Universidade do Minho Escola de Engenharia Departamento de

Universidade do Minho Escola de Engenharia Departamento de

"!$#&%(')*,+-' *,./#10324#
56' 7,#-089#-:';*<89&%,'>=?*(@"0:BA1832$ #
CD
EFHG3IFJKMLB,NPO;
QR
IS
TU <PV/SXWZY
F
\[]
^SIJ_F
`Ua/bcFdfeHcFg<hia,jkDlPgnmHopg
oFlPdrqsd_ltgvu
Rw xyxyFzP{}|~x€ƒ‚P„†…ˆ‡D‰P‹ŠŒxŽyƒ‚P„Œ‚x‚†‘‹‰P’P
“ „”•„–;{x‰}—€˜Œ†‚ˆ™Œ•„”z]‚Px›š;z;ix€|Mœ‰PžŸŒŽ|ˆ ”ƒ¡€„}¢ x£‹„Œ{1;Ž„;‚P„~yF;{6„~ŒŽ‹x€‰ Ž„;—€˜”~‚
¤_Ž”žŸxyŽyŒiš;z;D¥Œ yF¦–§J„Œ£‹;yZ¨PxŽx€‹•„–>„Œ‹„ˆ©DxŠŒx3y
ª/««Jª
dikg
cd;jolPa/kd&jDa aRtPblPgvu<a
a(l}a a `)lPgDo,d kDgvl1og~gd_lPa/o
`Ua/bcFdfeHcFg<hia,jkDlPgnmHopg
oFlPdrqsd_ltgvu
56' 7,#-089#-:';*<89\%,' R2$€89' :#-†%,'>=?*(@-03:#-
#-:\"7 !, %,$' #&%!,(0 ';:
)*,+,+.-/+0*21 !,2 :B#-(0 -' 3"0€48 !,+"#-!
566798;:<:>=<=<=@?BADCE?FGHEI<5DJK?L76M:ONP7QJR<6OS,T
7Q<J>R6OS,TVUAMCE?LFGEI<5JK?76
ISBN 972-98839-2-0
9 789729 883927
=•@-,! #-* !$
2 *<89 89.,'>' ' %(]-@892 :'/#-*,% 3# .(2$ . +"09#-2 *
2$! !J+"0 #-*,%
.,2 . 2 !$!*,-8/7' #B83.,' * !,*<89\:'
2$! !$2$#-: R./#1' 7' #-03'
2
2 B+-09#183 #- 3›0-@' 3"0U56,!(83"0--(' #-0!$"/' 003' 2 09#n#-24#]' "' Z:\'!"02$';*v89#-%,"0 _7"0 89';0
2$*M !,' *( 24#1%, :\'!S2 *v83' 0' 3' */#XA103'# %/# =?*<89';!$2 +! *,;24# #]0892#"/ 2$#-! 7';!$" '!,\' *,2$*/#1:';*v83" :\-892 -#>- ' #-;"*,' !$.,#-:';*<89 %$' : ":\&*/#\;"*&"_#1*"#('<!,'>3' :\7,0' %(' 7"32 89,! ' : :2 : -<' !,';03 %,' 2*),#10‘%,'&#-+"03#-%,' ;' 0 #H' €892$:#-%/# ;"*<8902+$"!,2 -H%("‘ "! ' +<#1‘%, !4#,$"09#}8.-"02$\%,'
&
=?*<89';!$2$+, *,;24# #60€892#/" 2$#-! 0/ !,21 ' *,%,'; #-03!$#2U2$! ' !$#n'3 !%4$(5~02 83 7-0 89
%/# #76;!,%/# 7,0' €8 #-%/# *,":\'#1%/#-:\' *<89' */#S7/#-0€892$! ./# %,' 03';!,03" ":\7"!(89#- 2 "*/#-2 8 #1:9$ ';: <' !,' 0#-+-09#-%,'; ';0n#--
-!$' +"#-D%,'›!,03 !‘: 0!4#-*(%, 3' 0' 2 09# ' #]*v8;"- *,2 &
,!,9# -%, 1 0;!,7]%,' R2 83' :#-562$€89032<"$ !%4 %," P7' ! #!)4 !$2$–@"03*(' 2 %, 3!($ 03' 32 89';:B#ˆ-7';09#1832 ">=@?BADCFE G:IHKJMLONQPSR,TVU %,'›7,03' R2 4-†%,# :\';83R%("!$"+-24#›%,'
WJXE!Y[ZDU\A&]^?BA&H _`J^T.UVa;R^H\NcbdT.J <@"2, ';%,2$%()+"';*<892$! :';*<89'†7"0 #-03! "e 2$+!,' 2 03' %( <%,)56' 7/#108 #1:';*v83
%,'30R%"!O- ' R2$€89';:B#- f : ';37' 2$#-!0' ;"*,.,'; 2$:\' *<83 ' %,' R2 %,H#- #-:2 +"&' -!$' +"#g 2 +,!,' !
/ R ./# d<' !,' 7,03';83,! !,: -#1!$"0"3 -*v83032<"$ !(89 ;": 3'!,;"*,.,'; 2 :';*v83"\3!,$ 0'ihdJ^j>klCNmR!n7opJ
qdr,J^stCua\?mJ^Alv,TO?QRU(wU\Ayx\Nz?ma;R|{
89' 7,0^6 ' Œ89>@"2,(!(7"0€8 #-%( 7' !$#}_~CpAl|R!n7opJ€k&R,TR9RghG?m‚\Aya\?QR(U>Rƒ„UVa\AyJ^s+J;…,?QR†z_€h>ƒ1‡ 1%,' %,'
ˆ7‰ˆKŠ!‰ˆK‹!‹ * #}84'gŒ + ‰,‹|‰!Š +,+ ˆ #18309# ,'; %/#$ "!$3#beŽ€1>‘V’“”>‘[•DW€–—•y˜!™Dš7›!™X•y›%š D'B';*%<' !/#-%,03#-%,
*,&7,0^6 ' Œ89œbSŽ€1>‘V’!•Dbc•DqSqG‘[•y˜!™,›pžV•y›!Ÿ {
2$*,#-!$:\' *<89'J%,';3'¡6 #1+"09#-%(' ';0£¢ :2 *,./#@F#1:4 !$24# _#-:2 +""]'¤¢œ6¥ *,+"';!4# 7-0689
%,H #-7"2$B'
' *( "03#736 #-:\' *<89 2
7";4 -' !†0' - 'X'<!/#- 2 "*/#-0 FV‡s7(03!$,! ' :#F.‡)(!&$p63#- ';*<89' ¢n89';:BA1832$ #%/# b T.U\rK?+H opJ pUg’~x\TO?mUVH
ƒ„U\j>kDJ^TR,?+H †zbS’0ƒU#18903# ' %,'6:\';83R%,-!$"+"2$#-K%,' 03';3"! !"1s%,' 7,03,$,!$';:B#-e'<!,'U';:B#1*/#-: %/#)A-03' #
2 ' *<.8 4#"/#U%,£# ‘\ADN¡U\st?#…p‚\Aya\?QR>TONQ? €a\?QR,s <#-32$: ":\U%,'ˆ@';0303#-:';*<8 #-K!&#-083';@F#-Œ89" !,3#-%,"*,#U7,03 !(09#‘%/#-0' 37' Œ892 -#1–"! !O
' <;":\>#- Ž1U;pUVH U\CpT.J^AlR,?+H >TONz? €a\?QR,?+H †zŽ H]'†"S>s …pJ^TO?BNQjJKH
wU\Ayx\NQ?maVJKHU}qdr,J^stCDa\?mJ^Alv,TO?mJKH † 9wdqeH $#6} Ž1 >H\4 1 #-*,%,2 %/#189#-U*/#1(8 !,09#12$U# !(:B# !(832$! 2 %># -
' : 7,0' 2$( -f"* -X! 2$*,' #-0 ' %* '<!/#1*v83“
'<!,'n-g
9wdqeH 7(03 2$%,';*, 2$#-: !,:#X7,0R !,09# #-%/#17(8 #1832 1# 3';*,%,&8 #-! ./#-%,-†7/#-09# !,:# "7(832$:\2 %># - +-!$! $/#1! : 7,03';3' *<83'U8909F# $/#-!$.()%,';3;03' -'$!,:B#>@"03:#>%,'6.,<2 $,032 %/# -)%('‘#-9: $"–"~7/#109#-%,2 +":#-›7/#-09#)#
bS’0ƒ@{l/"03#-: ';@' Œ48 !/#1%,"†89';89';];":\7/#-09#}892 -"ˆ;": : ';89
%,"~ "* "';*, 2 "*/#-2 %,'>7,03' R2 4 -' + >st?+H R,jU\ADN¡Jœq EXkDJ^AyU\Aya\?QR,sˆ' #n:\';83R%("!$"+-24# %,' W>JXE!Y[ZuU\A&]^?BA&H7‡ ' : %,2 @';03';*v83' )( ' 02$'; 03' #-2$)'
#-0€89<2 ", 24#12$ "*,€8 #189#-*,%, - 3
' '<!,' "&:\R%,';!$"s2$*,7,2$03#-%," *,# ]#148 !(03' % # "% - "07 # :';!$.,-03' 7,0' 2$R'; D' 7'; 24#1!$:\' *<89¤' '<!/#-*(%, 4 - -*,32 %,' 03#-%,">32 83' :#-‘ ":\7,! \' )R"' + D; ' 032 ' >M* -H! 2 *,' #-03';)' ‰ , !f ,# --832$#1V ‡ 3"0(! 892 : Z' €89' ):
%,';!$"U@"03#-: 89#-9: $' : #17,!$2 #-%,-£ ¢ 7,0' 2$( - %,'
' -' *<89-S '<!,' "7' 03#-: ' : 83' :\7603'#1! ""*(%,'†:B#12$ !(:B# -'% #-d Ž H6#-7(03' ' *<8 #109#-: ":';!$.,-03' 03';( !,! 8 #-%(" D'<!/#-*(%,;":\7/#-09#1%,"† -: , !(8303"†7,0R;' %,2 :';*<89"†%,'>7,0' 2$( - ' *O';892 "' "-! !,;2$"*/A1032$-
,#]*/A-!$2 3'†%,' ' 30 2 ' e8' :\7"03#-2$<303' 2 4->' :
8' :\7 / '#-!D/ ' %,'; '!,0"*/#-2 #60832<"/;24#-2 OR' ! ' -\%,' %,' ! " ~gfaM #6!$+-"032 89:\" 1
R2 2
2$2 2
]' C#-! 89';03*/#1832 -' #-7,7,0<#- .,';–@"09ƒc?BjU€’~U\T\?mUVH _@J^T.UVa;R^H\NQ?BAp…† ƒ’%_ ' :\' 0+"' % @0": 89.('>>TONQ? €a\?QR,s
‘\ADN¡U\sBst?#…pU\AyaVU #-0' */# .,' 0'X-7(892 :2 %#1832$"*:\';83.,
%, 2$*,7,2$0' %"* */#184!(09#-!‘7,0R;' 3' >(!, . #1
>TONz? €a\?QR,s U\CpT;R,s U\NzP J^T.]KH}†  ”H‘#1*,% wU\AyU\NQ?maR,Al qdr,J^stCNQ?mJ^AlR,T >s …pJ^TO?BN pj}H† 9wdqeH #-0'
7"7"!,!$#-0 G UH #-0']7-89';*<8924#1!,*,"*,! 2$*,' #-0#1*,%,2$%,#189';›@-0›@-03' #-832$*,+ .,2$! 'wdqG>HU7' 0€@"03: #-*
#-%/#17(892 "'>3' #-03 . D$ ' 2 *,+&(!,2 89';% @"0†+-!$!/$ #1!J"7(832$:\2 % #1892 "* †8 .,'ˆ7,0' ' *<8 "0 >03';7-089"*)83.,'@!(3'ˆ-@%$ -83.s7/#109#-%,2 +":\D@-0 ƒ’%_ -:7/#109#1832 "'›89';83 2 83.
-* -' *<892 "*/#-! :\';83.,R%( F' + 1q EXkDJ^AyU\ADNQ?QR,sd’ujJKJ^N p?BAp… #-*,%S89.,' WJXE!Y[ZDU\A&]^?BA&H :\';83.,
%,"!$-+&‡ 7' 0@-03:\' % "*f3' -' 03#-!ˆ03' #-!ˆ#1*,%S#-0832</" ;24#-!' 02$' K@F# ""0' %r89.,',$ 2$ - 2$*,7,2$0' % :
%,';!$ 37' ;24#-! ! .,';*C./#-03%(' 089#- vH#103'#}8 89#-'U2 ' .,';*C*,"*,! 2$*,' #-0\#-*,% ./#1-892 n3';032 ' #103'n;"*,2$%,';03' % 2 */#-!$! v89.,'‘:\
%,' ! ~';03')#-!$&#-7,7,! 2$';% 89&03' #-! - 892$:\' @"03';#-€892$*(+ %$ ' 2$*(+ 89.,'£$ ' 8 0' ;!,! 83 +-2 "';*
$ 89.('} H g sd_l1k #]0892#/" 2$#-!l] '!,09#-!y] 'Œ8 ~"0 v
1 ' *,'Œ892$U#-*,%H "-! !(832$"*/#10 #6! +""032 89.,:\
%,';! R' ! ' ;832$"* %/ '#-! - †8 2$:\'/ "0' #-832$*,+ &†8 2$:\' R' 02$' #]*/#-! 2$ 2#)
)
e_lPa/kg<ofg
jtd
m gb f
d
DoFo
e p;tlPa-t
oh
–o;taXkDg
†oblPaM
hH
–o;taXkDg ~ a(pgRcaM
d/ta, ,d
-"*,2$:\"
4 }$"! " 1
#† 0
$:
j tlPdikb,,d
hDoh
' 03#-2$ˆ'$# ,03' R2$#184!(09#- $
ˆ ˆ -832 1#1 ˆ Š =?*<89' ! 2$+!;*, 2$# #60€892<", 24#1! ˆ Œ : 2$:\' *<83 -*,'\)R2$-*,2$€8 # ˆ Œ ˆ =?*(37,2 09#- 5~2$"!<-"+"2 # : ';03' $(03 !,:#-*, ˆ Œ Š 5 ' *,'Œ@ 4$ 2 "†%/#-Ž  ˆ Œ Œ # =?*<83' !$2 +! *( 24# #]0832</" ;24#-!')#1 Ž H ˆ Œ ) #]0;<' !,2 89' Œ84!,03#- %,' / ';%,' ˆ Œ 0 #]7,03';*,%,2 %#-+"';: ˆ Œ 3' 037' ;832 1#]2$€8."- 02$ # ˆ ) ":\7"!(8 #>- 1 ' *"'Œ892$ # '> -"! !( 2$-*/A-032$# ˆ ) ˆ =?*(37,2 09#- ~5 2$"!<"- +"2 # ˆ ) Š –2 #10324#1*v83' †%/# ":\7"!(89#1 1 ' *O';892 # ' ""! !, 2 "*/A-024#
ˆ ) Œ 5]":4 *,2$-~%,'$#67(!$2$ #,,$ 2 !$2$%,#-%,' R) 2
hZhDo
) )R2
) )R2$2
)
ˆ
*
‹
‹
ˆ!ˆ
ˆ7Š
ˆŒ
ˆ)
ˆ
ˆ*
)R2$2
ˆ 0 :$p6' Œ892 -" ˆ U: 03+<#-*(2 %#>- %/#¤8' '
Š
Š
Š
Š
Œ
Œ
Œ
Œ
ˆK‹
Š+
dikg
cd;jolPa/kd&jDa a(tPbDl}gvu<a
ˆ / ';%,' ”
' !,0"*/#-2 f *,2$%(2$03'; ;2$"*/#12$ Š )
Š ˆ ˆ ' !,0 -"*,2 #]083<2 "/;24#-!, ! ]
%, Š )
Š ˆ Š # #];0 '<!,2 89' Œ48 !,03# f *,2$%(2$03'; ;2$"*/#1! Š Š ˆ Œ : #6! +""032 89:\s%,' / ';8303 - 3›0"7/#-+"#- Š,‹
Š ˆ ) #]! 83' 09># ' #-2 #6! +""02 89:\s%(' / ';8303 - 303"7/#1+<#1 Œ +
Š ˆ 0 #]!$+"-032 83:- %,$' #†%/#17(8 # - 3D
#1! Œ Š
Š ˆ 02 (8 ' 032 "ˆ%,' 3#-09#-+-' : Œ )
Š ˆ 3;0 ' - 7(03
' 9#-:\' *<83%,-]56#-%," Π0
Š ˆ * #17/#- 2 %/#-%,'; ' 3i2 :2 8 # R'; Œ
Š #6! +""032 89:\" 1 ';"* ';832$ - ' "-! !,;2$"*/A1032$- Œ *
Š Š ˆ : #6! +""032 89:\¤ :U032 +"2$*,#-! Œ *
Š Š Š : %,' ! 1 ' O* ' 032 Œ ‹
Š Š Œ / ' 7(03' ' *<8 ># ' 1 ';"* ';832$#1 )+
Š Š ) :U7' 03#-%,"0' 1 ';"* ';832$;" ) ˆ
Š Š 0 / ' *( 1#-&%/# 3""7 !(!4# - ) Œ
Š Š 30R;' 3%(' ' !$'; - ),)
Π#69
: $(2$' *<83' %,' 303"+"03#-:# - )<0
Š Œ ˆ #]9: $,2 ' *<89'‘%,' 303-+"09#-:# - %,' / ';%,' ]' !,03-*/#-2$ #]0832<"/;24#-2 ) Š Œ Š #]9: $,2 ' *<89'‘%,' 303-+"09#-:# - %,$' #6! +""032 89:\" 1 ' O* ';892 "†' "-! !,;2$"*/A1032$- ) ‹
)
"*,;! !,R'; 0 ˆ
dikg
cdkDg` l}gDo,dXkDgHvl}ogV2~gd_lPa/o
ˆ #6*/A1!$2$'U%,'V';032$';18';:7"09#12$ Œ ˆ ˆ 5]' -:7"32 - Œ ˆ Š 003&%,' 303' 2 4 - Œ ˆ Œ ' 032 ' 1 8' :\7"03#-2$ Š ';83R%(" "* "' *( 2$-*/#-2$ %,' 303' 2$4 1 Œ Š ˆ #]!$2 9#-:\' *<89& )R7"*,' *( 24#1! Œ Š Š # ';89
%,"! "+"2$#s%,' 5~ ) - -' * 2 *, Œ / ';%,' ”
' !,0"*/#-2 #]083<2 "/;24#-2 ) #6! +""032 89:\" 1 ';"* ';832$ - ' "-! !,;2$"*/A1032$- 0>)
,0 0
0
0*
!Œ
!Œ
+
)(2 2$2
Π0
Œ
Œ
';*,' 03#-!$2 %#- R' ! ' -&%,"
%,';!$"†%,' 303' 2$41 Œ ˆ #]!$2 9#-:\' *<89& )R7"*,' *( 24#1! Œ Š ';89
%,"! "+"2$#s%,' 5~ ) - -' * 2 *, Œ Œ R%,';!$"†=?*(37,2 09#-%,- *,# ]#148 !(03'% #
562$ !,4 -\' "*,;! !,R'; 1
DtPofoFu<a ,(dfkDg
id kDgRcd&kg` lPgDo,d
) ˆ 8903#184';+"24#1†%,' 3›0R!,09# ) Š :U7(892 :2 %#- %, %,' ! ]' !(03"*/#1! ) Š ˆ / ' %(' ”]' !,03"*,#-2$ ""! !, 2 "*/A-024#- 303-7"€89 ) Š Š R%,';!$2
) Š Œ )R7' 03<2 *,;24#- %,' ! \ -"! !( 2$-*/A-032 ) Œ :U7(892 :2 %# - %,
) Œ ˆ ';8 # - #6! +""02 89:\" 1 ';"* ';832$;" ') -"! !,;2$"*,A-032 "
303-7"€89 ) Œ Š R%,';!$2
) ΠΠ)R7' 03<2 *,;24#- ":\7/#-09># - ';*v8303}' %,' ! " ) )
"/ A- 2$# %,' 3›0' 2$( - ) ) ˆ G
) ) Š 8' :\7"†%,' ":\"7 !(8 ># - ) 0 562$ !,4 -\' "*,;! !,R'; `)lPgDo ,dXVg ~g dXm gva/c
0 ˆ ]"02 %;"*<89' 8' :\7"09#-2 0 Š V' 02$'; 8';:7"09#12$†' : 8';:7 / ' #-! 0 Œ R2$€89';:B# %,' 303' 2$4 1';: 8';:7 / ' #-! 0 Œ ˆ #];0 '<!,2 89' Œ48 !,03# %,' 3›0' 2$( -\' : 8' :\7 / '#-! 0 Œ Š -R"% !(!$ %,' 303' R2 4 -
0 ) )(7' 02$:\' *<8 ># - -&* "/,+ !,03# 1\%( R2 83' :# 0 ) ˆ
0 ) Š / ' ; !,! 89#-%," 0 0 562$ !,4 -\' "*,;! !,R'; j <cFb JVg &g l}a(pa/c Dd DbDtblPd
q)d
ˆ 4$*<83' 3' Š 562$ !,4 - )
ˆ
)
0
0
Œ
*
*
*,*
,* *
‹+
|‹ Š
‹*
‹*
‹!‹
ˆ+ˆ
ˆ+Œ
ˆ+Œ
ˆ+
ˆ +,0
ˆ!ˆ +
ˆ!ˆ,ˆ
ˆ!ˆ,ˆ
ˆ!ˆ )
ˆ!ˆ 0
ˆ!ˆ ‹
ˆ!ˆ ‹
ˆ7Š +
ˆ7Š ˆ7Š ˆŒ+
)R2
Œ 3';0337' Œ892 -#1 %(' 809#F$/#-!$.(M!(8(!,03
e jko " ge ;taRtŒtPo "a
e jko " g q)aM d ` l(tPo "d
ˆŒŠ
5 ˆ / ';%,' ” '!,0"*/#-2 f *,2$%(2$03'; ;2$"*/#12$ 5 Š #6! +""032 89:\" 1 ';*"';832$ - ' "-! !,;2$"*/A1032$-
ˆ)Š
e jko "g q e pog
jtg kgn`)lPd _l}a"fa,,d
ˆ / ';%,' ” '!,0"*/#-2 #]0832<"/;24#-2 Š #69
: $(2$' *<83'‘%,' 3›0"+"03#-:B#>- %,'$#]!$+""02 83:" 1 ;' *"';832$;"†' -"! !( 2$-*/A-032 "
Π303' 2 4 -&%,
' V';032$';1 8';:7"09#12$ e jko "
g m g •gvlPgRj <oa/c
5 ˆ 303' 2 4 - 5 ˆ ˆ -*(@' 0 *,;24#- 5 ˆ Š 3i2 R0" 5 ˆ Œ / ' 2 8 #1 5 ˆ ) / ' !,03" !$' Œ890 -"*,2$;" 5 Š / ';%,' ” ' !,0"*/#-2 #]083<2 "/;24#-2 5 Š ˆ -*(@' 0 *,;24#- 5 Š Š 3i2 R0" 5 Š Œ / ' 2 8 #1 5 Š ) / ' !,03" !$' Œ890 -"*,2$;" 5 Œ ":\"7 !(8 ># - 1 ' "* 'Œ892$ # '> -"! !( 2$-*/A-032$# 5 Œ ˆ -*(@' 0 *,;24#- 5 Œ Š 3i2 R0" 5 Œ Œ / ' 2 8 #1 5 Œ ) / ' !,03" !$' Œ890 -"*,2$;" e jko "
g q)l kotd opcFoFd _lPa a
jko "g
ˆ )0
ˆ)‹
ˆ+
ˆˆ
ˆ0
ˆ0
ˆ0
ˆ0
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ*
ˆ*
ˆ‹
ˆ‹
ˆ‹
~ ˆ ˆ U: ˆ890;;];":\7"*(' *<89'; @ !(*,%/#-:\' *<8 #12$†%,'$!,: 2$€89' :# %,' ‘; ˆ Š 890;!(84!(09#&%,'$!,: *,'!,0;-"*(2$&*/#18(!,09#-! ˆ Œ U: †%,2 @';03' *<83' 892$7"ˆ%(');"*,'\) ' ˆ ) #60' !(2 89';;8(!,09# %,'$!,:#Ž @{ ˆ 0 #60' !(2 89';;8(!,09# %,'$!,:#Ž ”Ž{ ˆ 890;!(84!(09#&7/#-03;24#-!%/#&:"! ' !,!4#s%(' #65 Š ˆ 890;!(84!(09#&+"' 03#-!Z%,'$!,: *(R%, Š Š () ';:7(!$"†%,'‘@ !,*O
' %,' #-;832 1#- Š Œ # @ !,*"-H\?#…,jJ^?Q 7/#109# 2$*,;!$2 */#
' ~%,'
'
Š ) 890;!(84!(09#&%,'$!,:B#Ž ;": # 89-7"! "+"2$#|YM™!Y ˜,Y p{ Š 0 $4 *(2$:\"~! R #-2$ˆ'>+"! !/$ #-2 1 #-! !4#-*<8 ˆK‹,‹ Œ Š 890;!(84!(09#&+"' *"';032 # %,'$!,: 9w Š 303
' 3\%,'>03';7,03';3' *<89#-%,&@' *%-- 832$7 / ./# ˆK‹!‹ Š * 890;!(84!(09#&+"' *"';032 # %,'$!,: 9wdq Š ‹ 0(!"% #-:\' *<89\%,'>%,"2 †7"*<83" Š ˆ + !(89#-(,$ 2 */A-024# Š ˆ!ˆ 303
' 3\%,'>03';*, -#>-\%/# 7-7"!,!4#>- Š ˆ7Š #6:\"8309#-+-' : ';83R A-832$# ;": (!&,$ 832 84!(2 1 "!]
' .(* ˆK‹!‹ ) Š ˆ Œ =?:B#1+"' *,†*("03:#-2$ #-;2$:#|‡ '> ": #1890,_" # #F/$ #-2#R) ‡ Š ˆ ) 890;!(84!(09#&%,'> !4#133'; %,g>beŽ 1 Š ˆ 0 n #183032 %‘%(' 7' " 7/#-03#2!(:B#Ž 1 q ] ' -' ]';8]#-! ˆ ‹!‹!‹ Š ˆ : #-0<' !"';832$7\%(>b„9wd#
Š ˆ # .,2$';09#-0<' !,24# %,' !$#-3' %,&2$*(%,2 p4$%O!, ' -' 6'Œ8]#-! ˆK‹,‹!‹ Œ ˆ V' 02$'U83' :\7"03#-!J*"-';89#- 2 "*/A-024# Œ Š V' 02$'U83' :\7"03#-!J;": @F#-Œ89"0†';89#- ) )
ˆ+
!ˆ ˆ
Š0
Š
)
*
ˆ
Š0
Š
Œˆ
Œ*
Œ‹
)+
) Š
) Œ
),)
)
‹
)
0+
0 +
)
)
0
0,0
) 2
Œ Œ
;4
#&!(83R;"030' !$#
' ˆ8 $7,2 #-ˆ%(' ;' 02$' †83' :\7"03#-2$ V' 02$';†9#;% "*/#-2 ;": 83' *,% ;*, 2$# a" a _g
oFlPd>' a"g
c V' 02$';†9#;% "*/#-2 fd_ltgU'XgRcpd_l}jg V' 02$';†*M- \' 89#- 2 "*/A-024#- l}g "d>'Jb o "a V' 02$';†*M- \!$2$*('#-0' fa/j DaM)'_d_pg V' 02$';†# -832$ #- ZbDa/kDl(tPo "a ' DgRjDdj 3 03
' 3\2 83' 09#}892- %/#&:'Œ89
%,"!$-+"24#
]#-* -' ' 2 893
Π)
Π0
%
z‡
.
* ‡
u‡
‡
,
‡
¤W Z /
ˆK‹ ‹
f]:# Ž ":\7,!$'Œ8 #-:\' *<83'H2$*<89';03!$2 +<#-%/# ": Š *,
%,"&%,' ' *<8903#-%/# Š
2$*<89';03:' %,2 " V!,: *,
%,&%,'>9#F4$%/# ( "*,'O) R';]%,' ?QR^H ' #189#-!$.,- 56' !$
#-:\' *<83"†%,'$!,:#&;' 02$'‘89';:7"09#1! 1 ';*,' 03#-!$2 %#- '9HKJ T.U\Y ROC H\NmR,jU\ADN¡J,{ Œ Œ Œ *
Œ ‹
Œ ˆ +
Œ ˆ!ˆ
Œ ˆ7Š
) ˆ =?*<89' 03#-R';]';*<8903'>" %,';3! R #-:';*<89"
) Š =?*<89' 03#-R';]';*<8903'>" %,';3! R #-:';*<89"
) Œ ;'<!,' :#&%,'> %,2<"/ #1\%(' !(:B#Ž )' /7 #-03#\#&(';032 ' lPg"d )' /7 #-03#\#&(';032 'Zba,kl(tPo "a
8
8
‹
ˆ ;'
<"
ˆ!ˆ
ˆ7Š ;'
ˆŒ
0 Š
0 Œ
0 0 )
ˆ
+
ˆ
Š
)
*,
%,"
‹
‹
0 0 *
2
2
*
„‡
;4
> q
9wdq
aM a_g
oFlPd
Š
‹&ˆ
‹&ˆ
‹|Š
‹Œ
‹)
‹0
‹
‹!‹
9Ž ”qSH
<"
U\NmR,YQ9wdq
p4
U\NmR,YQ9wdq
¤- (Ž œ
'
*
%
V ' 02$';ˆ89' :\7"09#-2 ˆ' : 83' :\7 0'#-! '_dpg(3l ' "d_l}a ,,d #&!(83R;"030' !$#
' †7/#109# %,2 @';03';*v83' 7' 0 R%("†%/# (';032$'_d_pg(9l #60 (! 2 89';;8(!,09# %,'>7,0' 2$(-';: 89';:7&03' #-! 3 03"+"0' 3\%/#&#-7,03';*,%,2 % #-+"';: 7/#-03#&#&;' 02$'$a" a _g
oFlPd =?*,89#-*<89';]2 *,2$;24#-2 %,\7,0R;' 3%(')#17,03';*,%,2 % #-+"';: 7/#-03#\#&(';032 '
3 03
' 3\%,2$**)-:2 %(' 7(03' 2 4- \' : 83' :\7&0'#-! –#-!$-03' ~03'#12$ '‘7,03' 2$ ' 24#
7,#-09#&# (;' 032$'_d_pg(9l –#-!$-03' ~03'#12$ '‘7,03' 2$ ' 24# 7/#-09#&# (;' 032 '&_d_pg(9l 0 0
0 !$
!$
‹
0
"083'>*!(: *,
%,&2$*<89';03:' %,2 ) )
"083'>*!(: *,
%,&%,'>' *<8903#-%/# ) 0
) <!,' :#&%,'‘@ !,*, 2 "*/#-:\' *<83\%(\2$€89' :# %,'>"7(832$:\2 %#>- *('!,0"*/#-! ) -7"! "+"2$#- %,' 03';%,' R892$%,#-67/#109# #-6(' 02$';U9#%;"*/#-2 U' ;": 89' *(% *,;24# aM a!
_gRolPdOa"g
c DXdltg"fg
cFpd_l}jg "Jb o "aH' lPg"d ) * -7"! "+"2$#- %,' 03';%,' (892 %/#- 7/#-03# #1 ;' 02$' *M-M!$2 *,'#103' fa,j a"_ dpg ZbDa/kl(to "a ' g
jDdj 303' 2 ' 24# 32 89';:B# %,' )7/#109#&# (' 02$' fa/j aM ) ) + <!,' :#&%,'> %,2 / #1\%($#
56' %,2 ,#-%(' !(: 2$*,%(2 $%"!( %,$#
) <!,' :#&%,'‘@ !,*, 2 "*/#-:\' *<83\%(\2$€89' :# %,'>"7(832$:\2 %#>- ' ""! !, 2 "*/A-024# ) 303' 2 ' 24# &:
%,' ! "7(832$:\ %#
7/#-09#&# (';032 '&_ d_pg ) ;'
0
ˆ ++
ˆ ++
ˆ+Œ
ˆ!ˆKŠ
ˆ!ˆ Œ
ˆ!ˆ 0
ˆ!ˆ ˆ!ˆ ˆ!ˆ *
ˆ7Špˆ
ˆ7Š,Š
‹ –2 #-!$-03' ~03'#12$ '‘7,03' 2$ ' 24#&#Ž 7/#-03#&#&;' 02$'_dpg(3l 0 ˆ + 2–#-!$-03' D%,' ' 003U7/#109#6#1%,2 @' 0' *<89';7,0' 2$R';K' : 89';:7 03'#1!R7/#109#6#
0 l
(';032$' _ d_pg
ˆ 6# 7,0' *,%(2 %#1+"' : %('¤Ž H 24# :\R%(' !$ 7(03"7"83&7"0>=~R,j R,T.aV] # 5
5 ˆ
5 Š
5 Œ
5
)
0
5 ˆ
562$€8902+$"!,2 -s*,"03:#-!Z;": !,:# : ';%,24# + '>%,'; 2$\7/#-%,0(- ˆ #-3- %('>8303';2$*,&7/#-03#&#&;' 02$'>7/#-9#-+"';2$0" 8-7"! "+"2$#)2$*(2$ 2$#-!7/#-09#\# Ž 2–#-!$-03' ~%,+-09#-%,2 ' *<89'‘7,#-09#&g# Ž 8-7"! "+"2$#)%/g# Ž #-l7 -" !,:# 2 89';09# - Ž1beŽ b ""! !"-&%,\' 003&%,'‘890' 2 *,
†#-&!$-*,+" %,' ˆ +,+ 2 89' 03#
' ""! !"-&%,\' 003&%,'‘890' 2 *,
†#-&!$-*,+" %,' ˆ +,+,+ +-' 09># ' ) 2 2
ˆ7Š,Š
ˆ7Š Œ
ˆŒ)
ˆŒ*
ˆ) Š
ˆ)Œ
ˆ)Œ
ˆ ))
ˆ ))
ˆ) ) 2$2$2
Š ˆ M !,*"
' %,' #-Œ892 -#>- Œ ˆ %,' ! "†%,' q 7/#109#&#- (';032$';†89' :\7"09#-2 Œ Š %,' ! "”Ž%#œ 7/#-03##-†;' 02$' 89';:7"03#-2$ Œ Œ ]'!,0;4 892 #-†7,#-09#&#- (';032 ' 9#%;"*/#-2 Œ ) ]'!,0;4 892 #-†7,#-09#&#- (';032 ' *M-&9#>% "*/#12$ Œ 0 / ';(!,! 8 #-%("†%/#-Ž ~)H 7/#-03##&#,$ "03%,#-+"' : ' :\7%4$02$ #¤¢&;' 02$' fa/j DaM Œ 56' ' :\7';*,.,\%," 02 8(' 032 "†%,'>3';!$';1%,'>:\R%(' !$-ˆ7/#-03#\#1 ŽH Œ Ž ~)H ": &:\' *,-0 -#1!$"0ˆ%(' Œ * / ';(!,! 8 #-%("†%,"9wdqe)H 7/#-09#&#&#,$ "03%,#-+"' : ' :\7%$4 02$#}&¢ ;' 02$' fa/j DaM Œ ‹ 56' ' :\7';*,.,\%," 02 8(' 032 "†%,'>3';!$';1%,'>:\R%(' !$-ˆ7/#-03#&->9wdqeH Œ ˆ + 9wdqesH ;": \:\' *,"0 1#-! "0ˆ%,'
2 #-!$-03' ~%," 7/#-0 )-:'Œ890"†%,\32$€89';:B# %,'>"7(832$:\2 % #-)*,'!(03"*/#1! ) ˆ –
#-09#1;89';0;4 892 #-†%(" :
%,' ! "ˆ%,'>7,0' 2$(-&!($ 832$%," 2$#\# "7R892$:\2 % #1 *,'!(03"*/#1! ) Š
2 #-!$-03' ‘%(")7,#-0 )-:\';8303"‘%( 2$83' :# ';: 89';03:\">%, 7,03
';33 %,'\"7(892 :2 %#-
) Œ –
' -"! !,;2$"*,A-032$# #-09#1;89';0;4 892 #-†%(" :
%,' ! " !($ 892 %," 24# "7R892$:\2 % #1 ' -"! !,;2$"*,A-032$# ) )
) 0
) 0 0 0 Œ
Š
# ˆ
5 ˆ
ˆ
":\7/#-09#>- ';*v8303' "†%,2 @' 03';*<89' :';89
%,"†%(' 7(03' 2 4- !,83;":\"7 !(8 #1 2$-*/#-!J%(' #-%/#&:
%,';!$ 7/#109#&#\;' 02$' aM a_g
ol}d #-09#1;89';;0 4 892 #-†%(" %,2 @';03' *<83' ":\7"!(89#-%,"0' 56' ' :\7';*,.,\%," %,2 @' 03';*<89' -:"7 !R8 #-%,-03' ":\7/#-09># - ';*v8303' "†%,2 @' 03';*<89' :\R%,';!$"~%,'>7,03' R2 4 -&';: 89' :\7 03'#1! 2–#-!$-03' ~%,' 7,#-09# %,2 @' 03';*<89' %* 4 "';2$ %,'>32 +"*,<2 ", )-*,;24# ,:\' 0 :';*,9#1!J7/#-9#-+-' 2$0"†%,' !,:#s;":7,#-*,.,2$# # ' 0'# 2$*<83' 03*,#- 2 "*/#-! F';: \: 2 !$./#103' .‡ )R2#)
Š
0
*
‹
*,+
,* +
Š
*
*
*
Œ
‹)
Š
‹
ˆ+Š
ˆ+Š
ˆ +>)
ˆ+
ˆ7Š Œ
ˆ7Š )
ˆ7Š )
ˆŒ‹
ˆ)ˆ
) )
5
5 Š
5 Œ
)
9wdq
3"7O!,!4#-&2$*,2 2$#-!%(
3"7O,! !4#- & ": "†*, "" 2$*(%,2 $%O!," 3"7O,! !4#- \#-7 " # 7,032 :';2$09#)+"' 03#- l-
p4
t‡
ˆ )0
ˆ)
ˆ)
e >s …pJ^TO?BNQjJ wU\Ayx\NQ?maVJ,{
e >s …pJ^T\?BNQjJ wU\Ayx\NQ?maVJœUqdr,J^stCua\?mJ^Alv,TO?mJ,{
e >st?+H R,jU\ADNMJ9q EXkDJ^AyU\Aya\?QR,s#{
e `ˆe >j ?mU\ADN¡U pUbdT.J;…,TR,j R!n7opJpU>s …pJ^TO?BNzjJKH(wU\Ayx\Nz?maVJKH9U qdr,J^stCDa\?mJ^Alv,TO?mJKH e ` m ne >j ?mU\ADNMU pUbdTVJ;…,TR,j R!n7opJpU>Ž”U;pUVH U\CpT.J^AlR,?+H>>T\NQ? €a\?QR,?+H {
e m >CN¡J^YmŽ1Um…,TVUVHVH\?Br,J,{
WJXE!Y[ZDU\A&]^?BA&H {
q hdJ^j>klCNmR!n7opJ wU\Ayx\NQ?ma;R Uqdr,J^stCua\?mJ^Alv,TO?QR|{
qeH\NzTR,N¡xm…,?QR^Hqdr,J^stCNQ?Br^R^H {
_`J^CTO?mU\TX{
;e ‘\ADN¡U\st?#…p‚\Aya\?QR}>TONQ? €a\?QR,s#{
P—‘OADNMU\st?#…p‚\Aya\?QR¤’~JKa\?QR,s#{
H Z&R,AyU\s#R ƒ„U\j>kDJ^TR,sl–}UVH\st?KR,ADNMU g<ta 9e # U\N[R,YQ>s …pJ^TO?BNQjJ wU\Ayx\Nz?maVJœU>q r,J^stCDa\?mJ^Alv,TO?mJ TpU\AlR!n7opJ >Cjx\TO?ma;R|{
` bdT.J;…,TR,j R!n7opJ}qdr,J^stCua\?mJ^Alv,TO?QR|{
) )R2
) )R2$2
` bdT.J;…,TR,j R!n7opJ wU\Ayx\NQ?ma;R|{
` bdT.J;…,TR,j R!n7opJ TO?mU\ADN[R||RRpJ UVa\NMJ ` bdTVU\rK?+H opJ pU ’~x\TO?mUVHœƒ„U\j>kDJ^TR,?+H {
m Ž R|,?QR,syW”R^H\?+H\Ym_~CpAya\Nz?mJ^A&H {
m Ž1U;pU U\CT.J^AlR,s#{
m e Ž1U;pU U\CT.J^AlR,sl>TONz? €a\?QR,s#{
m Ž1U;pU U\CT.J^AlR,syqdr,J^stCDa\?mJ^Alv,T\?QR m m Ž1U;pU U\CT.J^AlR,syŽ1UVaVJ^TOT.U\ADNMU {
m Ž1U;pU U\CT.J^AlR,
s cAD?Q,?BT.UVaVa\?mJ^AlR,s 8903#-%"!"-M#-%,"7R8 #-%/#r%,S2 *,+"!+; _`UVU;L J^T\PSR,T U\CTR,s
U\NzP J^T.]%‡ m ` Ž1U\NQTVJ^YmbdT.JVk&RK…|R!n7op
J F%,\2$*,+-!+ ”WRpaV]^YmbdTVJVk&RK…|R,NQ?mJ^Ay‡ m ` m ` Ž1UVH\?Bst?mU\ADN VRpaV]KbSŽ b RK…|R,NQ?mJ^A m m Ž1U¡klT.UVHKU\ADNmR!n KUVH p
U DR,s+J^T.UVHŽ1U;R,?+H {
` €Cp?maV]KbdTVJVky{
!
"#%$ H
@ !,*O-&3,$,03')# -#10324A -' ! $ & %,": $4 *,2 %,' "#'$ ()+* ; "*,'\)O-\' *<8303' \*(R%,,B'‘\*,
%,.- "0/ @ !,*O-&%,' #-Œ892 1#- 12) -#1!$"0†%,'>2 *v83' +"03#1 %,*(R%,.- 34) 1#-! "0ˆ%,'>3#,4$%/# %,&*,
%,.- 3 - 65 #%$ 1#-! "0ˆ%,&2$*/#-!J%,' $ ) )R2$2$2
"*76;!,*<89\%,'>*,R%("†%,'>' *<8903#-%/#
C -*^6;!,*<89\%,'>*,
%,"†%,'>2$*<83' 03:' %(2$" "*76;!,*<89\%,'> "*,'O) R';]7' 3#-%/#- !,*,2 %,2$0' ; 2$-*/#-2$ -*^6;!,*<89\%,'>*,
%,"†%,'>9#F4$%/# -^* 6;!,*<89\%,'‘@ !,"* R';]%,' #-Œ892 -#>- #-0%,2$*,#-!$2 %/#-%,']%,;"^* 6;!,*<83 @ !,"* -%(' ';030 5 ) &":B#}.8 -"02$ %,- *(R%,- %(' ';*<8909#1%/#\'>2 *v83' 0: ';%,2$" ()+* # H7# 6;!,€8 #-:\' *<89#-" 7' " 7/#-09#&# 2 83' 03# - %,';032 -#1%/# 7/#-03;24#-!J' : "0%,' : # $
" %,' 02 1#-%/# %/# @ !,*O- " 8 #7),#&%,' #-7,0' *,%(2 %#1+"' :
3 1 # - H;"*^6;!,*<83%,- *(R%,-”'<!,'>0' 'X$';: "*('\) R';6# 7/#10892 0†%,&*,
%,.- ' jJ^jU\ADNzCpj 8 ^# )(#&%,(
;"*,€8 #-*<89' %,\#-! +""032 89:\s%,' €Cp?maV]VklT.JVk 7/#-0 )-:\';890"†%,\#-! +""032 89:\ Ž1beŽ b ' 003&%,'‘890' 2 *, " @F#1#2 )(# %,'‘890' 2$*( # 7,0"+"0' 3%('>8303';2$*,&7/#-03#&#&2 89';09# - ! :';%,2$%/# %(' ';030\%(' ';89#-%,\' 89#- 2 "*/A-02$ " * ,:\' 0&:B^A )R2 : %(' 2 89';09# R'; $ 1#-! "0ˆ
: ' %,2 ) )R2
3 '# $ H%,' R2 7,#-%,041 - 5 1#-$! "0~:4 *,2$:\ / $ 1#-$! "0~:BA^)R2 : *<!,:\' 0:A^)R2$:\ %,'>+"';09#R'; 7-"7 !,!4># -&7/#-03#&#&+-' 09#>- #1890+2 $"!,2 - -/
@ !("* -\%,' #-7(832$M% 1 / f"7';09#-%("0†+"' O
* ';892 1 / 5 "7' 03#-%,"0†%,'>;(0 !"% #-:';*<89 5 -C2 *,%,2 4 "% !, 1 H"7' 03#-%,"0†%(' : !(8 # - 1#-!$"0ˆ#-!$' #1.
8 -"02$ 7' 0€89';*, ';*,%, #1\2 *<89' 0 1#-!$ 8 #-:#-*,.( %/#\7""7 !(!4# - 8 7# ),#&%,'>( !&$,832 48 !(2 1 1#-!$-0ˆ%,' ' !$2 892 3:\ &
8 7# ),#&%,'>+"';09# -&%,'>%,' ' *(%,' *<89'; * ,:\' 0\%(' 7(03"+"';*,2 83"03'; $ ; ' 02$'U89';:7"03#-! $ \
: R%(' !$s%,');' 02$'U89';:7"03#-! @F#-Œ89"0†3#% -*/#-! #!(83R;"030' !$# - 7,#-09# \%,' !$
#-:\' *<89
';0303&7/#109# 7' 0 4$
%, 3-:B# %,( '<!/#-%,03#-%,\%," ' 003" :' %,2$# %,('<!/#-%,03#-%,\%," ' 003" 03#-2 %‘%/# :' %,2$# %, '!,#-%,09#1%,&%," ' 003" : ';%,24# *,"0:B#1!$2 % #-%/# %,
'<!/#1%,09#-%(\%(" ' 030" #-!$2 9#-:\' *<89s\' )R7-*,' *,;24#-!i7,#-09# &7';;0 4 R%, ' €892$:#1832 1#s7/#-03#&# 83' *,&
% *,;24D# {
#&' €892 :B#1832 1#s3# % "*,#-! "*(8 #1*v83')%(B#-! 2$3#-:';*<89 O' )(7"*,';*, 2$#-! ;"*,89#-*<89' %/#&' 832$:#1892 1#s7/#-03#\# 83' *,%
% ;*, 2$# -*,89#-*<89'>7/#-03## ' €892 :B#1832 1#s3# % "*,#-! $,3';0 1#
' ! $(832$%/#1†"% !,09#1*v83' #&';89# - : ';%,24# %/#1 ,
* (:';03\:B^A )R2 : %(' ';89# ' # H:
%,' ! Ž%#œ {
"*,€8 #-*<83')%,\:\R%,';!$(>Ž%# ) X' ", 2$';*<89' %,&:\R%,';!$ >Ž * X' ", 2$';*<89' %,&:\R%,';!$ #œ 63#-*,' !$# 89' :\7"09#-!%,' !$2 %#-*<89'>;"*<89' *(%,- %(' 3! R #-:\' *<89" ) {
) 1#-! "0ˆ03' #-!Z%,\+"';*,
' -–%(' !(: 0":-33-:B# 032 48 ';032$ %(' =?*R@"03:# 1 %,$' # }#-2 1' 032 48 ' 02$ %,'>=?*(@-03:# - %(' 5~# -' * (:';03\%,'>\' )R' :\7,!$-†%,'‘8903';2$*, * ,:\' 0&%,'>7/#-0 )1:'Œ8903-†!$2 0' †%,$
' !,: :\
%,' ! 5 * ,:';03\%,'>' *<8903#-%/#- %,$' !,: :
%,' ! 5 ) * ,:\' 03\%,'>*,
%,"†2 *v83' 0: ';%,2$" ) )
) ) R2
-#1!$"0ˆ%('
7/#-03# " #-"]%('>8303';2$*, -#1!$"0ˆ%('
7/#-03## 7,0' 2$(-&%,'>!,0€89\7,09#>% @F#-Œ89"0†%(' 0' "% !O-\%/# 89"7"! "+"24# "0%,' : :^A )R2$:# %,&:\R%,';!$ "0%,' : :^A )R2$:#s%,&:\R%(' !$
1#-!$-0ˆ%,' 7/#-09#&#&7,03' 2$41\%(' !,0837(09#%; .("032 % "*<89'U83' :\7-09#-! * (:';03&%,'>7,03' 2$ ' ' : @03' *<83|' {
& %,' !$
#-:\' *<83\%,># 63#1*,' !$# %,' 2 3+2 $(2$!$2 %/#-%,' ;":7(032$:\' *<83 %/# 63#-*,' !$# %,' R2 3<2 $,2$! 2$%/#-%(' 4$*,%(2$ '‘%(2 *,%,2 p4 "% !, %/#&7""7 !,!$# - %* 4 -' !i%,'>2$+"*,#2 "/ )1*, 2$# l ~ 8†.,' 0'
$2 ]*,-89.(2$*,+ \: "0')%,2\!,! 86898 #1' 2$*.,#-*,% :"0's7' 02$!$!, 83 -*,%"!,Œ8Z"0
:\"03'@!,*, ';089#-2$*&2$* 2 98 ;!, ;' 3 R83./#-* 89‘8 #-'ˆ89.(' ! '#-% 2 * 89.,'†2 *v8303
%"!,Œ892$-* -@#>*(' "0%,' 0†83&83.,2$*(+" l #- .,24# -' !$! 2 #
^J Nz?Br^R!n7opJe‘\ADN¡U\st?#…p‚\Aya\?QR>TONQ? €a\?QR,s
# ^J rK?BjU\ADNMJhdJ^AyUE!?mJ^AD?+H\N[RhdJ^j>klCpN[R!n7opJ wU\Y
Ayx\NQ?ma;RU qdr,J^stCua\?mJ^Alv,TO?QR|{ UVa\Nz?Br,JKH9U zT …|R,AD?KR!n7opJ(|R ƒ„UVHKU {
65 ';3%,'-89';:7"&7,02$:\"03%,2$#-2$}'!('f' 0B.<!,:#-*, 89';*<8 #f;":7(03' ';*,%,';0Bf: !,*,%, @ 4$32 '<!,'
n0R%(' 24# ';: 89' 0:-)%, ":\ 7-0;'<!%B'%,'<!,'B#- -*v83' ;' 09A # 3';!$' - */#18(!,09#-!›7' 0:2 892 !
H%,';3' * -"! 2$:\' *<83 %(' 3' 0' >2$*<83' !$2 +"' *<83' J"*,%,' # 7' 0 ';7 - D#-*<89'; 2 7/#1H' 7,!4#-*('#-:\' *<89B%,'
' -' *<89-3' 83"03*,#-09#-: @F#1;89-03' ;0 !, 2$#-2$7/#-03#6#6! $,03' 2 !;*, 2$#6' : #-}: $,2$';*v83' .,"832$'~%,2 "* )-:\2$ - ]^ 6'\' : %(24# i;": 89
%, 7(03"+"0' 3 83' ;*,"+! --+"2$; '&;2$' *<;8 4<"/; #H7,0' 2$( -n;"*<892 * !,# #H89';0
'\)
8303' :#H03';!$' )-*( 24# U">';@';2 89-‘' 7,03¡' 6;!%4 %;">%,' #189A-8303-@'; F' + D2$<* !,*,%/># ' >, ! 89';0309#1:-83"V ‡
7R%,';: 3';06:\2$*,"03#-%," /#-B';89';U7"33#-: 3' 0 7,0' 2$€89"6#189';:7/#1%/#-:\' *<89'7,0' 2$R';]7(03' ;2$3#-
3, $,03' * ,:\' 03 %,' :#-*, ./#1 3"!$#-03'; 4 - 2 89#-2$s7/#-09# #n83":B#1%/#%,'H%,'; 2$R';&3! $,0'H:2 3R';
' 7/#-;24#-2 –']#);"!$
># ->%,' 9#1(8 ' ! 2 89';›' —
: -"0 $,2 89# v+<#-*,.,- ;"*,32 %,' 03A "' 2 7
%,' : ' 0~, $(892 %,"›#-
3'B "*,2$+<#7(03' -' 0&#n' ""! !"1 %,' 2$*(%,2$ #-%,"0' ",*/#-*,;' 2$0" ' + 2 &* _# - G4 *,%,2 ' )%/# $"!$3|# ‡ ';83 ˆ
Š
:U09# $ /* #184!(09#-! 7,03';3;!,7-0g'<!,' #- -03+<#-*(2 %#>
' \' 84- 2 *v83' 0' 33#-%/#-B' : !$(89';0B7,0' 2$R';
@ !,*,%,#-:';*<8 #-%/#1!$,03' 3'! @ !(84!,0 !,';0*,# 83":B#1%/# %(' %,'; 2 ' '!(' 0\*,f7,!$#-*,' #-:';*<89 89-03*/# - 3' *,' ;' 9A-02$ 7,0' -' 0U';: '<!,'s 2$0!,*(8 )1*, 2$#-]';89#- 'K‡]'s2$0(-\%,' ' * ""! "';0 ‘89#B*,'; ' 32 %/#-%,' ,# $(09#-*,+-'U89
%/#- #- A-0'#- %,' 1 ' 48 - # v032$%,# v2$% .,';' ! 032$+-.v8 ˆK‹ * ‹ '
,% ' ;2$ ' >'!(' 7
%,' : 3';0U32 +"*,2#"/#1832 1#-:\' *<89' :\' !$.("09#-%,#-] #-3H' *,.('#\# +"09#1*,%,'% #\'> #-09#-Œ89';0;4$€892 #-†%,\:\' 03 #-%,
*/#b T.J ,Cn7opJ‘# *(@F#-' ' %/#-%/# †"* - 09#109#- "'% ' 6*/# 7,03
!(09#f%,' !,: *, " 7,0R%O!(89 #183' *,%(' *,%,#&7"; 4 "' 2 †' -"! !"R';]%(\:\' 0#-%(
*/#1]A103'#1 _0?BAlR,AyaVU\?BT;R^HU'>%,' wUVH\N[opJgqdj>klT.UVH R,TO?QR,s (*/#&7,0^ 6' -\%,'>09A-;2$"†'>+<#1*,.,",'
A '<!,' 's! 2$%/#-0 ;": 7,03! $(!$' :#- %,' ,# $(3' * */#+"' €8 -%," Ž1UVa\CpTVHKJKH>Cj R,AyJKH ';: '!(' ./
832$3:\H, ! 7,03
"% !(832 2$%,#-%,' i';: 89';03:\">%,' @F#-;83"03';> ":\H48 !,0*,">%,' 8903,# $/#-! ., i03';!$2 +"2 -B'
@"0:B># - R' *<890'>: !,2 83"†, !(8303" *, #
R,T.]|U\NQ?BAp….,A
" *<84!(%, #- ' :\7,03';9#-&*M1 %(' "';: ' *(#-03#-0&' 83'H@' *%-":\' *( ›,!S3'M63# # 7,0' 2$(- › -:
!,:
9#1*v83B0' :' %,2 ,:#- 32$: ":\\#\:\' ! .,"0†:#-*,' 2 09# %,'>'\)
8309#-7"!4#10 #-]0' !$#
' '\)R2 89';*<89' ]' *<890'
#- %,2 "' 09#- 1#-024A "';2$†' * -"! 2$%,#- :Ui' 030"i%,'›7,0' 2$( -†4 - };":\ '' 2$%,';*<89' }2$*(' 2 89A -' 2 89';*,%, - 3' -:†!$ 6' ;832 - :\2$*(2$:\2 %A !$-
,2 ' , %(' 3¡' 6%(' ;":\7,03';' *,%,';0 \7,#-33#-%,\'‘7,03' "' 0 @ !(48 !(03 2$:\"7 !,! 32 "*/# # 7,0R !,09# %,'>! ' 2$
'<!,'sO' )R7,!$<2 '!(' : \ ":\7-08 #1:';*v83&%,');' 0€89" @' %* --:';*," , !#-;"*<89'; 2$:\' *<83" ')( -;"*,.,'; 2 %/#-)#->' '<!/># ' s%(';89';03:\2$%* 4 832$#1 '<!,'B">O' )(7(!$2$ #-
: ';*<8 - '&' : 7,02$*,X 4$7,2 i' €8 #- 7R%,';: 3';0
!(832$!$2 %#-%,#-67/#109# 7,03' "' 0 03';( !,! 8 #-%, %,2
' !,:#H%/#-%/# \' )R7' 0+2 *( 24# i%,' %,
' '<!,'&3¡' 63#-: ;"*,.,'; 2$%,#-
#- -*,%,2 R';†2$*,2 2$#-2$ G]&';*v89#-*<89 _*/#&# !(; *( 24#&%,'>03';+"09#1 '!(')%,\' "/*/#-: ;":7"0€8 #-:\' *<89s%,'
!,: 32 83' :# K7,0R !,09# - 3'%,';83' 03:\2$*,#-0>3' !r ":\7-08 #1:';*v83 @ !R48 !,0 #n7/#-0€892 0 %(' ! $,' 0 1#R';
-*, 0';892 %#-%,#-›*,>7/#-33#-%, e ' €8 #-›32 48 !/># ' <!,:#‘%/#-K(8 ' *(2$#1–:#-2 K ": !,*, ' #>%,¤# bdT.U\rK?+H opJ
pU£’~x\TO?mUVHœƒ„U\j>kDJ^TR,?+H¤†zbd’0ƒ '<!,')£' $/#-3';24# ' : , $,3';0 1#
' ;03"*,-!$"+"2 #-:\' *<83'U"03%(' */#-%,#- %/#
1#-032$A "' !i';: ' €48 !,%( ./#18 "/' ! % ˆK‹ * ‹ ":\;"*,3X' '<!% *,;24# */#}48 !,03#-!D%/#\2 :7"0€8 )-*,;24# %/#\7,03' 2$4 1 1#-032$#-%/#-†(8 ' *(2$#16%,¤' bS’0ƒ @ 09#1: ' *,%,H%(' 3';* ""! R2 %/#- i"032 !,*,%/#-]%,' %,2 3;2$7,! 2$*/#- -:Hg
# ‘\ADr,UVH\NQ?#…|R!n7opJ kDU\T;Rpa\?mJ^AlR,s # qeH\Y
NmR,N+H\NQ?ma;RB' # ‘OA L J^TOj v,Nz?ma;R
#6*<89'; %,"s#-*," Š + # 7,0' 2$( -';09# 'Œ@' Œ48 !/#-%,##18903# ,' s%,' !(:B# 32$:\7,! ' >\' )
8903#-7"!4# - %,'
!,: 1#-!$-0]+"! ! $/#-!DK# 6;!,89#-%, ';: @ !,O* -%,B89';:7 # ';09#B:\
%,' 0*/#%/
# bd’0ƒ ":\' ;, !'<!/#1*,%,
!,! ' ˆK‹|Š 2$* -' *<89, !X :\
%,' ! >CN¡J^YmŽ1Um…,TVUVHVH\?Br,J † Ž D"*,%,'& 7,;0 - )R2$:\ 1#-!$"06%,' 7' *,%(24# %,'
!,:# 3":# 7' 9#1%/#H%,' 1#-!$"0' ‘#1*v83' 02$"0' i7,#-09#H7,0' "';0>H* (:';03 #-<* !/#-!K%(' :B#-*( ./#-‘3-!4#-0' Œ
!
5 !,03#-*<89' #-s%"' #-%/#- ' +,!,2 *<89' –#n"7,2 *,2 - 03';2$*/#-*<83' ' 03# #n%,'œ'<!,' ;":7"0€8 #-:\' *<89 %,' !,:
&
32 83' :#&%(' 7' *,%,2$# %,'>%,"2$†;":\7"*(' *<89';]7,02$*,;2$7/#12$ :
%,';!$"†! 2$*,' #-03';ˆ'>0(!%4 %, : :' #-%,">%," #-*(" 0+ D%,"2 >#- "*<83' 2 :';*<89" #-! 89' 03#-09#1: %,03#-:B#}892$ #-:\' *<89' #1:7 %/#
7,0' 2$( - S: 7,02$:\' 2$0‘@"2J# 2$*<890RO% !"-)%,&' !(: ;"^* 6;!,*<83 %,'](8 ' *(2$#1~%,' >st?+H R,jU\ADNMJ£q EXkDJ^AyU\ADY
a\?QR,s † >q e'<!,'';09#-: 32$:\7,! ' ‘%,'\3' !(892 !$2 %#-0 Z\' )R2$+-2$*,%, 7, !,; A-!$ !,!$ i';9: $"09# 89';*,./# !$' 1#-%(
';03 #s%,' Π+ #-*," #1(8 '6+<#-*(./#-03';: !,: 03' ;"*,.,'; 2 :';*v83 'U#1%,"7 -)+"' *,';09#-! 2 % #-%/#- G/' ! 2 % :\' *<83' v
3';,+ !,*,%(\+-09#-*,%('‘' "';*<89\*," #-*,- 0+ @"2#1% "';*v83&%,& ":\"7 !(89#-%,"0 (7' 03:\2 832$*,%(s03' ""! !, 2 "*/#-0
#n#17,!$2 ,# $,2 !$2 %/#-%,' %("s: ';83R%,-)%,'7,03' 2$4 1 G'<!,'B'B89-03*/#-03#-: #1%/# -'% :#-2$>7""7 !,!$#-03';s*/#1
"0+<#-*,2 %# R';s' *,- :';2$"):2 !$2 8 #-0' `¢:\' %,2 %/# '<!,'Hn !,€89 %,' ;":O7 !(8 # -2$# %,2 :2 * !(2$*,%,
n# v032 %/# v2$% .(' ' ! 032 +".<8 ˆK‹ * ‹ 5 !,03#-*<89' "&#-*," 0+ ' + ›., ! "' !,:#7,03
!,03# 7"0 !(:B#89';"032$# !,*,#2 "/#-%,# %(' 7(03' 2 4 - &
: ˆ ‹ ( !,0+"2 !#:\';89
%,"! "+"2$#&%(
' WJXE!Y[ZDU\A&]^?BA&H†zW Z „'<!,'s2$*,;"037"09# 1#%(2 "';03"U' ! ' :\' *<89-
%,'\8 #-!89';"032$# H89#n:\';89
%,"! "+"2$#@"03*(' 2$# !,: 7,0R;' %,2 :';*<89 32$€89';:BA1832$; 7/#109#n# #-*/A-! 2$' %,'
(';032 ' ˆ89';:7"03#-2$d '!(' ';09# ; !&"/ 2 ' *<89';:';*<89'>+"' 03#-!Z7/#109# !$2 %/#-0 "
: 2$0€48 !/#1!$:\' *<89' '<!/#-<! '<!,' 0ˆ832$7
%,'>! $,' 0 -#>
' ' :\%7 4$02$#1 3"0 , !(8303\!4#-%( ,' : ]!$+"X' $,09# (89';: - 3' '!('s#&!$2 *,'#-02$%/#1%,' ' %,X' "/*(2$%/#&' : 83' 03:\"†%,'>@ !,"* R';
'<!,' ( !%$, 0' "';: #^# )R2 ":BA}892$ # "#'$
"#'$ "#
"# / $ /6"#%$ G6 <"
ˆ ˆ ‡
# #18903#-- 7';!$":\R%(' !$-!$2$*('#-0' ' ;!,832 / #-%/#>7';!4#‘32 :7,! 2$;2$%/#-%('~%,' #-*/A1!$2$'†'] A-!$!,!$ "* 48 !(%, _' R2$€89';: %(' "';09#-632 8(!/#R';]"*(%,'s\:
%,';!$&!$2 *,'#-0 ')89-03*/#&2$*/#1%,' <!/#-%( (!,0+"2$:\' *<83
%/#
"';2$ # %,' €8903-*/#-0s 7/#-03#-%,2$+-:B#H!$2 *,'#10 %,' :\"*,€8909#1*,%, <,! '2$* ,:\' 03- @' * ":\' *("U -:7,! ' R"]' # 1892$;" 8 - V!(!$+<#-0' U*( :';2$B@ 32 ' + i#84(! 0 ",! ! *,;24#B';: "! $%,-
,! )* ,:';03 %('U "*(892 7/# R'; –7
%,' : 3';0~+"';09#-%("ˆ#s7,#-0832$0–%,'6' ,! #
' ˆ2$:\7,!$'; *"- !$2 *,'#103' 3 ' 2 89+"';* 'Œ8]#-! \)
' ”:
ƒ„UVJ^TO?QRpJ heRpJKH
'
%\) ,4
;$ <
%4
V‡
X'
ˆK‹,‹|Š
3"0'\R) ';:7,! P": 'Œ89
%,"i' €8 #18;4$€892$;"D "* -' *,;2$"*/#12$ 1 ":\ >q P7
%,' 0(- *M- 3';0"D:#-2$
#-%,'X<' !/#-%," 7,#-09## 7,03' R2 4-n%,' !(089 7(09#%; K7"0s' 03';: 2 *,#-7,#% '; %,' 0' -*,.,' ;' 0 7' '<!,';*/#-
1#-032$#
' ' + -#10324#>
' &%,'n7(03';f%,'n#-R';;-8 #1%/#-\*/# $ "!$3#|‡9'<!,'n2 04- 89';0 !(: +-09#-*,%('
2$:\7/#-Œ89&# !$-*,+" 7,03#% .,"*,'X"$ !,03+ ˆK‹!‹ + ]f :#‘#-! 83' 0*/#1892 1#]7/#-03#‘#}bd’0
ƒ '†%/#-%/#U7' !$#£‘\ADN¡U\st?#…p‚\Aya\?QR>TONQ? €a\?QR,s† ‘; -"*(%,'ˆ@"09#1: %,';3';* "-! 2$%/#1 !,: ;"*^;6 !,*<83B%,' 84' ;*,2$ #- 7/#-09##0' 3-! !"-B%,' 7,0!,$ !$';:B#1 /2$*(37,2 09#-%/#1]*/#6#18(!,03'%# -:H#1 Ž1U;pUVH U\CT.J^AlR,?+H >T\NQ? €a\?QR,?+H†zŽ H \'s"£>s …pJ^TO?BNzjJKHgwU\Ayx\NQ?maVJKHU q r,J^stCDa\?mJ^Alv,TO?mJKH
† 9wdqeH &<' !,' #-7,0' ' *<8 #-03#-: 0' ;!,! 89#-%,"ˆ2 *<89' 0' 9#-*<89'; *!(: 1#-83 !$' <' !,'6%,'>#-7,! 2$#>
' ~;2$';*v8;4<" )
$ #1 '>%,'>';*,+"' *(./#-032$# › 56';*v8303\%,' €89' "*<83'\)
89 _ & !$#!,;!,!4#-%( ' *<8309#-!D%/# 89';3' >' %/#-%,&7"0 :Ԡ:\
%,' ! "~2 *,37,2 09#-%("ˆ*/#(6#}84!,0'%#
7/#109#&# 7,03' R2 4-\%,'>(';032 ' †89';:7"09#12$ ! : ,$p6' Œ892 - %/# ‘\ADN¡U\st?#…p‚\Aya\?QR >TONQ? €a\?QR,s† ‘; 7/#-9# 7' !$ %(' 3';* ""! R2 :';*<89 %,' 7/#-09#1%,2$+":#-)'
#-! +""032 89:\"7/#-09#‘0'#-! 2 %#108 #-0';@F#-›;"+"*,2 892 1#- <#-0'<!/#-2 ›4- #-Œ84!/#-! :';*<89'†'\)R';!(89#-%/#-–7';!$"' 0' .<!,:#-*,"D%,' !,: :\R%, '\/" 2 ' *<89' #67' 3#-0%,' ' 0 !,:# %,2 3;2$7,! 2$*/#~0' ;' *<89' @"2-@"0:B#1!$:\' *<89'2 *,2$;2 #-%/#U';: ˆK‹ 0 |‡ 189' : 2$*,%O!"% 2 %,U%,';3' * -"! 2$:\' *<83"›32$+-*,2</" #1892 ""' : %,2 @';03' *<83' –A-03' #-K%,'†;"*,.,'; 2 :\' *<89 <*(":' #-%/#-:\' *<83'ˆ*/#U -:7,0' ';*,4->%/#U!<$4 *,+!/#6*/#18(!,09#1! -*( 03#- 2 RX4$*,2 ]!<-"+"2 - :B#183' :A1892 */# 89';"032$# %," 6 "+""†! *(" 32$€89';:B#-†%('s#-7"2 ¤\¢ %(' 2 4- / !(33';!$! ] "0 R2 + ˆK‹,‹ 0 ]f : 32 89';:B#]%,'1‘;S
 %,' -'†3';0K#-7,#%ˆ%,'ˆ7' 0€@F#% ';0890 K0' <' !,2 32 83" 6# v2$* ˆK‹,‹!‹ z 2 +,!,09# ˆ ˆ ‡ 7,0 R2 %,' *( 24#1: ,! :# #-! 83' 0*/#1892 1#s:B#12$~'\"/#>%
Representação
Aprendizagem
Raciocínio
2$+,!(09# ˆ ˆ S:U†890;;
":\7-*,' *<89'; @ !(*,%/#-:\' *<8 #12$†%,'$!,: 2$€89' :# %,'}‘;
#-0:B#>% ' *,#-0† "*(.,' ;2$:\' *<89 T.U¡klT.UVHKU\ADNmR!n7opJpJœaVJ^A
DUVa\?BjU\ADN¡J!‡ #-7(!$2$ #-0ˆ& -*,.,' ;2$:\' *<89\#-%&'!(2$032 %,&7/#-03#&0' "! -' 0 7,03,,$ !$';:B#- TRpa\?mJKa BAD?mJ!‡ ('
#-%&'!(2$032 0ˆ*, "\ -*,.,' ;2$:\' *<89#18309# ,';]%/# 'O)(7' 02+;*, 2$#R\klT.U\Al,?KRK…pU\jg‡ :C7,032 :';2$03]03'X'!(2$32 89U';* ""! "' !,:#9TVU¡klT.UVHKU\ADNmR!n7opJ>pJ}aVJ^A DUVa\?BjU\ADN¡J ,<' !,' 7,0 ' : %,'†%,"2 892 7"
%,'>2$*R@"03:#1
0
&' €8 #-%(;"*,.,'; 2$%( /03';7,03';3' *<89#-%,B7"0ˆ@F#-Œ89" !$,03'>('<!,'
‘' '<!,'>3' "*(.,' ;' _'
!$(3' 0 1#
' ‘,!n:';%,2 R';U3!$(03' #-:}$,2$';*v83'„'!(' 7
%,' : ;"*<89' 0‘0;!%4$%( ' ' €8 #-06(!^6';2 8 #1
# ' 003" :3';+,!,*,%,>0' '<!,2$2 83U%,2 % 03';37' 2 83‘#-9 TRpa\?mJKa BAD?mJ -%(X' "/*,2 %,‘ -:6#U#-7/#1 2$%,#-%,'~7,#-09#U9# T.UVHKJ^stCn7opJ
pU€klT.J s+U\j R^H l'<!,'>7
%,'‘' 0 2$89# ":\ !,: 7(03! $,! ' :#s%,' klT.JKa\CTR|{Sf]:#s@"03:#s%,'>!$2 %/#-0 ":
# 7,03
!(092# '‘ !,%(' 0' +"03#- (%/#-%," / "*<8303"! \ ! 03#- 2 RX 4$*,2 7,0! $/,# $,2 +! 4 892 3"0 ,! 892$:\ Z83' : - 3'\# R\klT.U\Al,?KRK…pU\j D7' 03:\2 832$*,%( # !,:\' *<8 #-0> "*,.(' 2 :';*<89 #18903# ' )%/#
'\)R7' 0+2 *( 24# # #-7,0' *,%,2 %#-+-' : 7R%,'&';* -"! -' 0)"% !/#->@"03:#-‘%,2 @' 0' *<89';)%,'\7,0R;' 33#-:\' *<89 %,'
2$*R@"03:# 1 (?BAl,CNQ?Br^R ' pU;,CpNz?Br^R]# 7,02$:\' 2$03# @"03:# D7/#-%,0R';s'\03';+"09#- 4 1%,';83' 0:2 */#-%/#-
#B7/#10892 0]%("6%/#1%,"U')\' )R7';03<2 *,;24# ' + GR\klT.U\Al,?KRK…pU\j VR^HKU;R||RU\j a;R^HKJKH^‡ ';%* '<!/#-*<89œ
'<!,'s*/#
,! 892$:# R#- 03';+"09#-†( - !(892 !$2 % #-%/#- 7/#-03#&;032$#-0†*, "" @F#-Œ89" ' + &klT.J^r^RgpU N¡UVJ^T.U\j R^H^‡ : !(890 #-7';;89 # 89';0 ';: "*<8 # 'U#>@"03:#‘ ":\ !,: :\
%,' ! )%,']#-7,0' *,%(2 %#1+"' : 3']03';!4#-;2$"*/#
-: ]3' ! #-9: $,2 ' *<89' ' €89'ˆ;"*<89\' )
83 "\' )R2 89';: 89;0 ;7/#109#-%,2 +":#-i@ !,*,%/#-:\' *<89#-2$' : '<!,'†#133';*<8 #
#&#-7,0' *,%,2 %#-+-' : 3#1889';033-* ˆK‹!‹ # $/#-€8 #-*<89'n7"O7 !,!4#-0 '<!,' ' * "-! "' !(: 7,03 ’uCKkDU\TOrK?+H\?mJ^AlR||R|{ 809#}8 # - 3'%,' !,:B# 48 ' ;*,2$ “
@';33-0 ~, ! M' 63# ˆ( -X@-03*,'; 2$%,#-0' 7"€8 #- "003';;8 #1B#-X32 89';:B# # #17,03';*,%,2 % #-+"';: '
'Œ@' ;(8 !/#-%/##7/#10892 0†%,' !,: "7* 6;!,*<89B%('s7/#-%(0 ' _"*(%,') #-%/¤# k&R|,T;opJ ,89#-9: $' : .,#-:B#1%,
%,' UEU\j>kls+Js ! a;R^HKJ pUNzT.U\?BAyJ O'6 ":\7-89s7"@0 !,: -' Œ89"0†%,'6' *<8903#-%/# 'U7"90 !,: "';;83"0
%,(' T.UVH¡kDJKH\NmR, !H R Q|R
: $' : ' #-3; !,:' # 7,0' 3';"* #\%,$' !,: 7,03 –9U>Ž”U L J^T nFJ e]';83'>832$7 %,' #-7,0' *,%,2 %#-+-' : 89#-9
@';33-0 s' 9: $"09#B# 03' 7-8 #H;"030' ;89# M* - M' 63# #-7,0' ' *<8 #-%,# #1 32 89';:B# #632$
: i#-7' */#1
' @"03*,'; ' !(:B#n2 *,%,2 # -3, $,03'H'H#03';37"89# %(' "-! 2$%/# 7';!$2$83' :# 'H -0303';;89#, !
';0309#1%/# ,' *,%,' €8 #&2$*(@"0:B># - !R892$! 2 % #-%/#s7/#109# :';!$.,-09#-0†# ; !/#\\' "/A1 24# ' !,:# ,# $"03%,#-+"' : %,2 @';03';*v83' ,-*,%,'‘M* - 'U@-03*,'; 2$%,# #-
opJ¤’uCKkDU\T\rK?+H\?mJ^AlR||R G809#189# - 'U%,$
2$83' :# !,:#62 *,%,2$ # 1]O' )R83' 0*/#‘#- ';03 #U%/#603';37"89#U "003';;8 # K3-0K "*(3' + !,2$*<89' <#U#-7(03' * %,2 %#-+-' : ' @';2 8 # 7';!4#6%(' 3;! $' 089#U%,'~ #-09#1;89';;0 4 892 #-*,"K%,#-%,"%,'ˆ' *<8309#-%/# <#-%/#-7R8 #-*,%( - '
# 03';,+ !,!$#-032 %/#-%,';†' 89#1.8 4 832$#1†, ! #-+"(0 !(7/#-:\' *<89" %,'>7/#1%,0 ' †%,- O' )R' :\7,!$" %,'‘8303' 2 *, # ,# $"0%/#-+"';: 2 *,2$;24#-!i' ,+ !(2$%/# */
# ‘ ;": R2 89œ
# ¢B! $(83' "* -H%,'s(8 ' *(2$#1U7/#-03#H#B03';3"! !"-B%,'
7,0! $,!$';:B#1 7,#-33# 1#B7"0 3's#-%,"7R8 #-0 !,:#,# $"0%/#-+"';: ' 3' *,;24#-! :';*<89' :B#183' :A1892 # (*/#;03' O* #
2$:\7,<! 4$ 2 8 #>%,&09#-;2$
4 *,2$ <! -"+"2 ;": !(: :B#103 7,#-09#&# 2$*<89';037,0';89# -&%/#&2$*<83' !$2 !+ *( 24# -*,%,'>
-*,.,' ;2$:\' *<89 '~0' 7,0' 3';*<8 #-%,‘7' ! !(36%(@' !,:#]! 2$*,,+ !,#-+"' : H\?Bj ^st?ma;R-#}8909# ' %(@' !,:# ;"!$'; -
%,'‘@F#-Œ89" '‘03';+"09#1 7,#-09# :#-*,2$O7 !,!4#-0 ' €89' '
$ " *<84!,%( U*, "- 7,#-09#-%(2$+":#-B7,#-09#r#r03';3"! !"1r%,' 7,03!$(!$' :#- 2 *,37(2$09#1%," ';: :\R%,';!$"
$,2 "!+-"+-2$ - ";!,03+"2 09#-: %(' *<890 %/#¤‘C;":\!,:#)0'#-- #-"–:
%,' ! "›32 :9$„--!$2$;" <;"*,2$%,';09#-%,-
%,';:B#-24#-%(f;0 4 +"2$%("&'n' 7'; 2$#-!$2 %#-%,- 3 !,+"' 0 84!%$&$,!$'\"/' ! % ˆK‹!‹ * : ' 8(!,%,r%,' 32 89';:B#1
7,0' 3';*<89' >';: 3';03'; R2 "" i ":\ H\?+H\N¡U\j R AyU\TOr,JKHKJ aVU\ADNzTR,s,! H%,# U\r,J^stC&n7opJ$ ?mJ^s ;…,?ma;R%('!
"02$+"';: #-- # J pU\s+JKH hdJ^AyUE!?mJ^AD?+H\NmR^H†1' ¢hdJ^j>klCpN[R!n7opJ wU\Ayx\NQ?ma;R U€qdr,J^stCDa\?mJ^Alv,T\?QR †Vh wdq , { ":
' €8 # : !,%/#-O* # –%,' : 'Œ89
%,"¤ $/#-'#-%("';: 03';+"09#-&7/#109# : 'Œ89
%,"¤ $/#-'#-%("';: %/#-%,- ˆ# ‘;
89-03*,, ! - 3' #-7R8 # 7/#-03#&! 2$%/#10~ -: 7,03, $,!$';:B#-†;":\ %/
# bS’0ƒ ' 2 +"' *(% 1 ';033.(' *(@';!$% ˆK‹,‹ ) !
#6(Ž1U;pUVH U\pC TVJ^AlR,?+H9>TONQ? €a\?QR,?+H †zŽ H 8 #1:9$ ';: %,' 2$+"*,#-%/#-)7"0¤H\?+H\N¡U\j R^H aVJ^AyUE!?mJ^AD?+H\NmR^H 41X:\R%(' !$- 32 :7,! 2</" #-%,"s%, 32$€89';:B# *,';0 "-3f;' *<8903#-! %, 3' 0&.<!,:#-*, if :B# Ž1 ' !,:
7,0R;' 33#-%,"0\' :\2$*(' *<89';:';*v83' 7,#-09#-! ' ! › ":\7-89 7"0&32$:\7,! ' !,*,2 %/#-%,';%(' 7,0R;' 9#-:\' *<89 %,';32$+-*/#-%/#- 7"0 *,'!,0"- *,2 "]!n*,
%," l<' !,')7-3(!(' : !,:#\7,0"7' *,(- */#18(!,09#1!i7/#-09##-03:#%;' */#-0
-*,.,' ;2$:\' *<89 ';:7&$4 032 )'689"0*/A - !$ #1 ' ;4 "' !Z#-!(892 !$2 %#-%,-0 #63' :\' ! ./# - '‘#- ;":7"0€8 #-:\' *<89
%,&';03'X,$ 03.!(:B#-*(\';: %,"2 #-37' Œ89" 6# 2 * ˆK‹!‹,‹ X "*,.(' 2 :';*<89'n#-%%<' !,2$02$%,X#f7/#10892 0&%,' !,: #-:},$ 2$';*v83' #18309# ,'; %,' !,: 7,03
';33f%,'
#-7(03' *(%,2 % #-+"' : ,'
' #103:#% ';*/#-%,S*/#-
M "*(.,' ;2$:\' *<89 f
H\?BAlR\kDHKUVH R' *<890')"†*(R%,- aVJ^AyUE KUVH 8 #-:}$ ';:
%,' 2$+"*,#-%/#- 7"0
st?#…|R!nKUVH
,!
5 !,03#-*<89' U7,03
';3U%,'ˆ#17,03';*,%,2 % #-+"';: }%/#-%,]7-0!,: R,s …pJ^TO?BNQjJ pU R\klT.U\Al,?KRK…pU\j ,!œpU NQTVU\?BAyJ &
"0kDUVHKJKHU%,#-~;"*,'\) ' 4- #K6;!,89#-%," %,' @-03:#)# 3'U#}892$*(+"2$0 !,: %/#1%,s!$ 6' ;832 -(2 ' s';8 #1%,
%,'› -*,.,' ;2$:\' *<89 %/# 03';%,'›:}$"03#†3'M63# ' €8 # # @-03:#~8909#1%,2$;2$"*/#1!-%,'› -*,830(!,2 00Ž H v89#-:9$' :
'67"; 4 -' !:
%,#2 "/#-0–# ( !/#s7(;0 -"7,024# ' 830(!(8(!,09#)2$*<89';03*/# F,! N¡JVkDJ^s+J;…,?QRp‡ p¢s3';:';!$./#1*"# %,9'<!,'6'
7/#-9#B*( ';03' $(03 "*,%,')"]*(' !,0 -"*,2$-67R%,';: :"003';0 ')*, 1#-62$*/#-7(3' F's:\' :\*,'!,0;-"*(2$".‡
3'>7R%(' : %,';3';* -"! -' 0 !"#$%&#'(*),+
-/.01023547689
: #12$"0U7,#-083'%/# 2$* -' 832$+<#>- ' : Ž HB@"2K2 *,37,2 09#-%,# '\2$*M!,' *( 24#1%/#H7';!$">32 83' :#->*,' 0 B
"-3"]%,"6' 0' 2 -" ' : 7/#10892 !,!$#-0†%,3' 0].<!,:B#1*, !,2 89" 2$* "';832$+<#-%("03';6#-;03';%,2 89#-: '<!,'
#- Ž H 1@' 03'; ';: # #-7(03 )R2$:#-):B#12$–7,03":\2$3"03#)7/#109# #s;"*,830(!"-&%,' -' 03%,#-%,' 2 03"~32$€89' #
:#-‘2$*<89';!$2 +"' *<89'; J83' *,%( #-7/#-;2$%/#-%(' 7/#-09# !,! 8903#-7/#-9#-0‘#H'O)(7(!$"(- ":9$(2$*/#18;-"032$# #-3
24#1%/#Ϣ
-:"7 !R8 # -&32$}: $„-"! 2$ # $/#-'#-%,#\';: #-0;'<!,2 89';;84!(09#- %,'(r,J^A U\Cj R,ADA 3#}8389';03"* ˆK‹!‹ [{
: 32$€89';:B# *,' 0 "" ' *<8309#-!@"03*,'; ' !,:B#>@"083'$,#-3'U%('6(!(89';*<8 #-&#s' €8 #)83' 'd: ';03' $(03
' !,:# ';83(0 !((8 !,09# #-! 89#-:\' *<89'H;":7(!$\' )(# –*M- ! 2$*,' #-0 ' 7/#-03#-!$';!4# 3"3;!,2 !,:B# #-7/#-;2$%/#-%('H%,'
"0+<#-*,2 %#-0 " ' !, ;"*,832 (8 !,2$*<89'; ;"*,.,'; 2$%(" 7"0s*,' !,;0 --*,2$" %,' :\R%(#\' )R'; !(89#-03';: ';089#-
8 #103';@F#1 ;":7(!$\' )(#- F' + 03'; "*,.(' 2 :';*<89s%('67/#-%(0 ' –, ! -,%K‡ (%,' !,:B#‘@"0:B#>2$*/#}892$*(!+ 4 -' !,7' ! -:"7 !R8 #-%,-0–:#-2 7-83' *<89']#1(8 '].,7 6'];"*, X' $,2$%( : 89';03:\"›%,' -' ! R;2$%/#-%(' %(']7,0R;' 9#-:\' *<89 !,: *,' !(;0 -"*,2 '] ' 0# %,' 0 # -'%;' :B#12$›!$';*v83 %,9
'<!,&' !,:B# 7-08 #)+! -"+"2 #‘%,'U2$<! 4$ 2 `8
%/# 24# > ';03' $(03$ !,! 8309#-7,#-33#>';89#>! ' *<892 M% - !R892$! 2 % #-*,%, !(:B#U';89;0 !(48 !(09#‘:B#1 2 #-:\' *<89'ˆ7,#-09#-! ' !$# €892$:# 3
' '<!,'
a ^TONMUEr<. !,:#-*, 7"( !,2– ';03 # %,' ˆ + $(2$!$2 R';‘%,'\*,' !,0 -"*,2 ")' + 8902$!$2 R';‘%,'\32$*,#-7,3';
6# 2 * ˆK‹!‹,‹ 2$+,!,03# ˆ Š ›890;!(84!(09#&%,'$!,: *,'!,0;-"*(2$&*/#18(!,09#-! f]: *('!,0-"*,2$ '
!,:# ';! !,!$#S;":\7,!$'O,) #“<' !,' 03';37"*,%,' #r32 */#-2 H' !$';;8303 - '!&4$:\2$ - 3';*,%,
-:7"83f7"0!,: A ua\s+UVJ 7"0!,: aVJ^T[kDJaVU\stCs#R,T ˆ7"0!,: *!(:';03"f -*^6;!,*<89 %(' pU\Al,TO?BY
N¡UVH ';*<892$%,#-%,' '<!,'s03' ;' $ ' : 2$*/#12$ %,' ,!(8303"6*,'!,0"- *,2 " 24#B2$*/#17,3'; Z' 7"0 !,: R E ^AD?mJ l'<!,'
8903#-*,:2 89'2!,: ' €8.$4 : !,!$ # ,!R8903-)*,'!,0;-- *,2$" K#18309# ,';s%/#1136 A 0';@';032$%,#-)2$*/#17,3';z 2$+,!,03# ˆ Š ‡
5~"3'&3i2$#-*,+ ˆK‹!‹ f]: ,*,2$; *,'!,0"- *,2 H7
%,' ';8 #10 ! 2$+<#1%, # ;' *<89';*/#- :\2$!$.,#-03'; J! :\' :H%('% ';*/#->%,' :\2 !$.,#-03';)*,'!,0;-- *,2$" !,: ' 03'X,$ 03n'\R) 2$€89' : ';890;!(84!(09#- #1*/#18.-- :2 #-‘%,'7'X<' !,' */# K: ';%,24# '#-! 89#
-:7,! '\R) 2$%,#-%,'\ ": %,2 @';03';*v83' @ !,*"
' 3';*,%, 7"34 "';2$ 7,#-03;' 032$#- U: s*,'!,0;"- *(2$" 89' *(%,' : #
#-+"0;!,7/#-0 - '‘' : #-:B#1%/#- /'OR) 2$832$*,%(&830;; 7(032$*( 2$7,#-2$~832$7"ˆ%,'>;"*,'\) ' z 2 +,!,03# ˆ Œ!‡ ,?Br,U\Tz…pU\ADN¡UVH ,"*,%,'$!,: *,'!,0"- *,2 \7
%,'>' 89#-0 !$2 +<#-%, #&,!(8303" *,'!,0;-- *,2$" 2$#2!(:B#&#-0$ "02 % #-&%,#^)"- *,2 ¥Œ;’P‰ˆŠŒ;‰~©x€zP|†„”‰}‰
?¢3|ˆ„”x|ˆ ”ƒ¡ K’ P‰P™ „”Ž „”|ˆx€Ž‹¡„”‰P zPxZŽx€Š;xJz}|ˆ„K™;Ž„Œ‰}‚xZ¡ ;‰;Ž‹{PzPƒ—€˜Œ‰1„
‚x }‰Pƒ—€˜” ‚}„†„” ;z} Žx¡?ŽzP•„~‚Px|ˆ zP ‰1Œ„ yDyx zPx‰}¡ ƒ„”ƒy€¢;‰}‚xzP| “ ŽŒ™;Ž„Œ|ˆ„ ¦›„”Ž|†„ x€‰}„;‚ ‰1„ˆ|~x3yF|†„ˆ|ˆx€| ;ƒ„
‚x›‚P„;‚;y zPx “ ŽŒ™;Ž„Œ|ˆ„–z‹£‹ 3„ D xKx€| ‚P‹„}¢ ;z1„ŒyxŽ‚;yi¡€Œ| “ z•„Œ‚;x3yJyŽ˜”ˆ‚ˆŽ “ †ŠŒ;‰]©DxzP|†„”‰P‰
$
%! '&)(
*
!
'
#"
+&
$ *
aVJ^ADr,U\Tz…pU\ADN¡UVH ("*,%(' 1A-02$"†*('!,0-"*,2$-†7
%,' : ' 89#-0 "*(' ;89#-%," #2!,: ,*(2$ &*,'!,0;--*,2$('
U\Aya;R|pU;R||R^>H ! a ma\st?ma;R^H /#- '<!/#-2 7
%,' : ' * ""! "';0 1A-02$"†*('!,0-"*,2$-†'>@-03:#-03';: 2 ! " Divergente
2 +,!,03# ˆ Œ S:‘
3-0U(!/#
N ^T\?QR^H Encadeada
Convergente
Cíclica
%,2 @' 0' *<89'; 832$7"†%,'> -*,'\) ' "'%D#-U;"*,'\) ' U(-H -*,832 84!&4$%/#- 7"06%,-2$]832$7" %,' 32 */#-7,' ?BAD? ?BN ^TO?QR^H ' U Ea\?BNmR,Y
:
"1 1#'
,
7 %,' 0s ":\7"!(89#- 2 "*/#-!–%,' !,:# Ž1 #1!$2$;' 0;# - 3'B';: %,-2$ #-7';;83" @ !,*,%/#-:\' *<89#-2$ *<!,:#
89-7"! "+"2$#'!(']7,0' :\' 2$# )7/#-09#1!$' ! 2$:U'R7"0›,!(8303)!4#-%, <*/#);!/#) #-7/#-;2$%/#-%(']%,']#-7,0' *,%(2 %#1+"' :
'\+"' *,';09#-! 2 % # - 2 ' "*(3' + !,2$0 03';37"*,%,';0)%,':
%, #-%,'X'<!/#-%,n# *, 1#-)32 8(!/#R'; ;": $/#-'
' : \' )R7' 0+2 *( 24#1U7/#-9#-%/#1 $O1H' 89#-U"% !,#-U#109#-Œ89' 0 4$€892$ #-> '<!,')89"0*/#-: 7-3; 4 "';!K#B0' 3-! !"-
%,'>7,0! $,!$';:B#1 '!(' /%,'>, !(8309# @"0:B# R3';0324#1: 2$*<8903#18 A -' 2$ =?83 "* - '<!,' 0›%,2 % ' 0 '!(']#1d Ž1 >H]3M' 63#1: #1#2 )(#-K:A-+"2 #-@ '!(' ;"*,2$+<#-: 7"0K32(%/#-0K0' 37"€8 #
# '<!/#-<! '!(' 0 7,0! $,! ' :# : -'% %,2 33 7,03'; 2$3#-: M* - 09#109#- "'%;' &%,'H' 03';: 2 *v83' +"03#-%/#-s ":
, !(8303" 32 89';:B#1~, ! 7,#-09#-%(2$+":#-–7/#-09#s#s03';3"! !"-)%,'U7,0! $,! ' :#- -* ' : /#-2 *,%/# v03'; "*(.,' ;' 0
'<!,'&3'\' €8 A #-2$*,%,# : !,2 83H!$"*(+"' %,'\#1832$*,+"2 0 !,:#H#-;0 '<!,2 89';;48 !(09œ# '<!,'2$: !(!$' ';03X' $,03 <. !,:B#1*,
6# 2 * ˆK‹!‹,‹ ]S' *<89#-*<89 6#- Ž >H #17,03';3' *<89#-: #109#-Œ89' 0 4$€892$ #- ,*(2$#1 >'<!,' M* 1M' ' *,;"*<8903#-: ' :
, !(8303" :\' #-*,2$:-ˆ, !H48 '; *,2 #- #&% ˆK‹,‹ 0 M 3#18383' 03"* ˆK‹,‹ ]# v2$* ˆK‹!‹!‹ R\klT.U\Al,?KRK…pU\j U€…pU\AyU\TR,st?KR!n7opJ v2 ' "*(3' +!,2$*,%(s%,';3 0' -' 0†)83R%( #)7,#-0832$0›%,'U#1!$+,!,:#-
7/#1089'; R "*,€892 84!,2 *,%, - 3'6;":\)@"0:B#-–'X," 2$';*<89' ~%,'‘#-7,0' *,%(2 %#1+"' : 'U#103:#% ';*/#-:\' *<89)%,'
;"*,.,'; 2$:\' *<83
klT.JKaVUVHVH R,jU\ADN¡J j Rpa\? n7R,jU\ADNMU k&R,TR,s+U\s+J 2 ' 7' 0:2 892$*(%, '<!,'8 #-0';@F#-) ":\7,!$'O)(#-)'M63#-:
0'#-! 2 %#1%/#-ˆ*<!,: !,083\';37/#> B%('>83' :\7 ‹
AlopJgst?BAyU;R,T\?Q|R|pU Z2 'i#189';*,%,';*,%, g# '<!,'&#
:B#12$"024#&%,"‘7,0!$,!$';:B#1603' #-2$U# ' '<!/#-;2$"*/#10‘'
0' 3-! "';0 4-\%,'>*/#18(!,03'%#&*M-&!$2 *,'#-0
R||R\klNmR ?Bst?Q|R|pU 2 ' 7R%(' *,%,n#-%/#-7R8 #-0)# ;!/# 89-7"! "+"2$# %,' #-;"03%(n -: : !,%/#-*O#-)%,
#-}: $,2$';*v83' T.J C|H\NMU UpUm…,TR||R!n7opJ H\C&R,r,U 2 ' ~7' 0:2 892 *,%, 7,0R;' 33#-0BX0(!%4 %, ,! 2 *(@"03:#- 2$* ;":7(!$';89#)%,']@"03:#)\' "/ 2 ' *<89' /#-32$: -: ' *,%( #-7/#>% ' †%('6:#-*<89' 0~ 3'!H%,' ' :\7';*,.,
'<!/#-*(%,.,A&%(' 9#1;892 1#-\%,' #-! ,+ !,:#-ˆ%/#-†; !/#- "*(\' ) R';]' ‰ , ! *,
%,"/'
UE!? ?Bst?Q|R|pU 4!"#,$"!
$ &%1 $##&(' ')$ *%,+'(#$ 1 .:0/(//21345/(4"76/8/4/9 ‘;:;*</8&=/e¢!/ Ž H>*?13/(%4@/&A4="O)
B=CD ˆK‹!E ‹ q EXklst?ma;R!n7opJF@ G ‘;H"6//8I 4JK/A/21L6/2138M#NA/8O1L!M
*/P/89$l-"#!/
C
13!Q,/8RC\ )/2.1 7ST5C/8O1L!M#NUC4O1L"V35SM#N!WVG138
"Gi
4JK// Ž HX/21L6::4/4I@"@*C4I1HY="/Z“
b T.JKaVUVHVH R,jU\ADN¡J
b€R,TR,s+U\s+J –£?+H\NQT\? C QpJF[843!Q,/8(5\O )"#MN]8! $+" -#&]/^J_4% -=/
4
13@/
qeH\NQ?Bs+JpU¤b T.JKaVUVHVH R,jU\ADN¡JF G ‘;`I@4"aB*/8/3=O1cbVNU3/?@4d/4
/8 'I7!"e&C4/= '*YNYO )/81Z5f4gbhQ,\ "&/T;
M */T/N
O )413g/ k&R^HVHKJ R k&R^HVHKJFji9/81k/81"lbkm47no4"7XF138d#n/8pI7!"?
"!133"a"qr//8sCS5/2131355C6pICStuFv xw>yz={vv
i9|I13/213!;="4"/=b4//847"a}/?~ ]G€>r/S/J_O13m>‚ƒ"
8ƒ/213dx?R?=„
†… €>‡Kˆ>y*‡Kyˆ8{R‰*w&~]w,Š;ˆ3wL€[w>v‡‹{ŒŽ*uF^Hl"6//8#]1"d#\C]"4‘/ƒ;q"#[4’C
4/8138133SpI/8T"„/213#r/8“>‚8/8/”*/=">‚/?581G/„ƒo"/
/8="4/XeI13689/S~A•eG€cY4–4=O1bU85!dYk/k4/8138133
I18T@!"P/A;/8/]/e/8/]>‚”4/r/eJ_C?@!"/P*Cb44/
_— $ ˜ 6 ‹%1 'r% 6 3 1š™ 1 1
›J_Ce=œ/V*/^/8PO1"O!ICœ4/8138133œž8žbž4=!eoP{ˆ8Ÿy ¡‡,wL¢>‡Kyˆ8{
£‡¤uLŠuF¥u¦ K{O§Si¨‚/2134©Iª=/1;/?CpI
1344133/xZ~A•eG€S£‡,uLŠuF¥u¦ K{F€O^#B
/ž/8/&q/(o147"!/4 i9 "O O138A/&#!17!/&/
* !"$#&%
]~ w‰*wL€x•w>y*ˆ3uFv;{ €('^v K‰ ¡ˆLwL¢L¢> uFv;{ €*)D~]•+' €-,/.10NS8Od#!/G;G5!/oo/GN
h‚/81)4"/4TpI?/Ph‚”4/e/08 /=80I5/qT4M#N2L¢LuFvtw>ˆ43
¦*w>v‡,wL€=H‰ ¡tw>ˆ¦*w>v‡,wL$€ 5h7 6G /ZJ_CZ5!/0/8="4/?5Z8=b=o/81LZ;C
¢{z={O‰O{U‰*wCw>v‡Kˆ8{O‰O{ / 88/0@!"8/œT/3„5/N+ 9‚/?h‚*138=O13! ToGC¢"{ 3
z={O‰O{U‰*wR€{ K‰O{: 6AZO1LO1 ;Ro/8/0C5kC/œ#C!/0O134=b/;/ 88/
*/e/N=/8!/]oe/eO134=b/ 2&;V <=5>
Camada
de Entrada
Camada
Intermédia
Camada
de Saída
3
6
1
4
2
7
5
¨3 < % œpI1>13=C5~]•'V§
;
]~ w‰*wL€T•xw>yˆ3uFv;{ €T~]wL¢LuFˆhˆLw>v‡,wL€>)D~]•œ~]€-,§S)4@?47 >‚/213=©/8/81C/xBA!C/
pIY5B/3„cZ "=O13km4fZ" =ffO13kc/8/
=/8C "=O13V47!!Q‹//8/© XC/013/J_4L–/+2C;¨3 ED!5>=e
4O13&"/*/(/3!„/&Nx/3N!xJ_M#N>‚"/
@!C4I1œ/ž4h‚”*/&O1G/I5!/
13ƒ;b eCT‰ ¡z5w>v€*u?‡,w>zGŠuFˆ8{-¥ FO
/21L6FQ‹/e08/8Mxej6"4"084/8@
pIeƒ;4360F13"=O13P0CG481L04M#NGeU4j0ª"1CA
13M#N!
T/4]=/3„T3T* HG $ 8/4 !!I/# J@KLNMPO/Q$RTSPUVMWOUPXYNMPO/MZOUZ[E\/]P^E_@`badcNcNegfhji-kml4i&e
&
V
P 1
!
3
5
Entradas
Saídas
2
4
6
V ED % G8p*134413CS~]•A~0§
;
$
"!$#
% = 86 J_A84J_4eC 8!cC;813O13U/ ~A•eG€YbfX/8X4c
8Ul2135n/4šRƒ4I1j 4d#4 k5:~]•e O@"
@l/4I1
/4pI ?47=4@4O13/ %
5 ~]•]‘b?4/813";e4@O13/œpIC x =Rƒ4I1"F
481/x A!C>13/x"@*4/^85!"=O13cu[€?ŠwL€[u[€=!/4>‚”*/4¨/3N!f"
13/?4©hQ
/8"13/213x/213„R" F
B~]•e`/8oTTC5J_855J_8O13Z /213„R"SpI@–U4//8C!ƒ4O13
4@*81/A"
1343M4”4/e/J_8/Po4"7T//213813=O138
&
&
&
9i /813x!4d4jb\h‚1L0!813¨P`4$88O13?ƒ;j–4??ˆ3w¦ˆ8{F€>L–5!
C{¥¦*uFˆh ¡‡Dz5u=‰*wR{>Š;ˆLw>v;‰ ('[{[¦*w>z)‡Dˆ3w> ¡v uF
©/8"–ln8p*134413lkn=b41lY8d#! bkm47Xo4"7 13>JK
8d#sC/8A/8=o4–5o4"7S~]•]? 6A/213R4O13h‚1S>‚/8134|C#!187/
84/ W¨!18138/ !!I F * !" # %
K{[¦v,+[€>‡K ¢LuF i9/21LTb0CR1L84JKR4@43/]4 6!#!/\/213I13/\4C.- w‰ ¢> ¡v;{
… v*¦*w>v /{ˆh K{= … ¢LuF¥u¦ K{10a3!13FQ,/8?//847"C4O13?CR1L84JKS¢>¥
{F€L€> 2\¢{ŒŽ*udF
D (§ 3h‚ž5œ8>1L?/8/*M#NœO138eO13/4pIe44/4I13`/ #/
s/21L 2_
o/8O13C/ 5>;s548/8oO13T7q/81 2K! o4M#! 5>5 4G
CBJ_85U"¨/C~]•e0€ /NkO1/ //21345/o47!/x="h‚/ 4O@" Q
@C13/\1b#!/A!4d4 2K! a{>Š;ˆ3w>v;‰( '[{[¦*w>z ŠuFˆˆ3w¦ˆ8{F$€ 5h
&*)
]~ wL¢LuFv/wL¢> ¡z5w>v‡,uR‰*w&Š{O‰ˆ
[wL€>;rC"=O13!/21L13>JKxW9hQ,/8GCxR84/8/;"
pI"* /"!N]4ƒœb\!1ƒ„œœ5]P@4// #F13/^o/8/„
@/¨i(
8=e"O[b&4/8/368A134! 5e8!&/V!”*/4/8/*/a}]/8o441@!
!134I/3NR"C4O1L/ž}GAJ_Cx8;4113
@! c!/ž13* NR[@Tb
J_84=}4rpI136=/8]#dxO1 9A!13487T8441L;!8
4|TJ_CM#N//8="7!
& ~]w¦ˆ3wL€L€*u žˆLw>t[ €*uFX“fb 4ƒ;=C ~A•e #d C*"CfJ_MN
4/4–4 (pI0/8?8#‚CAJ_M#N 9R;ž $ 88I1Tœ@>138/
>13pI>1L/ Fx
œ4=o/213/Z;Z ZO13ŽQ,/3!„AfJ_85lpIn/8j1 A!
w>y¢>¥ K‰ K{v;{C/- 8T„ 9C1/]/]O13!/ ( %
"$#&%(' ) # *+ # '-,/.
2 5
. /8O1L g@!"8#"e8q#‚CUd4 “44//NXbUCY13>JK;¤Q
J_41Lx8d#! /8o48@*/8 6œŠ;ˆ3w>t[ €*uO#/8R!813"9x/8/3N
841hQ,/81 02@*– 2Rc4C;21L=O13ZJ_1B5©B//21345 ©ƒ/C
/8U=o81L!C4I1T/8/3 2K! 3 546 5h
&87 uFv‡Kˆ3uF¥uF0i9/813C1L84JK54O@"
@Ts84//8 fCC!8138„13#=s//81C5pI
1 e/495O1 2K 5 /ƒ8eO1" 9.84"*ƒ 88441@?5¢LuFv‡Dˆ3uF¥
{O‰*uFˆAbPJ_4
/P8/ž//&R //813450I1"GAJ_CRp*?R/3!„R/81
4=–G5O13T?>J_@ ?47 % =h‚4C"/\1=/\TI1"Tt;w :¢>y*¥u[€
{y*‡ +Fv uFz5u[€>]ˆ3=u <;>[€UlŠ;ˆ3u[¢LwL€L€[u[€ ‰*w ?4@{ <ˆ> ¢LuF( /S~]•]G€U1 ? /k13"d/R
ƒ!/81L!I1/4//8
z 7 uFzGŠ;ˆ3wL€L€*u5‰*w‰O{O‰*u[€>( 9<134= 2(¥ ‡Kˆ3uS/8"C4I14/5 /8o/81@
&BA ¡¥ ‡Kˆ8{[¦*w>C
X"
13=Zp*S>‚*13(J_CM#NUCO134/8/5c213C / 88O13fC/
4 ƒ13 pI5!4/O13© 481 „WVx/8S@4d X¢LuFzGŠ;ˆ3wL€L€*u5O@"
@=C
8MNSs/8ME DrQ,C4/" 3Cs/MG F5Q‹=/"/8G DIHJFk
œƒ/^/ 13>JK/ / 1š!813"=O1¨=;813O13/ p*]>‚/8134‘pIO134/
4=/]!/AT/8|84/8/3/ 2_*4//3!C4I155/ 5>
&
;% SR UT NI%WV P ’>m>‚N9"/q"9#T/ƒxT/8 ?47Tp*" qNTpIRT4O13b3T4/4T
/ž="r!/*)/ 9"q/!J_/ž/Px/4)/žC48/(4/;"7ž/ƒ80x"*#"d#!M#N
LK
M ON QP
Z b P £"C 9 –4=O13£/ƒ=£:4b4ƒ£J_4›b/8"13£›O@4/813OMN
J_
1LY/=ª"1=/ ! / G =q % 8" C [E! <J_]C48 Y8o5k134
/58q/ % /8"D !"$# 4G4/k4I13N]I=//5J_3 /C/8//5ƒ13/C
C84/3NZSJ_=O1SZb44ƒ –IC % /?F‚q/4 /048134/^/G//4/
x/A41@!M4”4/e"441!Q‹p*„=#!/ G $ 8!/ !"I$# ‘TC*8R!/œ~]•]G€x/8Z4)133!ƒ"–R B % ""*L–SW91813/ < $# 4/84@ 6"4""q4?x~]•e0€GpIG7/&/81/žƒ"q4/ $+¦ ¢"{ 3
-k{‡¤w>z ‡K ¢{ 4G4/=O13N 8CT8/8/Z134 /ZJ_
13SZ4"7ƒ;M#N5ƒ!/
/?6!#!/ 2134"7!œ4/813pI3C// !E T/TY“/8/8=O1Z
O14//84 ~]•]e/r O1ƒM4”4/e @4/3!/AJ_8O134/ %
& 94" E@$# /4O@"
@[@13;~]•]G€ƒ/= ~]•A~A€4|>‚”4/
/8=b4138/b 6œGC4/=G;„Ž/8j/¨84/ Nœ/;2@*//¨A13o Tu /uFv w>v
– E@# & 9 JK!C/8x"1Cœ?~Aw>‡Kˆ3$u 3 žˆLuLŠ{[¦O{ŒŽ*u0/8;"x13ƒ!"–? G C4"–!81# O1
†""C/ E!I$# 1!Q‹/="
13=R?15!/\;"\!3/0~]• 'A/
8C–= P EE # /884@4 /ž4/]~e{O‰ K{¥ œ{F€> P€ 3 A y*v ¢>‡D uFv€ )D~ A -€ ,FJ_hQ
&
4C/8/5"
134!1@!}/0~]+• ' €>
& 6AZ„C// ! /4?T//?"ƒo3/ "@$# !4/O13 C5;4/
4"7/8/R4/0/8;8@*//4 4/!/0) 4ry[ŠOŠuFˆh‡ ;wL¢>‡,uFˆ -k{*¢ /* ¡v wL€O 3C5hQ
8/8/3N==84–4=O1C!”*/4
/
88“7=*3TQ,/8RN5/qS84/?5/œP 9O134/?=C13ƒ;bs="–4/0"
13=/
?138 0–! G =" !"I$# PWa]138"7/8o43FQ‹/xp*R="#!M#NT~]•e0€
13/¨6/¨0–4=O13œ/\4"d!/- 80} -w‰ ¢> ¡v;{} … ¢LuFv uFzT K{} €*u&ŠuFˆ 7 uFz 3
Š;y*‡‹{O‰*uFˆhr}5~]=u < +F‡D ¢{CGy*‡¤uFz={ŒŽ*uF3"b … €>‡{‡ :€>‡K ¢{ 4C/8"P B814d ! /# !#"%$
&('*)
+-,/.10#2435'
6879;:4.=<?>40
7A@CBD'*E?,;>F<G'D9;HIJ<?0
¨i ‚/81œ1 /88O13RG/213!13b47/žG8/8"MNRG8ƒ"45!/&pIAJ_3! m47!/
;G84/8//?T>@"M#N!S/?4/;b/4 “2134"7!œ;"/G4/4ƒo4813/? 40 ] #?
K
ML
NPO R
M Q4SW\UT V MXWCMP^ZY\[P]_^G`Xab[dcGeRfhg%iUjk@O[lUnmo/[ `CY&UP^EUP]W[E`CY MDm `CX$MP\po/UW^rqslUP\topmPlT[EOU XumT^EU`vm@Q*Y&LNMRw$MP^xo/U `&UGw/LbmU
@L /L UZm\tmTLb{PUW`PqP[ `&UP^ M4\$OUU \pm@Q/LbSP\/[EUZm Om@`blU?w/L&[E\$OU|lUGQZU UW` [xQZX/Q/^ `&UW` \pmTLb{PU`CU` `&SPU Y L MP\$`vQZ[HY&[ OUW`s}P`slyk@^HQ$^EMW`
O~
U lyk@LzmPw/L Uti
 V€o$M4L ^m@`~Y‚O UGwumTL&Yƒg…„M4Lb† [H\/Y\[d]G‡?cXaƒ[P]G]_`GgyiFˆMjY&Q$L MP^H[ `gYNM[H\/]W^H_ `Kq‰QQ/\$O/[EMP^xQ4mT\YbmlykT^mKw$LzmXumT^ MOm@`blU?wŠm@LCYNM
O$M
`zmT^ mPlTR@S4UZ\$M4Y&Q/LNM4^ q$M4u
X SW`bM M4t
\ ‹P^H[ `zm OpmZm@`&XŠkdl[Q4m@` \ M~Œ=Q4kTL [l@MOUQ$^rq"OQ/LNM4\Yzm M `&Q$MZ^EUP\/]MF{[ M4]?mKQ M~w UWL O/UZO/U
lyk zmPw
<
J
;wLuFˆh K{S‰O{ … t uF¥ yŒŽ*u5‰O{F€ … €,Š L¢> wL€
6
9
&
4P
& 03
! '(*)&+$ " & )'457689 :# );
D /# 9
,$ - . #!" #< 5=
ƒ ep
F‚
ƒ
/$'
$ &
!" #%$ " $&
$0 "
%
& ,$021
' )>#)"?7? 4@ "A
' " 5=61
i
&
‚
BC$& DD ! &
" (D?7( $&5=6
?
&? 0
&
Rp
S(
" (
&J ' ! "
' ! #
P–
#< 5=N<O
ƒ
'
kp
& ! H$ I
? &
"
( ' "L ƒ
? " # Q$
*„
#$P& ,$06Q*# #)
– žp
9
SV
L–
"
U ' ?7 7X " Y'E? '&V? V ' ?7 \ " ! ](
'$#
?7P'$&?=
: K
&? %$ T$ 6U$0
) " 576
6/[)
&
Iª
¥ y‡{Z‰*w0€[u=<ˆ3w>t[ ¡t >v ¢> K{
E? &&
?71
M)&5=6
,$ ‚
EF$ G" `
,$=5
?7(^'$
$0#W
–
–
€[w>¥wL¢8ŒŽ*uv;{‡Dy*ˆ8{¥
/
W' "
' "L HR
2,' ! #
Z1
ƒ
5 \$&&
" 5712 ,$0 %$& ! 7
^_
&p
" " 5=T6
" $12OER
!" 4 W Q<O'5=
'$aR
) " 5=6b
$ " 1
 6owLuFˆh K{5‰O{ … t uF¥ yŒŽ*uC‰O{F€ … ,€ Š L¢> wL€
q 7 >v >¢ K{F€G•?{‡Kyd3
ˆ8{ €
] uF¥u¦ K{
ƒ
A ¡ ¥u[€[u2ž{ 3ž~Aw>¥ ¦ K*u
;q
u zGŠ;y‡{"3
7 F
ŒŽ*u œw>v >‡D ¢{fw … tuF¥ yr¢> uFv ˆh K{ ) 7 … , 3
§ 4
4„
ƒ
–
! /#
 7 …
ƒ
„ q
F
”
4”
R}
ƒ 9p
 7 …
(p }
–
5p
3q
&
”
p Cp Ap
ƒ
ƒ
ƒ
” 0
ƒƒ 9 ! /#
cd?7(;
-$ ) " Y#(
? $#
9V_$0
]
?= U<Og ?7&7h -
kj
j
'
V
j
$#( L 576
6l & ) '
]
7" $H) NJ1 1Ho6p%$ '
VE
"
5=
?=P'$#?71
?7 $ "
E? & \/# /' " 5
'(#&'3
- & #" 5=6
&b
K—
6\ 6_$
! 5=6
sCN
V
)& #" 5
j
? >? & " 5
"! ! ? Rn($ (P$#?7 " C&>? &&
k & #" 5=6
) " $#)
6 G a$ '& ! ' -
&?7'$ (h$ S' )>#) 7B?= $0
)E k^
#$ " & b %$6)P'
>$ "
7# " ,$
"
"
"
'$aR
('$&
& "L rRn ,?7,$&&
" 1
It9uwvyx rvwzV!P,
9 ?=576
" 7L e?7 f{F€L€[w y{O‰O{
" ( ' " 5=6
\$M { [EUo|q}sm@M4]W^xmr~ƒi
&q1
&
1f-P'4
1
" m&>? &&
T$ ] - & ,$0
! Q^ " 5
,$& &e
G'E? 7
2? " $0 7ie " ! #U
JK
) #" 5=6
$ " <O&`&^'$&
& & " 576
VD)E
$#9
%$&
L < $_ 1#
%) )>#
#! &H$7E ?7 '? #
4a$E
6b '{
G<O&(5=6
"
€[w y{O‰O{ Z6
'{
1
! $#?=
/('
¦*w>v uFz={5
rp !ƒ
2
#&b?='
"
< #$0
!
<O&(eG &#$&
b(T'$ M Z b ƒ
?c$ &47&6
! & " (
F$ " &
<O&(5=6
¨
? ,$&?771
'? ,$ N 7
¨i
?7 M& ! #$&71
Cp
n(^F$0V < '\ a1
B'$ "" (
B'$p " !G
ƒ
›{>Š;‡D K‰O*u
"
,$ # >? " ( "
Rƒ
#)> "
$ &
,$,$w< $
ƒ
9&2$
‚
–
1
I 5 –
L <

9
”
? &?7
'V L 
?
?7'4576
" ?7%$ " ƒ
P&#?=
p
ƒ Tp
<
i
$
B
ƒ „
‚
T^ p
_
ƒ
Z
4
6
%
71
¦*w>v w
]–
/9 &bb>?7&
?
?
"
?7
! $?7
?=& < " 576
,) )> : '$ C€[w>¥wL¢8ŒŽ*uRv;{‡Ky*ˆ{¥
p
„
„ 9
 4 6 2&;
6/
?=&? $ #'$&?=
? ,$
?78 e<O
!" ‚
b
1
Bp
?='(; 7 ;
?7^'$&2^
5c
–
" ( '$0
" ]?7$8 " %$&
Pi
!!
B
"
Tvyr¢>¥w +F‡K K‰*u[€ ^p
#
!" #
c
2 5
<O'V5=6
¢>ˆLuFz5u[€L€[uFz={F€ Žp
?7'&'V7 ) ,$&1
F$0PQ? &#( B
4
6
,$0;
'$ D e#'$& " 576G
&e
"
'$&,$07 ' ! 9 G? (
" (
p
–
p
u
71
? ?74
" 7
"
"
?
! $&?7
 46`p

„ ƒ
p
"
_&'2
#
9 ?7,$&aRn ! " /?7 7 7"
?7
^ "
2 % 5c1
?7#$&&#
3 ,$0 \9 " ( < I
R
4 6 –
‚
? $8 " ,$\?7 E
" & # 71
$&&#
" (?7,$ U" 5=6
Rƒ
"
3)>#'$\?7
,$ " 3
c
0 %
%
5Š{ˆ‰*w<L{F€[wL€ p
ƒ
2K
 5
12 0
M
?7
7 ?7576
&?jX M # ? "
( %
,$ " 3 )EH)_9 ‚
" & 7 %$ "
%
$ (^
Z1
E #?=576
! (^ M)>H)M?7 E7h?72
3
" $ '
P&#
"
p p
% 
#'$'
P?7 19+
($ &4 ! $#?7
$'
kƒ
8
'$ &
 ‚
&? ,$ 1
e'E? '&
9 ?= "
F J1 1HI? N
&6
?7
" #
5=6
1
" $&&$&^
V
*„ Zp
q
$&(71
# #)
? %$ T ' ! ”
< #$&: # $ &#
#$& 7
" S ! &1 3
'$0/#'$& " 5
Pª
" (
" $5
) #" 5=6E)>4Q '6
F$0Q^…
?7'$H$ " #,$ * –”
4”
M ( " '?7
"$#
$_ 1H
I
&M?7'4
$
ƒ
?7y
4 6&?7
F$ " 5
D
%
" ? 4#71
" C? F$
G& ! #$& e6@$&&#$ (
?7,$& f€[w>¥wL¢8ŒŽ*u
E ?7QD'E? &'
E ?7Dp&>? &'
8
E &#$ ! $?7
3Q) 7L 7WD
'{
&( )'4576
7 #(#
w
‚
4P#
&
? ,$ 7
? "
5=6
' #'$&?=E1
? $#$&#)i 'E? &'1

=p
Rƒ
?7
ƒ ƒ „
q
<O&(
$ " $ PQ ')W&#
" $#9
R€[w y{O‰O{ 3
ƒ
T-? ,$&P&# ' " 5=6
_<O,$ \&#?7#
8 V?7&e &
9&l
lV#&
>?7' D
?7&('&( o& "L Rn ( &? ,$ ¢>ˆhy'[{z5w>v‡,u§
zTy*‡‹{ŒŽ*u i
Rƒ
P 1
ƒ
?7%$&&
" "M b9FR
WGM Q4m@` „ mK†smKT
MjY `&UP\5Yv[Pc_`R] gyi Jm@\pmY [lT[E`CY M ˆ UPL&Yzm Œ=Q4mTL [l@M4\/UŠq Qpm=mPQ [dc?^p[ `zm=Q Q$OUPQX M4LNM M \/[{Gm@L `&[xa
O/MWOm Opm=V MGQ w/L [ O]Gm?q UW\$OmsmT^m€m U[H\$]P^E_@` /LNM4\tlT[E` V L [l Om@^H[E\pm M4LNMRQ M1m `gY L&Q/Y&Q/LNM=QZUP^mPlTQ/^ M4L OU…Œ1„JˆZqXm X/^E[lTM4\ OU
Y GM Q wukKQ UZ`zmTQ Q4mPl@M4\/[ `vQZUOm LbmTX/^E[lTMPR@S4UŠi
d[E]P^ MVO/U‹Gl[ OUZOm@`&U [HL L [xw"UP\QtlT^xm@[lTUti
[H^ opmPQ =Q$
O {[E] WGU o$MP\/\$`zmT\ Y\[d]?^ a4[Pc_` Gg%i-} U4Y P\/[lUm ]?mT\pmTY&[l[ `gYNMpq \$MP`bl[ OU5mPQ(V UPXumT\po$MP]WMtiŒ` `&Q$MW`
m u
X mTL [H_@t
\ l[ MP` X/[EUPt
\ mT[EL MW` lGU Q mT[ W _m =
` lUW\Y&L x[ w/Q HLNMRQ Om UWLzQMZOmPlT[E`&[{ MVX$MPL MVUOm `vm@\_{WUP^{[xQ4mT\Y U O/M Jm@\pkY [l@Mpi
%$
&
(
*)
+
'$
/. 10
,
!
#"
32
,
4.
%$
5
I
!#"%$&'()+*-,-./
0213)451)16
)789'1()4":515;=<5$/)-(8$1
>
5?A@$B)1&'
5AC=)ED11$
FA;GIHAJEKMLONQPSRT#)(U3JEKMLONVPSRT(#$F$W'$1')5$
XY" U3JEKMLONQPSRT[Z\$])'1$"^3_($"%))1)`$G$%$^)'1)^)a"b$621"^$c*ed))gf
02)')%$G')Ofh)2
A;&'8$`)1$"iCj)'1$lk3)i"^)E0)%)'
)^&^
1"^>
5$mn$/"
$)15
$W#"o)')'1)'13)qpr$F$$s2$C$7HAJEKMLONQPSRTY)1#$$1Ot16
$%)+A')<uf
5A+$v)u;2wx;)5()"y$615"%$#*z)5)'?A@$`12
E
m$v)%$|{})'1~$€Z\)1@$|1$
)'1~
5n$3_$%k3)+$#{})1~$aZ}$$n$3_‚&/1))'w5$^2
#)$=?A@2$^v5$~
ƒ„}…Y„V†
‡lˆ‰Š‹ˆŒ‚GŽ’‘4ˆ”“[•‚–˜—-™Fˆšn›•zœŽŒ4žMGŠ‹ŸMˆ Ž¢¡m£•¤‹™4ŸnŠ‹•ŒY¥‰Š‹ˆ
*§¦W¨‚©$16
)'"^sª$G4"^Y&'5)q)q&'1I44)$?@$-)q$v)"^'C)')16;$5;=
)«{}$"i¬51)'n)'1)16)­1$®$is$®$]¯-')A1$c*°s±16$Cª51
2®1$²$G')$c)
)';$?A@$12
2M~5$8$W))F;G>;$'pr$°;)³')C#>{}))'1?A8)'16
)+)'
)'ª$5"^$1@$
&/)';)
241<>
Cu
5151$2f´)7))'1"%)16
)/)s#{}$"i#)/)')')16
?A@$i)B)'
?@$%)
1$x;2F$5?µ=)'C)'1$%18{}$"^
¶¸·Y¹ U3TOº»P\NQ¼iTx½m¨YJEKM¾ENQPÀ¿0Tx½mÁ · ¨‚½hÂO8Ãj
2
Ofh)#;216
)8)[¦W¨‚©z"^4$1d)5C)')'1Gf
;$5;=l1$
$%XY1$'CÄ8$«
v2d$l)`Ū$1ÆgxÇ3ÈÉËÊÀ²¯e5$5
"%$
$51Ì5³AA;2^"^i)))'160?@$`v1wsDÍC!{Q³)'1$®"Î$m"^5?$$®$n)'
Of
Z b %$&14
?7 "L *$@?7 $#V
! $&? 7
"
P 9 ?75 /<Og? '? %$ b ,$06d)P&\ ?= 7
D#) 79
? ,$& " # F$ " $ " &<O'V
Q " ? '&
),$ D$ &
j"!$#$&%'
& ! '$ $#9
;
" ?7 ! ' " 5F 7
&
^
"I!I #
$&^
#(H$0 7 _$&^
,$0576e^ " $05=6
"DjcX
$& ! "
'$&&#?=
<?7 $&&
<O ,) )> e9
@? %$ BA
&#
G "
= F$ E
0E? ?
" $& L =)_ " E$ L 5=61BOB
$0 71PD\((#D$0 N9 " 5F ? (#
576
' ! #
#7< " %$ ? ( ,$0 #?=Q
! $&?7 "
9 ? ' !
7 " " V! L 5=6K "
%
?= `
^
%$&
H)
" D<O
A W? ( " $0aR
&- #79
&&
$'
e ,$' "L 7N&'
'$& !" Rn e SDj
" V( ,$05=6T
" $ L ?7 9 ?==)
[); H)
" ! &5=6 " %) )>#
6-? &^- " R
# #)
" "
! $#?=1QD_R);)
?7 9 ?=576
^W '(H$ N#
< ! H$0#7
)&P) #?7,$1 " i ,$0 U9L
"
&>? &'
F< 5 , ^
&T) '6
? (:[) @ E? " 576
HDjT#?74I
=)bR
?7J
5=6
,$0,$&o?7
#)
" Q' ! #
1
" $5=6
) )
,) )E T & ,$0 )> bD$& @? ,$ '5 # (
" D?7'4 D9*
576
Q
&
1$ Rn 1
^'$ &#&
j )N1D
7 $&_)'4,$ I
" $& L
,$ F$0D$ ?7#?=M$&& " Rn ,$ -" $& L
1>6_
"
H< 57
Mu #
? ? L !
A `$ " b ?
" $5=6_
6
,$0576 )/$:12n&:2G)*,+
*2 ));) ,a1 4
G
" (&>=E(5=6
!" # " IN W
$ " #71
& &
" $&&G ! '#$&(#(^'$,$ " VT?7 9 ?=576E#
P&1 \
6 -/)N=? (T6
7 V#T& ! ,$ 1
! & 2 2 7 @ <?c$6 ! W Djc14_aR
#?= + 7 5=6bCDjc1/DE " J
'? 9 H < 57b&& 7 D?7&5=6
7!" / F< %$5=6
(!")*,+-%$&# & ).Dj)/-,#PQ
01322546
7)8*,+9%$&# :2
) ;) ,< 9
&
!
e
e " aR
WT " $0576b #)
" 71
01322546
&
j"!$#$:&%12
! #
L
,$0
\ "! &&
0h
! V 1
('$&b
? '$&#$ "
) \j,a16_bDH$
)>4U =)>4E*<O
V : 7"
(9\ H)
" $& " 5F V
&
& ) <O'VU?7(M ' ) 2
"l '$ " $ " "
" " &
$(
5
" (
#Q,) '$& !
P') ) &
'pl ?7 ? ? e
6\
! & 1
\j 3
& V1
M$0 <E1
6_'V
" $ L
D #
V
&
9'$jA?7
" $& L [Rn (" (k9 " 576
? 9 ?7
%
%
7
L ll&#
V)'4P=) V "
?
$ '(#
6
,$
" g? $8 " ,$
#)
" #FR
) 4 l 7
,$ %*#'$& " 5F W6M?7 HR
9
?7
P') 9? " '
8 / /?7' '9 ]
' " 5F w)I&6
&
4
,$ -" $ L
rv
v"#
D 7"
" ! &5 (
S#
U
#
? (^F$0aR $& "L &
" = 71
2
" `
! 5
#71
5
D
D J14
,$&&
" (
$'
j )
7 &>? " &
?7( " $0? R
? ,$ E
= $&
'$ R
,$ " '5 V/?7
?7$8 " %$&
$&HR
! >?=
L- &?7
$& L 5=6
" $ WF
J1 1H
'$ " M" (?=& #" 5=61ED\'&2^
6e
F$
#&&
?7P ? " ? $8 " ,$&
"
%$]S#
' " 5 <?7 ,$ &) N" (/< " 576\8 ?c$#)
$ ? ?7-?7%) ? 6
j )
7 'E? " Ei
" V
<O&(5=6
6G ? '&H$0
! (VW)'$
'5 # (71
& " 5F 3 & #" 5=6
" $&3
9 $0b
$&'5=6
$&V $& h ? U H) &&$&^
:7(' 2546
^ %
" : ? 4576k "
5
V31%' @!$ c
< " 5 _b$#( L ^ \ ?7 b
H< 5=7C " #( L "
$ _?7,) ?7#
#
$& /b 7! T'5
# '$&?=
&
! 2
?7 " $5=6b
#7 E1
"
DT;?7%$&P'
OB'$
6/')>
9 " 576=5
"
Y'E? &'
&#) &
)'$
W" (_' " 576
? $ L //<O&(5=6
$06
(=E L '5 V
>?=#7X G ?7 b
< " 5 _
VP=E#(
"
" $5=6
5 )>?=? Q
Q & " 576
,$ I
' ?74 5=8 ? $&#)
2
<O
] 576G_
&\\'E? " j )
7 2O
H< 5=
" ' 9&1H) /& #" 5 3'$ = #'$ " Y? F$V? $8 " ,$&
E
G
! &
j )
7 ,$&
? 9F$0P=) ,$0e? '$
zP, rz
N
D' " 5 D^&3#) ,$ P') E MU & 1
$#( L 576I 9-&
< " 5761
! & B)>4-(# " 5=6
5 /&5 M '$ 71ED_
_ "
'$ 1
? $8 " ,$&?7,$'@ " < ? 1 _
D &'2
'5 V7 "
7 j) $ &5 ' +NV$&%12"!
! A +
#-4 !'< /Vb'$jA?7
e^ " ((< " 5=6G5=8 ? $&#) 9
#
3159
58 ?c$H)
# .-
/ + %
& ]
" "
j )
7 ! ?7,$ %$ w" $ L
'5 V
$& L 5=6
$#&%(') *U #,+ % $ " eV<O&(E
$ &
Tb) 0/ %"
2
1
"
5
-?=&
'5 V
T" $&?=B?7,$0# " 7 '$0P[Rn U 5=
'$0
? ,$ "
&
&P)
"
" 7
G
< d
?
" ?
$ ? $ " &
q
$_
57 #! '#$
"
W #'$'@ " 5=6
>
)'4 )> bF$ 9 ?7 ,$ !#"
D\
6
< q 1
*6?=
2
%
G
=
$& A ?74
'$0G$ h<O
( %
H$ " ?
^,$ - "
D 5c1
_^$ ? 4 HR
" (G?7^ ,$ d9
#$&UV
? 7 #$
" $'
,$ " R
!I q1
? $8 " ,$
" =)E W" ,$ Dj)< 9 4 7
?7 ? ? ,$
$ 7
? aR
$&$ V1 " HR
$#( L 576
"
! <OFR
j5 " )> U w #?= &? &#$ ! '$#?7M
J1
? 546@
"
1
! 5 "
? ,$ ,$ R 3e " $'
?7 /9
"
& [Rn 6\$
%$
" L
&
"
" V %$5=6
'(H$ &?7
? ; E$0U
7 '& '
U ) " 5=6b
$ " R
$0i$ " &iC546 )> /?7
? " (&>? " &b $$H)
"
7 2
$ &
'$ LM $- 1#
" ! '7
(
1 ! 1H )>&6(? &5=E9$H) ^T)%$ ! ?7
6
A
)> ? 9
#$*2
7 W?7( " $0? *#& TT&>? '&
' B o)EH)B
_" S?7$8 " %$&
" $ L
'$& " $ " j )N
7 +NV$&%121 OBF$0
s7>|.=<RBn'"!
?75=6
L #
:7(' 2546
?=&? $ 3FR
4-@$ !$2 ! ! 7 2'$ 2%12546
4 7 " $& L " (2 L
g? $8 " ,$& ! V$&^K !7<<< !$#9&6
O? &' 9
?7
_
?7(
"
?
j )
7 w
" $ Rn'E? && 0!$# ! (' 2 !$<
%
!$# %127#/ 2!$#9 ! ! *!;:&%$+
@ "
" 7(' 2546
7 1<# 2+:21 O =#'$ " ! & L '
?7Y' (^ W)>4b 7 j)"3?7(b 8&. !' %12@$3
%12 2
%$
!M2 !
!'C,7 !
1# qE 2@ %12546
!
! %12M2B%'
$
"
?
>?
692'! ?F2 !
! ) !' !$#/9<(DE "
A $'\ ? D
&
D
%S'
"
!I q1
" " $ &? ,$0# " M "
? L # F$0b
$ " L
# 2!$#9 ! !G&20! ?F2
D
?
#?
:7(' 2546
7 1<# 2+:2M<
5 iG'5 V L Rn 7 c
'5 # (
;X
< " 5 U
? '5 V
" = ? 7 7? ? 4((V ?75=6
$&$aRn M" ((P 9
V=#( L 5761 /
6 o?=&
#(
Dj)/(?7g
woH$ ,$
?7(/ L
" '
= ?7H$0
E
j )
7 ! l
_ 7 8 P=) 71
>?=#W &
,$5 M 7i? F$0/$ ? ?7\ &6
$( +6b *V#W^ " &? &#$
#) "!
1
9&
$ 9
#& ? (h
F$ W $& " &
b'E? &'
P
D
"
! ` P
^&3#) 7
! ?7
,$&&
&
? Dj);M?
$&^
$ " &
!#"
I
D0#9
Dj)/c$
< 40*2435'
$ b ?7,$&aR F$ " $ " & b?= # $ " ,$&& " $ &
'
A " N* $&&
M
&
$&
$&&
)/ < 0
& #" 5=6
6_$
" &H$*?7 " $?7#
#71
8&
$ (^: ;0
7
!
3
H) 7
" 7L a " !
D_&&#`
%
6_
#$ " _ 1
46
F
S$ '(
?7J
5=6
Dj)/
`)>F$0b " ?75=6G546F
& D$ 9&M `$ 9b ?7 !" F
G # < ,$ /
F$ $ ?7#?=h?7%) ? 1
7
DV?= #$
" ! L
G !" #%$ <O&(& =E? # " "!$#%'&)(*&+-,./!$0&1*$3245$.#768
;
&
L
? Rn T" V
G
6
'?7&#5=6-'5 T h$#9 7" '
#
_ # ? ?7#
# D
3
'(H$ " $ L U )>& U "Dj)/
)>#6
- !$&2
Dj)
k" 1
)>#6H "
%$ E
" $& L
;?7 ? ?7 e 7 ($ '(
'
U" (
%$
N( ? (h " $0 3$ ?7
&
$ +)> (D p )>&6
'E? " - #7E? " # b )>&6
$&^
<
E?7" 1F$#?= 5 "
? $8 " ,$
'5 # (7a & ( 7 i&# i
#M " $0 5$ D 7 k&#'$ (
&
D
F$ 9 #5=6
' ?7 )b
b
? # $ " " $& L - 7 \#&# \
6_$ " 7L G
V
= &*$& L 5=6
&
%
F$ ( 7 D
&
7@? _<O'V
'$ " Ue
Dj)/ 3o
/ ^5=6
? ,$ E
= $&X %$ '$ $^ ! 4E1 w ,$ \ " _(Q)>4( "
= !- ) T " E
" (k1 " H$ ? $ " "
!$+
0# 2@)*,+-%$&# :2
&?7'#$b
&# T
6\$ " L X$&=) 4
& " 576
" &e$& L pG
A 7 ?7#
? Dj)/U
&Q'E?
! ! !'
W_/
$
_ 1
" &
H) L
'^'$&
Dj)
9 ? "
" $&
bF$ #,) F$ !
@? h$#9
U
U E$0 V 7 '$(U9 " '
G/ 546@
( Q&F$ V
_ :" E< &#
&>? " &
" $
&5 (>? %$&aR '$ $0( g^ 9
" `^ " ?7
-oD? ?
Dj)-
U "
9 ? "
_(
4
! &#$&(
L
$#?7
! OB)
&# 6_$ " R
" ?7
P&#71
?= " '$ W I ,$0[Rn &?7'#$&\_( ,$ &bb ' " 576
M " Q?7'$H$ " #5=6
' ! &V5=6 "
&5 (
N
( '(H$ " $ L D/ 7 < " ?7
,$1
3
9
2E&6
,) ) U #?=5F <O'VPa$?7
`?= " &1
"!$#%'& !$# .#$, &
!$#7. ,#7& # './, &
6
= #?= ? ? #$&G
P&? E
G
P & B$ (^
?c$
?7%) ? &# M
\$ " L '$ " 1
;X&
& \$ 9#7^ ; ,$0 M
'?7'5=6M'5 ? R " (
I
:(^M ?= U
$& 7 5=6
)>&6
M & $ (^& 1
1$,, 68
3!$#
"!$#7 '&)!#.#$, &
= ?7 UM ? && E
'5 VM;
F$#
F$&$ ! 4 $0aR
D
$#?7
Oo)
$0#N'E? '& 1
&? &#5=6
!"
7 #
" ? P&7> V(
h8 $#( w? & & N?7Q ?c$
$ (^
&>? &'N? " $0?7
B ' " 576
7 U'& -
\$ " L h : ,$ QM&?7
&>? " &1!
' ? Rn *" (
! &H$
$& L 5=6
$#( L 576
_
L
O ) #" ?7#
P'4 W " &
o
'$0$ ? ?7/ #?= W
&
" (M? 5=6
_ F$ " S$ &
\ ( ,$ ?
#< ,$ &&#y?7
? ( " $0576-<
$
. #$, &
#
6
# % # /
'& -
?=&
F$#? " )>6
Q )>&6
$ 9 L
?
H< ,$ ! & L ,$ -$ ^#\
GG&>? &'
y$ (^Q % < ? $ "
1
%$ " S? ( " ,$&
)>&6i#? #" e
" (Q1 " #$ ?c$ " &Q
&Q&#'$ V
= &*)7? 4I?7S
/ E
#< ,$ 1
+
'*-,8 &. #7&1#/ .021$3$".
"
L [Rn < ?
?
($&
? ,) )> ^
" $0 5$& 5= Rn 7 ,$ " &>? &&
P # UM &? " &&6
/
D$&
@? D< " $ " &1
!
"$#&%(')%+*-,/.102,435*-%7698:6;3502<>=?.1*-62@-8A8A3CB9<ED-09.1FHG+<I8J69.1G('1<I026IKML;N-<?OP<RQSN-%+F-%(BT3U'5<I026V3CB9%+G+%(BWO
B9NX3CBYD-@HB96;BVN-<ZF<I62B[=I.58AD-@SBV<I0;DH09.1,109358\B9.U69NX358:<5K^]
_a` .1N-*bcKdbT.1G+G+35*-efgih4j5kSK
lnmpoRqsruturwvyxir(+)z2|{)ruxitwoR}.4~)m€xim5IoVr€{)mp}+xU‚ƒ}…„XmixA{)r:z€mI{)rw†+mix:{)rS2w„oVrwq{5}(‡ 2iˆ)rwz‰}ŠqHxW„}Šv
3o 24{)mixEq 2/B
‹ 25:‚ +SoVr9‡ 24ŒYYr9{)rux[‹c$r +)oVmpq 25}+xŽnqX}ƒ{5}ŠoVrututw}ympq 25}+x>r[†‘ˆ)mpoR}Š‚’z€mix/“[rwqs”w‚’}ytumixcr
•—–5mp,† +Xtw}ympq˜5ow}ymixI™cš 253o 2›1t 24M{ 2 +)z{)ruxw‚Wruxz€mI{)rw†+mi(x 2w„oVruxirwqX‚ 25vyxi(r 2€$x +2›tumpqHxw‚’}Š:‚ +).} 4~)m
rTz€mI{)mc{)rœ +Sqstw}ympq 25z€rwqX‚Wm5™šYmpožŸz¡ &xI~)mc{)ruxitwoR}Š‚Wmix¢mix 25z:I}yrwqX‚$ruxY{)r£„oVm9ˆ51o 25z 254~)m
¤ +Xr&„Xrwowz/}Š‚Wrwz¥{)ruxirwqX–5mp†¦–5rw;o 2w„†¦}y1t 254C§iruxŸ}Šq¨œ¨mpoRz:˜5‚ƒ}y1t 2px„ 253o 2 2oVruximp,† +N4~)m{)r&„oum5I†+rwz 2px
+)‚’}Š†¦}(‡ 25q{)m€mix>z€mI{)rw†+mix¡rwz‰1t 2+4x 2 K
© .18:.ª«.1%S09<?ª«<?09%7e-.E*-.E=¨3CD-¬7B9@-G+.35*4BV<I02%+.10?f1<wQS%762BV<B9.SeH.¢@-8­=?.1*p®2@-*4B9.>eH<¯BV°?=I*-%7=¨356£=?.18ADH@HBu35=?%+.1*-35%+6
± @-<aª«.10V3C8²%+*S³X@-<I*H=I%´3CeX356/D.10/D-09.)=I<?6962.16Ue-<P<?'1.5G+@-µI¶5.·*X3CBV@H0V35G’fMDH09¸1D-02%+.16/eH.16/69<?09<I6U')%7'5.16IK!¹
ª«@-*-=?%+.1*-358A<?*4BV.Ee-.E62%+62B9<I8A3¢*-<I0º'1.162.c=?<I*4BV0935GX8:.5BV%('[email protected]<?69<?*»'5.1G7')%78A<?*»B9.ZeX356 Yr9{)rux‹>r$+SoVmpq 25}+x
oR‚’} žtw:} 25}+x/¼’Y‹YxW½ fH<?* ± @X35*4BV. ± @-<Z3<?'5.1G+@Hµ¨¶5./*X3pBV@-0935G¾%7*H³X@-<?*-=I%7.1@P3¡=?09%´3Cµ¨¶5.e-3|¿ mpz„ +S&‚ 254~)m
“[rwqs”w‚ƒ}y1t 2r¢•—–5mp,† +dtw}ympq˜5oR:} 2¼ ¿ “—•&½ K
À <?62BV<=¨3CD-¬7B9@-G+.|62<I0V¶C.Áe-<?69=?09%7B9.16U<I8ÂD.1098:<I*H.10/e-@X356/B9°I=I*H%+=¨3C6:D.1D-@HG´3502<I6If ± @-<69<I0º'1<?8Âe-<
<wQS<?8AD-G7.AD-350V3/=¨[email protected]')%+8:<I*4BV.56;=I.18:D-@HBV35=I%7.1*X35%76;%+*-62D-%+0935e-.16;*X3 À 3pBV@-02<Iè3Sį356 Yr9{)rux
‹>$r +SoVmpq 25}+xŽ&qX}ƒ{5}Šourututw}ympq 25}+x/¼’Y‹aŽxW½ <>.56 †‘ˆ)mpoR}Š‚ƒz€mix:“[rwqs”w‚ƒ}ytumixrE•—–5mp,† +dtw}ympq˜5oR}ymixU¼«“—•ŸxW½ K
Å5Æ
Å
(*)
+
GCHJIKHLI
!"#$%#&'
,.-/-0213-45687:9<;=0?>@7;
/;A5-BCBD;=687E9F;=0
MONQP%RSKTUVXWYR[Z[U]\^_U`abVKPcMdVfeV
8 qsmI{)m fXB9<I098:.:@-6V35eH.DX35093:e-%762B9%+*-,1@H%+0;<I*4B909<¡@H8 *H<I@-02¸1*-%+.:*X3CB9@-0V3CGn<c350ºBV%ih-=I%´3CGyf-°c3A@-*H%+eX35eH<
e-<ZD-02.S=?<I6969358:<I*4BV.A=uNX3¨'1<¡D-350V3U3U.1D¾<?0V35µI¶5.Ue-<>@-8€3 Y‹; Kkj£8F.10V3/<RQH%762BV358e-%7'5<I0269.16YBV%7D¾.16¯e-<
*-.)e-.16?f <I8 DH09%+*H=I¬+DH%+.-f=I.18:D.102BV3mlW62<=I.18:.@-8‰=I.18:DX350935e-.10 ± @H</D-09.)e-@-Ã/@-8A3€6935¬+eX3 ± @X3C*-e-.P.
<?ª«<?%7B9.=I@-8¡@-G´3CB9%7'5.€eX356<I*4BV0935eX3€<RQH=?<Ie-<U@-8 eX35eH.€'C35G+.10TG+%78A%(BV<CK g 8‰*H.Se-.€D¾.)e-<¡62<I0¢eH%+6962<I=I35e-.
e-<>35=?.109e-.U=?.18 .U<wQSD.162B9.€*X*3 n %7,1@-0V3 Å K7bg oqpT.p®93C6If gih1sh rmt’Ä
x y{zC|~}= fd=¨35eX3:@-8A3:<wBV% ± @-<wBu35e-3AD.10Y@-8 „Xruxi[m € %’K <CK7fd@-8‚* -8:<I02.
u Ž&ztumpwq v+SqX‚Wm{)ratumpqsJr xS§iruF
02<¨35G».1@cF-%+„* ƒC09%+. y <I8F.10V3Y69<W®93[8A35%+6 =?.18@-8 *X3;ª«.1028€3Y09<I35G  ± @-<—B9<I8@-8<wª«<I%(BV.<RQS=I%7BV3CBV¸509%+.
DX3C0V3¡'C35G+.509<I6—D¾.569%7B9%7'5.16<¢%7*-%+F-%(BV¸102%+.ZDX35093¡'C35G+.102<I6—*-<I,43pBV%7'5.16IKK …[6969%78f). xw}Šq 3 † .1@ ruxw‡‚ †Š7z +)†+m
<Œ
y‰ˆŠ}
 =I.58A.P<I*4B90V35eX3eX3P=I.1*-<RQH¶5.°:8@-G(BV%+DHG+%+=I35e-.AD¾<?G+.=I.10209<I62D¾.5*-e-<I*4B9<€D<I69. zC|‹} f .5*-e-b
e-<?*-.5BV3Z.E*H.Se-.E.5F)®2<I=wBV.Ze-<;<I6ºBV@-eH.>K< >.E*-.)e-.Ee-<;.1*-eH<;DX3502B9%+@/.E62%+*X35G’K Žn.SeH<Y35%+*-e-3¢<wQS%+6ºBV%+0
@-8A3;=I.1*H<wQH¶5.<RQ)BV0V3Sf5e-<?*-.18:%+*X35e-3YeH< I:} 2px fp=I@p®93Y<I*4B90V35eX3YBV.18A3;.T'C35G7.10 ’‘1f ± @H<—<?62Bu3CF¾<?G+<I=?<
@-8A3Á=?<I0ºBu3 BV<?*-”e “?*-=I%+3 .1@ %+*H=IG+%7*X35µI¶5.·*-. D-09.)=I<?6962. =I.18:D-@HBV35=I%7.1*X35G € %’K <CK7fY3Ce-%+=?%+.1*X3 @-8A3
=?.1*-62BV35*4BV< y{zC|–•A DX35093 ± @-<U69</<I6ºBu35F<IG7<IµI358356E=?.10902<I=wBu356E=?.1*-e-%7
µ —)<I6E.1D<I0935=I%7.1*X35%76DX35093.
*-.)e-.-K
6 ˜ 3509,5@-8A<?*4BV.16>e-<<?*»B90V35e-3 y <?62BV¬[email protected]  3@-™
8 -*-%7=I.'Cm3 l
u g 8 }ŠqX‚Wryˆ53o 24{)mpoV ± @-<€09<IeH@-Ã.18
G7.10IK À 3C6 Y‹aŽx °@SBV%+G7%+ÃI35eX3P3ª«@-*-µI¶5. 24{5.} 4~)m y‡š" f D¾<?6V35*He-.›BV.)eX356c356<?*»B90V35e-356¡*»@-8A3
=?.18F-%7*X35µ¨¶C./G+%+*H<¨350?K
q 4~)m{)(r 2)tw‚ƒ}Š– 254~)›m yœ'žŠŸ f ± @-<cD¾.)e-<¡=?.1*-e-%7=I%7.1*X350;.A69%+*-35G&e-<¡6935¬+eX3Sf%7*4BV09.)e-@-Ã?%+*-eH.
u g 8€3 œ +S@-8A3/=I.18:D.1*-<I*4B9<Ee-<Z*X¶5.:G+%+*H<¨3502%+eX35eH<*-.:D-09.)=I<?6962.A=?.18ADH@HBu35=?%+.1*-35GyK
j£8JBV<?098:.16;ª«.1098A35%+6MBV<?*
8 l 69< ± @-<Z<I62B9<c*H.Se-.U°Ze-<?69=I02%7B9.:D<IG+356;69<?,1@-%7*»B9<I6T< ± @X35=µ —S<?6IÄ
y Å K7g 
|_¡O¢¤£ ‘F¥ zC|§¦=¨©ˆ«ª ¥ zC|¬ªA¨©ˆk­ ¥ zC|§­w¨
®i®¯®i¨Jˆ„° ¥ zC|–°±Ÿ
g
Å KÅ 
DX35093:@H8 *-.)e-.*Œ—=?.18.˜·<I*4BV0935eX356T<Z@-8A3U6935¬+e-3HfX.1*-e-< | 09<?D-09<?69<I*4BV3A.:,435*-N-.Ue-.:*-.)e-.bŒM< ² | 3
x2s†ƒ{M2 e-.:*-.)e-.-K
…L 35F<IG+3 Å K(g>8A.16ºBV093:3CG+,1@-8A356;eX3C6Tª«@-*Hµ
—)<I6Te-<¡3C=?BV%('C35µ¨¶5.:8A35%+6;@HB9%+G7%+è3CeX356IfS.1*-e-<µ´eH<I*-.5BV3
3 }Šqstw†¦}Šq 254~)m eX3ª«@-*-µ¨¶C.-f·¶E¸m¹·.09<I6ºBV.|e-<€@-8€3e-%7')%76V¶5.%+*4BV<?%+0V3< ² Œ‡ºŠ˜ £‰ˆ_Ÿ’¡ ¼ »» ¼ ¨ 62< ˆ¾¡À
½ ¿ <
² |'¡Oœ'ž³£ |‰Ÿ
y
Åk
±Y#K:%F f%%LY%##f #L
x0 = +1
x1
w i1
x2
w i2
...
n Entradas
w in
w i0 = Bias
Nodo
i
Σ
ui
fa
Saída
si
xn
n
%+,1@-093 Å K(g1ÄKj£62BV02@HBV@H0V3U,1<I0935Ge-<Z@-8 *H.Se-.HK
!#"%$
&(')*
+-,./10325476%478:9-;7<>=@?1ABCEDF<HGI/FJ1K>L<>CMD1<N2OP3,RQS2K>TB16
År
!"#$%#&'
+% ,1@H0V3 Å K Å  o‹…ÃI. fg¨h1h t’K#…­D-02%+8:<I%+093Uª«@H*-µ¨¶5.HfBV358F°I8e-<?69%+,5*X35eX3€D.10Yª«@-*-µI¶5.
e-< r 5–i}+xw}ƒ{)ru °*-.1028€35G78A<?*4BV<¡@SBV%+G7%+ÃI35eX3U<I8 *H.Se-.56Ee-.BV%7D¾.= © @-G7G+.)=uN[lŽ£%7B2BV6µo(gih 4Æ t’fs<I8 ± @-<
3A6935¬+e-3UB9.18€3/.:'53CG+.10#’‘3CD¾<?*X356T69<¡.A,435*-NH.:ª«.10Y*X¶C.lW*-<?,43CB9%7'1.HfXe-<35=?.109eH.A=?.18 @-8€3!hXG7.169.shX3
e-. ‚+H{)mm+q 24M{ 24™ j£869<?,1@-%+e-3Hf35DX3502<I=I<[email protected]@HB90V356Yª«@-*-=µ —S<?6[G7%+*-<I3509<?6IfX=?.18 3 -G(BV%78€33UBV<?0
=I.58A.U=I.5*»B90V35eH.18A¬7*-%+.¡.:%7*4BV<I0º'C35G+. ¿¨ ‘ƒK
L 35F<IG´3 Å K7g1KÄ nX@-*H
µ —)<I6Ye-<>35=?B9%7'C35µI¶5.-K
!#"$%&'
‘ ¨ |) ¿
†¦}Šz/:} 25o
(
¿¨ ‘,
¿ ¨ |*¿
+
%-/. ¨ 0.1
†¦}Šqs1r 25o
|
‘
¨ |) ¿®76
4 23 ´ | ¨ - ¿[®768*
¿¨ ‘
„XmpoZ‚ƒoVFm 4Cmix
|* ¿®96
¿
¨ |: - ¿®96
35 ª
¿¨ ‘
†+m9sˆ †+xw‚ƒ}y1t 2
O-8‘ ¨ ‘
&‚ 25q)ˆ)rwqX‚WF
r E)}…„XrwoIH Gp†¦}y1t 2 IKª%JM;=L=<?>!N @B£ AD´ C | Ÿ
O-8‘ ¨ ‘
xirwqsm
PRQSL £ | ¶E¸¹UT!V Ÿ
O-8‘ ¨ ‘
tumixirwqsm
WYXP £ | ¶E¸m¹UTZV Ÿ
>\A^C]
[ ]@]
O-8‘ ¨ ‘
ˆ 2+4xuxw:} 25q 3
M
­
- ² Œ‡ºŠ˜ £ | Ÿ |
%-/. ¨ 0.1
¤ + 24{53o 24M{ 2
… *X¶5.TG+%+*H<¨3502%+eX35eH< °Ÿe-=< h-*-%+eX3Y<I8 BV<I028A.56ne-356&09<I6ºBu35*4B9<I6&ª«@-*-
µ —)<I6?f5.1*He-<Ÿ@-8€3;<?69D<I=I%+35G»3CB9<I*-µI¶5.
e-<w'1<62<I0—eX35eX3 _Zª«@-*Hµ¨¶5. †+m9sˆ †+xw‚’}y1t 2 f)BV358F°I8=?.1*-N-<?=I%7eX3cD.10Ÿª«@-*-µ¨¶C. xw}(ˆ5z€mp}ƒ{ ·K j£6ºBu3>ª«@H*-µ¨¶5.HfS=?@p®93
ª«.1028€3T°35D-02.¨QH%78€3CeX3TD.10 @-a
8 `Bbdc °—e-<G+.5*-,1<—3[ª«@-*-µI¶5.¢8A35%+6&@HB9%+G+%7è35e-3T*-.@-69.¢eH< Y‹Yx fK e·@-8A3
ª«@-*-µI¶5.=?09<I62=I<?*»B9< ± @H<<wQS%+F<¡@H8‰FX3CG´35*-=?<¨358:<I*4B9.€,10935=I%7.169.A<I*4BV02<@-8 =I.18:D¾.502Bu3C8A<?*»B9.AG7%+*-<I350T<
*X¶5.cG+%7*-<¨350 y n %+,5@-0V3 Å K Æ  o ` .102eX35*f g¨h1h4k t’·K …;.c69<['C3502%´350M3 }Šqstw†¦}Šq 254~)bm y ´  .1FSB “I!8 lW62<Tª«@H*-
µ —)<I6—=I.18
e-%(ª«<I09<?*4BV<I6:e-<?=IG+%('1<?6 € *-.·G+%78A%(BV<5f£<?8 ± @-›< ´ 62<35DH09.¨QS%+8A3›e-.Á%7* hX*-%(BV.-fM3|ª«@-*-µI¶5. B9<I*-eH<DX3C0V3·3
†¦}Šz/:} 25o K
² Œ‡ºŠ˜ {£ ¿ ŸC¡
12
GCHJIKHG
W
¿ yn
WYRgCPU Z[NQ^³Z[P%R`ih
T%ULe%U]R”NQ^'^_UVT%`Ka
6 Y‹Ž x =I.5*-62B9%7BV@H<I8 @H8€3;eX356 8A35%76%+8:D¾.502Bu3C*»B9<I6<£D.1D-@HG´3502<I6 =IG+356962<I6&e-< Y‹Yx fp=I.18 @-8 'C3562B9.
G+< ± @-<›e-<|3CD-G+%7=¨35F-%7G+%7eX35e-<Cf—@HB9%+G7%+Ãwƒ¨'5<I%+6:<I8 D-02.1F-G+<?8€3C6Ae-< z€rwzGpow}:2 2pxuximitw}:25‚ƒ}Š–2 f tw† 2pxuxw} žt1254~)m f
oVrutumpqEXrutw}Šz€rwqX‚$mU{)r;„ 24{5oV§irux < ouryˆ5oVruxuxI~)m f-<?*4BV09<[email protected]Ž 3pB9BV<?0962.1*f gih1hsrmt’K
j£8 B9<I098:.16Ÿª«.1098A35%76If»<I6ºBu35669¶5.e-< hX*-%7eX356¯D<IG7.cB9@-D-G+. y%jb¨Kkk¨ml¨on*¨opµ orq>35G7G´35*4BIfXgih1h Æ € pY.p®9356If
gih1sh rt y n %+,1@-093 Å K  fX=?.1*4BV<?*-e-.-Ä
{ 2 y'j’ f4.5*-e-<;D.1*4BVi% h-=¨358¥.16£<I6ºBV¬78@-G+.56 <I*4')%´35eH.16Ÿ3¢DX350ºBV%+0
u @-8=I.1*®2@-*4BV.Ze-< qsmI{)mix[{)r¢rwqX‚ƒ3o 24M
…
Åj
±Y#K:%F f%%LY%##f #L
k=0.5
k=1.0
k=2.0
1
0.8
0.6
0.4
0.2
0
n
-10
-5
0
%+,1@-093 Å K Æ Ä… ª«@-*-µI¶5. xw}(ˆ5z€mp}ƒ{ DX3C0V3/%+*-=?G+%7*X35µ
—)<I6¯e-<8´
Camada
de Entrada
Camada
Intermédia
Camada
Intermédia
5
¡O¿[®76[¨ ´ ¡
<
‘ ® ¿ 8´ ¡
Camada
de Saída
3
atalho
1
4
7
6
2
atalho
8
5
n
10
%+,1@H0V3 Å K ÄKj£62B909@HB9@-0V3Ue-<Z@-8A3 Y‹Ž =I.183B9.1D¾.5G+.1,1%+3 v1v5v ™
T ®¿
K
Å
!"#$%#&'
e-.:358¡F-%+<?*»B9< €
u @-8 =I.1*p®2@H*»B9. e-< qsmI{)mix›}ŠqX‚WrwoRz€”9{5}ymixYy'k[ fT@-*-%7eX35e-<?6%7*4BV<I02*X356ae-<·D-02.S=?<I626V358:<I*4BV.Hf ± @-<
35@H8A<?*»BV358 3U=¨3CDX35=I%7eX35e-<EeH<c3CD-09<?*-e-%+ÃI35,1<?8 e-<EBu3502<?ªƒ356;=?.18:D-G+<RQ-3C6 €
{ 2 yBlK f ± @H<>eH<?'1.5G7'1<?8 3/09<I62D¾.562Bu3UeX3U09<?e-< €
u @-8J=I.1*p®2@H*»B9.AeH< qsmI{)mix>{)r¢x 2s†ƒM
{ 2px +SqX}ƒ{5}ŠoVrututw}ympq 25}+8x y'nµ f4e-=< h-*-%+e-.56MD<IG7.EBV@-D-G7. y Œ9f  ¨ z .1@
u @-8­=I.1*p®2@H*»B9.ceH< tumpqsJr xS§irux „Xrux 24M
35FH09<?')%+35eX358:<I*4BV< zC|~} f-<?8 ± @-F< Œ k l ‚f  jk ‚f  * ŒŸ< z € <
q 4C§irux>{)Br 2)tw‚’}Š– 254~)m y'pµ fH*-.1028€3CG+8:<I*4BV<Te-.BV%7D¾.c*X¶5./G7%+*-<I350—<EeH%7ª«<I02<I[* l
u @-8 =I.5*p®2@-*4BV.Ue-< œ +)=?% ƒ¨'1<?Gyf-62<I*-e-.€3ª«@-*-µ¨¶C. †+m9sˆ †+xw‚ƒ}y1t 2 @-8A3eX356Y8A35%+6@SBV%+G7%+ÃI35eX356 y L 3CF¾<?G´3 Å K(g  K
¹ 69%+*-35G eH</<I*4BV0935eX3D-02.1DX35,43 lW69<¡356962%+8 DX35093a3Aª«09<?*»B9<5f&3CB90V3¨'1°?6EeX309<?e-<5fs=¨358A35eX3€D.10¢=I358A35eX3Hf
*X¶5.P<RQH%762B9%+*-e-.P=?%+=IG7.16IK À 356Z09<?e-<I6>8@-G(BV%+=I358A35eX3€3C6>@H*-%+eX3Ce-<I6 qX‚WrwoRz€”9{5:} 2p›x y'k[ e-%('S%7e-<I!8 lW62<<I8
69@-F=I.5*p®2@-*4BV.16?f.1@=¨358A35eX356?f y'kmª ¨^k
­w¨ ¨Kk K e =?.18@-8 09<?D-09<?69<?*»BV350E356T=¨3C8€35e-356[D<IG+3Uª«.5098A3
j - k ª - - k - l fH.1*-e-< e-<I*-.CBu3:3U=I3509eH%+*X35G7%+eX3Ce-<e-.:=I.5*p®2@-*4BV. K
g 8A3 T‹Ž e-<I62%+,1*-m3 lW62<>D.10 tumpz„†+rw&‚ 25z€rwqX‚$r¢}ŠqX‚$rwoR†¦}(M
ˆ 24M{ 2 ± @X35*-e-.:=I.5*»B9°I8 B9.SeX3C6Y356YG+%+,135
µ —)<I6
D.16962¬7'1<?%+6Ÿ<I*4B909<Y.16£*-.)e-.16Ÿe-<;e-@-356Ÿ=¨358A35eX356Ÿ3Cep®935=I<?*4BV<I6 y n %+,1@-093¡g1K  K © 3569.Z=I.5*»B90 ƒ502%+.-f4eH<I69%7,1*Xm3 l
69<>D.10 „ 25oVtw:} 25†¦z€rwqX‚$rZ}ŠqX‚WrwoR†¦}(Mˆ 24M{ 2 KK Ž .10Y'1<?ÃI<?6<wQS%762BV<?8G+%7,435
µ —)<I6¯e-%+02<I=?BV356Y<I*4BV02<¡3C6T<?*4BV0V3CeX356T<>.56
*-<?@-09¸1*H%+.16Me-<6935¬+e-3c.1@ ± @H<T"$6935G7BV358U]=¨358A35eX3C6 y n %+,1@H0V3 Å K  K j£6ºBu356=?.1*-<RQ —)<I6¯e-<I62%+,1*X3C*8 l 69<YD¾.50
25&‚ 259† EXmix oqŽ£09<I=uNH<IG7BIf gih1h tyK
… *-¶5.¡G7%+*-<I3509%7eX35e-<Cf»3c<wQS%762B “?*-=I%+3ce-<T*-.)e-.16M%+*4BV<?098:°Ie-%7.16Ÿ<.>69<[email protected],50V35@:e-<=?.1*-<?=?BV%(')%+eX35eH<
BV.509*X3583350 ± @-%(BV<?=?BV@H0V3 Y‹Ž 8¡@-%7B9.D.SeH<I09.56V3=?.18:.@-8A38 ƒ ± @-%7*X3eH<€35DH09<I*He-%+ÃI35,1<I8EK Ž .50
[email protected]´35e-.Hf)69¶5.¡<?62BV3568:<I698A356Ÿ=¨3C0V35=wBV<I02¬+6ºBV%+=I356 ± @H<¢e-i% h-=I@-G(Bu358@H8 <[email protected]<[=I.18:D-G7<wQS%+eX3Ce-<T35.
D-02.S=?<I6962.AeH<¡35DH09<I*He-%+ÃI35,1<I8 o b[3¨O »%7*f gih1h1h tyK
… B9.1D.1G+.1,5%´3%+eH<¨35G y <?8BV<?098:.16ceH<A=I358€3CeX356If *-.)e-.16><A=?.1*-<w[
Q —)<I6  e-<A@-8€3 Y‹aŽ e-<ID<I*He-<
ª«@-*-e-358A<?*4Bu35G78A<?*»B9<Ue-.DH09.1F-G7<I8A3P369<?0c02<I62.1G7')%+eH. ™ jŸ8,5<I0V3CGyf BV<?*»BVm3 lW62<A02<Ie-@HÃI%+0>.Š* H8A<?09.e-<
<I62=I.1G7NX356 y .1@a<I62DX35µI.Ue-<EDH09.)=I@-093  35e-.5DHBu35*He-.=I<?02B9.16;D-09<?6962@-D¾.562BV.56Ifd=I.18:../@-62.Ue-<E09<?e-<I6;=?.1*8 l
D-G7<?Bu3C8A<?*»B9<%+*4B9<I09G7%+,43CeX356If¾<?')%7BV35*-e-m. lW69</*H<I62B9<U=¨3562.3DH09<I.)=I@HDX35µ¨¶C.62.1F-02< ± @H<:=?.1*-<RQ —)<I6Ze-<w'1<?8
<wQS%762BV%70IK/L 358F°I8‰°:=?.18@-8 35e-.1DSBu350 lW69<:35D<I*-356Z@-8€3=I358A35eX3a%+*4BV<?098:°Ie-%+3H'f hX=I35*-e-.3a<I62=I.1G7NX3
e-.16:*-.)e-.16U%+*4B9<I098:°IeH%+.16:3·69<I0:e-<?=I%+eH%+eX3|D.10U09<I,50V356:<I8:D-¬+02%+=I356IK!L 093CBu3 lW69<Pe-<@-8A3 <?62B90V3CB9°I,1%+3
± @-<UG+<w'53a3 ± @-<U69<U<?62BV<W®93D<I0935*4BV<Ue-%(ª«<I09<?*4BV<I6Z62.1G+@-=µ —S<?6EDX35093P.aDH09.1F-G7<I8A3Hf62<I8@-8 =I09%(BV°?09%+.€e-<
e-<?=I%+69¶5.¡=?.1*4BV093CBV@X3CG+%+ÃI35e-.-f5eX35e-. ± @H<*X¶5.>69<3CBV02%+F-@H%-,10V3C*-e-<T%+8:D¾.10ºB 5*H=I%´3E3C.c8:.SeH<IG+.Z<?8BV<I028A.56
e-<Te-<I62<I8:D¾<?*-N-.-fS<I8 DX3C02BV<Ye-<w')%+e-.¡35.c<?*-.1028A<TD¾.)e-<?0Me-356 Y‹Ž xI™ j£62BV093CBV°?,1%´3C6M8A35%76£<IG´3CF¾.10935eX356
DX35626V358JD¾.10YD-02.S=?<Ie-%78A<?*[email protected] ƒCBV%7=I.16¯e-<ZD-09.)=I@-093Hf ± @-<>69<?0V¶5.Ue-<?69=I02%7B9.16Y*-. © 3CD-¬7B9@-G+. K
Åh
±Y#K:%F f%%LY%##f #L
GCHJIKH
WaKVR”U Z
V
eN
N'ZŠR”V
R”V`K`KV
?< *»B909.Ee-.56 35G7,1.109%(BV8:.16 e-<MBV09<?%+*-.[69@-D<I0º')%+69%7.1*X35eH.16If1.[8€3C%+6nD¾.1DH@-G´350&<—8€35%76 @H6V35e-.°¯.E35G7,1.102%7BV8:.
e-< Yrw‚ƒoumpvyš—oVmu„ 2iˆM254~)m ¼’Yš&½ .1@ 62<I@-6:e-<I02%7'C35e-.56o9qZ35G7G´35*4B¨f¾gih1h Æ tyKj£62BV<35G7,1.102%7BV8:.DH09<?'C35G7<I=?<
=I.58A.@-88A3509=?.DX3C0V33P=I.58@-*-%7eX35e-<UeX356 Y‹Yxu ®©ƒ ± @-<A=I.1*-6ºBV%(BV@-%Ÿ@-88:°?B9.Se-.<=h-=I%+<?*4BV<:e-<
=I.58AD-@SBu35µI¶5./DX35093.BV09<?%+*-.¡e-< Y‹aŽx f-D-02.S=?@-0V35*He-././8A¬7*-%+8:.>eX3ª«@-*-µ¨¶C./e-<E<I0209./*-./<?69DX35µ?.Ue-<
D-02.S=?@-0V3/e-.16YD<I62.16YeX356YG+%7,435
µ —)<I6—<I*4BV02<Z*-.SeH.16IfXFX3C69<¨3C*-e-. l 69<Z<I8 8:°?B9.SeH.16;e-<Z,10V3Ce-%+<?*»B9<Ee-<I62=I<?[* l
e-<?*»B9<5KK … =I.18FH%+*X35µI¶5.>e-<D<I62.16 ± @-<¢8:%+*H%+8:%+è33>ª«@-*-µI¶5.¡eH<<I0209.°T=I.5*-69%7e-<I0935eX33>69.1G7@-µ¨¶5.>DX35093
.¡DH09.1F-G7<I8A3>eH<¢35D-02<I*-eH%+è3C,1<I8K 35eH. ± @-<¢<?62BV<[8A°wBV.)e-.><wQS%+,1<[.¡
= ƒ5G+=?@-G+.>e-.¡,50V35e-%7<I*4BV<Cf)B9.109*-m3 lW62<
*-<?=I<I626 ƒ502%+. ± @-<Z3cª«@-*Hµ¨¶5./e-<E<?0902. y ‚ 69<W®93=I.1*4BV¬7*»@X3<Ee-%7ª«<?09<?*-=I¬% ƒi'5<IG’fH. ± @-<Z35=?.1*4BV<?=I< ± @X35*-e-./62<
@-69358Jª«@-*-=µ —S<?6Ye-<¡3C=?BV%('C35µ¨¶5./eH%7ª«<I02<I*-=?% ƒ¨'1<?%+<6 oqpT.®9356If gih5±h rmt’K
…¥35D-G+%7=¨35µI¶5./e-.:35G7,1.109%(BV8:.¡e-< Yš D.SeH<E69<I0Ye-<?69=?09%7BV3:*-3Uª«.1028€
3 oqpY@-8A<?G+NX3C02B;<wBT35GyK(fgih rtyÄ
u •—z­œRoVrwqX‚Wru .1*-eH</.P'5<I=wBV.10Ze-<U<I*4B90V35eX3 y‰ˆ_ °ª«.509*-<?=I%+eH.3C.16E*-.)e-.16Ee-<U<I*4B90V35eX3aeX3a02<Ie-<Cf
D-02.1DX35,135*-e-. l 69<E<?8Jª«09<?*»B9<5fX=I358€3CeX3D¾.50;=¨358A35eX3HfSe-<>35=I.509e-.U=I.58 356Y< ± @X3C
µ —)<I6 Å K(g>< Å K Å f
<?8 ± @-<c.U%7*»B9<I,10935e-.10¯@HBV%7G+%+ÃI33/ª«@-*-µ¨¶C.A3Ce-%+µI¶5. y š  € %yK‘<5K(f
y Å KÆ 
|'¡d¢ ² } zC|‹}
}
<?8 ± @-< ² •%¡ ‘ y 'C35G+.50TeH<<I*4BV0935eX3€e-3€=I.1*H<wQH¶5.ae-< I}:2pxm f ² ªf¡ˆ«ª ¨ =¨ ² °*¡ˆ„° f¾DX350V3 ˜
*-.)e-.16EeH</<I*4BV0935eX3 y ˜ ¡ j  Kµj£8 69<?,1@-%7eX3Hf =¨3CG+=I@HG´3ml 69<¡.a<?0902.-f =I.18‰FX3562</*X3ª«@-*-µ¨¶C.ae-<
[email protected]*-.1028€35G78A<?*4BV<¢eX3CeX3/D¾.10?Ä
‘
­
¢ £
° C - ² Ÿ
yÅ K 
8¡
T
.1*He-< e-<I*-.CBu3U.:'5<I=?B9.10Te-<c6935¬+e-3UeH<I69<W®935e-.-f l .:=I.5*p®2@-*4BV.Ae-<Z*-.SeH.16[eH<>6935¬+e-3:eX3U09<?e-<><
˜ <‡| .a62.18€3pBV¸102%+.:e-.16E*-.)e-.16[e-</<I*4BV0935eX3<%7*4BV<I028A°?e-%+.56 y ˜ <‡|·¡ j  k  K
@-0V35*4B9</<I62B9<
DX3C6969.HfX.16YD¾<?69.16YeX3U09<?e-<Z<I62BV¶5*. hHQS.16IK
Yrw‚ƒoumpvyš—oVmu„ 2iMˆ 254~)mi .5*-e-<.><I0209.c°[D-02.1DX35,135e-.¡D-350V3>3CBV©0 ƒ56If)e-<?69e-<3c6V3C¬+eX3>3CBV°T.16M*-.)e-.16Me-<
<?*»B90V35e-3HK <69<?,1@-%7eX3Hfd.16D<I62.1669¶5.a3®[email protected]62<I,1@H*-e-.a3:09<I,50V3AeH< }ƒ{5oum £v m #K Ž 35093
@-8 -*-%+=?.UD¾<?69.UBV<I!8 lW62< ± @-<5Ä
zC|~}£ JŸK¡ £ JŸ
y Å Kk 
zC|‹}
!
u
#"
&
('
*),+.-
/0214365879;:6<=5><@?BA8CDFEHGJIJKLNMPORQSUT4V8KXWKPYRZ[TP\^]
'
$
%
Æ
!"#$%#&'
<?8 ± @-< 09<?ª«<?09<AlW69<·3 @-8A3 %(BV<I0935µ¨¶C.ae-. 35G7,1.109%(BV8:.ÁeH<›BV09<?%+*-. < e-<?*-.5Bu3 3 BV3pQH3 -e <
35DH09<I*He-%+ÃI35,1<I8K·…[6[e-<?09%('53CeX356;DX3502=I%+35%+669¶5.U=¨35G7=I@-G+35eX356;62<I,1@H*-e-.:.A=?G´35@-62@-G´3Ce-.-Ä
j
² |
¡
y Å Kr 
zC|~}
² | zC|~}
.1*He-<
² | ¡dœ'ž £ |‰Ÿ 
y Å Kj 
²
zC|‹}
Ž 350V3 62<|.1FHBV<?
0 C fT.1@ 62<$®93 3 %+*S³X”@ “I*H=I%´3 e-3 6V35¬7eX3 ² | e-. *-.)e-. Œ/*-. <?0902. ,1G+.1F-35G fY°
*-<?=I<?696 ƒC09%+.A3CB9<I*-e-<?0T35./BV%+D./e-<>*-.)e-.-f-.1@P62<$®93HÄ
)
'
-
-
-
-
-
-
-
-
-
² |
¡
4
- £m| ° C - ² {| Ÿ
¨ Œ l
š } | '
œ ž £ } ŸLzK}L|À¨ Œ l
5
2
.1*He-< ²w £ Œ Ÿ 02<ID-02<I69<?*4Bu3 . =?.1*p®2@-*4BV. eH.16€*-.)e-.16µ eX3 =¨3C8€35e-3Á=I.58 ± @-<›.Á*-.)e-. Œ¡62<
02<IG´3C=I%+.5*X3 y .1@P<?62Bu3CF¾<?G+<I=?<ZG+%+,135µ
—)<I6  K
…*4B9<I6/e-<62<a%+*-%7=I%+350Z.›BV09<?%+*-.e-<@-8A309<?e-<5fŸN„ƒ ± @-<aDH09.)=I<IeH<I0U_›<?69=I.5G+NX3eH.16'C35G+.102<I6c%+*-%7=I%´3C%+6
e-.16¯D¾<?69.16;3C6969.)=I%+35e-.16 _56¯G7%+,43C
µ —)<I6M<I*4BV02<¢*-.)e-.16If ± @-<¢e-<w'1<I09¶5.U69<?0D¾< ± @-<I*-.56;<,1<?0V35e-.56e-<[ª«.5098A3
35G7<¨3CB9¸109%+3H›K Žn.SeH< lW62<a<I*4Bu¶C.|DX3502B9%+0>DX35093›.BV02<I%+*H.›eX302<Ie-<CfM=?.18:<Iµ¨3C*-e-.l 69<D.10¡62<IG7<I=I=?%+.1*-350@-8
=¨3C69.eH<:B909<I%7*-.-fn*X3ª«.5098A3P%(BV<?0V3CB9%7'C3Hf&.1@·BV.)e-.16>.16c=I3569.56If *-3ª«.1028€3 rwz†+mp‚$r K À .1098A35G+8:<I*4B9<5f
=I.5*»'5°I8 ± @-<T<I6ºBu3E69<?G+<I=?µ¨¶5.>69<W®93c3CG+<¨3pBV¸102%´3HK j£869<?,1@-%7eX3Hf4=¨3CG+=I@HG´m3 l 69<;.Z,10V3Ce-%+<?*»B9<;<T3®2@-62BV35!8 lW69<;.56
D<I69.56IK g 8A3 }Š‚Wrw3o 254~)m BV<?098:%+*X3 ± @X35*-eH.¡BV.)e-.16M.16M=¨3562.16e-%769D.1*-¬7'5<I%76ŸB9%7'5<I09<?8\62%+e-.>=I.5*-69%7e-<I0935e-.16?K
¹D-09.)=I<?6969.a°ceX35e-.€=I.18:. hX*He-.D<IG´3A35D-G7%+=¨3Cµ¨¶5.:e-<¡=?09%(BV°I02%+.16Te-<cDX350V3C,1<I8 y <CK ,HK7f ± @X35*-e-.P3C6
8@-e-35*-µ¨3C6*-.16[D¾<?69.16[<¡*X3Uª«@-*-µI¶5.e-<c<I0902.Aª«.102<I8%7*-69%7,1*-i% h-=¨35*4BV<?6  K <¡*-.5BV350 ± @H<¡.a35G7,1.102%7BV8:.
D.Se-<=I.5*»'5<I02,1%+0:DX35093 @-8Â8:¬+*H%+8:.|G+.)=¨35G y n %+,5@-0V3 Å K…k  € *X3·D-0 ƒpBV%+=I3Hf¯D.102°I8f¯=I.5*-62BV3CBum3 l 69< ± @-<
± @X35*-eH.€69<cDX350ºBV<>e-<c@H8Š* H8A<?09.€<?G+<w'53Ce-.AeH<¡=¨3C69.16Te-<cB909<?%+*-.-fX<?62BV3 ± @-<I6ºBu¶5.€*X¶5.€62<c=?.1G+.)=¨3SfX.1@
<I*4BV¶5.A*-¶5.U69<>356962@-8:<>=?.18:.:@H8 D-09.5F-G+<?8€362°I09%7.-K
GCHJIKH
Wa ZN«R`fN
`KV
WaKVKRU Z
VXe%N
YN'ZŠRV
8
R”V`K`KV
53 D-09<?69<?*»BV35µ¨¶C.e-.c35G+,1.509%7B98A.e-< Yš 35G(BV<I02.1@:.cDX3C*-.10V3C8€3EeX3>%+*4'1<?62BV%7,435µI¶5.c<?8 T‹Žx <Te-<I62e-<
<I*4BV¶5.›B “?8²69@H09,1%7e-.›@-8A3›8A%709¬+35e-<Ue-<a*-.i'1.56U35G+,1.509%7B98A.56>eH<BV09<?%+*-.HK jŸ6ºBu3›<RQHDHG+.169¶5.|e-<?'5< l 69<3
e-@X3C6[0935Ã
—)<I6?KŽ .10[@-8G´35eH.-fX.35G7,1.102%7BV8:.e-< Yš °cD<I6935e-.-fe-<>=I.1*4'1<?09,±“?*-=I%+3€G+<?*4Bu3HKfŽn.10T.1@HBV02.
…
?FA8CDFEHG!>7#"U?BDF?%$X3'& G( <)"*(;1* <+(VTXL,.1/ 0 <6A#23(54? 5><6( ?FAC6DBEXG879(;DB<)"*(;1* <:4KPY L,.-
Æg
±Y#K:%F f%%LY%##f #L
Erro
Mínimo
Local
Mínimo
Local
Mínimo
Global
+% ,1@H0V3 Å K…kSÄ ¬7*-%+8:.16G7.S=I35%+6<Z,1G7.1FX35%76orq>3CG+G´3C*»BIf¾g¨h1h Æ t’K
G´3Ce-.-fnFX3569<?%´3ml 69<:*-.›,10935e-%7<I*4BV<:e-<I62=I<?*-e-<I*4B9<5fŸD¾<?G+. ± @H<ABV.)eX356c356>BV°I=?*-%+=I356¡eH<€.1DHB9%+8:%+ÃI35µ¨¶5.a*-¶5.
G+%7*-<¨3C0e-.U,10V3Ce-%+<?*»B9<ZD¾.)e-<I8\69<?035DHG+%+=I35eX356 o ¯.569< ­# %´3C*-,-fgih5h±rmt’K
À .cD-%+.10£eH.16—=I3569.56IfS3¡35D-02<I*-eH%+è3C,1<I8eH< Y‹;¢x ° ‹Tš—v9tumpz„†+rw‚ 2„€ %’K <CK7f».><I6ºª«.109µ?.¡=I.58AD-@SBu35=?%+.l
*X35G»<?*»'5.1G7')%7e-.¢=I02<I62=I<e-<—@-88:.Se-.T<wQSD.1*-<?*-=I%+35GS=?.18 .¢35@H8A<?*»B9.e-.56 DX350 58:<?BV02.16&G+%('S02<I6 y D<I62.16  K
…6269%78f <wQS%+6ºBV<<?69DX35µ?.|DX35093›3D-02.1D¾.562Bu3e-<a35G(BV<?09*X3CB9%7'C356 ± @-<D.16969358 35=I<?G+<I09350¡.D-09.)=I<?6962.|e-<
35D-02<I*-eH%+è3C,1<I8fS<?8F.10V3>69<$®93c69<I8:D-02<¢D¾.56969¬('1<?Gs<I*H,435*X350—.>"$8:<IG7N-.10$];8:°?BV.)e-.c=I.18 @-8A3ceX35e-3cBum3 l
09<wªƒ3/e-<¡3CD-09<?*-e-%+ÃI35,1<?8f-eH<I69eH< ± @-<Z69<>=I.5*-N-<IµI358.16Y69<?@-6TD¾.1*4B9.16;ª«.102B9<I6;<Eª«0V35=?.1F6 o pY.p®9356?f gih1±h r tyK
Ž .50;=I.1*-62<I,1@H%+*4BV<CfXe-%7'5<I0969356;'C3509%+35*4BV<I6¯0 ƒ5D-%7eX356eH.A3CG+,1.102%7B98A.>e-< Yš f ± @H<E69<ZFX3562<I%´3C8J*-./@-62.Ue-<
@-8A3BV.1D.1G+.5,1%´<3 hHQH3Hf-ª«.10V3C8JD-02.1D¾.562Bu3C6T*H.16 -G7B9%+8:.1635*H.16IK
L .)eX3¨')%´3HfBu3C8F¾°?8 <wQS%762BV<?8ª«.1098A356&69%78AD-G7<I6 e-<—35=?<IG+<?0V350&.35G+,1.509%7B98A.¯e-< YšŸ *H.18A<I35eX358:<I*4B9<
356Y69<?,1@-%7*»B9<IF6 o‘b3¨O )%7*f gih1h5mh t’Ä
g1K 2wxL2c{)rŸ„oVrwq{5}(‡ 2iˆ)rwz K ¢@X35*4BV.8€35%76 D< ± @-<?*X3¢ª«.10 >8A<?*-.102<I6 'C¶5.¢62<I0£356 8@-eX35*Hµ¨356£*-.56
D<I62.16ce-356c=?.1*-<RQ —)<I6?f e-<:8A.)e-. ± @-<€3D-09.)[email protected]:¬+*-%78A.€,1G+.1F-35G 69<?0 ƒPªƒ3i'5.109<?=I%7eX3D<IG7.
@-62.AeH<>6935G7B9.168A35%+6¯69@X3¨'1<?6IK¹¥D-02.1F-G+<?8€3° ± @-<Ze-<?62Bu3/ª«.1028€3¡B9<I!8 lW69<E@H8€3U35D-02<I*-eH%+è3C,1<I8
8A35%+6aG7<I*4Bu3S?
K Ž .10.1@HB909.!G´35eH.-f62< 69<Á35@-8:<I*4BV350<?8 e-<I8A3562%´3 . 'C35G7.10ae-< ¾fE<?*»BV¶5..56
<?G+<?'C35eH.166V3CG7BV.56€*X356€8@-eX35*Hµ¨356eH.16aD¾<?69.16€D¾.)e-<I09¶5. D-02.'5.S=I350%7*-62BV35F-%+G7%+eX3Ce-<P*-. BV02<I%+*H.
y <5K‘,-K7fX8:.i')%+8:<I*4BV./.162=I%7G´3CB9¸109%7.  K g 8A3/ª«.5098A3e-<>35@-8:<I*4Bu350Y3BV3pQH3:e-<>35DH09<I*He-%+ÃI35,1<I8J69<I8
D-02.i'1.)=¨350Ÿ%+*H62Bu3CF-%+G7%+eX35eH<—°T35G(BV<I09350£3Z09<?,10V3Ee-<T35D-02<I*-eH%+è3C,1<I8e-<Y8A.)e-. ± @-<T<I62BV3E%+*-=?G+@X3E@-8
B9<I098:.Ue-< z€mpz€rwqX‚ +)z Ä
zC|‹}m£ JŸK¡ £ JŸ 
zC|‹}£ -‘ Ÿ
yÅ K 
zC|‹}
w
n
)
&
)
'
)
+.-
'
&
'
Æ4Å
!"#$%#&'
.1*He-< P09<IDH09<I62<I*4Bu3c3¢=I.1*H62Bu3C*»B9<Ye-< z€mpz€rwqX‚+)z¡ @H69@X35G78A<?*4BV<;eX35e-3ZD.10 @H8­'C35G+.10 D¾.569%7B9%7'5.
<?69=I.5G+N-%7e-.Pe-.P%+*4BV<?02'C35G+. ¿¨ ‘YyK*j£62B9<:B9<I028A.Pe-< z€mpz€rwqX‚:+Sz ª«@H*-=I%7.1*X3a=I.18:.P@-8A3P8:<I8:¸l
02%´3 ± @-<·3C=I<IG7<I093 e-<I62=I%7eX356ae-. ,10935e-%7<I*4BV<CfYB9<I*-eH. @-8 <wª«<I%(BV. <?62Bu3CF-%+G7%+è3Ce-.10:<I8 69%7B9@X35µ=—S<?6
.162=I%7G´3CB9¸109%+356IK
Å K mI{)m¢{)r oVrw}Šqsm K @H0V35*4BV<¯3[3CD-09<?*-e-%+ÃI35,1<?8f@-8A3 }Š‚Wrw3o 254~)m =I.50909<?69D.1*-e-<¯3T@H8€3;=I.58AD-G7<?BV3
35DH09<I62<I*4Bu3Cµ¨¶5.ce-<TB9.SeH.16—.56M<RQS<I8:D-G+.16Me-<YBV02<I%+*H. _Z09<?e-<5K © .1*4'5°I8 ± @-<¢3>35D-02<I69<?*4Bu35µI¶5.69<W®93
35G7<¨3CB9¸109%+3Hfne-<ª«.1098A33 ± @-<a*-¶5.›<wQS%762Bu3›@H8€3B9<I*-”e “?*-=I%+3›DX35093'C35G+.102%+ÃI350c=?<I0ºBV.16/=I3569.16¡e-<
B909<I%7*-.-KK j£62BV3A3CD-09<?69<I*4BV35µ¨¶5.:D.Se-<Z62<I0Y<?ª«<?=?BV@-35eX3Ue-<Ze-@X356;ª«.1028€356?Ä
u z€mI{)mTxir ¤ +Xrwqstw:} 25† fC.1*He-<69<—=¨35G7=I@-G+358.16 3®2@-6ºBu358:<I*4BV.56£35.16nD¾<?69.16 G+.1,1.[35D¸16 3T<I62=I.1G7NX3
eH<c@-8\<wQS<I8:D-G7.:eH<>B909<I%7*-. € <
u z€mI{)mUrwz †+mp‚Wr .1@ „XmpoY}Š‚Wrw3o 254~)m f).5*-e-<T.16M3®2@-62BV358:<I*4BV.16—35.16ŸD<I62.16—62¸¡69¶5.c<wª«<[email protected]
3CD¾¸16T3U35D-02<I62<I*4Bu35µI¶5.€eH<ZB9.SeH.16;.16Y=¨3562.16Ye-<EBV02<I%+*H.-K
¹ D-02%+8:<I%709.>8A.)e-.>e-<[B909<I%7*-.¡°[8A<?*-.16—<wQS%+,1<?*4BV<<?8 BV<I028A.56¯e-<[8A<?8A¸102%´3EG+.)=¨3CGyf4DX3509335G7°I8
eX3 3CD-09<?69<I*4BV35µ¨¶5.!35G7<¨3CB9¸109%+3 eH.16=¨3C69.16ae-<BV09<?%+*-.ÁBV.102*X350e-%(ª«¬+=?%+G ± @-<|. 35G7,1.109%(BV8:. h ± @-<
D-02<I62.<I8 8A¬7*-%+8:.16G7.S=I35%+6?f 69<?*-e-.eH<?'1<?0V3586 HBV%7G ± @X35*-eH..=I.1*®2@-*4BV.e-<Ae-35e-.16Ze-<UBV02<I%+*H.
°U<IG7<?'C35e-.<U<wQS%+6ºBV<:FX356ºBu35*4BV<:%+*Sª«.1098A35µ¨¶C.09<?e-@-*-eX3C*»B9<5K j£8=?.1*4BV0V3C62BV<Cf .8:.Se-. rwz†+mp‚Wr
8:<IG7N-.10V3A3€<I6ºBV%78€3CB9%7'C3Ue-.€'1<?=?B9.10Ee-<¡,50V35e-%7<I*4BV<Cfs62<I*-e-.aBV358F°I8 @-8 D-09.)=I<?6969.a8A35%76T{ª ƒ5=?%+G
e-<Z62<>D-350V35G7<IG7%+è3C0IK
Æ K •Ÿxitump9† E 2 {)mixašYruximix qX}ytw:} 25}+xId™ g 8€3 F¾.13Á<I62=I.1G7NX3ÁeH.16€'C35G+.509<I6:%+*H%+=I%+35%+6¡e-.16D<I62.16€D.SeH<
35=?<IG7<I0V3C0¢FX356ºBu35*4BV<U.PD-02.S=?<I6962.Pe-<:35D-09<?*-e-%7è35,1<?8K¡¹ DH09.1F-G7<I8A3<I6ºBu3a<I8‰e-=< hX*H%+0E. ± @-<U°
@-8A3¢F.43E<I69=?.1G+N-3HK M35G7.109<?6£<IG+<w'C35e-.16£D.SeH<I8.102%+,1%7*X350 @-8€3¢693CBV@H0V35µI¶5.ce-3Z02<Ie-<Cf)3CBV09356V35*He-.
.aD-02.S=?<I6269.Pe-<U35D-02<I*-eH%+è3C,1<I8K À .a<I*4BV35*4BV.-f'C35G7.109<?6e-<?8€3562%´35eH.aD¾< ± @H<I*-.16ED.)e-<I8‰G+<?'C350
3 ± @H<¡.3CG+,1.102%7B98A./e-< Yš .1D¾<?09<>*»@-8€3 ƒ509<I3Ae-<?8€3C69%´3Ce-.ADHG´35*X3UD.10T'5.1G7BV3AeX3:.109%7,1<I8JeX3
62@-D¾<?02ª«¬7=I%+<:e-<A<I0902.-EK …6269%+8 ± @-<?0¡'C35G+.509<I6Ze-<?8€3C69%´3Ce-.<?G+<?'C35eH.16c.5@ e-<?8€3562%´35eH.D< ± @-<?*-.16
e-<w'1<?869<I0><?')%(Bu35e-.56IK g 8A3aF¾.43a<?62BV093CBV°?,1%´3a°U,1<?0V350E'C35G+.509<I6Z3CG+<¨3pBV¸102%+.16[=I.18@H8€3a8:°Ie-%+3
e-<:ÃI<?09. ± @-<AeH<ID<I*-eX3C8 eH.‚*­ -­8:<I02.e-<:=I.5*-<w[Q —)<I6>e-<A@H8*-.SeH.-K Žn.10Z<wQS<I8:D-G7.-f q>35G7G´35*4B
o gih1h Æ t 69@-,5<I09<Z.U%+*4B9<I02'C35G7
. yfHDX350V3U@-8 *H.Se-.U=?.18 ´<I*4BV0935eX356?K
GCHJIKH
WaVRU]Z
V eN
W
e%`%Z[`KV’Vf^'`Ka
6['53C09%´3C*»B9<I6Te-.a35G7,1.102%7BV8:.Ue-< Yš D¾.)e-<?8 62<I0¢=?G´356269%¯hX=¨35e-356<?8 eH@X356¢=I3CBV<?,1.109%+356Iįe-</35eX3CDHBu3ml
µ¨¶C.,5G+.1FX3CG .1@·G7.S=I35GCoqpT%7<Ie-8:%+G7G+<?0Ifdgih1h tyK¹¢6>DH09%+8:<I%709.16[@HBV%7G+%7è358@-8 =I.1*-NH<I=I%78A<?*4BV.P,1G+.5FX35Gne-.
…
1Æ Æ
<I6ºBu35eH.:=?.18:D-G+<wBV.eX3/02<Ie-<Cf-=I.18:.U3e-%709<I=?µ¨¶5./eH<¢BV.)e-./.'1<?=?BV.50TeH<Z35=?B9@X35G+%7è35µI¶5.¡eH.16;D¾<?69.16?KjŸ8
=I.5*»B90V356ºBV<Cf.16HG7BV%78A.56T69¶5.FX3C69<¨3Ce-.16E*X3€%7*Hª«.1028€35µI¶5.:<I69D<I=?¬ihX=I3e-<¡@H8‰D<I62.-fs=?.18A.€.=I.18:D.10Ll
Bu3C8A<?*»B9.:B9<I8:D¾.50V35Ge-3:62@X3Ae-<?09%('53CeX3:D-3509=?%´35G’KDj£6ºBV<ZBV%+D.Ue-<><I62B90V3CB9°I,1%+3/<I62B ƒA8A35%+6;DH09¸¨QS%+8A3Hf-<I8
BV<?098:.16Y=I.18:D-@HBV35=I%7.1*X35%76IfX3U@-88:.SeH<IG+.U*-<[email protected]*X35G 69<?*-e-.8A35%+6ªƒ3C=I%+G78A<?*4BV<EDX350935G+<?G+%7wà ƒ¨'1<?GyK Ž 35093
35G7°I8e-%76969.Hf¾<?62Bu3C6[BV°?=I*-%7=¨356TBV<?*-e-<I8‰3A62<I0[8€35%76Y<=hX=I35ÃI<?6E<c02.1F-@-6ºBu356?f35D<I69350e-<c@-6V3C09<I8 8:<I*-.56
%+*Sª«.1098A35µ¨¶C.-K
À <?62BV<:=I.5*»B9<wQ)BV.Hf %+8:D.102BV3€e-<I62=I02<?'1<?0¡e-.5%+6>35G+,5.109%(BV8:.16[%78AD.10ºBu35*4BV<?6Ee-<:35eX35DSBu35µI¶5.PG+.)=¨35G’Ä¢.
+)}yt iš¯oVmu„ <>. YšŸ —š Ä
±Y#K:%F f%%LY%##f #L
d35N-G78€35* o(gih t£D-02.1D 16E@-8A3€'53C09%´3C*»B9</e-. Yš =uNX358A35eX3 +)}yt iš¯oVmu„ ¼ šn½ f ± @H<ADX3C09<I=?<UG+<?'C350
3·@-8€3|0©ƒ5D-%+e-3›=I.1*4'1<?09,±“?*-=I%+3Á*X3·8A35%+.102%´3eX356:69%7B9@X35µ=—S<?6IfM69<I*He-. D.10/%+6269. FX356ºBu35*4BV<P@HB9%+G7%+è3Ce-.-K
Ln0V3CBV3mlW62<¡e-<@H8‰8:°?B9.Se-.Ae-<62<I,1@-*HeX3.109eH<I8f ± @-<62<=I.58F-%+*-3A=I.58‰=?<I02BV356¢N-<?@-09¬762B9%+=¨3C6IKŽ 3502B9<
e-<Ze-@X3C6[3C6969@H*-
µ —)<I6 ± @-<c*H<I8 62<I8:D-09<Z69<>D.Se-<?0V¶5.'5<I02i% hX=I350IÄ
n
u
u
. ?< 0909. –5rwoVx$+4x 3 =I@-0º'C3 e-. D¾<?69. DX35093 =¨35e-3 =?.1*-<RQ-¶C.!D.)e-<›69<?0P35D-02.iQS%78€35eH. D¾.50@-8A3
DX3C0 ƒ5F.1G´3/3CF¾<?02Bu3/DX3C0V3/=I%78€3 € <
3/8@-e-35*-µ¨3U*-.UD<I69.:*X¶5.U°>3Cª«<?=?Bu3CeX3:D.10B9.Se-.56;[email protected];D<I69.56 ± @-<Z<I6ºBu¶5.A3/69<?035G(BV<?0V35e-.56IK
¹ 35G+,5.109%(BV8:.E=I.18:D¾.502Bu3 lW69<T=I.58A.c.35G7,1.109%(BV8:.¢BV0935e-%+=?%+.1*-35GXe-< Yš fS@SBV%+G7%+ÃI35*-e-.Z@-8A3c=?.18F-%7*X35µ¨¶C.
eX3/8:<I698A3/09<?,10V3/e-<>35D-02<I*-eH%+è3C,1<I8 y < ± @X35µI¶5. Å K k  <>=?.183/69<?,1@-%7*»B9<Z09<I,50V3Ue-<>35D-09<?*-e-%7è35,1<?8Ä
j £ JŸ
zC|~}£ -‘ Ÿ
y Å K…h 
zC|‹}£ JŸ¡
j £ - ‘ Ÿ j £ JŸ
<I8 ± @H< j £ JŸK¡ C K Ž 35093[35G7°I8 e-%+6269.-fpe-<Ÿ8A.)e-.Y3Y<?')%7BV350 <IG7<?'C35eX3C6&'C3502%´35=µ —S<?6If.Y6V35G(BV.T35=wBV@X35G
e-.16>D<I69.56c°:G+%78A%(Bu35e-.3@-88 ƒpQS%+8:.ae-< ·'5<IÃI<?6<I802<IG+35µ¨¶5.35.6V3CG7BV.35*4BV<?09%7.10IbK …6269%+8fn<I62B9<
35G7,1.109%(BV8:.Z=I.1*4BV°?8Je-.5%+6DX3C0 58:<?B909.16?Ä ¾f)Bu3pQH3e-<Z3CD-09<?*-e-%+ÃI35,1<?8\DX3C0V3¡./,10935e-%7<I*4BV<¢eH<I69=?<I*-eH<I*4BV<
< ¨ @-8\G+%+8:%7BV35e-.10Me-.UBu358A35*-NH./e-.U6V35G(BV.-fHB9<I*-eH.A./'C35G+.50DX35e-09¶5.Ue-*< ‘ ® 6 K
&
'
'
'
('
'
&
('
)
!
!#" ¹ *-.58A<;e-.c35G7,1.109%(BV8:.
'1<I8 eH.c%7*-,1G¬“?6 " ur xw}Š†¦}yrwqX‚ '2)t
2iˆM25‚ƒ}ympq ]Vf1BV0V3pBu35*-eH.lW62<
e-<Z@-8A3'53C09%´3C*»B9<E69.sh-62BV%7=¨35e-3UeH.€35G7,1.102%7BV8:.>e-< Tš o pY%+<?e-8A%7G+G7<I0 ¯0V3C@-*fgih5h Æ t’K
!
!#" !
!#" Æs
!"#$%#&'
09<I,50V3/e-<Z=wƒ5G7=I@-G7./°ZeX35eX3UD¾.50EÄ
…
&
4 2333
|‹}£'JŸK¡
;
)
) 33
¥
&
&
|~}s£(' -
‘ Ÿ
|~}s£(' -
‘ Ÿ
£ ' - ‘ Ÿ ¥ C £('JŸ ¿
C
C £ ' - ‘ Ÿ ¥ C £('JŸ * ¿
C (£ ' - ‘ Ÿ ¥
C £ 'JŸK¡O¿
¨
¨
|‹}£' -‘ Ÿ
&
35
¥
¨
Å K(g
y

XD 35093 ¿ * * ‘ * ; K 3C; 69<¨3Ce-.16<?8²=I.5*-69%7e-<I0935µ
—)<I6eH<a.109e-<?8 B9<I¸102%+=I3<<I8:D-¬709%+=I3Hf <?62B9<I6
ªƒ35=wBV.102<I6ª«.109358 hHQH35eH.16/<I8 ¡ ‘ ® T|< ¡@¿®76 K ¹¢6/D¾<?69.16UeX3C6/G+%+,135µ
—)<I6c<I*4BV02<*H<I@-02¸1*-%+.56
D.Se-<?8 <I*4BV¶5.U69<I0[35G(BV<I0935e-.16¯e-<>35=I.102e-.:=I.183/02<IG´3Cµ¨¶5.-Ä
) )
) )
&
zC|‹}£'JŸK¡
4 2333 
&
&
|‹}s£('JŸ
¨
|‹}m£'JŸ
¨
33 ¿
¨
35
(£ 'JŸ¿
C
(£ 'JŸ *¿
C
£'JŸK¡O¿
C
y
Å K(g1g 
£[email protected]=?.18AD-350V3CB9%7'5.16c8:.16ºBV0V3C0V358 ± @-<<?62B9<a35G+,5.109%(BV8:.a=I.1*4'1<?09,1<a8A35%76>0935D-%7eX358:<I*4BV< ± @-<
[email protected],1.102%7BV8:.16Me-.:,1°I*-<?09."o pY%+<?e-8:%+G+G7<I0?fg¨h1h t’KK…G7°I8 e-%76962.-fXe-<ID<I*He-<¡3CD¾<?*X356Ye-<>e-.1%+6;D-350 ml
8:<?BV02.16If • < » f1=?@p®93¢<I62=I.1G7NX3Ee-<¯'C35G7.109<?6 *X¶5.E°8¡@-%7B9.¢=I02¬7BV%7=¨3HfC69<?*-e-.Z@-83CG+,1.102%7B98A.Ye-<w'1<I09356
09.5F-@-62B9. € %yK‘<5K(f109<?,10V3¢,5<I0V3CGyf1*X¶C.E°;*-<I=?<I69©6 ƒ509%+3E*-<I*-N»@-8A3E35G(BV<I0935µ¨¶C.E35.16 'C35G7.109<?6£35=I.5*-69<?G+NX35eH.16 DX35093
• < y •C¡d¿® ‘Z< ¡ 6s¿® ¿  K
»
»
j
&
&
&
&
GCHJIKH
&
R”U Z«R”UV &
e%NE`R”`KN
¹ BV09<?%+*-.e-<a@-8A3 Y‹Y eH<?'1<?09%+3·62<I0B9<I098:%+*-35e-. ± @X3C*-e-.·69<P3CB9%+*-,5<€.›'C35G+.50¡8:¬+*-%78A.e-.|<I0209.-K
Ln.SeX3¨')%´3Sf-<I6 ± @H<I8A356[eH<>D-350V35,5<I8 8A35%+6¯<IG´3CF¾.10935e-.16B©“I8 eH<>62<I0[35e-.1DSBu35e-.56If-eX3Ce-. ± @-<c3ª«@-*-µI¶5.
e-<Y<I0209.>D¾.)e-<Y35DH09<I62<I*4Bu3C0—e-%('1<?0969.56M8:¬+*H%+8:.16 G7.S=I35%+6 y n %7,1@-0V3 Å K k  KŽ .50£<wQS<I8:D-G+.Hf‚ŽŸ02<I=uN-<?G7Bo(g¨h1h t
e-<wª«<I*-e-<>.U@-69.:e-<Ze-.1%76;=I02%7BV°?09%7.16;e-<ZDX350935,1<I8\DX35093 Y‹;¢x Ä
K … %+e-<?%´3¢°BV<?*4Bu350M3¨'C35G+%+350 .ED-02.1,102<I6962.ceH.ZB909<?%+*-. € %’K <CK7f ± @X3CG
u l 259† E 2¡{)r;š—oVm9ˆ5oVruxuximc{)m oVrw}Šqsm 3e-%78A%7*»@-%+µI¶5.ceH./<I0902./69.1FH09<E.16=I3569.56;e-<¢BV02<I%+*H.-f fHeH@-0V35*4B9<E@-8€3ceX35eX3 Fœ 25} xL2A{)rE‚ƒourw}Šqsm f
e-< œ %(BV<?0V35=µ —S<?6I·K … ª«@-*-µI¶5.¡e-<TD-02.1,109<?6962.-f-3¨'C35G+%+35eX3¢<?8 =I35eX3 œ %7B9<I0935
µ —)<I6?f»B9.18A3c3Eª«.1098A3HÄ
š
£ Ÿ
L£ JŸ¡ ‘ ¿±¿±¿ £ œ ¶ Œ˜ ;_ª ;_ª £ Ÿ -‘ Ÿ
y Å K(g Å 
¹ D-09.5,109<?6969.P*-.aB909<I%7*-.a°/<IG7<?'C35e-.a*-356¢ªƒ3569<?6E%+*-6ºB ƒ¨'1<?%+6?f .1*-e-</.P<I0209.a*-.56E=¨3562.16Ze-<BV02<I%+*H.
62.1F¾<¡<I8‰'5<IÃ/e-<¡e-<I62=I<I0?K À .<I*4Bu3C*»B9.-fBV<?*-e-</DX3C0V3€Ã?<I09.3€G7.1*-,1.€D-0V35Ã?.-f3*-¶5.a69<?0 ± @-</.
B909<I%7*-.62<¡BV.102*-<.162=I%7G´35*4BV<CKZ¹BV09<?%+*-.A°DX350935e-.a62< J£ JŸ/* fs<?8 ± @-< °@-8A3€8A<?e-%+e-3
e-<Z<?0909.Ue-<Z<?62Bu3Ce-.A<?62BV35=I%7.1„* ƒ502%+.-K
'
'
('
+
' +
'
'
'
Æk
‹Sz€rwoVm |˜wx1}Šz€m {)r ‚Wrwo3254C§iruxI™ j£62B9<›=I02%7B9°I09%7.·°›35D-G7%+=I35e-. ± @X35*-e-.Á. =?09%7B9°I02%+.Á35*4BV<I02%+.10
ªƒ35G7NX3Hf1eH<T8:.)e-.Z3E,4350V3C*»B9%+0 ± @-<Y.EBV02<I%7*-.EBV<I028A%7*-<5K…6269%+8f1.EBV02<I%7*-.Z°YB9<I028A%7*X35e-.¢62< * f
<?8 ± @-< e-< hX*-<>.U*ŠH8A<?09.U8 ƒQH%78A./eH<>%(BV<?0V35µ=—S<?6IK
±Y#K:%F f%%LY%##f #L
u
'
GCHJIKH
R
8%R”Vf^'N
Š`
NQTZV¾eV `e%V ¹ DH09° l D-09.)=I<?6969358A<?*4BV.Ze-.16£eX3Ce-.16£e-<w'1<T69<I0£62<I02%´358:<I*4BV<;=?.1*-62%+e-<?0V35e-.Z3C*»B9<I6Ÿe-<B909<I%7*X350 @H8€3¢02<Ie-<CK
j£8F.10V3¡*-¶5./69<W®93<I6962<I*-=?%´35Gs<I8 =I<I0ºBV.16¯=¨3562.16If-B9.109*X3 lW69<T')%7Bu3CG¾*[email protected] bH¶C.'sƒC09%´3C6356.5D¾<?0V35µ=—S<?6
<I8 ± @H<c62<>D.)e-<Ee-<I62e-.1F-09350T.:DH09° l D-09.)=I<?6969358A<?*4BV."oq…[ÃI.M f gih1h4k € bH3502G+<5f¾gih1h1hmtyÄ
{ 2 qX‚Wryˆ5ow}ƒM{ 24{)rY{)mix 24{)mix KnL 093CBu3 lW69<;eH<;@-8­D-02.S=?<Ie-%78A<?*4BV.Ee-<'C35G7%+eX35µI¶5.¢e-.56
u rwoR} ž1t 254~)m>M
eX3Ce-.16If-'5<I02i% hX=I35*-e-. l 69<Z69<><wQS%762BV<?8 <I0209.16Ye-<>35G7,1@-8A3¡<I62D¾°?=I%7<5K
x 24{)mix %K j£62Bu3:ªƒ3569<<?*4'1.1G('1<@-8A3A=?.1*4'1<?096V¶C.eH<¡eX35eH.16IK 35e-. ± @-</3C6
u YrW„oVruxirwqX‚ 254~)m{)mi
Y‹;¢x 35D<I*X356ZG7%+eX358 =I.58‚* -8A<?09.16?f .56>e-35e-.16EBV<?0V¶5.Pe-<:69<?0Z=I.)e-i% hX=I35e-.16?f&D¾.10E<RQS<I8:D-G+.-f
@HB9%+G7%+è3C*-e-.@-8A3/09<?D-09<?69<I*4BV35µ¨¶5.AF-%+”* ƒ509%+3¡.1@e-<I=?%+8A35GyK
x 24{)mixI™ ¹.5F)®2<I=wBV%7'5.€e-<?62B9<cD-02.S=?<Ie-%78A<?*4BV.:°c02<¨35G7%+è3C0@-8A3UB90V35*-6ºª«.1L0 l
u •Ÿxi1t 25†+mpq 25z€rwqX‚WmA{)mi
8A35µ¨¶C.*-.16EeX3Ce-.16¢e-</8:.)e-.a3a35=?<IG+<?0V350[</8A<?G+N-.50V350T.aD-09.)=I<?6962.e-<35D-09<?*-e-%7è35,1<?8FK j£62B9<
<?69=¨3CG+.1*X3C8A<?*»B9.Ue-<ID<I*-eH<ce-./B9%+D.:eH<>e-35e-.16?Ä
Á•—qX‚ƒ1o 24M{ 2px K¹J<I62=¨35G7.1*X358:<I*4B9.eX356>'C3509¬% ƒi'5<I%76¡e-<A<I*4BV0935eX3B9<I8e-%7'5<I0269.16<wª«<I%(BV.16>=I.1Š* l
ª«.5098:<.16£e-%762BV%7*4BV.16 35G+,1.509%7B98A.56 e-<Y3CD-09<?*-e-%+ÃI35,1<?8K <;@-88A.)e-.¢DX3C02BV%7=I@-G+350If535G+,5.109%(JB l
8:.16Ye-<>,10V3Ce-%+<?*»B9<ceH<I69=?<I*-eH<I*4BV<Cfs=I.58A.:.A=?.1*-N-<?=I%7e-. Yš fX6V¶5.AFX356ºBu35*4BV<>69<?*-69¬('1<?%+6[35.
<?69=I35G+.1*-358A<?*4BV.-K …[6969%78f»=I35eX3c'C3502% ƒ¨'1<?G¾e-<[<I*4BV0935eX3¡eH<?'1<E62<I0—<I69=I35G+.5*X35eX3¡eH<[ª«.1028€3>3
± @-<3>62@X3c8:°IeH%´3Z69.1F-02<[.>=I.5*p®2@-*4BV.ce-<[=I3569.56¯e-<YBV02<I%+*H.><?62B9<$®983 _E'1.1G(Bu3Ze-.Z'53CG+.10ŸÃI<?09.-f
D<IG7. ± @-<;.E<I62=¨35G7.1*X358:<I*4BV.ED-350V3¢.E%7*»B9<I0º'53CG+. O-8‘ ¨ ‘Hª«@H*-=I%7.1*X35©0 ƒ¢8A<?G+N-.10 e-. ± @-<;DX35093
.¡%+*4BV<?02'C35G+. ¿[¨ ‘ ® j QS%+6ºBV<?8\e-@-356¯ª«.1028€356M=< h-=I%+<?*4BV<I6¯e-<¢09<I35G+%7è350Ÿ<?62BV<<I69=I35G+.5*X358:<I*4BV.-Ä
r ruxw–i}ymš 24{5o2~)m Á”9{5:} 2 rwouma
ˆ - ˆ
y Å K(g Æ 
*¡
² ¹ £ ˆ_Ÿ
.1 *-e-< ˆ e-<I*- .CBu33P8:°IeH%´3e-< ˆ < ² ¹ £ ˆ_Ÿ .e-<I6º')%+.DX35e-09¶5.Pe-< ˆ € %’K <CK7f ² ¹ £ ˆ_Ÿ¡
šC » C » ]
fXDX3509!3 ˜ <RQS<I8:D-G+.16;eH<ZB909<?%+*-.-K
° ª
m
25†+mpo †ŠqX}Šz€m/v r 25†+mpo ·w˜ x1}Šz€
ˆ - £ ¶ ž±ˆ  ¶Œ˜ Ÿ T
*¡
y Å K(g 
£ ¶ ž±ˆ - ¶Œ‡˜ Ÿ MT
'
'
'
Ær
!"#$%#&'
I< 8 ± @-<F¶Œ˜·<<¶ ž±ˆ 02<ID-02<I69<?*4Bu358 .U8A¬7*-%+8:.¡<Z8 ƒpQS%+8:.eX3/'C3509%¬ƒi'5<IG ˆ K
2s†ƒ{M2px K·j QS%+62B9<I8 e-@X3C6Mª«.10ºBV<?6—0935Ã
—)<I6MDX35093><?69=¨3CG+.1*X3C0—3C6—6935¬+eX3C6IKj£8 D-02%+8:<I%+02.EG+@-,1350If
± @X3C*-e-./69<[@-6V38A35%76MeH<@-8A3c6935¬+eX3><62<E3cª«@-*-µI¶5.¡eH<¢<I0209.¡°69<I*H69¬7'5<IG _¡<I62=¨35G+3HfS=?.18:.
3C=I.1*4BV<?=I<*H.=¨3562.€eX3€35D-09<?*-e-%7è35,1<?8e-.,10935e-%7<I*4BV<>e-<I62=I<?*-e-<I*4B9<5f <I*4BV¶5.a3AeH%7ª«<I02<I*-µI3
eH<Á<?69=¨3CG´356<I*4BV02< 3C66935¬+eX3C6D.)e-< 3Cª«<I=wBu3503 ª«.1098A3 =I.18:.!3!02<Ie-<Á35D-02<I*-e-<C?
K Ž .50
<RQS<I8:D-G+.-f)69<@-8€3Z6V3C¬+eX3ZBV<I8 'C35G7.109<?6—<?*»B909< ¿ µ< ‘[<I* ± @X35*4B9./.1@HBV093>B9<I8 'C35G+.102<I6M<I*4BV02<
¿ < ‘ ¿±¿±¿s¿±¿±¿¨ <I*4Bu¶5. . 35G+,5.109%(BV8:.e-<aBV02<I%7*-.·%+0 ƒ|e-%769D<I*-eH<I0:3|8€35%7.10DX3C02BV<aeH.Á62<I@
<?62ª«.102µI.*-3A35DH09<I*He-%+ÃI35,1<I8e-3:62<I,1@-*HeX3€6V3C¬+eX3HDK …6269%+8fd356T6V35¬7eX356 ± @-<>©B “I8 3:8A<?698A3
%78AD.10ºB 5*-=?%´3e-<w'1<?8 62<I0¡<?69=I35G+.1*-35eX356>DX350933P8A<?698A3<?69=¨3CG´3HK À <I62B9<€=I3569.-f e-<?'5< l 69<
DH09.)=I<IeH<I0/3@H8 <?69=¨3CG+.1*X3C8A<?*»B9.=?.18²38A<?698A3<I62=¨35G+3.1@ e-<I6º'S%7.|DX35e-09¶5. y @-6V35*He-.
D.10A<wQS<I8:D-G+. 3 < ± @X35µI¶5. Å K(g Æ  K j£8 62<I,1@H*-e-. G+@H,4350If¯D¾.)e-< l 69< ± @-<?09<?0a3®2@-6ºBu350a3C6
'C3502% ƒ¨'1<?%+6[e-<¡6935¬+eX3A35.16T'53CG+.102<I6Te-.€=?.1*4BV0V3Ce-.18:¬+*-%7.AeX3Uª«@-*-µI¶5.e-<¡35=?B9%7'C35µ¨¶C. y <CK ,HK7f¾3
ª«@H*-µ¨¶5. †+m9sˆ †+xw‚ƒ}y1t 2 D-02.SeH@-Ã'C35G+.102<I6¢eH<:6935¬+e-3e-<I*4BV02.Pe-.ae-.18:¬+*-%7. ¿¨ ‘  K À <?62BV<U=I3569.-f
°P%78AD.102BV35*4BV<A=I.1*-NH<I=I<?0A.56/G+%+8:%7B9<I6c8 ƒpQS%78A.16c<P8A¬7*-%+8:.16>eX3›'53C09% ƒ¨'5<IG<?8²'1<?Ãe-.56
'C35G7.109<?68 ƒpQS%+8:.16T<8A¬7*-%+8:.16;e-.56¢=¨3562.16¢e-<cBV09<?%+*-.HK À <?62B9</=¨3562.aD¾.)e-<I0 lW62< lƒA@HBV%7G+%+ÃI350
3U69<?,1@-%7*»B9<Eª«¸1098@HG´3HÄ
| °‚Ÿ
£ - Ÿ
£ˆ 
y Å K(gk 
’¡
» - |–°
D-350V3@H8<?69=¨3CG+.1*X3C8A<?*»B9.¢*-.¢eH.18A¬7*-%+. ¨ yf162<I*-eH. » < |–° .16 G7%+8:%7BV<?6 8 ƒQH%78A.
<¡8A¬7*-%+8:./eX3A'C3502% ƒ¨'1<?GyK bS</3:'C3502% ƒ¨'1<?G eH<6V35¬7eX3:B9%7'5<I0G7%+8:%7B9<I6;e-<?69=I.5*-N-<I=?%+e-.56If <I*4BV¶5.
°€D-09<wª«<I09¬('1<?G—@HB9%+G7%+è3C0Z3ª«@-*-µI¶5. †¦}Šqs1r 25o y .5@ .1@HB90V3*-¶5.›G+%78A%(Bu35e-3  DX3C0V3.16c*-.)e-.16>e-<
6935¬+e-3HK
Yr9{+N4~)m M{ 2 Z}Šz€rwqHxI~)m KÁ¹ ‚* -8:<I09.|eH<<?G+<?8A<?*»B9.16*»@-8²'5<I=wBV.10/e-<P<?*»B90V35e-3HfM3›69@X3 {5}Šv
z€rwqHxI~)m .1@ 1t 25o2{5}Šq 25†¦}ƒM{ 24{)r f D.SeH<P3CBV%7*-,1%+0Z'C35G+.509<I6¡e-<I8A3569%+35e-.›<?G+<w'53Ce-.16IfŸD-02%+*-=?%+DX3CG+8:<I*4BV<
± @X35*He-.P*X¶5.a<wQS%762BV</@H8 ,10935*-e-</=?.1*-N-<?=I%+8:<I*4B9.62.1F-02<U369@X3a*X3CB9@-09<?è3a</09<?G+<w' C*-=I%+3HFK jŸ8
,1<?0V35G’f09<IeH<I6n=I.18@-8 <IG+<w'C35e-.TŠ* H8A<?09.Te-<Ÿ*-.SeH.16&e-<—<?*4BV0V3CeX3Y©B “I8@-8A3Y35D-02<I*-e-%7è35,5<I8 8A35%+6
e-%(ª«¬+=?%+GyK g 8A3eX3C6cª«.1028€356>e-<€35G+%('S%+350E<I6ºBV<AD-09.1FHG+<I8A3P=I.1*-62%+6ºBV<*X309<?e-@-µ¨¶C.›eX3e-%78A<?*-6V¶C.
e-.56Y'5<I=wBV.102<I6Te-<Z<I*4BV0935eX3HfX=?.1*-69%7e-<I0935*-e-m. lW69<>35D<I*-356T3U%7*Hª«.1028€35µI¶5./09<?G+<w'53C*»B9<5K
lŸ}Š†¦‚ƒ3o 2iˆ)rwz {)rP +[†ƒ{)m5™ Žn.10€'5<IÃI<?6IfYBV.102*Xm3 l 69›< SBV%+GY. @H69. e-<BV°I=?*-%+=I356e-:< hXG7B90V35,5<I8ÂDX35093
3›<?G+%+8:%+*-35µ¨¶5.e-<a02@-¬+e-.Hf£69@X3¨')%+ÃI35*-e-. 3ª«@-*-µI¶5.|e-<P35DH09<I*He-%+ÃI35,1<I8f ªƒ35=?%+G+%(Bu35*He-..›B909<I%7*-.-K
© .18:.U<wQS<I8:D-G7.UB9<I!8 lW62<c3 25q˜5†¦}+xirruxW„Xrutw‚ƒ3o 25†… @-8A3BV°?=I*-%7=¨3/8@-%(BV.U@-6V3CeX3:*-3:8A35*-%7D-@-G´3Cµ¨¶5.
e-< %+8A35,1<?*-6If.1*-e-< @-8 69%7*X35GEe-< <I*4B90V35eX3!°ÁeH<I=I.58AD.162B9.<?8 .1*-eX35669%7*»@-69.1%7eX35%76If¢D<IG+3
‚ƒ3o 25qHx«œ¨mpowz 24M{ 2A{)rEl m +)oR}yrwo?™
u
u
Æj
±Y#K:%F f%%LY%##f #L
GCHJIKH
’U;
``K^'Ue`KeN N
U]Z[`fN
A8 302<Ie-< T‹Ž B909<?%+*X35e-3D¾.50 Yš D¾.)e-<:69<I0c'S%762BV3=I.18:.@H8€3Pª«.1098A3D-0©ƒCBV%7=¨3DX350V3<?ª«<?=?BV@-350
@-8A3 ± @X3CG ± @-<I0U=?.10902<I69D.1*-e“I*-=?%´3Á*-¶5.ÁG7%+*-<I350IK … ± @-<I6ºBu¶5. ± @H<62@-09,1<°5ÄeX35eX3·@-8A3›ª«@-*-µ¨¶C. º
e-<?69=I.5*-N-<I=?%+eX3 ± @-<Yªƒ35Ã;@-8A3¢=I.10209<I62D¾° .5*-e”“I*H =I%´3Z<I*4B909<YDX35e-0J—S<?6Ÿe-<;@-8<?69DX35µ?.8˜klWe-%78A<?*-69%7.1*X35G)DX35093
@-8 <I62DX35µI. ¶ l e-%+8:<I*H69%+.5*X35Gyf”º fs62<I0 ƒAD¾.16269¬('1<IG <I*-=?.1*4BV09350¢@-8A3 Y‹Ž ± @-<09<I35G+%7ÃI<c3
=I.50909<?69D.1*-”e “?*-=I%+3/<wQS%+,1%7eX3.1@PD<IG+.¡8A<?*-.16;69<>35DH09.¨QS%+8:<¢e-<IG+3=I.18J35G+,5@-8€3c<=hX=
ƒ5=I%+3 "… 02<I69D.16ºBu3
'1<?8 e-. rumpoVrwz 2 ŽnqX}Š–5rwoVx 25†[{)rP¯„oV=m x1}Šz 254~)m {)rl +)-q 4C§irux ± @-<|<?62BV%7D-@-G+3 ± @-<|@-8A3 =¨3C8€35e-3
%+*4B9<I098:°IeH%´3°Ÿ69@ h-=I%+<?*4BV<¯D-350V3;@-8A3 T‹Ž =I.18:D-@HBV350 @-8A3T3CD-09.¨QS%+8A35µ¨¶C.;e-<—@H8€3 ± @X35G ± @H<I0 ª«@-*-µI¶5.
=I.5*»B9¬+*»@X3Hf4<?8F.10V3.¢B9<I.102<I8A3¢*X¶5.Z3 h-098:< ± @-<Y<I6ºBu3¢<I6ºBV02@HBV@-093E69<$®93E¸1DSBV%+8A3[<?8B9<I098:.16 eH<BV<I8:D.
e-<·35DH09<I*He-%+ÃI35,1<I8 <|,1<?*-<I0935G+%7è35µI¶5. o‘b3¨O )%7*f gih1h5mh t’KL 358F°I8 <I62B ƒ D-09.i'C35e-. ± @-<·=I.58 e-@-356
=¨3C8€35e-356;%+*4BV<?098:°Ie-%+356;3CB9°Eª«@-*-
µ —)<I6Ye-<?69=?.1*4BV¬+*»@X3C6[D.SeH<I8 62<I0Y09<?D-09<?69<I*4BV35eX356?K
¹¢@HBV02.·3569D<I=wBV.·%+8:D¾.502Bu3C*»B9<€e-%7Ã09<?69D<I%(BV.·35.›B9<I8:D¾.|e-<P3CD-09<?*-e-%+ÃI35,1<?8K … 35D-02<I*-eH%+è3C,1<I8
%+8:D-G7%+=¨33ZDH09.)=I@-093>e-.56M<?G+<?8A<?*»B9.16Ÿe-<I62=I.1*HN-<I=?%+e-.16Me-<Y@-8A3 T‹; *-.1028€35G78A<?*4BV<D<IG7.c3i®2@-62B9<[e-.56
D<I69.56IKT¹¢0V3Hf3:35D-02<I*-e-%7è35,5<I8*»@-8A3:02<Ie-<c=I.13
8 ‘ ¿s¿ D<I62.16°>FX356ºBu35*4BV<>8A35%+6YD<I6V3CeX3A<?8 BV<I028A.56
=I.58AD-@SBu35=?%+.1*X3C%+6¡eH. ± @-<3|e-<P@-8A3›09<?e-<P=I.18 ‘ ¿ D¾<?69.16?f¯69<?*-e-. @-8A3›09<IG+35µ¨¶C.|F¾<?8 8€3C%+.10ce-.
± @-<:.Pªƒ3C=?BV.5!0 ‘ ·‘ ¿ D¾.)e-<?09%´3a62@-,1<I02%+0?K bS<I02%´3a8@-%(BV. HB9%+G ± @-<:.aBV<I8:D.eH<A3CD-09<?*-e-%+ÃI35,1<?8 ª«.16962<
G+%78A%(Bu35eH.:D.10¢@H8€3€ª«@-*Hµ¨¶5.aD.1G+%7*-.18:%´35Gs69.1F-02</.a‚* -8A<?09.ae-<'C3502% ƒ¨'1<?%+6?K À .a<I*4Bu3C*»B9.-fBu3CG *X¶5.a62<
'1<?09¯% hX=¨3HK
j£62B ƒ>%+,1@-35G+8:<I*4BV<;DH09.i'C35e-. ± @H<.>D-09.1FHG+<I8A3E,1<I0935GXe-<[35D-02<I*-e-%7è35,5<I8<?8 T‹;x °T%+*4BV093CB ƒ¨'1<?G €
%yK‘<5K *X¶5.ED.Se-<¯69<I0£02<I62.1G7')%+eH.¢e-<ª«.1028€3T=< hX=?%+<I*4B9<;DX350V3B9.Se-356£356 %7*-62B 5*-=?%´356?K À ¶C.E°=I.1*HN-<I=?%+e-.Z@-8
35G7,1.109%(BV8:. ± @-<:=I.1*-62%+,43P09<I35G+%7è350Z335D-02<I*-eH%+è3C,1<I8*»@-8B9<I8:D¾.D¾.5G+%+*H.18A%+35Gyf69<?*-e-.%+8:D-09.i' ƒ¨'1<IG
± @-<BV35Gs3CG+,1.102%7B98A.E'1<?*-NX3/3¡<RQS%+62B9%+0?·K …6269%+8fHeH%+à l 69< ± @H<¢<I8 ,1<I0935G.D-09.5F-G+<?8€3>e-<E35D-02<I*-eH%+è3C,1<I8
<I8 T‹;x ° ‹Tš lW=I.58AD-G7<?B9". oqpY.p®9356If g¨h1±h rmt’K
© .1*[email protected]<w'S%7e-U. _56¯=¨35DX3C=I%+e-35e-<I6¯e-<¢=I.50909<?69D.1*-”e “?*-=I%+3¡*X¶5.¡G+%+*H<¨350M<I*4BV02<EDX35e-J0 —S<?6IfH356 Y‹Ž x
B “?8Â69%7e-. @HB9%+G7%+è3CeX356=?.18Â69@-=?<I6269. <I8 e-%('1<?096V3C6Ae-.58A¬7*-%+.16?f—%7*-=IG7@-%+*He-. š¯oVmituruxuximix{)r ¿ mpqX‚ƒoVmp†+m
q{ +4xw‚ƒow:} 25† f Ym5H Gp‚’}y1t 2rZ
 +)‚Wmpz 254~)m f •Ÿxw‚ 25{‚ †+xw‚ƒ}y1t 2 f r9{5}ytw}Šq 2 f “[ruxw‚y~)mr ¿ mpqX‚’oVmp†+maM{ 2š—oVmI{ + 4~)m f
•Ytumpqsmpz/:} 2 f£<I*4BV02<[email protected] o Ž 3CB9B9<I0269.1*f[gih1±h r € bSNX3C09eX3 pT358:DX35G¢g¨h1±h rt’K À .1098A35G+8:<I*4B9<5f£DX35093
@-8 F.18 =?.1*p®2@-*4B9.€e-<ZeX35eH.16Ye-<>B909<?%+*-.-fH@-8€3/02<Ie-<>=I.18 35D¾<?*X356T@-8A3 y .1@ ± @-35*4BV.:8@-%7B9./e-@X356 
=¨3C8€35e-3 y 6  %+*4BV<?098:°Ie-%+3 y 6  69<?02'1<cDX35093:3CD-09<?*-e-<I0Y@-8A3/eX35eX3BV3509<wªƒ3U=?.18 8:<I6ºBV09%+3HK
g
Æ
!"#$%#&'
86<5; 680
c-7 ;=B 6µ0 - ’6
4EB ; 687
(*) (
GCH GCHLI
WaKVR”U Z
V
5;=680
R”UKUT`Ka
+% e-<?%´3¢.102%+,1%7*X35GyfC=I.1*HN-<I=?%+eX3>D¾.10 †‘ˆ)mpoR}Š‚ƒz€m“[rwqs”w‚ƒ}ytumA¼«“ ½ <[D-02.1D.162BV3>D.10Mb[.1G7G´35*Hef4D¾.)e-<Y69<?0
09<?69@-8:%+e-3T*X3%n %+,5@-0V3 Å K r8orqE.1G+e-F<I02,-fsg¨h hmt’K£¹ “ %+*-%7=I%+3mlW62< =I.18@H8€3 „Xmu„ +S† 254~)m e-< }Šq{5}Š– †ƒ{+dmix f
69.5G+@-µ=—S<?6AD.16962¬7'5<I%+6ADX35093 .ÁD-09.1FHG+<I8A3Hf—,1<I0935e-.16:e-<ª«.5098A3 3CG+<¨3pBV¸102%´3HK …‰%7*Hª«.1098A35µI¶5. ± @-<›@-8
%+*He-%7')¬[email protected]%+69D.1*-%7F-%+G7%+ÃI3Hf1< ± @-<3CBV<?*-e-<E3C.16—'C35G7.109<?6—e-.56¯DX350 58:<?BV02.16Me-.D-02.1F-G+<?8€3Z<I8 < ± @-35µ¨¶5.Hf
°E09<?D-09<?69<?*»BV35eX3:D¾.10;@H8 twoVmpz€mixuximpz 2 fSe-<E@-8 8:.SeH./<I8\[email protected]*„ƒ5G7.1,1.U_/<?62BV02@HBV@H0V3')%+,1<?*»B9<Z*-.
… À K g 8‰=I02.18A.56969.58€3°CfnD.10E62@X3'1<IÃCf =?.18:D¾.16ºBV.aD.10E@-8=?.1*p®2@-*4B9.eH< ˆ)rwqsru’
x y =¨350935=?B9<I09<?6  K
g 8 'C35G+.10€D¾.16269¬('1<IGDX350V3 @-8 ˆ)rwqsr °|e-<?69%+,5*X35e-. D.10 25†+rw†+m K … ± @X3CG+%+e-35e-<›e-<·=I35eX3 69.1G7@-µ¨¶C.
y =?09.18:.16269.18A3  °Ÿ8:<Ie-%7eX3D¾.50 @-8€3ª«@-*Hµ¨¶5.Y=uNX358A35eX3;e-< 2w„‚ƒ}ƒ{4~)m I 69<?*-e-.T.16&%+*-eH%7')¬[email protected] 3¨'C35G+%+35e-.16
e-<>35=?.109e-.U=?.18 <I6ºBu3HK
j£8 =¨35eX3!=I%7=IG+.HfDX350ºBVA< lW69< eX3 D¾.5D-@-G´3Cµ¨¶5.!35=wBV@X35G y { K 69<?8A<?G+NX35*Hµ¨3 e-. ± @-< 69< DX35626V3
*-. 8¡@-*-e-.Á09<¨3CGyf.16A%+*-eH%7')¬[email protected] „Xmu„ +S† 254~)m 6V¶5. 62@p®2<I%(BV.16€3Á@-8A3Á62°I02%+<eH<›.1D<I0V3C
µ —)<I6IfBV35%+6
=I.58A. xirw†+ru3t 4~)m eH.16UD-09.1,5<I*-%(BV.102<I6If two +1‡ 25z€rwqX‚Wm <?*4BV09<DX3502<I6:e-<PD-09.5,1<I*-%(BV.102<I6U< 7z +S&‚ 254~)m e-.56
e-<?69=I<?*-e-<?*»B9<I6?K © .18:.c02<I62@-G7BV35e-.>e-<I6ºBV<DH09.)=I<I6269.-fS@-8A3>*-.i'C3c,5<I0V3Cµ¨¶5.>e-<T%+*-e-%(')¬[email protected]°T=I02%´35e-3HK£¹
D-02.S=?<I6962.a09<?D¾<wBV< l 69<Cf<I*4Bu¶C.-fse-@H0V35*4BV<>' ƒ509%+356[,5<I0V3C
µ —)<I6Ifs3CBV°c6V3CB9%+6ºªƒ35ÃI<?0@-8A3€eX35e-3€3€=?.1*-e-%7µ¨¶5.Ae-<
DX350935,1<?8f-eH=< hX*-%7eX3Hf-D.10;<RQH<?8ADHG+.-f-D<IG7.UŠ* H8A<?09.U8 ƒQH%78A./eH<>,5<I0V3C
µ —)<I6 y K
$À © ¹
*-%7=I%´3C0./BV<I8:D. y ¡O¿ 
qE<I0V3C0Y3UD.1D-@HG´35µI¶5.U%+*-%7=I%´3CGyf»e-<Eª«.1098A3/35G7<¨3CB9¸109%+3 y •A K
– 25†¦:} 25o • K
j À
g … À LT¹ y * nŠ…«jKp
rw†+rututw}ympq 25o .56;D-09.1,5<I*-%(BV.102<I6T3/DX3502B9%+0e-3:D.1D-@-G+35µ¨¶C.U35=?B9@X35G y ‡ K
…DHG+%+=I350 two +5‡ 25z€rwqX‚$m 35.16;D-02.1,1<I*H%7BV.509<I6YDX3C0V3/,1<I09350;e-<?69=I<?*-e-<?*»B9<I6?K
…DHG+%+=I350 7
z +)‚ 254~)m 35.16Ye-<?69=I<?*-e-<?*»B9<I6?K
– 25†¦:} 25o 3U*-.i'C3/D¾.1DH@-G´35µI¶5. y ;_ªJ K
…;=?B9@X35G7%+è3C0.:B9<I8:D¾. y ¡
 ‘  K
…
('
('
n
('
'
+% ,5@-0V3 Å K rHÄKj£62B909@HB9@-0V3U,1<?*-°I02%+=¨3/e-<Z@-8 “ K
¹ DH09.)=I<I6269.·e-<a02<ID-02<I69<?*4Bu35µI¶5.ÁeH.›ª«<I*-¸5B9%+D. y 62.1G+@Hµ¨¶5.  <I8 ,1<I*-¸CBV%+D. y =I02.18A.56969.58€3  f£°e-<Al
69%7,1*X35eH.!eH< tumI{5} žt1254~)m fT69<?*-e-..5D¾<?0V35µI¶5. =I09@H=I%´3CGEDX350V3 @-8A3 F¾.13 02<I62.1G+@-µI¶5.!e-.16PD-09.5F-G+<?8€356
@HB9%+G+%7è35*He-. “—x’y n %7,1@-0V3 Å K…j  K b[.5G+G´3C*-:e o(gih1j1mk tXe-<wª«<I*-eH%´3 ± @H<3Z8A<?G+N-.50 ª«.1098A3Ee-<Y09<IDH09<I62<I*4Bu3Cµ¨¶5.
69<?09%+3:3/=?.Se-%¯hX=¨3Cµ¨¶5.UF-%7„* ƒ509%+369%78AD-G7<I6eH.16;'53CG+.102<I6;D.16962¬7'1<?%+6YDX35093/=¨35eX3/DX3C0 58:<?B909.-K
n
0 X
( 1
<
4<A#2#( 4? 5><6(
"! 9+$#%#-
?BA8CDFEHG87 <1
Y \
Æh
8f
K f"f# f# PROBLEMA
POPULAÇÃO
Codificação
FENÓTIPO
GENÓTIPO
Descodificação
Função
Objectivo
Função
Avaliação
VALOR DE
APTIDÃO
CUSTO
7% ,1@-093 Å K j)ÄKŽŸ02.S=?<I6269.€eH<>02<ID-02<I62<I*4Bu35µI¶5.€eH.:ª«<?*-¸5BV%7D¾.EoqpY.S=uNX3Sfgih1h4j tyK
¹¢@HBV02.3562D¾<?=?BV.¡%+8:D¾.10ºBu35*4B9<;e-%+ÃT09<?69D<I%7B9.8_Zª«.1098A3E=I.18:.¡3Zª«@-*-µI¶5.¡e-<
„‚’}ƒ{4~)m °=I35G+=?@-G´35e-3Hf»3
DX350ºBV%70 eX3¢02<ID-02<I69<?*4Bu35µI¶5.Z<I69=?.1G+NH%+eX3HK j£62BV3Eª«@H*-µ¨¶5.E02<I=?<IF<;.¢,1<I*H¸5BV%7D¾.¢eH<@-8­%7*-e-%('S¬7e-@-.[<09<wBV.102*X3
@-8'C35G+.50;*)@H8A°?09%+=?. y „‚’}ƒ{4~)±m  f ± @-<c8A<?e-<3 ± @-35G+%7eX35e-<ZeX3:69.1G7@-µ¨¶5.ADX35093A09<?69.1G('1<?0[.AD-09.1FHG+<I8A3Hf
69<?*-e-.:e-=< h-*-%+eX3/ª«.1028€35G78A<?*4BV<D.10?Ä
Œ¹ž ¸ [w˜
¸ Œk¸
y Å K(g r 
À 3a62%7BV@-35µ¨¶5.a%7e-<¨3CGyf 3€ª«@-*Hµ¨¶5.Pe-<:3¨'C35G+%+35µ¨¶5.Ae-<?'5<I©0 ƒ69<?0Ee-=< h-*-%+eX3ae-<U8:.SeH.69@X3¨'5<A</02<I,1@-G+350Ifse-<
8:.Se-.3 ± @-<E=I02.18A.56969.58€356—69<?8A<?G+NX35*4B9<I6BV<?*-NX358 'C35G+.509<I6—e-<Z35DHB9%+eX¶C.¡D-02¸iQS%78A.16?·K …G7°I8 e-%+6269.-fH3
69.5G+@-µI¶5.P¸1DHBV%78€3*-¶5.eH<?'1<:69<?0c@H8D¾.5*»B9.%769.1G+35e-.ae-<:35DSBV%+e-¶5.P<IG+<w'C35e-. € %yK‘<5K(f&<I62BV350Z09.)e-<¨3CeX3ae-<
69.5G+@-=µ —S<?6T=?.18 FX3C%(QS.16'C35G+.509<I6;eH<c3CDHBV%7eX¶5.-K
n
GCH GCHG
¤Vfe%NQaLV
NQT «
RU^'V
'
'
?< 69e-< ± @-<ª«.1%n=I02%´35e-.Hfs.a8:.Se-<?G+.A.109%7,1%+*X3CGneH</b[.1G7G´35*He69.Cª«09<I@·e-%('1<?096V3C6Z35G7B9<I0V3Cµ
—)<I6If¾e-</8:.Se-.€3
35@-8:<I*4BV350Z362@X3P,4358A3PeH<A3CD-G+%7=¨35F-%7G+%7eX35e-<><U69@-=?<I6962.-K … <I6ºBV02@HBV@-093eH<I62B9<A8:.)e-<IG7.a,1<I*-<?0V35G7%+6ºBu3Hf
e-<?69%+,5*X35e-.ZD.10 †‘ˆ)mpoR}Š‚’z€mU“[rwqs”w‚’}ytum/r•—–5mp†Xtw}ympq˜5oR}ym:¼«“—•&½ oqpY.S=uNX3Sfgih1h4j tX°;09<?D-09<?69<?*»BV35eX3>*X3
n %7,1@-0V3 Å K K © .58A.Ue-%(ª«<I09<?*-µ¨3C6TDH09%+*H=I%+D-35%+6MBV<I!
8 lW62< ± @H<5Ä
8 lW62<¢[email protected];BV%7D¾.56e-<Z09<?D-09<?69<I*4BV35µ¨¶5.€,1<I*-°wBV%7=¨3 €
u 35=?<I%(Bu35!
u 3/D.1D-@-G+35µ¨¶5./%7*-%+=?%´35G¾D¾.)e-<E62<I0Y=I02%´35eX3/D.10;[email protected];8:°?B9.SeH.16 ± @-<c*-¶5.U.A3CG+<¨3pBV¸102%+. €
u 35eH8A%(BV< l 69<¢@H8€3/N-%7D¾¸5B9<I62<>eH<>=?.1*-e-%7µ¨¶5.Ue-<ZDX3C0V35,1<?8J8A35%+6—³X<wQS¬7'5<IG €
!"#$%#&'
,1<?*-<I0935G+%7è3ml 69<.·=?.1*-=I<?%7B9.Áe-<P.1D<I0935e-.10/,5<I*-°wBV%+=?.-f ± @-<<?*-,1G7.1FX3|356U.1D<I0935µ
—)<I6Ue-<P=I02@-è3 l
8:<I*4BV.U<Z8@HBV35µ¨¶C. €
u 69¶5.Ze-=< hX*H%+e-.16Ÿ*-.i'5.16—D-350 58:<?B909.16 ± @-<Y=?.1*4BV09.5G´358.>DH09.)=I<I6269.ce-<Y09<I*H.'C35µI¶5.>eX3ED¾.1DH@-G´35µI¶5.-f
.1@P62<$®93HfX=?.18A.U62<>D-3569693:e-<Z@-8A3/,1<I0935µ¨¶C.:eH<>%7*-e-%('S¬[email protected];D-350V3U3/69<?,1@-%+*4B9< € <
u .16YD-02.S=?<I6269.16Te-<Z69<?G+<I=?µ¨¶5.:6V¶C.:,5<I*-<?0V35G7%+è3Ce-.16IK
$À © ¹
*-%7=I%´3C0./BV<I8:D. y ¡O¿ 
qE<I0V3C0Y3UD.1D-@HG´35µI¶5.U%+*-%7=I%´3CG y•A K
– †¦} o • K
j À
g … À LT¹ y *X¶5. © ¹ À
¹ n $À …¢#  n[… «jKp
rw†+rututw}ympq o .56;D-09.1,5<I*-%(BV.102<I6T3/DX3502B9%+0e-3:D.1D-@-G+35µ¨¶C.U35=?B9@X35G y ‡ K
…DHG+%+=I350 mu„Xrwo {)mpoVrux[ˆ)rwqs”w‚ƒ}ytumix 35.16YD-02.1,1<I*H%7BV.509<I6;D-350V3/,1<?0V350;*-.i'5.16[%7*-e-%('S¬[email protected]?K
– †¦} o .56T*H.'5.16T%+*-e-%(')¬[email protected]
rw†+rututw}ympq o .56;69.1F-02<?')%7'5<I*4BV<?6e-< DX3C0V3:3U,5<I0V3Cµ¨¶5.U69<?,1@-%7*»B9< y ;_ª© K
rw†+rututw}ympq o <E%7*-69<?09%70;.16Y*-.i'1.16Y%+*He-%7')¬[email protected];<I8 ;_ª K
…;=?B9@X35G7%+è3C0.:B9<I8:D¾. y ¡
 ‘  K
u
('
n
('
n
'
%+,5@-0V3 Å K ÄKj£62B909@HB9@-0V3U,1<?*-°I02%+=¨3Ue-<Z@-8 “—• K
YN RN[NQTZ`
GCH GCH
fN
NQT '
Z[U^'` A8 3€eX3C6 ± @-<I6ºB —)<I6E%+8:D.102BV35*4BV<I6 ± @-<69<'s“I8‰e-%+62=I@HB9%+*-e-.€e-<I62e-<U3€=I02%´35µI¶5.e-.56 “—•Ÿxu °¡69.1F-02<
69<Z302<ID-02<I62<I*4Bu35µI¶5.UF-%+*”ƒ509%+3¡69<?0 ƒ/38A35%+6¯35e-< ± @X3CeX3/[email protected]%7D¾.eH<¢D-09.5F-G+<?8€3HK b[.1G7G´35*-e
e-<wª«<I*-e-%+3 ± @-<¡62%+8f4®2@H62BV%¯hX=¨3C*-e-.l 69<¡=?.18 .3502,1@-8:<I*4BV.€e-<¡62<I0¢3 ± @H<IG´3 ± @H<8€3QH%78A%7è3.*‚-8:<I02.
e-< rux ¤ drwz x D.10[FH%7BTe-<¡%7*Hª«.1028€35µI¶5:. o9qE.1G7e-F¾<?09,-f¾gih h ty#K Žn.10[email protected]´35eH.-fX<I6ºBV<¡B9%+D.Ae-<c09<?D-09<Al
69<?*4Bu35µI¶5.:ªƒ3C=I%+G7%7BV3¡./BV0V3pBu358:<I*4BV./B9<I¸102%+=I.HfHD.5BV<?*-=I%+35*-e-.:3Ue-=< hX*H%+µ¨¶C.:eH<>.5D¾<?0V35e-.509<I6Y,1<?*-°?B9%+=?.16IK
L .)eX3¨')%´3Hf¾3A02<ID-02<I62<I*4Bu35µI¶5.aF-%7„* ƒ509%+3:D.16269@-% 35G+,5@-*-6T%+*-=?.1*4'1<I*H%+<I*4B9<I6IK Ž£09.1F-G7<I8A356 ± @H<¡09< ± @-<I% l
0V3C8 @-8€3c35G7BV3>DH09<I=?%+69¶5.-f).1@=I.5*»B9<I*-N-358\@H8 ,10V35*He-<‚* -8:<I02.e-<['C3502% ƒ¨'1<?%+6?f).509%+,5%+*X358­=I09.58A.16269. l
8A356—eH<[<?G+<?'C35e-356—eH%+8:<I*-J6 —S<?6If»BV.102*X35*-e-.>.¡<?69DX3CµI.e-<[D-09.)=I@H0V3Ze-<I8A3569%+35e-.><wQ)BV<?*-69./D-350V3 ± @H<@-8
“—• BV<?*-NX3U69@-=?<I6269.-K 35%7609<?=I<I*4B9<I8:<I*4BV<CfdB9<I8 62%+e-./eH<?ª«<I*He-%+e-. ± @-<>3/@HBV%7G+%7è35µI¶5.¡e-<EeH%7ª«<I02<I*4BV<?6
35G(ªƒ35F¾<wBV.16[e-<02<ID-02<I69<?*4Bu35µI¶5.-f 8A35%+6TD-09¸¨QS%+8:.16[eX3<I6ºBV09@[email protected]+<?8€3A3€09<?69.1G('1<I0?fªƒ35=I%7G+%(Bu3/.
e-<?69<I*4'5.1G7')%+8:<I*4B9.Ae-<Z.1D<I0935e-.102<I6Y,1<?*-°?B9%+=I.56T8A35%76=< hX=I35ÃI<?µ6 or%7=uNX35G+< Y%+=?Ã5f gih1sh rmt’K
g
#
+ 3+@K !PA 3 1*(71(HG(XA "4369X:P<8?BA61U? 3#! 5 (A8? 5>< 7^<61 73
! ! !<6A5#(=< G <DF<" 78A?# 4X3 4;< %$ 36DF<1 <67& -'JNG G?%
(;A"N1( <67#"U1N<G5!!<!G8(XG,!+ 7#(@36G-) . ).(/) 0 1.) -
736581N:6< 5 ( G <DF<!G 97 (;1"(XA34 (XA"(XG
! ^7 <61 (( ( 678DB<3!2< 4;1U< =
<!GUGU< @3*) 4;<6A 78A"N<
)94;<6A"5
36<
!
g
…6269%+8fS35.G+.5*-,1.¡eH.16 -G(BV%78A.16M35*H.16—B9<I8 <wQS%+6ºBV%+eH.¡@-8A3cD-02.1G+%(ª«<I0935µ¨¶5.>e-<¢eH%7ª«<I02<I*4BV<?609<?D-09<?69<?*[l
Bu3Cµ
—)<I6n,1<I*-°wBV%7=¨356?f5@-8A356&8€3C%+6 ,1<?*-°I02%+=¨3C6If5.5@HBV09356&8€35%76 D-09¸¨QS%+8A356&e-.[D-09.1FHG+<I8A3Y35G7'5.-K <—<?*4BV09<—<I6 l
Bu3C6IfCB9<I8!lW62<—3 YrW„oVruxirwqX‚ ~)m¢{)r †+mpoVruxMYr }+x¼’ Ÿ½ DX35093Y'C3502% ƒ¨'1<?%+6n=I.1*4BV¬7*»@X356If ± @-<—B9<I8eX3Ce-.
F.1*-6M09<[email protected]<I8 ƒC09<¨3C6—e-<[35D-G7%+=I35µ¨¶5.EeH%+62B9%+*4Bu3C6 y <5K‘,-K(f)B909<I%7*-.>e-< Y‹;¢x o M.S.1*H% <?BT35G’K7fg¨h1h t  K
À <?62B9<=¨3562.-fŸ3   <I62B ƒ›8€3C%+6ZD-09¸¨QS%+8A3eH.›<I62DX35µI.|eH<69.1G7@-µ
—)<I6ce-.›D-02.1F-G7<I8A3Hf *X¶C.›NX3¨'1<?*-e-.
*-<?=I<I6269%7eX35e-</e-</=?.1*4'1<?096©—)<I6?f eX35e-. ± @-</@H8‰,1<?*-<=?.Se-%¯hX=¨3Ae-%+02<I=?BV358:<I*4BV<c@-8€3:'53C09% ƒ¨'5<IG eH.aD-09. l
F-G7<I8A3HK
8f
K f"f# f# GCH GCH
#µN«R`KeVR”N
NQT 'Z[U^'V
À 3>'1<I026V¶5.U3CF-0V35*H,1<I*4BV<CfH@-8 .1D<I0935e-.10—,1<I*-°wBV%7=I.D.SeH<69<?0¯e-< hX*-%7e-.=I.58A.@H8€3Zª«@-*-µ¨¶C.8€3pBV<I8 ƒml
BV%7=¨3 ± @-<:35=?<I%(Bu3 ”ºD-02.1,1<I*H%7BV.509<I6<=I<?02BV.56EDX350 C8A<wBV09.56¢e-</=I.5*»B909.1G7.-fs,5<I0V3C*-e-.E¹ e-<?69=?<I*-e-<?*4BV<I6
o À <?'5<I6[<?BT35G’K7fg¨h1h1hmt’Ä
[ ž ¹‚¸ s¸ º [w˜'Œ ¸[ ² ¥ n ¸m˜ s¸
¸
[ ² [w˜«¹ [w˜ [ ²
y Å K(gj 
© 8 ª <?ª«< e f = 56 e 6 “—x f4BV< ¬ C8 6£e 6 D< 5e <I6If two 5‡ z€rwqX‚Wm y ”º ¡ ¹ ¡ T 
< z )‚ ~)m y º ¡ ¹ ¡ ‘  f CD-G = 5e 6<I8 ª 562<I6e ª«< < »B9<I6Pe 5G BV8 K À 8 eH<IG 1< -° = fT= 5
e “—• D e-<›e-< h ! 6 D< 5e <I6 ± @-<›@SB G à Hf69< -e B e 6A<IG7<I"6 5DHG = 5e 6
»@-!
8 8:<I69!8 ª C69<5f e-<I6 #5e eH< oVrutumpz:I}Šq ~)m€ˆ)rwqs”w‚’}yt 5K © 8 %$ &»'B 1<?8e-<I6ºBV<<?6 ± @-<I!8 BV<?8 6 >D 626 F G e 5eH<e-<@SB G à e ª«< < 4BV<I6 D< Ce <?6 »@-!8 c8:<I62(8 )5D-G = Cµ¨¶ f4D e-< -e lW62<
e-< h * D< 5e <I6>e ª«< < »B9<I6>e = 8@-8 y <5+K -K(f eH=< h , @-8= @-à 58:< 4B ± @-< <?B #-5D< C6
@-8 eH<I69=?< -eH< 4BV<  K
… D< 5µ¨¶ e-< two 1‡ z€rwqX‚Wm BV< 4B [6 8@HG <ID e-@-µ¨¶ 69<RQH#
@ 5e e 6 69< <?6 $.,$ 6IKŸ¹ F)®2<IA= l
B /$ °Z= -62< 1@ 6Te-<I62=I< -e-< 4B9<I6E@-!8 /= 8F 5µI¶ e (8 CB9< 50G 5< -°wB = e 6YD 5< B <I6IK
<?62BV<8 e fŸD <?B9< -e-A< lW62<D <I69< $ Hª (8 5µI¶ 1< -°?B = Sf—BV<?62'B -e l 69<e ª«< < »B9<I6:= 8¡F l
5=µ —S<?6IK À <I62'B BV<I62<5fn69< ƒ15e DSB 5
e 1ª (8 !8 6[= 8¡@-8 e-<?62B9< D< 5e f e-=< h# e 1CB $ °?6
e-<@-(8 ·ª«#@ -µI¶ ± @-< <I=?<IF<›e 6AD 1< B <?6If;@-8 = p®2#@ 4B eH<D 58:<?B 6:e-< n ¸m˜ s¸
¸)f
<wB -e e 2
6 3$ 6 -e /$ ¬7e-@ 6 y e-<?69=I< -e-< »B9<I6  Ä
n 54 ž ¶[w˜ ¸ k ˜'¹ Œ76 ¥ k ˜'¹‚Œ86 ¥ n ¸ ˜ ¸&
¸* k ˜'¹ Œ76 ¥ k ˜'¹‚Œ86
y Å K(g 
-eH< k ˜'¹‚Œ86€e-< 'B :#
@ 9 -e /$ ¬+e-@ K
À <?D < :; 4'B 5µ¨¶ ; 9F „ƒ =f < >: >e ; &9*l?:;5@f ;9D #<I¬7D f¾B “ :>D :: F G e C#e ; :[#e ;A< B l
à &9!;C D
Ä < B à 9!;EC >e ; )z ; {)mp}+xE„XmpqX‚$mix Ff ;!< B à 9G; EC )qX} œ¨mpoRz€r o9q H #e I=; -fsgih h t7J¹
K 9G; ! K ; 5e ° 5e K CCe K b HH -ef K L $ ; :V¶ " H e : “—•Ÿx J>¹ two 5‡ v
'
'
'
'
'
'
ȁ
!"#$%#&'
z€rwqX‚WmA{)r Sz­„XmpqX‚Wm :; H ; << HfXe#;*9 e H ;CV¸ f B 9! K : µ¨¶ e>;)< C;* : < 9 :: 9(:
e : K ; C ;: J… :: 9f:V¶ ; 5e: ± B &C : B I[l :; ± B “#< :If ± B ;2:; ¶ *H E5e&:F;9 K ; :?f4e#;
9 e !< ;9*l?:;Ze : 3$ : < 9 :: 9(&: J À two 1‡ z€rwqX‚Wm{)r/{)mp}+xY„XmpqX‚Wmix f : < 9 :: l
9!: :V¶ D$ :C :2< 9 -° :?f>< 9 :2;RQ C ;9 : H 5e :?f :; -e G :; B ª B #< , 9G; EC ;wQ K H <5e n B# Å J >
h J·Ž h9f C';9*l?:; < B à 9!;EC *B ª 9G;5f -e#;;° I>C e B 9! 9 ƒ&:< I „ƒ Hf
; 5
e ) H ;&C 9!;EC';J À &: K : µ —.; : H#e ; )9 ƒ:< < ECV° 9 $ H g y B 9  f e>; :<; -e>; EC';
C 9( $ H e ;#;e K 9!; K ; C f <: < EC ƒ fC 9! $ H e ; #;e :; B -e K ; C JM¹ :; B -e #
e ; :< ;-#e ; EC;*° ; 5e K ; H K ; 5µ¨¶ A $ ; :'>J
Pontos de Cruzamento
Pontos de Cruzamento
Progenitores
1010001110
0011010010
Descendentes
1010010110
0011001010
Å J hHÄ ©B Ã9G; EC #e ;Ze : K C : J
¹ ; : C B e : I ; :@9A° C :e>; < 5e B 9 e#;:C';: < B Ã 9!;EC :F He2X¶ K e B Ã B) ;: B#H C5e :
< #< H,B : /$ :µo ; : H ; ; C H J(fsgih5h Æ t’f ;9DI A:;$®! 9! H 9!;C;)< ; C'; ± B ; < B Ã9G; EC < 9
e : K EC :ce#;!< C';:°(9! : $ ECi® : e ± B ; < B Ã9G; EC e#;( K ;: B 9 K C JEj :C; :
K ; 5e ; :(C'9DI° 9 K e#; 9 :; LB C H à 5e :! B C : ; K ; :;EC5=µ — ;:I
f K ; : e#; C'; ; 9 : e < #< ;I e : K H e < 9 H ª&I=; C : I „ƒ :J À ; : C'; < ; ”ƒ , f < B à 9!;EC e>; : K H ;C K ; &:
B 9! ; < 9DI 5µI¶ e#;*; >; :Ifd
e Ce ± B ; #; B 9 $ H ;*; >;>)° H C'; # J
À < : ; ; K ;:; EC'5
µ —.; : ; :s° ; :;$©® ƒ $ ; H ± B ;D 3$ : ; >; ::;W® 9 ; # : $ L K ;Al
Cµ¨¶ ;-< B à 9!;EC ; 9 # ; K H, 9G; H A ;: K 5µ ; K < B# ; : H,B µ —.; :J ¹
two 1‡ z€rwqX‚Wm oR}Š‚’z€”w‚ƒ}ytum ° B 9 ; ; 9 K H, ;:C'; C K ; K ; # or <# H ; <Ià ±r t7J j :C;
K ; #2B C H, à B 9( < 9DI 5µ¨¶ H >; > : K ; C ; :IÄ
n B> ; ˆ«ª ; ˆk­ ; C9
ˆ ª ¡”ˆ«ª 
£‘ -
_Ÿ]ˆk­
ˆ ­ ¡”ˆk­ 
£‘ -
_Ÿ]ˆ«ª
±B;
Å
y J 
; K ; : ;EC9 < 9 :: 9! # : K ; C ; : ˆ ª
; ˆ ­ : $ ; < C ; : # : ;:<; ;EC'; :2:; # B 9 $ H, H ;&C , K ; C; #<; > # 9 , ¿¨ ‘8J j 9 ; H < ; :< ; ; EC;:h< < 9 B 9!-< #:C C B> ; C <-9! : K 9( ;
B 9 # : K ; C ; :J &9DI 9 ; : C'; K :: I ,H ; ; 9DI : ; :< ; ; EC';:*:; ; 9 B :
: $ ;<C ;:
¾°
9¸
µ¨¶
H°
¸
A¬
4Æ
8f
K f"f# f# 5µI¶ :;$®
; $ ; : 9 K 3$ ƒ $ ; H J
K B 9 K ; > B ”ƒ , B ; ; <; I5; B 9
y ¡d¿®76s #;9DI DC H : C B S‚ ~)mµy
…
°
'J
C : ;*< E
C H, ;*9 > ; 2B (
9 3$ : H,B
'
¬
±
µ¨¶ Ä
¸
¸*
k ˜«¹ Œ76 ¥ n ¸m˜ ' s
>,$ #B> ; K 9G; l
ÅÅ
k ˜«¹ Œ86
y J9 
5µ¨¶
Sª 9!5µ¨¶ ;-°C < # K l
5µ¨¶
K B#H 5µ¨¶ 9 K ; > # ± B ;
®
; B 9 > ;#;:° B H
± W®
±
K C K K B#H 5µ¨¶ : C B 5µ¨¶ 9 K ::9¬ $ ; H ; :; H C; &C $ °: # < B à 9G; EC C > < , H ; :C';*:; 9 K ;) K :: I H, ; # :; B $ H, :; H C; #D$. B 9!A9 B C5µI¶ J
À ; K ; :;EC5µI¶ I „ƒ K ; ml :; : I ; B 9 K C ;9 B C'5µ¨¶ >:; #AD$ H, H C'; >
K :; B $ ; : y n B# Å J  J8Ž 1: ; K ;:; EC'5
µ —.; : ; :0; : C'; K ; # K ; (:; ±
B 9! K ; B ; ; H ; : 'C ; K ; # H C'; ; C J%… 9 B C' < EC I B> K "
B 9G; E'C >,$ ; : ; K % H ; H : B ;(:; 9 K ; > # :J … :: 9 @9G; :9 B # %$ H, j 9
Ponto de Mutação
Progenitor
1010001110
Descendente
1010101110
Å J Ä
n B# ; h > < 9 A
B 9 $ H,
; EC'EC ; : C'; K ; #
:;G; >< EC % B 9 ;:C' #
<
H ; < o ± rt : B ;
:; ; G K C ; B
?Ã
¹
GCH GCH
YNQTV` KV
9¸
H ;&C , ;EC #
5µ¨¶ I „ƒ >J
# 9:¬ , ; $ H ; :
B C'
9¬
À
“—•
K : : $ ; : K ; >;J < K H 9G; E
C; B >
K ; ƒ :; ;9(: > ; : C B C ,$ K #
# &C' # ;A< $ ; ±“ #< >J Ž B#H C K &::' ;:C; #< $ ; ; E
C';
5µ¨¶ L > < , y B
ª ;:C'&CV¬,:C < J
B LB : ; B 9! K ; C B# I 9! # : C I B# C 9! #
µ¨¶
e`
EVP%aL` V
±
: B I>C  ±B;
;$ ;
z qEXm:{ šYmu„)† ~)m|¼ š&½ Cª ; < C ± B ; ± B H ; G: HB µ¨¶ h H ± B ; C'; 9 K ;
„ )† ~)m K ; ± B ;° K I ;A; 9 C; 9 : ; #/$ ; : ; > :*:; B : ; H ; l
K <; ::9G; EC J g 9( „Xmu
9G; EC : < #: C C B# C; : K ; H ± B ; &: : H,B µ
—.; : ; : C; ; 9 -¶ :; : 9G; H ;: JŽ B C H # B 9( „Xmu
„ S† ~)m < 9 B 9 ; H ; $ # ‚#9G; ; #,$ ¬ #B# : C'; 9 B 9!D9( K II ,H ;
; K #B à 9G; H ; : ;: B#H C > :#;9DI _A< B : C ; B 9 9! ; :ºª µ < 9 K B C< # H J
±
!"#$%#&'
V°
oVrw}ŠqHxirwo ~)m;„ )o ; ; 9
5µ¨¶
¬
5µI¶
¬
¬ #B# :
µI¶ ;
À
{)r -wxw‚ƒ}Š‚ S} ~)m¼ 1½i :C ¬ ± °
¬
5µ¨¶
À
C';9 : ; : C &CV° : ± B ; ;wª ; ;9 (: B I#: C C B# µI¶ ; B 9 9:¬ 9 ; #,$ ¬ >B# : y ;J+#J K ; &:
B 9 K  o C H ; mt8J·… # K µ¨¶ #)$ H ; H ;
:; ;#< EC ;9 # :< B ::V¶ X¶ ; :C #AB 9 $ H &< ; C'; B /$ ; :' H 9G; EC';&J
Ž G$ ;?à ; : ; : C'; EC; ;::; ; K ;:; $ ( :G9G; H ;: #,$ ¬ #B# : B :;W® ± B ;-;:C; :
K ::;9 B C 9!&C <&9!;C; K 1; 5µI¶ :; B> EC';&Ja¹ ‚#9G; ; #,$ ¬ #B# : ± B ;! B ª ; ; 9
;:C'; K ,$.H ° , ° ; : > ; † Ÿ•¯† Š‚ U¼ •&½ JC¹ B C 2;:C &CV° < #: :C'; ; 5µI¶ ; B 9 ‚#9G; ; < ; ; EC ƒ ; ; :< ; ; EC; :2:; > :; H ;< < , >B 9 ‚#9!; 9G; ;
< # < 9 $ H ; K C ¶ ;2< #/$ ¬ #B# $ JKj :C; K < ; :: 2
° < EC H # K B 9!
x ¢
“ X!‚ [¼ “ ½ J Ž  H C 9 C9 I¾° 9 :; K ; ;=h @ ‹ "
#
$š #9ˆ %Š!‚ #:¼’‹Tš&½ ± B ; ; C'; 9 ‚#9!; ; #,$ ¬ >B# :2:; H ;< < , > : K ; K #B µ¨¶ ; 9 < ; 5µI¶ J ¹ 9 ; H, ; H > K C # ;# H I ;CV¶ C &:(; : C:Aª B #< , H, ; :
y šŸ - •M “ ; ‹Tšn½i 9 C > ; h µI¶ ; # ª ; ; EC';:; :C &C9° : y n B> Å J 
o À ; $ ; : ;C H J mt8J
À
1°
9 ; H H ; HH > K C B 9(; : C &C ;
B H ; 9 : B I>:C C B # : K 3$ : #/$
< L; C # : #/$ #B# : ; B 9( K K >
;=h A< 9 K K oqŽ H #; 9 ±r t7J ;:C'; <: 5 x #,$ >B# : B ; L: B I#:C C B %
H #- K
; 9 < ; C'; 9 B 9 $ H ; ‘ ¿±¿ J
Selecção
Selecção
População
P
t
NP
TP-TSxTP-VE
TP
Progenitores
VE
TGDxTP Recombinação
Descendentes
TSxTP
Selecção
n B# ¹
GCH GCH
R”Vf^'N ŠV
IµI¶
Å J1Ä·Ž
População
Pt+1
TP
5µI¶ <; :: ; ; 3$ eN'&fNQaNQ^ V
Ã
¢ª
±
5µI¶ J
K K B>H ¬
¶
; H # ; 9! B ; : #
/$ # B# : < 9 !
9 K C K < ; :: ;:; H ; < ; $ ;:; 2
$ ,$ ; D
C';9 K K < , H 9!; C; 9! : K C; :; : ;:; ; K #B , ; : I ; .
J j : C; 9 >,$ ; : :
()? U" 739;:P</+!7#( < 4<1U1*( A<G+*$, - 4<A#2#(54;?B58<G7 <1/. Y +4K012.^Y KPY +-
#
¸
Ã
Š
K*:
K # "F
9C # : ;G:; H ;< > :C # B# > l :; K ; H 9 # ;A< $ ; : #
K <; :: ; 9 : C &; 9%J
; K ; H,
B C H, : K !< H < B#H B 9 … : C < <&: ;D< $ ; : # : $ H ; : ;A K C : "
>,$. # # l?:; ; 9 >B : < H ::; : K #< K : ; # Jx † ; ; # "B #
: I ; $ H, ; K C ; %$ B & C $ B ;
† !J K 9!; < : B C ,H B 9!
:; B # < : DB C H, ml :; B 9(*C #:&" 9! ) # ; <C' ' D I E # <wƒ H < B#H, #)$ H
;*:; H ;< J
g 9!(" 9! : 9 K H ;: ;2< $ ; C'; : $ H ;
$. _ 9G; # (
$ B ; K < ; :: ; $H,B C / $ EC; : K ; H, $ B ; 9 K H C B ; # : $ H ; : ;2
: ; K C : ; B C ,H (" B %
; EC ;J
9 l
;< ;E H B #: H ; H, :@C'; ; 9 C l :; #
K C # 9 B#
H ;EC>JDŽ B C AH # : #,$*) #B# : < 9 B 9 $ ,H ;) K C # 9 9 : H < : 9!:2' $ H ; :,+ K C 9 :#< I K Ž G< H 9!&C' ; : C: # h< B#H ;: ;:; $H,$ ; B l?:; K 3$ <& #*B !
9 < $ ; s “ #
< < #: C C >B # 9 ƒ l
; H; $ #
K K B>H J
# o :; B $ H ; K ; H,
.-
C H; t0/1 ;:C;(9C # : > ,$*)#B> :*: ; # : K ; H
$ B ;
$ H ;*:; H ; <. ; K ; ; ; B 9(2" B # H, #; B ' #: I ;*; : C ; J
: 93 C # :29! : < # ;< # : K K <; :: ;*:; H ; <. * 4 56
g 9 >
#7 " 8 o ; :9 t7J"….n B# ; J<; ;:< ; $ ; B 9 ; ; 9 K H ; : C-C< < ,$*)> B# : Jj :C'; 9C > # K C : K #< ) K :=$ B ;D;:C : B IŠl
K B 9! K K B#H ; ; D #
> H ;C' ;%< #,$*)>B# ; :C ƒ :: < # B 9
" B #< &9!;C >
> <; EC';:L < 9 K C 9!;EC 0
< 9 B 9!ƒ ; K K < , H :; B? 0:; # ; : C'; : $ H ; :
: ;*9 # @$ B ; :; B : 9!&C+ :; > G B ;&J
9( H #
,$*)> B# :< 9 9( , K C : :29G; H ;:< # &C :
… C* D&:: B 9 ,B l :;A$ B ; : #
B ;G: I ; $ /$ “#< >JCB D
_ ; K #
$ B # % : K I H ;9(:* ; : H,$ ; : ;A9 9 ; $ ; 9 :; ;:< H # : : # ,$*) # B# : < 9 9G; ;: $ H ; : ; K C J… :: 9 E #; : C'; < C;. C A$ H ; K C > EC'; : ;*:;)< H < B>H :; B
C ml?:;#;< ;:: ƒ ;." ;<C B B 9( < $ ; : #
$ H ;:; H ; < J g 9(E" 9! : 9 K H ; : ; : 9! : B C HF :
< #: :C';;9 9 # h< $ H
;) K C K :; B% $ ; : J B # :; B C HF > ;:CA< $ ; : I:C' # H C'; ; G ;< ;:<; EC'; K < ; :< ; EC;J
K ; ƒ :; ; :#; <; ::©ƒ 5
(*)&H
E;.K7
JI
0
DK
/LKNM
56 F59
9EOQP<6
: :(9DI ; E C';: ; K 9! > (
G
;:C' :;< :; ; K H < #
: 9 ; H : #: K #
: C B# ; ;:< C :2EC; , 9G; EC; >: I B 9 K EC ; $ :C' < >< ; K C B H # B # l : ; K 0
R
<6A#23(54? 5><6(
SX0214365879;:6<=35><
?FAC6DBEXG87^<61SUKP\MPZ \!W
7 "436583
5><
-
?BA8C6DBEXGDT TU ;
+YY
+2V ,#++WU -
!"#!$%
r
Valor de
Selecção
9 10
1
8
5.3
4.4
2.1
1.5
1.4
1.4
1.3
1.3
0.8
0.5
7
Indivíduo
6
5
4
Indivíduo
2
1
2
3
4
5
6
7
8
9
10
3
&
0
B> @; J<;
'
; : C <)(: C < < 9
9 : C ; 9
: B I#: C C B# +*-, ;# /. J
C; :; B 9! ; :< K 9!; F ,) $ ; H ; B C HF 21 ' K43 # < ;6587 J
9
9;:=<:?>
@BADCEFHGJIKFDLFNMPORQTSORUAVUTW%XTQVLFZY[FHL#FH\^]NFH_#OQTGUTE\`@aOKIKEcbd%EUTE\
fe hg
# ji kiml on hp rq"
#4i e s2ti vu e gnp e;w yxmz;{|}~|€‚mxmƒ„Kz…{Rx
† xˆ‡‰xvŠR‹~xˆŠ m}jz…Œ~x{R|2ŽˆR‡k|‚ŒŽ/‹‘ŽvŠ‹~x’{RŒ“z„’z”{•Žˆ{|h{RR‹~Žˆ‚Œ“|2xv{R|}j|‚mxˆƒ…’z”‡k|‚Œ“x–{R|2ŽˆŠƒ”z † Ž —’|}
† xˆ‡ n!p e˜r™TšŽˆ‹~Ž›ŒŽ/ƒœž{R| † z”{Rz…KŸc}j|Ž/{RxmŠŒ“Žˆ‹Žˆ}JŠ4xˆŒ~| † z Žˆƒ…z”{•Žˆ{|}T{Rx¡ŠRŽˆ‹“Žˆ{z”¢m‡£Ž{•Ž gJ¤“¥ ¤jiˆ¦kiml¨§’¥
© ¤«ª¬r­ i‚®‚i¯i’¥ © =°)¬± ¥²u=g ©³© w´œ žR| tŽ † z…ƒ”z„ŒŽ x–R}jxRœJŠRŽˆ‹“ŽvŽˆƒ ‡‰{|+Š4|‹j‡£z„Œ“z…‹µR‡‰{|}~|€‚mxmƒ„Kz¶Ÿ
‡k|‚Œ“x‘z” † ‹~|€‡£|€‚ŒŽˆƒ=œR}~|€R{RxkŠ·xm‹8z…}~}jx£z…R{Rz † Žˆ{RxŠ•Ž/‹“Žx£{|}~|€‚mxmƒ„Kz…‡£|€‚Œ“xk{R|¸}~z”}?Œ“|€‡hŽˆ}8¢ˆ‹“ŽˆR{|}!|
† xˆ‡£ŠRƒ…|r¹Kxm}€™
ºe gTn!p e † xˆ‡£| xm+Ž}~|€‹ † xm † |»Rz…{Rx‘|‡½¼¿¾ˆ¾mÀœ † xm‡kx y|‹~‹~Žˆ‡k|‚ŒŽ{R|³}jRŠ·xˆ‹jŒ“|›Žµ|€}jŒŽŒ“|€}~|/™
Á |€}~{R| /ÂmÂmœ;ŠRŽˆ}~}jxm²Ž¯}j|‹h{z…’Rƒ”¢mŽˆ{RxRŽ¯{Rz…} † z…ŠRƒ”z…•Ž{R|¯Ã ª ˜ ¬r¦ki ˜hÄ ­ ¬ ª ¬r­ ¬ ˜¿Å)œÆŒ~|R{xÇ}~z…{Rx
ŽˆŠRƒ…z † Žˆ{RxŠ4|ƒ…xm}o}j|R}2Žˆƒ…RRxm}£|‡ {Rz…ˆ|‹~}jxm}ŠR‹jx | † Œ“xm} 1 |ˆ™È¢R™…œ³Ã ª ˜ ¬r¦ki ˜ ®’¬²ÉHªt®‚i e ¤ ª s;±rªti ¸|Px
n¬±¥´­Ê•¬±rªË¦h¬r­ ¥2Ì ª±¥o®’¬hÍTiˆ¤ji’± ¬r¤“¬ ˜´7«™8Î}jŒ~|µŽˆ‡µ»z”|‚Œ~| yxˆzό“Žˆ‡µ» ‡ÐŒ~z”ƒ…z Ž/{RxŠ•Žˆ‹~Žkx2Ñ ªti
­%Ò ˜ ª±¥Ó¯Ô~®ˆª±¥Õ#i ˜ ¬~i‚®’¥h¬r¦×Ö·¥´¦h¥ ¤jijsJi ÍJ¥´¦ q ¥´¤«ª„Ø¿i‚®‚i 1 & z”¢ˆR‹“Ž K™„¼¿Ù‚7«œRxm»Œ~|R{Rx£‹~|€}~Rƒ„ŒŽˆ{Rxˆ}
ŽˆRz…‡hŽ/{Rxm‹~|€} * 'ƒ…ˆ|}€œ /Âm¼ . ™
·ڌ“|€‹~‡kxm};{R|³z…‡£ŠRƒ…|‡k|‚ŒŽ ˆxRœ yxmz%{R| † z”{Rz…{RxŽˆ{RxˆŠŒŽˆ‹Žµƒ…z”R¢ˆ•Žˆ¢m|€‡Û{|³ŠR‹~xm¢ˆ‹“Žˆ‡£Ž /x Í;ܳÜ
*-Ý Œ“‹jxmR}jŒ~‹~RŠ%œH¼¿¾m¾¼ . ’||‡µ»4xm‹“Ž  ˆxP}j| ŽPR‡£ŽÞƒ”z…R¢m•Ž/¢m|‡ßŠ4|‹ y|z…Œ“ŽÞ{R| g ©³© œ yxmz † xm † |»Rz…{•Ž
† xˆ‡£x8R‡£Ž y|‹j‹“Žˆ‡k|‚Œ“ŽŠ‹“(/Œ~z † Ž;ŠRŽˆ‹“Ž;‹j|}~xˆƒ…m|€‹ÏŠR‹~xm»ƒ”|‡£Žˆ}à‹j|)Žˆz…}œ¨}~|€R{Rx!Œ“z…ƒ”z Žˆ{•ŽŠ·xˆ‹HR‡hŽ;¢ˆ‹“ŽˆR{|
Š•Žˆ‹?Œ“|v{•Ž^z”{RáR}jŒ~‹~z”Ž™V'ߋ“Ž ˆxâŠR‹jz” † z”Š•Žˆƒ#{R|}?ŒŽ`|} † xmƒ”ãRŽâ{|€m|€KŸc}j|äâ}~RŽâ| 0 † z 3  † z Ž 1 ž•Žˆ{Rx
å“æ%çrè¿éjê-ëìçTè¿íÆîï´ç«ë=ð=íçrñ¨íTòóéjôð=êóõríè¨çJöžê÷ôéjñ´ôê÷çðï¨ëçè¿éùøúñ´ûré?ñ´ü´ç«ëêóçè¿éý)ê÷þtð=é?ÿ8ç€þ4éËñ¶írëÿð=ê÷ô?çùñ¨ê-õ€é?ëìþtê÷è¨ç€è¿é
è¿í
³êóñ¨ü¨í
B
7
4
"
+
4
7
B
$
1"
F
.
2"
;
"
4
4
>
4
;
;
G
$
:"
'
>
W"
D"
"
$
6
’a ÆT‘+BT³ !³ ›
& z”¢mR‹~Ž K™„¼¿Ù c‡£Žˆ¢m|}!xm‹~‡£Žˆz”} 1 Ž † z”‡£Ž‚7| † xˆ‡ÐŽ/Œ“‹jx 0 Ž 1 Ž/»•Žˆz„¹Kxž7«™
† ˆx R}~z…{R|‹~Žˆ{•Ž|‡×‹j|ƒ”Ž ˆxvŽxmKŒ“‹“Ž/}ƒ”z”¢m•Žˆ¢m|€R} g ©³© † xm‡kxvŠ·xˆ‹µ|r¹K|‡kŠRƒ…x¯Žƒ…z”R¢mRŽˆ¢m|‡ i ´i
* '‹~x
¯|z”}j}œH¼¿¾ˆ¾mÀ . 7rœ{RŽˆ{Rx žR|¯Žâ‡hŽˆz…xm‹oŠ•Ž/‹jŒ“|–{Rxm} Žˆƒ…¢mxm‹~z„Œ“‡kxm}h{|ŽˆŠ‹~|{Rz Žˆ¢m|‡ Œ 3 ‡
¢m‹~ŽˆR{R|€}‹~| žRz”}jz…Œ“xˆ} † xˆ‡£ŠRKŒŽ † z”xm•Ž/z”}™ Žˆ‡µ» ‡ yxmzÏ{R| † z”{z”{RxhŽˆ{RxmŠŒ“Žˆ‹!xo}~z…}jŒ“|€‡hŽkxmŠ4|‹“Ž´Œ“z…ˆx ª
­•q Š4xm‹ÏŒ“|€‹R‡£Ž#{Rz…}jŒ~‹~z”»Rz ˆx#¢ˆ‹“Ž/Œ~Rz…Œ“Žœ/}j|‹»•Žˆ}jŒ“Žˆ‚Œ“|;‹jxm»RR}?Œ“x| † xm‚Œ~|‹|«¹ † |ƒ…|‚Œ“|€} y|‹j‹“Žˆ‡k|‚ŒŽ/}
{R|!ŠR‹~xˆ¢m‹“Žˆ‡£Ž ˆx6|€‡ Í;Ü³Ü 1 }~xm»£ƒ”z † | )Ž¸{•Ž p
7«™5Æxˆž ‡ Žˆz”{•Ž›‹j| y|€‹~z”‹ žR|!Œ“x’{Rx¡x † {Rz”¢ˆx
yxmzà|€} † ‹~z…Œ~x£|€‡ z”¢mƒ 3 }œŠ4xm‹8R‡£Ž žR|}?Œ ˆxk{R|¸RRz„m|‹j}“Žˆƒ…z”{•Ž/{R|ˆ™
!
#"
&"
%$
('
21 *) ,+
.-
%3
0/
4+
3
+
>"
Classe Abstracta
5
7698;:
)
&+
<"
3=
?
ANN
Aprendizagem
SANN <WeightMatrix> Supervisionada
UANN
Não Supervisionada
Tipo de Rede
Kohonen
...
FF
RC
RBF
...
@A%BDCEGFHJILKMON<PQSRTETCRTCOEGFUOVW3X%FQTQSV3QYUOZ\[^]<_(`a[I
bdc
A%V3ETFETeCOA%FUVfW3X%FQTQSV3QgUOZ>[f]<_(`([hV3QSRGijESV3kOESV3QTV&lmR?FUnFolOFp@AqBDCOEGFHJILKMOrZDlUOVfF2QsW3X%FQTQSV3QutTi
v0wTx9y{z}|~€‚„ƒz}…Sy‡†z‰ˆ;€‚Šƒs‹Œƒ€‚~&ŽTˆO‘}’4“•”g– ˆ9“•ƒ˜—™”™~š€œ›3Ÿž &†š…4‹…Sˆ¡€&~š¢gƒs£z}€„…S€z}ƒ£šz¡ƒ¤¥…SyŸ—}ƒ‹Œ…4£š¢z;—}€Ž‚¦š¢z‰¢?—}†€œ—‰¢
‹Œ…„§‡¨¥©‰ª%«*¬?­}®{¯
‚À
"!$
{R|€}~|‚ˆxmƒ…’z”{RŽˆ}6}j|£|€ † xˆžŒ~‹“Žˆ‡ß{|‡£Žˆ‹ † Žˆ{•Žˆ}¸Š4xm‹¸R‡½Œ“‹~Ž † |~Žˆ{Rx † xm‚Œ”žRxR™!Ž † ƒ”Žˆ}~}j|hŽˆ»}jŒ“‹~Ž † Œ“Ž
‹“Ž/z 1#"%$&$ 7¡} ˆxv{R| 0 z”{•Žˆ}£Žˆ}‘z”‚Œ~|‹ tŽ † |} † xm‡µRR}€™'!x¯…m|€ƒ8}~|€¢mRz”‚Œ~|+Œ~|‡Ÿc}~|2xvŠ•Žˆ‹~Žˆ{Rz…¢m‡hŽ
{R|2ŽˆŠ‹~|{Rz Žˆ¢m|‡+œ }j|R{Rx–Ž žRzÆ{R| 0 z”{Rxm}6Œ“x’{Rxm}µxm}µŽ/Œ“‹jz”»RŒ~xm}µ| † xm‡kŠ·xm‹?ŒŽˆ‡k|‚Œ~xm} † xm‡µRR}µŽˆx
Š•Žˆ‹~Žˆ{Rz…¢m‡hŽK™(â{R|‹j|)Žˆƒ )Žˆ‹ žR|ˆœ•Ž/Š·|€}“Žˆ‹J{R|}~z…{Rx † xm‚Œ“|‡kŠRƒ”Žˆ{•Ž¡Ž/Š·|€•Žˆ}8ŽµŽ/ŠR‹~|€R{Rz Žˆ¢m|€‡Û}jRŠ4|‹j’z¶Ÿ
}~z…xm•Žˆ{RŽ 1 † ƒ Ž/}~}~|*) "%$+$ 7rœ•|}?ŒŽk|}jŒ~‹~Œ~R‹“ŽkŠ·|€‹~‡kz…Œ~|³R‡hŽ|«¹ŠRŽˆR} /xŽkxˆŒ“‹jxm}Š•Žˆ‹“Ž/{Rz”¢m‡£Žˆ} 1 |ˆ™È¢R™…œ
ŽˆŠR‹j|R{z )Ž/¢m|‡  ˆx+}~RŠ4|‹?Kz…}~z…xm•Žˆ{•Žm7r™šùxm‹ 0 ‡ œHx+…m|€ƒz” y|€‹~z…xm‹œ%Œ~|‡Ÿc}j|‘Ž2{| 0 Rz ˆx2{RxŒ~z”Š4x
{R|‹j|{R|/™#x2ŠR‹j|}~|€‚Œ“|ˆœÏx2}~z…}jŒ~|‡£Ž † ŽˆŠ•Ž {R|ƒ”z…{•Žˆ‹ † xm‡ np ˜ 1 † ƒ Ž/}~}~|-,.,7| np!n ˜ 1 † ƒ”Žˆ}~}j|
/10 7r™
5Æxm‡kx yxmzH‹j| y|€‹~z”{x£•Ž Ý | † ˆx K™„¼mœúR‡hŽ np e † xm‡kŠ4xm}jŒ“ŽkŠ4xm‹R‡ † xˆ2jR‚Œ“x£{R| † xmR|r¹K—’|}€œ
Rx’{Rxm}‘| yR €—K|€}k{| Ž † Œ“z„/Ž ˆxœxˆ‹~¢‚Žˆz )Ž/{Rxm}žR‡£Žv{RŽˆ{•Ž|}?Œ“‹~KŒ“R‹~Ž™[šŽˆ‹“Ž‹j|ŠR‹j|}~|€‚ŒŽˆ‹k|}?ŒŽ
z” yxm‹~‡£Ž /xRœ yxmz%{R| † z…{Rz”{RxµŽˆ{RxmŠŒ“Žˆ‹;{Rxˆz”} † xm‡£Š4xmR|€‚Œ“|}8»R(ˆ}~z † xm};{|³‡hŽˆz”ŠRRƒ”Ž /x6{R|³{RŽˆ{Rxm} m| † Ÿ
Œ“xˆ‹~|}8|‡hŽ/Œ~‹~z |}€™3 Š‹~z”‡k|z…‹~x6{R|}?Œ“|}xm»4j| † Œ~xm}~(µ}~|³|€ † xˆžŒ~‹“Ž)/Ž{R|}j|‚mxmƒ„’z”{Rx‘{R| yxm‹j‡hŽ6| 0 † Ž
*65 R}j}~|‹ Ý Ž/z”Rz=œ·¼¿¾ˆ¾87 . œ%Š4|ƒ…x žR|Ž/Š·|€•Žˆ} yxˆzù| † |€}~}~(ˆ‹~z…x † xm † |»4|‹#xo}~|«Ÿ
•Žh»z”»Rƒ…z”xˆŒ~| † Žoà Ö
¢mR{RxRœ•{R| 0 Rz”{x † xm‡£xkR‡Úˆ| † Œ“xm‹!{R|¸m| † Œ“xm‹j|}€™3ÛÃ Ö –Žˆ{xmŠŒŽR‡£Ž yR † z…xm•Žˆƒ…z”{•Ž/{R|{Rx Í;ܳÜ
† 㕎ˆ‡£Žˆ{•Ž {R|:9 ¬r¦;=<„i 9 ¬ œ {R| 0 Rz”{•ŽPŠ4|ƒ”ŽÞRxˆŒ“Ž /x?>A@BDCFEHG¸œ žR|Š·|€‹~‡kz…Œ~|£z…R}jŒ“Žˆ † z”Žˆ‹6Œ~z”Š4xm}›{R|
{•Žˆ{xm}!ŽˆŠ·|€•Žˆ}!Ž ž•Žˆ{Rx£{RŽ † xmR}?Œ“‹~ ˆxk{R|¸R‡ xm»4j| † Œ~x JI ™
Á |‚Œ~‹~xh{|}jŒ~| † xm‚Œ“|«¹KŒ~xRœ•R‡£Ž n!p eN{R|›ŽˆŠR‹j|R{z )Ž/¢m|‡ }jRŠ4|‹j’z…}~z”xˆ•Žˆ{•Ž 1 ) "%$+$ 7 † xˆžŒ ‡
%$
T
S+
%$
"
q
g"
%$
G
%$
n
+
7)
+
+
J+
&+
O
2$
q
76
7
)
%$
m+
&
q$
^+
-
8Ÿ8
\"
+
-
>+
"
$
"
8
%$
T) .
K R‡£Ž ¦ki 9 ¤rª„ØÞ®’¬*;•¬ ˜ ¥ ˜ 1 † ƒ Žˆ}j}~|%LNMPORQ=SUTWVXTZY2O\[ù7 *6] Žˆƒ”ƒ”Žˆ‚Œ)œ%¼)¾m¾mÙ . œ ’|+{| 0 R|2Œ“x’{•Žˆ}‘Ž/}
† xmR|r¹K—’|} 1J^`_ba 7dc
g"
K R‡£Ž ¦ki 9 ¤rª„Ø£®’¬­%¥®’¥ ˜ 1 † ƒ”Žˆ}~}j|-eXgf=M4Yih)7rœ žR|‹~|€ŠR‹~|€}~|€žŒ“ŽÞŽoxm‹j¢‚ŽˆRz )Ž ˆxo|€žŒ~‹~|xm}³xK{Rxˆ}
1j2k!lnmoldprq 7scK|
9"
q$ 3
K R‡ ˆ¬± 9 ¥´¤6®’¬ut«q’­úliv¿¬ ˜ ®’¬¡i’± 9 ª ´iml¨§’¥ 1 † ƒ”Žˆ}~}j| $&wyx zM h¿7rœ•Š4|‹j‡£z„Œ“z”{Rx žR|6{z y|‹j|‚Œ“|€}#xK{Rxˆ}
Š4xm}~}~Žˆ‡  Œ~z”ƒ…z )Ž/‹Æ{Rz y|‹~|€‚Œ“|} yR —’|}!{R|›Ž † Œ~z…/Ž /x #1 { 7r™
>"
0
%$
L+
a+
q+
|~} z”¢ˆR‹“Ž K™„¼Wµ{R|‡kxmR}?Œ“‹~Ž † xm‡£x ›¢m|‹~Žˆ{•ŽR‡£Žk‡£Ž/Œ~‹~z {R|6Š4|}jxm}!Š•Žˆ‹“ŽR‡£Ž‘{•Žˆ{•Ž np e xmR{|
x€…R{Rz † |{Rxm}JRxK{xm}Jxˆ‹~z”¢ˆ|‡V}jR‹~¢m|#•Ž6ãxm‹~z xm‚ŒŽ/ƒœžŠ·|€ƒ”x žR|x”R{Rz † |{Rxm}JRx’{Rxm}{R|}?Œ“z”xµŽˆŠ•Ž/‹~| † |
•Žµm|€‹jŒ~z † Ž/ƒ™
Î}jŒŽ–|}?Œ“‹~KŒ“R‹~Ž¯{R|+{•Žˆ{Rxˆ} +Š•Žˆ‹?Œ“z”ƒ…ã•Žˆ{•ŽPŠ4xm‹Œ“x’{•Žˆ}£Žˆ}‘}~» † ƒ Žˆ}j}~|} 1 |/™-¢R™„œ.,.,Ú| /10 7r™Tšxˆ‹
R‡£Ž žR|€}jŒ /x{R| ¬ ˜ ;•¬±rª s;±rªt®‚i‚®’¬ œ•xmP}j|‚~Žœ·{R| 0 Rz”‹#‡hŽˆz…}#z… yxm‹j‡hŽ ˆxkäh‡k|{Rz…{•Ž žR|µ}j|µ{R|€} † |¡{R|
† ƒ”Žˆ}~}j|ˆœ yxmzώ/}~}~x † z”Žˆ{Rx‘R‡ƒ9 ¬r¦;=<„i 9 ¬ äk‡£Ž/Œ~‹~z {R|¸Š·|€}~xm}€œ4{|›‡kx’{Rx žR|6{z y|‹j|‚Œ“|€}‹~|{|}!Š·xm}j}“Žˆ‡
Œ~z”ƒ”z )Žˆ‹J{Rz y|€‹~|€žŒ~|}8Œ“z…Š·xˆ};{R|³‡£Ž/Œ“‹jz |€}8{R|³Š4|}~xˆ} 1 |ˆ™È¢R™„œ•R‡hŽ np Œ“z…ƒ”z Ž¡R‡£Žµ‡hŽ´Œ“‹~z {R|¸Š4|}jxm}
„#„jæy……†ˆ‡Š‰d‹ˆŒs‰d#ŒŽi‘“’8”6‰•‡\–˜—š™‘#‰•› „Rœ‘RírëÏ鑞)éjÿ`Ÿ¨ò-í/ç;òóê-ñ´ü´ç8è¿éô‘ )è¨ê-û€í2¡o¢ˆ£¤s¥§¦i¨Z©rªD«8¥­¬¯®°²±i³•´’è¿é‚µ/ñ¨éTí8õré~ôcðír듶vè¿éñ·´ÿÆéjë=íþàê-ñðé?êóë=íþÏôí€ÿ`ï¨ÿ
ðçrÿ8ç«ñ¨ü¨í8è¿é¸ )
%$
q$
"
\)
\"
?
+
O+
q$
3
%$
q+
%$
\"
>"
76
q+
%$
q$
z Camada de
Entrada
&
Camada
Intermédia
‚¾
Camada de
Saída
+1
w i,j
w5,3 +1 w
3
5
4
5,0
3
1
WeightMatrix
1
2
3
4
5
j
5
4
2
0
i
Bias
Conexão Unidireccional
Conexão Recorrente
} z”¢ˆR‹“Ž ’™…¼W 5 Ž/Œ“‹jz ³{R|¸Š4|}jxm}#ŠRŽˆ‹“ŽR‡£Ž n!p e³™
>
%$
RRz…{Rz”‹j| †€† z”xˆ•Žˆƒœ•|€ ž•Žˆ‚Œ“xžR‡£Ž np!n | }jŒ“Ž ¡‹j| † xm‹~‹j|‚Œ“|
r™ | }~R» † ƒ”Žˆ}~}j|,., † xm‚Œ ‡ “Œ x’{•Žˆ}Ž/}
xmŠ4|‹~Ž —’|}JŠ•Žˆ‹“Ž¡Ž6‡£ŽˆRz”ŠRƒ Ž ˆx¸{R| np r˜ œK|}jŒ“ŽˆR{Rx¡{Rz”}jŠ·xm…m|€z”}TŒ“x’{Rxm}Jxm};Žˆƒ…¢mxm‹jz…Œ“‡kxm} {
| Œ“‹j|z”x
{R|€} † ‹jz…Œ~xm}!Žˆ‚Œ“|‹jz”xm‹j‡£|€‚Œ“
| t|/™-¢™…œ ng œ g | n gTn © g r™
O"
)
9;:=<:9
3
T)
76
@BADCEFHGJIKF L#F MPOQTSTOUAVUW·XTQ L#F"@?STQOREìIAVQT\BFHG%IKE?d·QT\BFTQ
?_#d%EQT
G OREQT\
šxˆ‹H}~•Ž;m| ˆœ´x#e ¦ª¬r­ 9 ¬J®’¬gƤ“¥ˆ¤jiˆ¦kiml¨§’¥#®’¬ e < ’¥´¤«ª 9 ¦h¥ ˜ ¬r­%Ô 9 ª±¥ ˜ ¬"! ˆ¥2< q•±rª¥´­$#ˆ¤«ª¥ ˜ u e g e ! w
% #|€ˆ|}#|€Œ!Žˆƒ=™…œà¼)¾m¾m¾'& yxmz † xmR}jŒ~‹~˜…{Rxh{|‚Œ“‹jxo{R|›R‡
|}~Š”‹~z„Œ“xk}~|€‡£|€ƒ”ã•Žˆ‚Œ~|ˆc4z™È|ˆ™„œ tŽ † z”ƒ…z…ŒŽ/‹8Ž‘Œ“Žˆ‹~| tŽ
{R|2{R|€}~|‚ˆxmƒ…’z”‡k|‚Œ~x¯{R|+ŽˆŠƒ”z † Ž —’|} † xm‡×e ! ˜+’z ŽR‡£Ž g ©³© |‡ Í;Ü³Ü œŽ † xˆ‹~‹~|€‹}~xm»‹~|2x
}~z…}jŒ~|‡£Ž+xmŠ4|‹~Ž/Œ“z„mx ªË­•q ™oÎ}?Œ“|oŽ/‡µ»Rz”|€‚Œ“| yxmzTŽˆŠRƒ…z † Žˆ{Rx † xm‡ß}j † |€}~}jxP|‡)(ˆ‹j|)Žˆ}¸Œ /x {Rz…}jŒ~z”‚ŒŽˆ}
† xˆ‡£xox gƤ“*¥ <”¬r¦ki2®’¥PÍTiˆª K¬rªË¤¥^ÉHªtij°€iˆ­ 9 ¬ %,+ x † 㕎œH¼¿¾m¾ -& ! ˜ ±~iˆ<”¥´­4iˆ¦h¬r­ 9 ¥o®’¬ Öúiˆ¤“¬Rt€i ˜ ®’¬µq’¦ki
ÖϪ ;•¥ ˆ¤jijsJi % + x † 㕎|rŒŽ/ƒ™„œ ˆÂmÂm- &R| i e9 ¤«.ª q’ªyl¨§’¥›®’¬;Ӗ¬ ˜ i ˜ ;iˆ¤ji£ÍJ¥´­ ¿ªt®‚i‚®’¥ ˜ ®’¬q’¦ ÍTi ˜ iˆ¦h¬r­ 9 ¥
% + x † 㕎|€Œ#Žˆƒ=™…œ /ÂmÂ/
¼ &=™
3fe g e ! Žˆ}j}~|‚Œ“Ž–|€‡ ž•Ž/Œ“‹jx»Rƒ”x † xˆ}µŠR‹~z… † z…Š•Žˆz…0
} } z…¢mR‹~Ž K™„¼Z17 rœxm‡£|Žˆ{•Žˆ‡k|‚Œ~|oxm} ªË­
™ 4;Žˆ{•Ž+R‡ {R|}?Œ“|} † xm‡kŠ·xˆR|‚Œ“|€}
®ˆª 32t®ˆq•¥ ˜rœŽ ;•¥•;4qP<„iml¨§’¥ œxm}µe ! ˜o|hx ¦hÒ®ˆqz<”¥Þ®’¬oi ´iˆ< ªtiml¨§’¥ 5
† Ž/‹“Ž † Œ“|‹jz Žˆ{RxPŠ4xm‹µR‡£ŽPãRz…|‹“Ž/‹ žRz Ž {R| † ƒ”Žˆ}~}j|}€œ † xmR}jŒ~‹~˜…{•Žˆ}µ{|oŒŽˆƒ yxm‹~‡£Ž žR|2Ž/Œ~‹~z”»Œ“xm}¡|
† xˆ‡£Š4xm‹jŒ“Žˆ‡k|‚Œ“xm} † xˆ‡µRR};} ˆxµ{R7| 6•Rz…{Rxm};•Ž/} † ƒ”Žˆ}~}j|};}jRŠ·|€‹~z…xm‹~|€}œ|«¹Kz”}jŒ~z”R{xµR‡ÛŠR‹~x † |€}~}~x{||}Ÿ
Š4| † z”Žˆƒ”z )Ž ˆxRœ‚万k|{Rz…{•Ž žR|!}~|#{R|} † |#Š•Žˆ‹“Ž›Žˆ}}~R» † ƒ”Žˆ}~}j|}€œ‹~|€{R/| 6RRz”R{x¡xm£Ž † ‹j|} † |‚Œ“ŽˆR{RxRx¿ˆxm}
Ž/Œ~‹~z”»Œ“xm9} 8 † xˆ‡£Š4xm‹jŒ“Žˆ‡k|‚Œ“xm}€™
| x˜…ˆ|ƒù{•ŽhãRz…|‹~Žˆ‹ žRz”Ž£{Rxz…R{Rz…z…{RRxRœ•Œ“|€‡‘Ÿì}~|6R‡hŽk‹“Žˆz žR| 6R‡£Ž † ƒ”Žˆ}~}j|µŽˆ»R}?Œ“‹~Ž † Œ“Ž † xm‡
R‡ 9 ¬r¦;=<„i 9 ¬ ŠRŽˆ‹“Žx¢m|€ Œ“z…Š·x™ | }j}~z…‡ œŽˆ}‹j|ŠR‹j|}~|€‚ŒŽ €—K|€}h¢m|€ €Œ~z † Ž/}} ˆxv{R7| 6•Rz”{RŽˆ}{R|2R‡£Ž
yxm‹j‡hŽµ}jz”‡kŠRƒ”|€}œ•Ž/Œ~‹~z…»RRz”{Rx/Ÿc}j|³Žˆx 9 ¬r¦;=<„i 9 ¬ Ž‘{R|€}~|‚~Ž/{•Žk‹j|ŠR‹j|}j|‚ŒŽ ˆ:
x } z”¢ˆR‹“Ž K™„¼ ;
«™
&$
Y5
o5
s
™+
*+
-
+
o5
>+
1
?
D
1
n
o5
"
o5
0
)
%$
n/
T"
g+
"
T
q$ 3
"
T"
+
=
q$p"
o)
O)
G
3
ˆÂ
Algoritmos
Genéticos e
Evolucionários
Módulo de
Avaliação
População
...
Problema
Indivíduos
} z”¢mR‹~Ž K™„¼Z7 3 Ž/‹ ž €Œ~z”Š4x‘{Rxoe g e
T"
O)
o5
!
%
#|€ˆ|}!|€Œ#Žˆƒ=™…œà¼)¾m¾m¾'&=™
Classe abstracta para indivíduos
Indiv<TGene>
Indivíduos com genes inteiros
Indiv<Real>
Indiv<int>
OBRIndiv
BBRIndiv
Rep.baseadas
em permutações
Rep. binárias
OrdIndiv
Representação baseada em reais
IBRIndiv
Rep. ordinais
Rep. inteiras
Instanciação de template
Sub-classe
} z…¢mR‹“Ž ’™…¼
RBRIndiv
| ãz”|‹~Žˆ‹ žRz”Žµ{R| † ”ƒ Žˆ}~}j|}{Rxkz”R{Rz„z”{RRx % #|rm|€}#|rŒŽ/ƒ™„œ%¼¿¾m¾ˆ¾ & ™
T"
z .
K¼
#xm}2‹j|}jŒ“Žˆ‚Œ“|€} ‡ {Rƒ”xm}€œ yxˆ‹“Žˆ‡ }~|¢ˆRz”{•Ž/}|}jŒ~‹“Ž/Œ ¢mz”Žˆ}}~z…‡£z…ƒ Žˆ‹j|}€œ!}j|R{xa|€}jŒŽ/»·|€ƒ”| † z”{Rxˆ}+xˆ}
† xˆ‡£Š4xm‹jŒ“Žˆ‡k|‚Œ“xm}» (ˆ}~z † xm} žR|Š4xK{|‡ }j|‹Þ‹j|{R|76•Rz…{Rxm}œ † xm‡kx`xaŠR‹~x † |€}~}jx[{R|–‹~|€Rx¿ˆŽ ˆxa{•Ž
Š4xmŠRRƒ”Ž ˆx2xm¯Ž |€}jŒ~‹~Œ~R‹“Ž+{Rxގ/ƒ”¢mxm‹jz…Œ~‡£xo¢ˆ|‹“Ž/ƒ™£šxm‹¸áRƒ„Œ“z”‡kxRœ ‘Rx ‡£x’{RRƒ…x{R|hŽ)/Žˆƒ…z Ž ˆx žR|
xkŒ“z…ƒ”z Žˆ{Rxm‹Æ{R/| 6•|6xkŠR‹~x † |€}~}jxh{R|›{R|} † x’{Rz 6 † Ž ˆxRœúxm+}~|‚~ŽKœ † xm‡kx † xmR}?Œ“‹~z”‹!R‡hŽ}jxmƒ” ˆx † xm‡
»•Žˆ}j|¸’‡ † ‹~xˆ‡£xm}j}~xm‡£ŽœK| † xm‡kx£Ž´Œ“‹~z…»RRz…‹Æx/Žˆƒ”xm‹8{| is; 9 ªt®‚§’¥ Ž|€}jŒŽ‘}~xˆƒ” ˆxR™
Y+
=
T)
."
2
9)
%$
3
3
"
O3
O3
#|€}jŒ~| † ŽˆŠ…Œ“ƒ”x yxmzT{R|} † ‹~z„ŒŽPŽ † Žˆ‹~Ž † Œ~|‹jz )Ž ˆx | yR † z”xmRŽˆ‡£|€‚Œ“xÞ{|h{R•Ž/}6Œ † Rz † Žˆ}6z”R}jŠRz”‹~Žˆ{•Žˆ}
•ŽHŽ/Œ~R‹~| )Ž ގˆ} n¬~®’¬ ˜ p›¬rqK¤“¥´­4iˆª ˜ Ï­•ªt®ˆªË¤“¬±±rª¥´­4iˆª ˜ u=np ˜cw|+xm}he < ’¥´¤«ª 9 ¦h¥ ˜ ¬r­%Ô 9 ª±¥ ˜ ¬
! ˆ¥2< qú±rª¥´$
­ #ˆ¤«ª¥ ˜ u e ! ˜cw´™
| } np ˜J} ˆx‡ ( žRz”RŽˆ}àRRz„m|€‹~}“Ž/z”}œ¨z…{R|)Žˆz…}àŠ•Žˆ‹~Ž8R‡hŽ8Ž/ŠR‹~|€R{Rz Žˆ¢m|€‡N}~Š·|€‹j’z”}jz”xm•Ž/{•Žœ¨}~|€R{Rx
† Ž/Š•Ž |€}³{R|‘ŽˆŠR‹j|R{|‹R‡£Ž ž•Žˆƒ žR|‹ † xm‹~‹j|}~Š4xmR{  † z Žo|‚Œ~‹~| † xˆ2jR‚Œ“xm}³{|µ|‚Œ“‹~Žˆ{•Žˆ}³|¡}“Žˆ…{•Žˆ}™
| } np ˜ † xm‚Œ €‡ Œ~xK{RŽˆ}³ˆŽ/žŒ“Žˆ¢m|€R}¡{•Ž/} np e˜rœ † xm‡kx }j|‚~Žˆ‡ Ž+ŽˆŠR‹j|R{Rz )Žˆ¢ˆ|‡ß ˆx+ƒ”z…R|)Ž/‹œùŽ
Œ“xˆƒ”|‹ ˆ † z Ž›Žˆxµ‹~”{RxRœ’Ž6Œ~‹“Žˆ}~Š•Žˆ‹  † z Ž¡| •|r¹Kz…»Rz”ƒ…z”{•Žˆ{|ˆœž}~|€R{Rx‘ŽˆŠŒ“Žˆ}ƊRŽˆ‹“Ž›ƒ”z”{RŽˆ‹ † xm‡ Ž6‹j|}~xˆƒ” ˆx
{R|¸ŠR‹jxm»Rƒ”|€‡hŽ/}8{R| ±s<„i ˜˜ ª s;±~iml¨§’¥ | ¤“¬ ˆ¤“¬ ˜˜ §’¥ ™
| Žˆ‹ žRz„Œ“| † Œ“‹“ŽœxmŒ~xmŠ·xˆƒ”xm¢mz”Žœ;{R|ޏR‡hŽ np
P{R7| 6•Rz…{•ŽÇŠ·xˆ‹oR‡ † xm2jR‚Œ~x^{R|Rx’{Rxm}œ
Žˆ¢m‹jRŠ•Žˆ{xm}Š·xm‹ † Žˆ‡hŽ/{•Žˆ}œ † xmR|r¹K—’|}#RRz”{z”‹~| †† z”xm•Ž/z”};Š4|}~Žˆ{•Žˆ}€œ·{R7| 6•Rz…{•Žˆ}!|‚Œ“‹j|6xm}!Rx’{Rxm}€œ4|›R‡
† xˆ2jR‚Œ“x+{R| yR —’|}›{R|kŽ † Œ“z…/Ž ˆxR™!3 z…žŒ~|‹j|}~}j|£RŽˆ} np ˜ yxmz|€}jŒ~z”‡µRƒ”Žˆ{RxŠ4|ƒ…x+{|}~|€‚mxmƒ„Kz¶Ÿ
‡k|‚Œ“x {RxPŽˆƒ…¢mxm‹jz…Œ“‡kxo{R|hŽˆŠR‹j|R{Rz )Žˆ¢ˆ|‡ß{R| n¬ 9 ¤“¥ gJ¤“¥•;3i ‚iml¨§’¥`u=ng w´œÏ|k{R|}j{R|o|€žŒ ˆxÞ{z…m|€‹~}~Žˆ}
/Žˆ‹~z”Žˆ‚Œ“|€}‡£Žˆz”}!/| 6 † z”|€žŒ~|}Œ~|‡ }~z”{xoxm»Œ~z”{•Žˆ}€œ † xm‡kxoxŽˆƒ…¢mxm‹~z„Œ“‡kx{R|¡Œ~‹~|z…Rx ngTn © g ™ | ‚Œ“|}{R|
}~|›Œ“‹j|z”RŽˆ‹R‡hŽ np
{R|rm|µ}j|‹ † xmR}jz”{R|€‹“Žˆ{Rx£R‡ ŠR‹ «ŸcŠR‹jx † |}j}“Žˆ‡k|‚Œ“x£{Rxm}#{•Žˆ{Rxm}€œ·Š4xm‹ yxm‹~‡£Ž‘Ž
tŽ † z”ƒ”z„ŒŽˆ‹JŽkŽˆŠR‹~|€R{Rz )Žˆ¢m|€‡ ™
šxm‹³xˆŒ“‹jxoƒ Žˆ{xRœ%xm}³e ! ˜} ˆx|«¹|€‡£Šƒ”xm}{|µ‡ ( ’z”•Žˆ}#{R|‘ŽˆŠR‹j|R{z )Ž/¢m|‡ žR|µ}~|»RŽˆ}~|€z Žˆ‡
|‡ ŠR‹~x † |€}~}jxm}¸{R|}~|€ƒ”| † ˆx2•Ž´Œ“R‹~ŽˆƒŠR‹ ŠR‹jz”xm}{xm}³}~|€‹~|}³’z…ˆxm}™€3}›e ! ˜k|}jŒ ˆxŒŽˆƒ…ã•Žˆ{Rxˆ}Š•Žˆ‹~Ž
Ž‹~|€}~xmƒ… ˆx2{R|‘ŠR‹jxm»Rƒ…|‡£Žˆ}³{R|xmŠŒ~z”‡kz Ž ˆxœ%¢m|€‹“ŽˆR{x+/Žˆ‹jz Žˆ‚Œ“|€} žR| † xm‡kŠ·|rŒ“|€‡½|‚Œ“‹j|‘}~zŠ•Žˆ‹~Ž
}~xˆ»R‹~|rKz„m|€‹|TŠR‹~x † ‹jz Žˆ‹Hx¨ˆxm}z…R{Rz„P…{RRxm}€œ † xm‚m|€‹~¢mz…R{Rx#Š•Žˆ‹“Ž‡k|ƒ”ãxm‹~|€}ù}jxmƒ” —’|}™ | z”{R|€z Ž;xm‹jz”¢mz…•Žˆƒ
yxmzTŠR‹jxmŠ·xˆ}jŒŽ Š·xm‹ #xˆƒ”ƒ Ž/R{¯|€‡ ¼¿¾ 8Kœù|h{|}~{|o|‚Œ /xRœ }~x y‹~|{Rz…ˆ|‹~}~Žˆ}Žˆƒ„Œ“|€‹“Ž €—K|€}œ{| yxm‹j‡hŽ+Ž
ŽˆR‡k|‚Œ“Žˆ‹hx^}j|²ƒ”| ’|P{R|ŽˆŠƒ”z † Ž —’|}€™ 3} tŽ † Œ“xm‹j|} † |‚Œ“‹~Žˆz”}oŠRŽˆ‹“Žx^}~x^{R|ve ! ˜v} ˆx ¯Ž
yxm‹j‡hŽ¡{|›‹j|ŠR‹j|}j|‚ŒŽ ˆxk¢m| rŒ“z † Ž xm}8xmŠ4|‹~Žˆ{Rxm‹j|}8{R|¸‹~| † xm‡¡»Rz”•Ž ˆxµ¢ˆ| rŒ“z † Ž xm}8ŠR‹~x † |€}~}jxm}{R|
‹~|€Rx¿/Ž ˆxk{•ŽŠ4xmŠRRƒ”Ž ˆx|¸}j|ƒ”| † ˆx£{xm}z”R{Rz„z”{RRxˆ} |›Ž y ˆxk{R|›ŽˆŠŒ~z”{ /x
} z”RŽˆƒ”‡k|‚Œ“|/œ¨} ˆx#{R|} † ‹~z„Œ“xm}ùxm}Žˆ‡µ»Rz…|‚Œ“|€}{|JŠR‹jxm¢m‹~Žˆ‡hŽ ˆxRœ´Žˆ‡¡»·xm} † xm † |€»Rz”{xm}}jxm»R‹~|xŠRŽˆ‹“Ž´Ÿ
{Rz…¢m‡hŽ!{•Ž gJ¤“¥ ˆ¤jiˆ¦kiml¨§’¥ © ¤«ª¬r­ 9 i‚®‚i›i’¥ © =°)¬± 9 ¥ Š·|€‹~‡kz…Œ~z”R{Rx#R‡"{R|}j|‚mxmƒ„’z”‡k|‚Œ“x³z… † ‹j|‡k|‚ŒŽˆƒ
{R|ŽˆŠRƒ”z † Ž €—K|€}TŠ•Žˆ‹“Ž † xm‡kŠRŒ“Žˆ{Rxm‹€™3e ¦ ª¬r­ 9 ¬®’¬#gJ¤“¥ ˆ¤jiˆ¦kiml¨§’¥¡®’¬#n¬~®’¬ ˜ p6¬rq’¤“¥´­4iˆª ˜;e ¤ 9 ª s;±rª
+
%$ 2
&$ \+
G)
6
5
6
o5
G
6
"
%$
$
"
q"
G)
6
q$
O3
T"
76
+
O
)
76
q$
+
3
6
n
+
G
š/
T)
(+
q$
o5
G
2"
%$
o5
=
O
"
%$ G
"
+
!
m
&"
+
3
?
2+
+
o5
O)
\+
2
3
G
>+
O
T
O
O)
n #"
2
0/

D
ˆi ª ˜ yxmz%{R|}j|R㕎/{Rx † xm‡Úx‘z…žŒ~Rz…Œ~xµ{R| tŽ † z”ƒ…z…ŒŽ/‹ÆŽ † xm † |€Š ˆxk{R|¸ŽˆŠRƒ…z † Ž —’|} žR|¸Œ~z”ƒ…z |€‡ n!p e˜rœ
z” † ƒ”z”R{Rx‘Ž/} np ˜r™ Á |›R‡Ð‡£x’{Rx}jz”‡kz”ƒ Ž/‹œ’xoe ¦ª¬r­ 9 ¬¡®’¬³gJ¤¥ˆ¤jiˆ¦kiml¨§’¥£®’¬ e < ’¥´¤«ª 9 ¦h¥ ˜ ¬
­%Ô 9 ª±¥ ˜ ¬ ! ˆ¥2< q•±rª¥´­$#ˆ¤«ª¥ ˜ yxmzÏ{R|ƒ…z”R|Žˆ{Rx‘Š•Žˆ‹~ŽhŽˆK¹Kz…ƒ”z Ž/‹;x£{|}~|€RãRxo{|¡ŽˆŠƒ”z † Ž —’|} žR|¡Žˆ{RxmŠŒ~|‡
e ! ˜6Š•Žˆ‹“Ž‘Ž‹~|€}~xmƒ… /x£{R|¸ŠR‹jxm»Rƒ…|‡£Žˆ}™
+
^+
3
2
s"
%$
5
76
+
o5
O
("
/
!#"$
% $& ''
(­|
(
+
O+
+
*)
 RR}jxmŠRãRz…}jŒ~z † Ž´Œ“|{ yxˆ‹~| † Žˆ}jŒ~|‹o}~|}}?ŒŽ/Œ~z”}?Œ“z † }oŽˆ}hŽÇ{R‹~ ˆ|€ ‡£ŽˆaR}~|€}ƒ Žˆ‡kŠKŸ
Š4xm}jŒ~}œ yxm‹8}jRŠRŠ4xm‹jŒ!‹~Ž/Œ“ãR|€‹;Œ“ã•Ž/ yxm‹8z…ƒ”ƒ…R‡£z…•Ž/Œ~z”xmà™
| ˌ“|€‹ | R{R‹j| ώˆ¢R™
.+
-,
+
&
à ’§ ¥o¬ ­;=< ª±~i‚®’¥ ˜ ¥ ˜ ±¥´­%±¬rª 9 ¥ ˜ # ˜ ª±¥ ˜ ®‚ioiˆ­$#ˆ< ª ˜ ¬¸®’¬ ˜ Ôr¤«ª¬ ˜ 9 ¬r¦;•¥´¤~iˆª ˜ ˜ ¬r­4®’¥£is;4¤“¬
˜ ¬r­ 9 i‚®‚i ˜ i ˜8˜ Ôr¤«ª¬ ˜9 ¬r¦;•¥´¤jiˆª ˜ ¥*=°)¬± 9 ¥¡®’¬³¬ ˜s9 qR®’¥ ¥´¤«­%¬±¬ ˜ ¬q’¦ki®’¬ ˜ ±r«¤ ªyl¨§’¥ ˜ ¥*¤“¬
¥ ˜ ¦hÔ 9 ¥®’¥ ˜ ®’¬;4¤¬ ¿ª ˜ §’¥Þ±¥´­ ˆ¬r­%±rª¥´­4iˆª ˜ ¬‘ªË­ ˜ ;4ªË¤ji‚®’¥ ˜ ­4i2p¸i 9 q’¤¬~Ø¿i ˜ ¬r4­ ®’¥2iˆ¦r¥ ˜
is;=< ª±~i‚®’¥ ˜ ­4ih¦h¥®’¬s<„iml¨§’¥k®‚i ˜˜ Ôr¤«ª¬ ˜ 9 ¬r¦;•¥´¤jiˆª ˜
/.
S1
"

/
/
n
"
#xWj|³|‡Û{Rz ŽµŽ/}~}~z…}jŒ~|rŸc}j|¸ŽµR‡£Ž¡¢mƒ”xˆ»•Žˆƒ”z )Ž ˆx›{•Žµ| † xmRxm‡kz Žœ’|³Š4xm‹ † xmR}~|€¢mRz…žŒ~|¸ŽµR‡ Ž † ‹ €} † z”‡kx
{R| † xm † xm‹~‹  † z Žµ|‚Œ~‹~|¸Žˆ};xˆ‹~¢‚Žˆz )Ž —’|}œ † 2~Ž/}8|}jŒ~‹~Œ~R‹“Ž/}œRŠR‹jx † |}j}~xm}8|Œ~| † xmƒ”xm¢ˆz Žˆ}€œ’}j|³xmŠŒ~z”‡kz„Ÿ
)Ž/{Rxm}œùƒ”ã|k{RŽˆ‹ ˆx/Žˆ‚ŒŽ/¢m|R} † xˆ‡£Š4|€Œ~z…Œ“z„/Žˆ}™-!x+|€‚ŒŽˆ‚Œ“xœz”x¨/Žˆ‹³žR‡ Ž/‡µ»Rz”|€‚Œ“|{R|kz” † |‹?Œ“| Ž
Š4xK{R|‘}j|‹¸{R|}~Žˆ}jŒ~‹~xm}jxRœùŠ·|€ƒ”x žR| ‘•Ž´Œ“R‹~Žˆƒ ŠR‹j|}~}jRŠ4xm‹ žR|£Žˆ}¸xm‹j¢‚ŽˆRz )Ž €—K|€}³|}jŒ ˆx+z”‚Œ“|€‹~|}j}“Žˆ{RŽˆ}
|‡Úxm»Œ“|€‹ŠR‹~|rKz…}~—’|} yRR{RŽˆ‡£|€‚ŒŽˆ{•Ž/}!}jxm»R‹j|›x‘}j| yKŒ“R‹jxR™
‡£ŽÞ{•Žˆ}6Œ † Rz † Žˆ}|‡ R}jx}~x † xm‹j‹~|rŸì}~|{•Ž gƤ“¬ ¿ª ˜ §’¥®’¬ à Ôr¤«ª¬ ˜ Ö·¬r¦;•¥´¤jiˆª ˜ u=g Ã Ö w´œ žR|}j|
»•Žˆ}j|z”Ž¸|€‡Vxm»R}j|‹?ˆŽ —’|}Š•Žˆ}~}~Žˆ{•Žˆ}T{R|!R‡£Ž{•Žˆ{•Ž³/Žˆ‹~z ()m|ƒ=™3}‡ €Œ“x’{Rxm} † xm‚m|€ † z…xm•Žˆz…}{|!Š‹~|€’z¶Ÿ
} /xRœ‚{R|}j|‚mxˆƒ…’z”{Rxˆ}JŽ³Š•Ž/‹jŒ“z…‹ {R|8{Rz…} † z”ŠRƒ…z”•Žˆ} † xm‡kx¸Ž›Ä ­ ˆ¬ ˜s9 ª ‚iml¨§’¥ © ;•¬r¤ji’±rª¥´­4iˆ< xmkŽ ! ˜s9 i 9 2 ˜s9 ª±~i œ
ŠR‹jx¨’z…{R| † z Žˆ‡ ŠR‹j|€’z”}j—K|€}ŠR‹~| † z…}“Žˆ}€œ ž•ŽˆR{Rx³|€}jŒ ˆx³|‚mxˆƒ…’z”{Rxˆ} {•Žˆ{Rxˆ}ƒ”z…R|)Ž/‹~|}€"
™ 4Æxm‚Œ~R{RxRœ ž•Ž/R{Rx
R‡|€ƒ”|€/Žˆ{x#¢m‹~Žˆ›{R|J ˆxƒ…z”R|Žˆ‹~z…{•Žˆ{R| z”‚Œ~‹~x’{R z…{RxRœ¨|}?ŒŽˆ}ùŒ † Rz † Žˆ}ù ˆx!} ˆxŽˆ}ù‡hŽˆz…}ώˆ{R| ’RŽˆ{•Žˆ}€œ
Š4|ƒ”x žR|kR‡£Ž Žˆƒ„Œ“|€‹~•Ž/Œ~z…/Žh}jR‹~¢m| † xˆ‡ßxm}¸‡£x’{R|ƒ…xm}³z”}~ŠRz…‹“Žˆ{Rxˆ}³•Ž&#Ž/Œ“‹~| Ž™!#|}?Œ“| † ŽˆŠ˜„Œ“Rƒ…xRœ
Œ“x’{Rxm}8|€}jŒ~|}!‡£x’{R|ƒ…xm};}j|‹ /x£{R|€} † ‹~z…Œ~xm}|›ŽˆŠRƒ”z † Žˆ{xm}8䑊R‹~|rKz…} ˆx™
!
q$ 3
$
T)
%$ 2
G
3$
"
0
\)
j"
a+
q$ G
+
G)
"

2
)
G
n
D"
O
G
4)
O$
D"
G)
"
n
G
&"
3$
G
G
ˆÙ

4'?.
2
0
& ‡£Žh} ‹~z…|¡Œ“|€‡£Š4xm‹~Žˆƒ µR‡£Ž † xmƒ…| † ˆx{R|¡xm»R}~|€‹j/Ž €—K|€}³‹~|¢ˆz”}jŒ“Žˆ{•Žˆ} l "! l #$#%#Dl '&.
#{R|µ‡ ‡kxK{x
}~| žR| † z Žˆƒ=™ ι|€‡£Šƒ”xm}o{|P} €‹~z”|€}hŒ“|€‡£Š4xm‹~Žˆz”}k}~R‹j¢m|‡ Rxm}o‡£Žˆz…}£{Rz„m|€‹~}~xˆ}o{Rxm‡ ”Rz…xm}œÆ{R|}j{R|vŽ
!±¥´­%¥´¦ªti œÑ ¬r¦h
¥ ˆ¤jijsJi œÏe ˆ¤rª±rqz< 9 qK¤ji xm !J­ ’¬r­Êiˆ¤rªti œH}j|R{xގ e ­$#ˆ< ª ˜ ¬k®’¬ à Ôr¤«ª¬ ˜ Ö4¬r¦;•¥´¤jiˆª ˜
R‡£Ž (ˆ‹~|Ž‘z…‡£Š4xm‹?ŒŽˆ‚Œ“|{•Ž ! ˜s9 i 9 2 ˜s9 ª±~i % 4Æ㕎/Œ 6•|ƒ…{àœH¼¿¾mÀm¾-&™
‡ ‡£x’{R|€ƒ”xÞ{|oR‡£Ž } €‹~z…|hŒ“|€‡£Š4xm‹“Ž/
ƒ )('& 6Žˆ}j}~R‡k| žR|2Žˆ}6xm»R}j|‹j/Ž €—K|€}} ˆxÞ{R|Š4|R{|‚Œ“|€}c
z™È|ˆ™„œ•Š•Žˆ{‹~—’|}Š•Žˆ}j}“Žˆ{Rxˆ}#z…‹ ˆx‹j| † xˆ‹~‹~|€‹#x yŒ~R‹~xœRŠ·|€ƒ”x žR|6Žk} ‹~z…| ›Š‹~|€’z…}…ˆ|ƒ=™ ‡hŽ} €‹~z…|›{z rŸ
}~| ®’¬ 9 ¬r¤r¦ªË­ 2 ˜s9 ª±~i ž•ŽˆR{x kŠR‹~|r’z”}„m|€ƒJŽv¼¿Âm+ *™ ùxK{•Ž)’z ŽKœŽ2‡£Žˆz”xm‹Š•Žˆ‹jŒ~|‘{•Žˆ}›} ‹jz”|€} † xm‚Œ ‡
R‡ |€ƒ”|€‡£|€žŒ~xâ|}jŒ~x † (ˆ}jŒ~z † xRœ}j|R{Rx`x yŒ“‹~x`ŽˆŠ4|•Žˆ}2Š•Ž/‹ † z”Žˆƒ”‡k|‚Œ~|Þ{R|rŒ“|‹j‡£z…•Žˆ{RxâŠ4xm‹o/Žˆƒ”xˆ‹~|}
Š•Žˆ}j}“Žˆ{xm}œúŠ4|ƒ”x žR|›ŠR‹j|€’z”}j—K|€}!|«¹Ž † Œ“Žˆ}#} ˆx‘z”‡kŠ·xˆ}~}„m|€z”};{R|¸}j|6xm»KŒ“|‹€™
| Žˆ (/ƒ”z”}j|£{|o} €‹~z”|€}¡Œ“|€‡£Š4xm‹~Žˆz”} † xm‚Œ ‡  (ˆ‹jz”xm}›xm»zj| † Œ~z…mxˆ}œ žR|o ˆxÞ} ˆxR| † |€}~}“Ž/‹~z Ž/‡£|€žŒ~|
] |‹j}~ãR|€ y|ƒ…{àœH¼¿¾m¾ *&
z”{ ‚Œ“z † xm}€œRRxm‡k|)Žˆ{RŽˆ‡£|€‚Œ“|³xm}z”{Rz † Žˆ{Rxm}Ž}~|€¢mRz…‹ % ¯|z…¢m|R{
S)
™)
&"
T)
0
T)
7"
G
"
+
"
)
S)
G
)
0
'
T)
%$
T)
G)
+
>"
T
T)
T)
<"
n
G
+
2
}
K ’® ¬ ˜ ±r¤«ªyl¨§’¥ œžxmR{R|}~|ŠR‹j|€Œ~|R{R|³{|} † xm»R‹jz”‹œ † xm‡ÛR|€R㞏R‡ÚxmŠ4xm † x † xˆRãR| † z”‡k|‚Œ“xµä ;4¤«ª¥´¤rª œ
{R|rŒ“|€‹~‡kz”•Žˆ{RŽˆ}ŠR‹jxmŠR‹~z…|{•Ž/{R|} yR{•Žˆ‡k|‚ŒŽˆz…}œ † xm‡kxox2’ᇣ|€‹~x{R|¢m‹~ŽˆR}³{R|ƒ…z”»4|‹j{•Žˆ{R|6xm
ž•Žˆ‚Œ~z”{•Žˆ{|›{|›‹j˜”{x˜c
^+
"
K ¬ ­;=< ª±~iml¨§’¥ † 2jxµxˆ»zj| † Œ“z…ˆx |€ † xm‚Œ~‹“Žˆ‹JR‡ ‡£x’{R|ƒ…x žR| † ŽˆŠŒ~R‹~| † Žˆ‹~Ž † Œ~|‹§”}jŒ~z † Žˆ}Æ}jxm»R‹~|#x
† xm‡£Š4xm‹?ŒŽˆ‡k|‚Œ“x{|›‡ }~z…}jŒ“|€‡hŽ‘Žƒ”xˆR¢mxŠR‹~Ž x˜c
S1
o)
j"
$
K ;4¤“¬ ¿ª ˜ §’¥ žR|¡Ž/ƒ”‡k|‚~Ž¡ŠR‹j|€ˆ|‹ † xm‡ Š‹~| † z”} ˆxkŽk|rmxmƒ… ˆx‘{R|¸R‡Ú}~z”}?Œ“|€‡hŽ‘Ž † R‹?Œ“xkŠR‹“Ž x˜c•|

"
T
O
2$
K ± ¥´­ 9 ¤“¥2<”¥ œRxmR{R|¸}j|¸Œ~|‚ŒŽ † xˆžŒ~‹~xmƒ”Žˆ‹;x † xm‡kŠ4xm‹jŒ“Žˆ‡£|€‚Œ“xµ{R|¸R‡Ú{•Žˆ{RxkŠR‹~x † |€}~}jxRœúŽ/Œ“|€R{R|€R{Rx
Ž † |€‹jŒ~xm}Š•Žˆ‹ /‡£|rŒ“‹~xˆ} t|ˆ™È¢R™„œ ž•Žˆƒ”z…{•Žˆ{R|
r™
n"
| |‚Œ“‹j|o|}?Œ“|}€œTŽ  tŽˆ}~|£R|}?Œ“|hŒ~‹“Žˆ»•Ž/ƒ”ãRx+}~|€‹9(Þ{•Ž/{•ŽPä ;4¤“¬ ¿ª ˜ §’¥ R‡£Ž z…‡£Š4xm‹?ŒŽˆ‚Œ“|Œ“Žˆ‹~| tŽ |‡
Á £
(ˆ‹j|)Žˆ}›Œ ˆxP{z”}jŒ~z”‚ŒŽ/} † xˆ‡£x+m|{•Žˆ}œTŠR‹jxK{ ˆxÞxm 6••Ž/ )Žˆ}€™ 3}µ‡kxK{R|€ƒ”xm}›{R|£ŠR‹~|rKz…} ˆx Œ“‹“Ž´ŒŽˆ‡
x2}~z…}jŒ“|€‡hŽ † xm‡kx}~|{R|‘R‡£Ž † Žˆz¶¹ŽoR|¢m‹~Ž}~|µŒ“‹~Ž/ŒŽ/}~}~|/œÏ ˆxŒ“|€R{Rx † xm‡kxxm»zj| † Œ~z…mx2{R|rŒ“|€‹~‡kz”•Žˆ‹
xm} tŽ † Œ~xm‹~|€} žR|6Ž y| † ŒŽ/‡Ðx£}j| † xm‡£Š4xm‹?ŒŽˆ‡k|‚Œ“x™ÆιKz”}?Œ“|‡+œúŠ·xˆ‹jm|€‚Œ“R‹~Žœ%Ž/ƒ”¢mR‡£Žˆ};‹~Ž —’|}!Š•Žˆ‹~Ž
|}?ŒŽ¡Š4xm}?Œ“R‹~Ž™ | ŠR‹~z…‡£|€z”‹“Ž³{R|rm|«Ÿc}~|Žˆx tŽ † Œ“x›{R|x6}~z…}jŒ“|€‡hŽ› ˆx›}~|€‹ÆŠ4|‹ y|€z…Œ“Žˆ‡£|€‚Œ“|!{R|€Œ~|‹~‡kz”RŽˆ{RxRœ
}~|€R{Rx{Rz R † z”ƒÏz”{R|€‚Œ“z 6 † Žˆ‹#Žˆ}‹j|ƒ Ž —’|}{R| † ŽˆR}~Ž´Ÿc| y|z„Œ“xh|€‡ jxˆ¢mxR™ | }j|¢mR{•Žo‹~|€}~z…{R|µRx tŽ † Œ“xh{R|
}~|¡{R|}j|‚~Žˆ‹³ŠR‹j|€ˆ|‹³x žR|‘Ž † xm‚Œ“| † |µ|µ ˆx † xm‡kxoŽ † xm‚Œ“| † |icùz=™-|/™…œ·|r¹Kz”}?Œ“|€‡ } ‹~z…|}Œ~|‡kŠ·xˆ‹“Žˆz…}#‹j|)Žˆz…}
z”‡kŠ4xm}~}§…m|€z”}{R|!Ž´¹Kz…xm‡hŽ´Œ“z Žˆ‹œ´ŒŽˆ¢8…ˆ|z”}䳊R‹j|€’z”} ˆx y|ˆ™È¢R™„œŽ³ŠR‹j|€’z”} ˆx6{RŽ›x † xm‹j‹ € † z”Ž¸{|#‡£Žˆ † 㕎/}
}~xˆƒ Žˆ‹j|}8xm ŽŠR‹~|rKz…} ˆxk{Rx † xˆ‡£Š4xm‹jŒ“Žˆ‡k|‚Œ“x{Rx‘‡k|‹ † Žˆ{Rxk{R|›Ž † —’|} % 5 † 4ƃ”} ˆ| ,mœù¼¿¾m¾m-Ù & «™
J+

?
O
+
O
G
n
(+
"
2+
$
j+
L+
2
7"
S+
+
+
O
%$
G
n
S)
T
T
)
z8 + 8
Hd·Q¡QT\?W·XTQ
· ¢m|‹~Žˆƒœ’Žˆ}Œ † Rz † Žˆ}TŒ“‹“Ž/{Rz † z”xm•Ž/z”}{R|Žˆ (ˆƒ…z”}~|{R|#} €‹~z”|€}JŒ~|‡kŠ·xm‹~Žˆz”}T»•Ž/}~|z”Žˆ‡Ÿc}~|!Rx6ŠR‹~x † |€}~}~x¡{R|
®’¬±¥´¦;•¥ ˜ ªyl¨§’¥ œ‚xmR{|}~|#z”{R|€‚Œ“z 6 † Žˆ‡ xm} tŽ † Œ“xm‹j|} žR|z” •| † z Žˆ‡ xm}T/Žˆƒ”xˆ‹~|}{R|#R‡hŽ¸} €‹~z…|#Œ“|€‡‘Ÿ
Š4xm‹“Žˆƒ=œˆ}j|R{Rx¸{R|Ƌ~| y|€‹~z…‹|‚Œ~‹~|8|}?Œ“|€}JŽŒ~|R{  † z Ž|8Ž}~Ž xmRŽˆƒ”z…{•Žˆ{R| % 5 Ž ’‹jz”{•Ž ’z…} ²ãR||€ƒ ‹jz”¢mれ)œ
¼¿¾mÀˆ¾ &™
| 9 ¬r­4® r­%±rªti { (´ŸcRxˆ}R‡£Žo‡£|€{Rz”{•Ž£{Rx † ‹j|} † z”‡k|‚Œ“xxˆ–{| † ƒD”Rz…xh{Rxˆ}ˆŽ/ƒ”xm‹j|}{|R‡hŽo} ‹jz”|ˆ™
‡£ŽÞ} ‹~z…| žR|Š4xm}~}j•Ž|}jŒ~|oŒ“z…Š·x {R| † xm‡kŠ4xm‹jŒ“Žˆ‡£|€‚Œ“x † ãRŽˆ‡hŽ/{•ŽÞ{R| ­4§’¥–¬ ˜s9 i’±rª¥´$­ #ˆ¤«ªti ™:#Ž
} z…¢mR‹“Ž³ÙK™…¼‹~|€ŠR‹~|€}~|€žŒ“Ž´Ÿc}j|R‡£Ž³} €‹~z”| ­4§’¥¬ ˜s9 i’±rª¥´$­ #ˆ¤«ªti Œn…ŠRz † Ž™ (ˆ‹~z”Žˆ} yxm‹ )Žˆ}T}j| † xm2jR¢‚Ž/‡ºŠ•Žˆ‹~Ž
žR||}?ŒŽ † xm‡kŠ·xˆR|‚Œ“|}j|‚~Ž † xm‡¡R‡V|‡º}~z…Œ~•Ž €—K|€} ’|!Œ ‡VŽˆ|‹ † xm‡Vx¸|€}jŒ“{Rx6{RŽ¸z… úŽ ˆxRœ‚{•Ž/}
‡µR{RŽˆ )Ž/}Œ~| † Rxmƒ ¢mz † Žˆ}œK{Rx † ‹~|€} † z…‡£|€‚Œ“xk{•ŽŠ·xmŠRƒ Ž ˆxxm+{Rxm}!ŽˆR‡k|‚Œ~xm}8{R|¸ŠR‹~x’{RŒ~z…’z”{RŽˆ{R|ˆ™
G)
T)
<+
s"
&+
0
)
$
)
T)
4
q
S)
S)
7"
)
T)
+
"
O
"
S
3
3
=
xt
Tempo
} z”¢mR‹~ŽµÙ™„¼ Ý €‹~z”|³Œ~|‡kŠ·xm‹~Žˆƒ% ˆx£|€}jŒ“Ž † …z xm ˆ( ‹jz Ž™
D
)
O
| ˜ i¿Ø´¥´­4iˆ< ªt®‚i‚®’¬ † xm‹jŠ·xˆ‹~z Ž–‡hŽ •Œ~•Ž /xŠ4|‹~z {z † ŽKœ † xˆ‡ R‡hŽ–{RR‹~Ž ˆxœ;Š·xˆ‹k|«¹K|‡kŠRƒ”xRœ
}~|€‡hŽ/•Žˆƒœ4‡k|R}~ŽˆƒxˆÞŒ“‹jz”‡k|}jŒ~‹“Žˆƒ=™3ºŠ•Žˆ{R‹ ˆxo‹~|€Š·|rŒ“|«Ÿc}~|/œHŽˆxoƒ…xmR¢mxk{RxhŒ~|‡kŠ·xœ%ŽˆŠ } † Žˆ{•Ž×Š·|«Ÿ
‹…xK{xm}œ·}~|{R
x x t€i’± 9 ¥´¤ ˜ i¿Ø´¥´­4iˆ< ™³Î}jŒŽo}jz…Œ~•Ž /x † xˆ‡µR‡+œ%}~|€R{Rx2{R|µ‹j| y|€‹~z”‹€œ%Š4xm‹|«¹K|‡kŠRƒ”xRœ
Ž † xm‡£|€‹ † z Žˆƒ…z )Ž ˆxv{R|PŠ‹~x’{RŒ“xˆ} žR|P{R|€Š·|€R{R|‡ {Rx † ƒ”z”‡£Žvxm žR|P}~| m|{R|‡ |‡ {R|€Œ~|‹~‡kz„Ÿ
•Žˆ{xm}µŠ4|‹…xK{xm}¡{RxPŽˆRxR™ | } z”¢m‹“ŽÞÙK™ ‹j|ŠR‹j|}j|‚ŒŽR‡£Ž–˜ Ôr¤«ª¬ ˜ i¿Ø´¥´­4iˆ< † xm‡ R‡ Š·|€‹”x’{Rx {R|
}“Ž xm•Ž/ƒ”z”{RŽˆ{R|{R| ž•Ž/Œ~‹~xRœ † xm‹~‹j|}jŠ·xm{R|R{xoäˆ} ž•Ž/Œ~‹~x‘|}?ŒŽ €—K|€}#{RxkŽˆxR™
‡£Ž y|‹j‹“Žˆ‡k|‚ŒŽ#|}jŒ“Ž/Œn…}jŒ~z † Žz…‡£Š4xm‹?ŒŽˆ‚Œ“|Š•Žˆ‹~Ž³Ž³Žˆ (ˆƒ…z”}j|Æ{R|;} ‹jz”|} Œ~|‡kŠ·xˆ‹“Žˆz…} ;x ±¥¿¬ys;±rª¬r­ 9 ¬
®’¬#iˆq 9 ¥¿±¥´¤«¤“¬s<„iml¨§’¥ œ‚{R/| 6RRz”{Rx † xm‡kx¸Ž † xm‹~‹j|ƒ”Ž ˆx³|€‚Œ“‹~|!Ž³} €‹~z…|8|8|ƒ ŽŠ‹ ŠR‹jz Ž y{•ŽˆRxŒ~|‹~‡kx¸ŽˆŒ~x rœ
{R|€}~ƒ”x † Ž/{•Ž{R
| 2Š4|‹§”x’{Rxm};{R|³Œ~|‡kŠ·x % x)¹ ˆ| ’z…R}œH¼)¾ ˆ'7 &
%$
=
T
=
7)
%$ 2
&+
7"
"
2$
0
"
("
f+
S)
)
.
)
T)
m
=
¡
'&
& '& '& '&
=ÙK™…¼-
!
& '& '&
xmR{| ‘‹~|€ŠR‹~|€}~|‚Œ“Ž xŒŽˆ‡£ŽˆRãx{•Ž} ‹jz”|‘| 'Æ
& x/Žˆƒ…xm‹‡ R{ z…x{•Ž} ‹jz”|µŒ~|‡kŠ·xm‹~Žˆƒ™ | }›ŽˆŒ~x † xm‹?Ÿ
*
"!#%$'&)(
!
,+
0/ +
.-
*
2+
.-
1
-
!
0/
0/
$'&
3
T)
)
T)
ˆ7
4'?.
& xt
4
} z”¢ˆR‹“ŽÙ™
‚J
8
Tempo 12
Ý €‹~z…|Œ“|‡kŠ4xm‹“Žˆƒ † mx ‡ tŽ † Œ~xm‹|}jŒ“Ž /x ™
)
+
‹~|€ƒ Ž €—K|€}¡} ˆxáŒ“|€z”}µŠRŽˆ‹“Ž Œ~|}?ŒŽˆ‹µ}j|R‡£Ž •{ Žˆ{RŽP} ‹jz”| hŠR‹~|rKz…}„m|ƒJ|oŠ•Žˆ‹~ŽŽÞ{R| † xm‡kŠ·xˆ}~z ˆxP{Rxˆ}
ŠR‹jz” † ”z Š•Žˆz…} † xˆ‡£Š4xmR|€žŒ~|}{R|¸R‡£Ž} ‹jz”|/œ † mx ‡kx‘Ž 9 r¬ ­4®r­%±rªti |›Žo˜ i¿Ø´¥´­4iˆ< ªt®‚i‚®’¬ } z”¢ˆR‹“ŽÙ™-Ù1
«™
T
T)
7)
%3
T)
\’X
3 r¬ ¤«¤“¥ {|›Š‹~|€’z…} ˆx ³{•Žˆ{xkŠ4|ƒ”Ž{Rz y|€‹~| )Ž|‚Œ“‹j|¸x‘/Žˆƒ…xm‹8Ž † Œ“•Ž/ƒà{•Ž} €‹~z”|³|¸x žR| yxmzàŠR‹j|€’z”}?Œ“xRœ
• Ž yxm‹j‡hŽ
G
o+
)
q+
T)
"
+
&
'& ('&
=ÙK™ ;
.-
#
š Ž/‹“Ž2Ž)ˆŽ/ƒ”z Ž/‹#x{R|€}~|€‡£Š4|Rãx ¢mƒ…xm»•Žˆƒù{R|R‡ ‡£x’{R|€ƒ”xo{R|Š‹~|€’z…} ˆxRœàŒ~xm‹~RŽ´Ÿc}j|µR| † |}j}9(ˆ‹jz”x+Œ“z…ƒ”z Žˆ‹
R‡£Ž6‡k|{Rz…{•Ž6{xµ|‹j‹~xRœ’}~|€R{Rx žR|R‡£Ž6{RŽˆ} yxm‹j‡hŽˆ}‡£Žˆz”}TŒ~z”ƒ”z )Žˆ}T‹j| † xˆ‹~‹~|Žˆx ž•Žˆ{‹“Žˆ{Rx¡{Rxµ|‹j‹~xR™
·fŠ•Ž/‹jŒ“z † Rƒ”Žˆ‹œ4Œ“|€‡‘Ÿì}~|‘ŽÞà ¥´¦kiÞ®’¥ qRi‚®ˆ¤ji‚®’¥2®’¥ ˜ !J¤«¤¥ ˜ u à ! w´œ%Ž Ó¯Ô~®ˆªti ®’¥ qi‚®ˆ¤~i‚®’¥2®’¥ ˜
!J¤«¤¥ ˜ u=Ó ! w´œ%Ž n;iˆª„Ø£®‚ihӖÔ~®ˆªti ®’¥ qRi‚®ˆ¤ji‚®’¥®’¥ ˜ !J¤«¤“¥ ˜ u=nÓ ! w‘|Ž ӖÔ~®ˆªtiop›¥´¤«¦kiˆ< ª„Ø¿i‚®‚i
®’¥ qi‚®ˆ¤ji‚®’¥£®’¥ ˜ !J¤r¤“¥ ˜ u=Ó+p ! w
G
>"
s+
q$
%$
o"
p k # _ * !
$
k
#
k
k

# k
"
#
%'&
"!$#
$
|‡ ’|-,[{|RxˆŒ“ŽxkžáR‡k|‹jx£{|›Š‹~|€’z…}~—’|}!Žk| y| † Œ“•Žˆ‹€™
"
+
=ÙK™óÙ1
(
%'&)(+*
+ 
D
1
1
0.5
0.5
0
0
rk
rk
z8 −0.5
−0.5
tendência e sazonalidade
−1
0
5
10
15
sazonalidade
20
−1
25
0
5
10
1
1
0.5
0.5
0
0
20
25
20
25
−0.5
−0.5
sem tendência
tendência
−1
15
k
rk
rk
k
0
5
10
15
20
25
−1
0
5
10
15
k
k
} z”¢ˆR‹“ŽÙ™-Ù | Œ“x † mx ‹j‹~|€ƒ Ž €—K|€};Œn”Šz † Ž/}8{R|¸} ‹jz”|€}Œ~|‡kŠ·xˆ‹“Žˆz…}™
T)
ˆÀ
4'?.
H\
)
& š Ž/‹“Ž‘ŽŽ)ˆŽ/ƒ”z Ž ˆxµ{xm}8‡£x’{R|€ƒ”xm}J{R|³ŠR‹~|r’z”} /xRœ yxm‹~Žˆ‡Ú|€} † xˆƒ”ãRz…{•Žˆ};{R| ¸} ‹jz”|€};Œ“|‡kŠ4xm‹“Žˆz…}œ’xm‹~z…RR{•Ž/}
{R|o{xm‡!…Rz”xˆ}6| yxˆžŒ~|}µ{z”}jŒ~z”‚ŒŽ/}™vÎ}jŒ“Žˆ} yxm‹“Ž/‡ † ƒ Žˆ}j}~z 6 † Žˆ{RŽˆ}¡|€‡ † z… † x † Ž/Œ~|¢mxm‹jz Žˆ}€œ † xˆ‡ {RRŽˆ}
} €‹~z…|}ϊ·xˆ‹ † Žˆ{•Ž † ƒ”Žˆ}~}j|ˆœ ’||€R¢mƒ…xm»•Žˆ‡Zxm} † xm‡kŠ·xˆR|‚Œ“|€} † xm‡µR}䇣Žˆz”xm‹jz Ž{•Žˆ}Ï} €‹~z”|€}HŒ“|‡kŠ4xm‹“Žˆz…}œ
Rxm‡k|)Ž/{•Žˆ‡k|‚Œ“|
2
G
+
+
&$
T)
o+
T)
2"
T)
2
ù‹“Ž/Œ“Ž´Ÿc}j|J{R|JR‡Œ“z…Š·x‡µRz„Œ“x † xm‡¡R‡ |‡} €‹~z…|}‡k|}“Žˆz…} y|ˆ™È¢R™…œ´m|€R{•Žˆ}9
r™ | } ‹jz”|TŒ“R‹§”}?Œ“z † Ž! XFh h­X#"
QoMzOJY w h#‹j|ŠR‹j|}~|€‚ŒŽµx¡žáR‡k|‹jx¡‡k|R}~Žˆƒú{R|ŠRŽˆ}~}~Žˆ¢m|z…‹~xm}t|€‡ ‡£z…ƒ”ã•Žˆ‹j|}9
{|#R‡£Ž † xm‡kŠ•ŽˆRãRz”Ž6Ž ‹~|Ž
z”‚Œ~|‹~RŽ † z…xm•Žˆƒ=œ4|€‚Œ“‹~|h¼¿¾ ‚¾k|o¼¿¾87mÂKœ·}j|R{Rx»RŽˆ}jŒ“Žˆ‚Œ“| † xmRãR| † z”{RŽh|µŒ~z”ƒ”z )Žˆ{RŽ‘ŠRŽˆ‹“Žh{|‡kxmR}jŒ~‹“Žˆ‹Ž
/Žˆƒ”z…{•Žˆ{R|›{R|µ‡ €Œ~xK{xm}#{|µŠR‹~|r’z”} /xo}“Ž €xm•Žˆz…} } z”¢m‹“ŽhÙK™ % x¿¹
ˆ| ’z…R}œÏ¼¿¾ ˆ'
7 &=™ | }j|¢mR{•Ž
} €‹~z…|ˆ$
œ X M%&#ŽˆŠR‹j|}j|‚ŒŽÇŽ/}£‡k|}j‡hŽˆ} † Žˆ‹“Ž † Œ“|€‹”}?Œ“z † Žˆ}€œÆ‹~|€Š·xˆ‹jŒŽ/R{Rx/Ÿì}~| Žvˆ|R{•Ž/}h{R| Š•ŽˆŠ4|ƒ8|‡
} ‹“Žˆ )Ž % 5 Ž ž‹~z”{RŽ žz”} ²ãR|€|ƒ ‹~z”¢ˆãžŒœà¼¿¾mÀˆ'¾ &=™
'
T)
T)
2)
q$
)
T)
)
G
)
(!
$

)
D
L
} xm‹“Ž/‡Ú|} † xmƒ…ãRz”{RŽˆ}Žˆ}} €‹~z”|€} % ,K{R‡hŽ/àœ ˆÂm¼7& } z”¢mR‹~ŽÙ™ ;
T)
!
*

K(' w YZTZMzhˆœú‹~|€ƒ Ž/Œ~z…/Ž‘Žˆxk’ᇣ|€‹~xh‡k|}“Žˆƒù{R|›‡£xm‹?Œ“|€}#| y|‹~z…‡£|€‚Œ“xm}¢m‹~Ž¿ˆ|}|€‡ Ž † z…{R|‚Œ“|€}•Ž/}
|€}jŒ“‹~Žˆ{•Žˆ}{•Ž ] ‹ ´Ÿ ‹~|rŒŽˆRãRŽc|
+
G
K(' M %*) w ,Y +“Múœ‚R‡£Ž›} ‹~z…|#‡k|€Œ~|xm‹jxmƒ ¢mz † Ž}~xm»R‹j|!/Žˆƒ…xm‹~|€}T‡ €{Rz”xm}T‡k|R}~Žˆz”}€œž|‡ ¢m‹~ŽˆR} ÍJ¬s<”±rªËq ˜rœ
{•ŽµŒ~|‡kŠ·|€‹“Ž/Œ~R‹“Ž‡ (´¹Kz”‡£Ž¡•Ž † z”{RŽˆ{R|¸ŽˆR}?Œ“‹~Žˆƒ”z”Žˆ•Žµ{R| 5 |€”ƒ »4xm‹~R|/™
S)
-. /01
*)
\)
=
x ƒ”z„K‹jx³{R| x)¹‘| ˆ|€ žz”R} % ¼¿¾ ˆ7'&œ yxm‹~Žˆ‡º}j|ƒ”| †† z”xm•Ž/{•Žˆ}T{R•Žˆ}} €‹~z…|}T ˆx›|}?ŒŽ † z”xm (/‹~z Ž/} } z…¢mR‹“Ž
Á ›
ٙ671
r™ | ŠR‹~z…‡£|€z”‹~Žœà{R|€}~z”¢ˆ•Žˆ{•Ž2{R|2YWM3 w hˆœ † xm‚Œ €‡ßxm}¸ŠR‹~| xm}›{Rz (ˆ‹~z…xm}³{R| y| † ãRx {•Žˆ}›Ž † —’|}›{•Ž
5
œ´|‚Œ~‹~|¼ !{R| 5 Žˆz”x!{R|#¼¿¾87¼| {R|r!x¿m|‡¡»R‹~x{|¼¿¾87 Kœ/|€ ž•Žˆ‚Œ“x ’|8Ž#}j|¢mR{•Žœ † ãRŽˆ‡hŽ/{•Ž
45/6 ' 8O 78Xàœž|€žˆxmƒ…ˆ|ƒ”|€z…Œ~R‹“Žˆ}{•Ž6Œ~|‡kŠ·|€‹“Ž/Œ~R‹“Ž›{R|‡ÛŠ‹~x † |}j}~x ž˜…‡£z † xRœž{R|#‡£z…’KŒ“x¡|€‡ ‡£z…’KŒ“xR™
m
m+
T)
G)
Œ
n
&
a
D
>+
O"
f"
>"
9;: <=>@?
š Ž/‹“ŽÞ|€}jŒŽ † Ž/Œ“|€¢mxm‹jz Ž yxm‹“Žˆ‡ |€} † xˆƒ”ãRz…{•Žˆ}¡} ‹jz”|}6‹~|Žˆz”}€œ  ˆx ƒ”z”|)Žˆ‹j|}œ ’|oRxm‹j‡hŽˆƒ…‡£|€‚Œ“|‘}~R‹j¢m|‡
|‡ÚŠR‹~x † |€}~}~xˆ} R…}~z † xm} % ’, R{R‡£Žˆàœ /Âm¼ & } z”¢ˆR‹“ŽÙ™ ;
+
Y+
!
S)
n
‚
˜
"
z8 + ˆ¾
700
600
500
400
300
200
100
0
20
40
60
80
100
120
140
1100
1000
900
800
700
600
500
400
300
200
0
} z”¢mR‹~ŽÙ™
20
œ
O
40
60
80
100
Ý ‹jz”|€}!}~Ž xˆ•Žˆz”} † xm‡ÚŒ~|R{ € † z”Ž *X˜h hX˜QoMzOJY w h¸|
)
$
120
XM% r™
7mÂ
4'?.
2800
2600
2400
2200
2000
1800
1600
1400
1200
0
20
40
60
80
100
120
140
30
28
26
24
22
20
18
16
14
12
0
50
100
} z”¢m‹“ŽÙ™  Ý €‹~z”|€}}“Ž €xm•Žˆz…}
J
)
$
150
'
w YZTZMzh|
' #M %*) w Y +
200
M r
™
160
& z8 + 7¼
650
600
550
500
450
400
350
300
0
50
100
150
200
250
300
350
18.5
18
17.5
17
16.5
16
0
20
40
60
80
100
} z”¢mR‹~ŽÙ™67 Ý ‹jz”|€}! ˆx‘|}jŒ“Ž † z…xm ˆ( ‹jz Žˆ}
)
O
120
140
Y2M3 w h¸|
160
180
415 6 ' O 87 X r™
7
4'?.
m
& 200
180
160
140
120
100
80
60
40
20
0
0
50
100
150
200
250
15000
10000
5000
0
-5000
-10000
-15000
0
50
} z”¢ˆR‹“ŽÙ™
‚J
100
Ý €‹~z…|} ˆx‘ƒ”z…R|)Ž/‹~|}
)
n
150
' @X +/7iS“XFh¸| w )M r™
200
z6 r.
. 7mÙ
K(' X + 72S X˜hˆœR‡hŽ¯} ‹jz”| ‡µRz…Œ~x † xmRãR| † z”{RŽœ}~xm»R‹j|Px^žáR‡k|‹~xǎˆž•Žˆƒ{|P‡hŽ/ † 㕎ˆ}£}~xmƒ”Žˆ‹~|€}
x † mx ‹j‹~z…{•Žˆ};|€žŒ~‹~|k¼ ˆÂmµ|‘¼¿¾ˆ¾mÀœRxm‹jz”¢mz…•Žˆƒ…‡£|€žŒ~| † ‹~z”Žˆ{•ŽŠ·xˆ‹ xmƒ |‡½¼¿À ‚ÀcR|
T)
L+ 8
„
2
w )Múœ žR| † xm‚Œ ‡ ˆÂˆÂ–xm»}~|‹?/Ž —’|}£}~z”}j‡£xˆ¢m‹9( 6 † Žˆ}k}~xm»‹~|+x¯Œ“|€‹~‹~Žˆ‡£x/Œ“x žR|PŽ/Œ~z”R¢ˆz”`Ž
† ”z {•Žˆ{| ~Žˆ·Š xˆR|}~Žk{R|!xm»·|/™
K
„"
G)
"
- >
Î }jŒ“Ž+áRƒ„Œ“z…‡hŽ † Ž/Œ“|€¢mxm‹jz Ž † xˆžŒ ‡ß} ‹~z…|} † xˆ‡½R‡½|€ƒ”|€/Žˆ{x+¢ˆ‹“Žˆ–{R|‘ ˆx2ƒ”z…R|)Ž/‹~z”{RŽˆ{R|ˆœ ’| yxˆ‹“Žˆ‡
¢m|€‹“Žˆ{•Ž/}!{|›‡Ð‡£x’{Rx‘Žˆ‹?Œ“z 6 † z Ž/ƒœKŽkŠ•Ž/‹jŒ“z…‹8{R|¸| ž•Ž €—K|€} † Ž Œ~z † Ž/} % š|€z…Œ~¢m|2|€Œ#Žˆƒ=™…œ%¼¿¾m¾ 3& } z…¢mR‹“Ž
ٙ-1À r™
| ŠR‹~z…‡£|€z”‹“Žµ} ‹jz”|ˆœ•{|}~z…¢m•Žˆ{RŽ‘{| 415 X x YTWO 78Xàœ ¸R‡hŽ} ‹~z…|³{R|€Œ~|‹j‡£z…˜”}?Œ“z † Žµ{R|€ˆ|‹~Žˆ} † xmRãR|«Ÿ
† z…{•Žœ}~|{RxŠ·xˆ‹¡|r¹K|€‡£ŠRƒ…xޏŒ~z”ƒ…z )Ž/{•Ž+ŠRŽˆ‹“ŽÞ‡kx’{R|ƒ”Žˆ‹¸ŠR‹~x † |€}~}~xˆ}µ»Rz”xˆƒ ¢mz † xm}y|ˆ™È¢R™„œŠ·xmŠRƒ Ž ˆx+{R|
‹“Ž/Š·xm}~Žˆ} «™8Î}jŒ“Žh} €‹~z”| † ‹~z”Žˆ{•ŽkŽkŠRŽˆ‹jŒ~z”‹{•Ž‘| ž•Ž ˆx '& # '& +
- '& /rœ4|‡ žR| # # |
(
(
# ™
šŽˆ‹~Ž¡}~|€¢mRR{RŽµ} ‹jz”|/œ † 㕎/‡hŽˆ{RŽ¡{R|S“M + w +Tœ yxm‹~Žˆ‡ ¢m|€‹“Žˆ{Rxˆ} ˆÂm¸/Žˆƒ”xm‹j|}Ǝ6Š•Žˆ‹?Œ“z…‹J{•Ž›| ž•Ž ˆx
{R|!ãR|xm '& # - &! '& !´œžxm{R| # # œ # # # # œ’Ž ! ž•#Ž "$! %"úŽ &'")(*")+•Ž &'
',.-j˜$ &/ ¢‚Ž/' !0!1" Ž +' %( &'"$!23-0"…»R' ( " 4+' -0,£Ž 56(* ,ß' ,.& !17"$98•Ž &'- 9"”¢m•#Ž 5Ž # «:œ & ,;&'2Ž
&'" 6(' 5<2Ž -;=
Ž 8/- 7")! R™
T)
S)
n
3"
S)
S)
%$
3
=
)
3"
T)
+
m
=
)
T)
"
3
,"
J+
a
3"
g"
q
3
+
T
G
> @? =A
CB @A :D
EF&' !G!H, I20F&' !J& 8'- 7"$! K8'L -12 ,M&'8'-0")+'()8'"$N& PO L ! RQ 8 -0" I+'(*"$L !H&'K8'L !0!0L &'K! - O'!0L &L !S+' %O/23O'-1'T | !0!1O', RU ! V L !0!1"$, V O L !S(* +'&'" IW ! O (* +'&'"$(I"$+'L -3L ,XY8'L !0!0L &'Z! - 7 ( 5$")&L !@+/ %OF23O'-1'T
| K5)+'[&L !J\'5<23"$,YL !6& *(]L#&L !H7*(#-0"$ !H20"$8^!_& , `23&'!H(* +P7 +'(I"$+'L "$!J8L -0LaLcbJd_e % -3L ,
& ! +f7 5)7"$&/!*TKg h +f23- = !12 ! V "),Y8^-2iLY& !123L (]L#-N&'"$!j, `23&'! V lk <nm$o*p qZr`s 9ut ! ­; t sr`sv`mwpˆ<
x k !Ey Lc, 23&'5)["zLN& { t }|r`s/~m€s/o x { |y V PO ! -3 K& !1(*-0"<23! ,X8^-1, +'-J& ! [O'")&L/T
'
)
T
"
+
"
%
T
("
T
+
)
\)
+
\)
"
1D/
0
‚
)
„ƒG… ‡
† -Hƒ „ƒjˆ
1
,C&'!;,Y‰`23&'!h& bJd_eX,YL ")! ,Š7 [fL‹‰9Œk ! V 23L ,c^‰*,C(I+'Ž (*")&'Œ8^-Zt < 9‘’ m€s 9 r`“3o V
” O ! ( +f23-0L ,•& 2 -0,;"$+L &'L !–(*L -3L#(I2 -)!123")(]L !—&L;!0‰I-0" #V (I,;Y! 0LZL `Q "$!2 I+'(*"$LY& ˜ L (I20- !
„u™`šI›œRŸž: ¡¢š`£¤¥ašI£¦¤:§w¨1©¨0©iª}¨1©I«`¬I­u®F¶E¯w°‘±² `šI²³š´¯‘ µ¶uš·±‘¸0¯JŸ š`¯º¹3»`¸1£8Ÿ#¸1£¼œ´²@¸0¡¢½¼¶1¾Rš—¡œ´œI¿À°º½»]½¡œ`¡¢¸H¯‘š`£œR±„»]½œ
²´œ@¿ušII°}œRÁI¸²Â¡¢š@ ·²@¸±ºš@¸6Á`±ºW Ÿ#š*¯„¡¢¸6²´œR¿}›œI¯„¯wšI£¼œ`±‘¸0¯·]¿ušI›¸0¿u½¡œrŸ#¸1£š*¯Ã·²³¸1±‘š*¯„¡¢¸6¥ašI£¦¤%®
!" # %$&'(
! # ) *! # 1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
150
200
1.5
1
0.5
0
-0.5
-1
-1.5
0
+
50
100
"$[O'-0L-,/T/.102F‰*-1" !´(]L3 20"$(*L !&4 45658769 1:<; 7 5 & =6>
+6? +@RT
1
# " # - & r`s `sv`mwp O o*p t s^p nm fp r V ” O !3 o*p qZr`s t @—!0/- !–7 L#5$- !Ÿ8L#!0!3L#&'!*T
! ˜ - IŸ(* ,Y8'OF2iL (I"$+L#5 V ! -6L !2iL +f2 ³
!0‰I-0" !—!3L I+L ")!*T ,;& 5)cL !  & ( ,
&
2
5
('&
&
#.-
&
8
+ ,
#
"!
#%$
& & u
& & & % &
&
& & & &
-
+
-
+ ,
#76
% &
&0/1
#.4
/& "$!120"$+'[ O'"$&L#!&/-0O $&'L#23-0L¢7 ‰*!c& O',YL9,;‰*&/"zL4 p nm 
7#L +f2iL 1!148 -j! -N!0"),Y8'5 !S& O'!0L - V - ” O - -N8^O'(I
(]L , 8/- 7")!0W !6& (*O'-23Ÿ8/-3L I V ,8L#-123")(*O'5$L -E(*,
L =(I5zL O'!1O'5zL#&' L )-1"$&L )")! Ž I 5 —-0"$[ ŽP2 V . 0
!* # $&
/ + ,
-
/
,
-(
+
- ( 4
+
/
(
4 ,FT @
(:
5 9
/<;
32
*+
(
/ 2
/ 5
6
(
32
)(*
'&
(
(:9
, ” O && +' 2iL Âk nm$o*p qZr`s t t sr`sv`mwp 8L -3L 8 - $&' V &KL !120"$,YL#23"<7 L‹8L -0L L
r`s `s v`mwp V &_L !123"),ZL23")7#L o*p t s^p pv t “Ÿo*p t s^p T
!12 ,;‰I20F&/ `Q "$[ ” O ( -120!Ÿ8L - , 23-1!j! 0L , "$+'")(*"$L 5$, +f2 L]7#L 5)"zL &' ! V (*,;4L !Ÿ(I+'! U
")20!0Ž V
2iL#+P2 !G&'a,;& 5) 4 V @ L ! !120"$,YL#23"<7 L#!_"$+'")(*"zL#"$! & (]L#&L(I,;8 + +f2 –L + . T j!N(I+'!2iL +f2 !!3 +'-1,ZL#5$, +f2 & 2 -1,Y")+L &L !ŸL#23-0L¢7 ‰*!& 8'-1F( !1!0!& r`s p m p  r 
r`“R“ t VF , ” O L,Y")+'"$,;" *L ] –&' -0-1K‰Sa  (`23")7 K8 -1! [ O'"$&'/T –,YLaL# -1&L [ , &'" ˜% - +f2 ‰
O/20"$5$" ]L &'LS8L#-3LŸL ! !120"$,YL#23"<7#L ! ")+'"$(I"zL ")!„&'!6(I,;8 + +f2 !*T L -3LNL ! !0‰I-0" !6+ N!0L * +L "$! V +' -0,YL 5 U
, +f2 O/20"$5)" ]L#, U ! !³7#L 5$ - ! # T –h(*L !0=& !1‰*-1" !—!0L *+'L "$! V ‰L (I+'! 5$ŽL#&'
V
O', ! ” O ,ZL=,ZL#"$! 5zL ^-3L#&'
0
,
>=@?A
D5
FE
H
G
-
(*
4
CB
2
I
6
KJ
*N+ O
P
S
T U
WX
,
2
#
Z[$
#
1^`-
+ a
1^`
a
9
` /
1Kc-
+ a
9
1Kj
1
5
gKhTi
ef
`
#
*
gKhTi
e
#
e gKhTi
1
5
#
*
e gKhTi
f
m
g hTi
K
1mn/1Kj
e
o
* ^
1 klklk 1
e
o
1Kjp1
1
gK
e h0i
7d'd0d
o
*
1^klklk 1
1
+ a
9
4 ,FT @
/
a
9
1mn/1Kj
f
f
d'd0d
9
1^klklk 1
*
e gKhTi
1Kj
f 1
c /
a
9
`
4 ,FT @
1^`
#ba
9
5
^]__(+
G\
9
1^`
RQ
Y
#
,
2
WV
0
T
#ML
m
gKhTi
*
f
4 ,FTrq @
1m
gK
e hTi
m
+'& & +' 23LŸL–,;‰*&'"$LS&/! 7#L 5)- ! 8L#-3LjL !2iL * V ! +'&' j+P\', -1
(
, Q "$,;Z& h !12iL *W !(*+/!0"$& -3L#&L !*Tcg - L 5 *L - ” O 8L -0L4L !120"$,YL#23"<7#LZ"$+'")(*"$L 5:&L‡2 +/& *+'(I"zL V
(* +P7 ‰*, RQ ")!120"$-´8 5$=, +' !´&'OL ! !2iL IW !S(I,;8'5 2iL !IT
ts
}|
uv#
y
$xw
N
*
(
`
v
w
1^`
`
v
(
1
(
9
%
9
9
T
9
¸1±‘²@š´¿ušI›¸0¿u½¡¢š@¸²Â½¼ÁI£ 0¯ #šI±
€
{z
9
‚ „ƒ
À®
W…0†ˆ‡'‰‹Š[Œ‰ŽŽŒ‘’†ˆ†”“Ž†
K~
!" # %$&'(! # ) *! # ‚ …:† "! „ƒ#ƒ$
‘V ” O ! L ! "$LY+PO', 8'-0 U
ŸO/23-1Z,;‰I20F&'Y8 8'O'5zL#-–& bJd_e ‰KY& Y{ | Q &% + P")+'! V
( !0!1c")2 -3L23")7 8L -3LL! $+f2 ! & 8L &'-1W !³L8L -23")-J& &L#&'!HŽ'"$!2 3-1"$(I! VP`Q ")[ "$+'&/ 2iL 8'L !G(I,;
Lc(]L#-3L (`2 -1" *L ] ˜ -0,YL 5 &/h!0"$!2 ,ZL 4%/2 + ]#h& O', ,;& 5)@ V !23"$,YL * c'& !´8'L - , 20-0!³L
5 L !0!1F(I"zL &/! L;!1OL;8^!2 -1"$-G7 L#5$"$&'L ] 4 + "$[ O'-3L ,FT @RT
\
#
(*
KJ
q
+
T K
H
*
Obtenção de um modelo
Estimação dos parâmetros
Validação
(O modelo é adequado?)
Não
Sim
Previsão
+
"$[O'-0L-,/T 0 _-0( !1!0Y")2 -3L#20")7 h&L;, 20F&/5$[ "zL { | jL#+ *
X
I
KJ
#
L
"<23!0(iŽ V
)(*
.
*+
T
, 20F&/5$[ "zL& { | 2 , (*,; 7#L +f23L [ ,C8'-0")+'(*")8L 5´ ˜ L (I20 & ! -Y'L !123L +f2 8'- (*"$!0L
!0 '- O',ZL‹[fL ,YL‹L 5zL#-0[fL &'L‹& !1‰*-0" !;2 ,;8^-3L ")!*T – +f2iL +f23 V 23-1+L U ! &'" ˜ )(*"$5G(*+/(*"$5)"zL -h !
8L - , 23-1!N(* , 9,;& 5)4"$+'")(*"zL#5$, +f2 (*-0"$L &'(' ,*),+.-/+L ” O.)10.24352768+L7+25696372lL7+ ” O.-;:<-/+256>=
-ºT?) T V 2A@*2B+.),C/2ED<)>@F+)G6H)>:9IJ)>:<-;2+-/K]LL@*),0MD<)8:H),3B-/6NDO2A2O V I.-;25:NL7-;0.+L V [email protected](@G2+.),C/2QK,:<-$L7+.2'T
R27:2OD<:<2SCzLL+.2 V LTK>250.6NDO:1O ]721+.)NO@U@G2+)>C/2V) Q -$[7)2cO.6<21+.)NO@U),6<IJ)>K>-$L7C/-;6HD3L V 6H)>0.+21D3L7@c^‰>@
@YL7-/6) Q -$[5),0MD<)9)>@WDO),:<@G256K>27@*I'ODiL7K,-/250LL-/6 ” O.)X256@;‰,DO2B+.256+) p nm$o*p qZr`s tT
Y@G2+.),C/2Z+.),6<-$[70L7+.2Z+.)Œk\[]O^ k_ V ‰`K,250.6NDO:0O /+.2 LaI'L7:HD<-/:b+.)‹O.@YLaK,25@c.-;0L *72ZC/-/0)]L7:
0.-cDiL+.)d3#L7C;25:<),6eIL76<60L7+.256 V KiŽL7@YL7+Lf+.)K>25@GIg270.)>0hDO)@ki t
[ r
j “3rioio`m p x k[ y T"k L7@K ‰,@lIg2B+.)>:
) Q -;6HDO-;: V -/6H25CzLL+L7@G)>0hDO)92Om)>@nK>250 1O.0hDO2QK,25@o2EK,25@*IJ250.),0hDO)cLL0MD<)>:H-/25: V O@ZLGK>25@c-/0L *72GC/-/0)]L7:
0.-cDiLS+.)9)>:H:<256ILL6<63LL+.256 V +)>6<-)[50L7+'LG+.)9K,25@*IJ250.),0hDO)8^4kpT
6H6<-/@ V 2@*2B+.),C/2@[5),:3L7C V Ig2B+.)q6H)>:r:<),)>6HK>:<-cDO2K>27@*2´O.@s@*2B+.),C/2tu9vstSwyxzO{8| V 6H)>0.+2+.) 0.-;+.2
IJ25: 0
O
Y
H
X
K
|
RQ
O
} ~€s‚*ƒ … „ t ~‰ˆ ƒ … Š vŒ7 ~‰ˆ ‹
‡†
‹<†
ŽHEš´½¼ÁI£ 0¯‘R’ H“ ‰” –•• ˜— R™ ‰”
š ›— >” ;R— N” ®
œ< ¿u±
ž`½¼²@š@½ÁI£ 0¯rŸ* ¸_¡¢¸1¯‘½ÁIœ³š³°‘¸±º²@šš — ¡”R— N” ®
a
y
‚
… “
‚
‘ ‹† ‘
ˆ‡
‘
ˆN… ‘
†”‰Ž…R‘ 
“ ‡ 
“ ‡ 
y a
`
Œ
y
‘’†”‰
‘’†”‰
`
‘
‘
4 ,FT . @
!" *
&)! * # !"
## # # q
)>@ ” O.)Sx )8{ +.),0.27D3L7@ L*25:H+.)>@n+.256K>25@GIJ250.)>0hD<)>6k[ )G^4k V t )Sv ‹ 256K>2B) K,-/)>0hD<)>6\+.276
@ 2+.),C/2566k\[ )^ k V 6<),0.+.2 ‚ O.@ 3#L7C;25: K,250.6HD3L70hDO)#T 6HDiL9K>270.6HD3L70hDO))256qK>2B) K>-/),0hDO)>6+.29@G2+)>C/2
G
63L2 )>6NDO-/@YL7+.276cLLD<:3L¡3‰,6T+.)ED0‰>K>0-/K]LL6T)>6NDiLLD /6HD<-/K*L76 4 ) T¦['T V @Y‰ DO2B+.2568+)E@ /0.-;@*256 ” OL7+:3L7+.276 @`T
@G),DO2B+.25C;2[5-$LSD3L7@c^‰>@ K>250hD<)>@GI.CzL‡L*Ig256H6<-).-/C;-/+L7+)V+.2ZO.6<2A+.)8D<:3L706 ˜ 25:H@ZL IW),66H2.:<)S276\+L7+.276
25:H-$[5-;0L7-/6 4y)#T['T V D<:3L70.6 ˜ 25:<@YL *721C/2[fLL: ;D<@*-;K]L @RT
y
G
O
"!$#%&
6<2A+.)SD3‰,K>0.-;K)(769-/06<I.-;:*(7+.276\0+( ,(LD-'.:<) )(bI+(7:-(.(0/2143 K,25@*) >25' 0.2 @F+.256(70.276X27-;DO),0hD6(87
K>27@ 2aD<*: ( 9 (7C$Ž.2Z+.;
) : (7IJ)>+.),6m) + (7:0J)>: . 7250.+.) [
<= o ˜ 25:*(7@ 'DO-;C/- &(7++(76EI+(7:*(ZI.:H),35),:
60‰,:<-;)>6f)K (37D<-/&K (76+.),D<)>:<@G-/0 /6HD<-/&K (7&6 >@?)X-/0 /K>-;2979(L6fD<)>0hD6(LD<-;3A(76+.)(7I.C;-/K)( ]72S+.)S[
<—k o (721@*),:<K)(L+.2
J25C/6H-/6H*D (\:<) 35)>BC (7*: (LD
@ C6<E) (7BC F72+.)>-6 (7Ig270M*D (7+.25-: (7&6 7B6<-c*D '+( ]72 ” '.)f6<) ˜ 25-I.:H25F5:<),6<6H-;3A(7@G)>0hDO))>61+(LD<)>0.+.28>
R27:") G)>@GI.C/82 7 S0.21-/0 ;K>-/2V+.25E6 (70.2760.2435)>0h*D (87 2FŽ.250.)Ig),-: F
:<) ˜ ),:<
) (S-/90 (7I.C/-;)K ( -/C/-;++ (7+.)+.276
@;‰,DO2B+.256),6H6D ( D /6NDO-;K>256K>270M37)>0.K,-/2590 (7-/6'76fI.:<) 3-;-6 HB)>6f+.)X&K '.:NDO2EI*: ( ,2*+.276fA3 (7C;25:<),6f),@•g27C/*6 (I> *: (87
)>0hD3792 7 3h3-;2 ” '.)m256*@;‰,D<2+2561+.) p nm$o*p qZr`s t )>-: (7@-/0)K (7+I ( >)>6*+.)(+.),D<)>K,*D (7J
: (L6*IJ) ” '.),+0 (76
3A(7:<B- ( &HB)>68+.)QI.:H) >2 +.276SI.:<2B9+ 'D<256 +0 (L0.K>),-/:<276S0.2 +.K- (L( +.K- (87 '6HDO- )K (L0.+.A2 C6<
) (76H6<-;@ M
2 '.6H2 +.)
0.24A3 (76 ˜ )>:H*: (7@G)>0h6D (L6f0)>6HD<)9+.25@ /0.-;92 >
(7I.C;-/&
K ( ]72m+.) [ <
N,OA+I (L*: (M( I.:H),3B-/6072 )>0h3725C;37)AD<2+0
2 '.@ K>250 '0MD<2 +.)b),*D (7+I (768K>25@G2 0P(
(70 LC/-/6H)V9
+ (Q60‰>:H-/)8D<)>@GIg27*: (7QC 7J2bI:0"‰ CI.:<2BK>),6<-6 (7@*),0hDO2b+.256++ (7+.256 7R(E),6<K>27C$+Ž (Q+.2b@G2B+.)>C;2*0.) '.:<27+0 (7SC 7
2*D<:<),-/0.2G++ (*:H)>+.)VT
) (1U3 (LC/-/9+ ( ]721+.2*+.)>6H)>@GIg),0'Ž.2Q+)>6H*D (8> f),KC (LD<-;A3 (7@G)>0hDO)X'G)>6<K,25C$9Ž (*+.2*@*2B+.)>C;92 7
) G-;6HDO),@ +.-c35),:<6<276DO-/IJ256+)V
[ <
N,OV+I (76<6 ;37)>-/6 +.)6<),:<)>
"
@ (7I.C/-;)K (79+ (76 ' /2143 7K>25@G2S6<) -(7
@ (76f[ %{ V O
/2FŽ.-r),W
D (7QC >X7
2 'Y(76GE[ <f
[ O fC$.:H-/KiŽh)D 7 7)>@Kg25-: (0( 5
@ (7-/25:HK- (A+.256S),6H*D '+.256S25ID<)QIJ)>KC (L6
[ <=ZO ?k (790 F + -/60Ž -;K [7 ,]= \ 27:HDO) 9),WD (7SC >^7
= + (7-: (7++ ()_ `\³+Ž (LD )>C/a+ 7 . >
6H*D '+.256ZŽ ” '.)(+I (7:H)>K>),@-/0.+-/)K (L: ” 'L
) (76Q
[ <J=RO *6 b7;
2 (761
@ (7-/6S-;0.+.-/&K (7++ (76S9I (7*: (c(d(70 7C;-/6<)
+.2SK,25@*IJ25:N6D (7@G)>0hDO28+.256@G)>:<&K (7+.256 +0 (70.K,)>-/:H25&6 > (7+I (7+52 '.*: ( B-;&6 7 2B+I (70.52 '++ ( M-/6
) e27D<6<K- (L6
,
'D<-/C/- )(7@&
[ <J=ROf9I (7*: (f(\I.:H),3B-/-6 b72+.)I.:H) ,256q+.)I.:H28+ 'DO256 +0 (70.K,)>-/:H25&6 77K>25@ :<)>6 '.C;*D (7+.256 )>0.K,25*: ( -(gC
+.25:H)>6 > f@W)>6N*D '.+2*+.276 ;0.+.-;K>)>6´J25C;6<-/6N6D (76+2G@G)>:H)K (7+
2 hf'+(LKC (i:R'.@G9I '.&: 7:H),37)>C/U2 ' ” '.)X)>C;)>@G)>0hDO276
+.)SDO-: ( + (7C)Ž.2A-/0hDO),:<),6<*6 (L0MD<)>6XIg2B+.),@P6<),:V2DO-/+2566<),j
@ '.
@ '.6H2mk) GK,)>6H6<-;372 +.)G++ (7+2569+.2A@*),:<)K (L+.2
2 ' +2EK>270'Ž.)>K,-/@G)>0hDO2E+.)>6NDO) lm(72 R2 ZŽ 7
5
> n'DO:H256&
K (76<276+.)T-;0hDO)>:H)>6H6<)T-6 b72Q:<) ˜ )>:H)>0.K,K- (7+.276
IJ25: + :<)>-;6<C;)*J)>0 ) -/I.IJ)>:
7r),@
” '.)1256:<),-6 '.Cc6D (7+2562D<-/+.2566<)1:<) 35)>BC (7*: (L@P-6 '.IJ)>:H-/25:H)>6 (7276
2D<-/+.276Ig25::H&) F5:H)>6H*6 b72GC/-;0.)) (7: >
IJ)>-6 (7:b++ ( @ (7-/25:G+I (7:NDO) +.276b)>6H-D '.+.25.
6 (L+.25I*D (7:<),@ [ <=ZO"7SŽ o(U'D<25:<),.
6 ( +.) ˜ ),0.+.)>:Ao
2 '.6H2
+.)52 'D<:<2 DO-;Ig2Z+.):<),+.)>6 >hNŽ.276D (L0 )(7+ ) 6<) '.6 K,25KC ( J25-: (7+.25:H)>6
(7: F5'@*),0M*D (7@ ” '.))>6N6D (
(7: ” '-;DO),K,D '.*: (X+0 b728IJ)>:H@*-cDO)2D<)>::<),-6 '.Cc6D (7+.276 ¡37)>-/6 7IJ)>C;2 ” '.)6<)6H2K,25:<:H)>-: (7@ +.,) '@ U2 'DO:H2XD<-/IJ2
'
ZY
> (*
+
q
T
N
N
X
p|
(**_N+
K
|
N
G
^
O
p
D|
L

(***+
ˆ
(**
}#
V
&
ŽJ
( **
+
(**
P#
(**
K|
G
+
D|
0
X
NJ
V
J
P
L
(**
#
X
(**
+
+
O
D|
> (**
K
|
F ( **
+
+
!" # %$&'(! # ) *! # .
+.)G:<),+.)>674(76G[
<f[
O"7 ” '.)(7I.C/-;K)(7:-(7@ 'AI.:<) 3B-/6*bL2 ++((K)(7:F (m+.)P'.@ 6<-;6HD<)>@((),C$‰>K DO:H-/K>287R2DO)>0+.2
)"GK,)>C/),0hDO)>6:<)>6 '.C;*D (7+.256> )>6'.C;D*(7+.256-/+ >0hDO-;K>2566*bL2*D6(L@c ‰,@(7I.:H)>6H)>0hD6(7+256IJ25: C).:<-;KiŽMD
7
) (L6E[ <J=ZOT(LIg),0+(76Ig2B+.),@UDO:-(LD6(L:&7),@W6<-;@T'.CcD 70.),297B)"GK>),:HDO276++(S61‰>:<-;)\DO),@*IJ25:*(LCS>
” '.)9K>BC (7@ ( ” '
C).:<-;KiŽhD K>270.6H*D (L6D (n(L-/0.++ ( ” ') (76
[ <f
[ OD ,@ (A3 (70h*D (UF5)>@ +.)IJ)>:H@*-cDO-;: ( ˜ 25:<
@ ( )bL2+.) )>6H*D (7+.256 +.)
@G)>@ 35:<B- (87 '.6NDO- )K (70+.2 (L6<6<-;@ 296<&) ''.6<2V+I (7-: ((I.:H),3B-/-6 b728+.)K '.:HD<2VI.-: ( >2 4yA) > F8>X7B+0 (9-/+.),0MD<- &K ( )bL2
+.) 'IG256X+.)1DO: ˜ &) F52 @">P\ 250h*D '+.92 7‘2m),6H*D '+.2m),@*I /:<-;K>2b+.) W(7C/BC (76P
) ?25: g0.),:
. K>270MD<*: (7[
I HB)
)>6N6D (7
6 ( :H@ ( &HB)>&6 7(72(),3B-/+)>0.K,K- (7: ” '.)E276X@G2B+.)>C;256 N\[ +0 b72 C;-/0.&) (7:<),&6 7 ˜ 25:H0.)>K,-/+.2569IJ)>BC (76TE[ <J=ZO"7
(7I.:H)>6H)>0h6
D (7@o),
@ F5),*: (7QC 7.:<),-6 '.Cc6D (7+.276-6 '.IJ)>:H-/25:H)>E6 (72562D<-/+.276Ig25:3 7:H-/256dDO-/IJ256+.)T
[ <fE[ O">
\ 25@GIg) DO- H),6R+) I.:H),3B-/6 b792 77K,250 ˜ :H250h6D (70.+2X
[ <
N,OK,25@ @Y‰ DO2B+.256eDO-: (7+.-/K,-/2590 (7-/6r+.
) /2143 7 :H)>IJ25: C
D6(L*: (7@P
@ (U'.6 4 U) > F9>X7‘K>27@*IJ),D<- )bL2
L( M:<-;+
+ ( M-/6 7 . @\);g270.69:<)>6 '.C;*D (7+.256 4yA) > F8>X7eK>27@*IJ),D<- )bL2
+.) 28(70h6D ( + ‰ ),B- F5),0.+ `e)>:<61Ž.)>0 ˜ )>C/a+ 7 @k> f2 I.:H-/@G)>-/:H2A)K (76H92 7 2m@ (U'`+.)>6H)>@GIg),0'Ž.2 ++ (L6
[ <
N,O K>52 'L(*+.) 35)>: C–6HU) 7 I:<24A3 (437)>C;@*),0MD<U) 7a(7
2 '6<2Q+.)X60‰,:<-;)>6@ '.-;D<2GK '.:H*D (76 4 (*
@ (7-/27:<K- (VK>25@
(
2.6H)>:NU3 ( &HB)>6 @k>kR2B++ (¡3BK- (87 K,)>:HD<256f)>6H-D '.+.256+.)>@G250.6NDO-: (7*: (7@ ” '.) (76E[ < N,OTIJ2+)>@oI.:H),35),:6D bL2
J)>@&U2 '(L-/0.++ (\@G)>C)Ž.25: ” 'W) (I.: LDO-;)K (f(7C;-/K,)>: &(7++ (90 (9@G),D<2+25C/52 F7K- ( 75+I (7-: (3 L:<K- (L6 +.)>6N6D (7661‰>:<-;)>6 >
R25:k) G)>@GI.C/92 7k (L90 FS) + -/61Ž -/K
, 'DO-/C;- &(7*: (7@ [ <J=ROX9I (7*: (TI.:H),37)>: 60‰,:<-;)>6DO),@*IJ25-: (7-/6
+ (9K>25@GIJ),DO- )b72 ;7MK,25@*9I (7*: (70+.29256d:H)>6 '.C;*D (7+.2562D<-/+.276 3B- (X@G2B+.)>C;2526 N\[]O.
+
^ Nf7MK>25@ (76
[ < NnOn(
˜ 25:H0.)>K,)>: 276 @G)>C$Ž25:<),6d:H)>-6 'C;6D (L+.25&6 >2B&) F5'.0+.2T25m6 (U'D<25:<),&6 72V+.)>6H)>@GIg),0'Ž.2S++ (L6f
[ <
N,O+)>IJ)>0.+.)+.)
3 7:<-;256 ˜ (7K,D<25:<),&6 7 K,25@G
2 (*),6HDO: '*D '*: (Q++ (E:H)>+.A) 7256+I (7: L@*) DO:<276+.)VDO:<),-/0.2*52 'M(E90 (L*D '.:H) &(Q++ (E60‰,:<-;)
DO),@*IJ25-: (7SC >
\³Ž.&
) F752 'IC–6H)9B- F5'+(LC/@G)>0hDO)'TK>250.K,BC '.-6 b72S+.) ” '.) (76
[ <J=6K>27@ K>270.") GIHB)>6+.
) K,25@c.-;+0 (7@
K>27@*IJ250.),0MD<)>6C;-/0.&) (7:<),6 4y++ (L+.2bIg),KC (76K>250.k) GIH),6X+
) @"7 )S+0 b72bC/-;0.)) (L:<)>6 4y++ (79+ (QIg),KC (Q)K (L@ (79+ (
-/0hD<)>:<@;‰>+K- ( @k7 ˜ '.0.K,-/25+0 (L0.+.2 K,25@*M
2 '@Y6 '.Ig),:1K>250 '0MD<2 +.256S@G2+)>C/27i
6 N[]O.
^ Nf> Wb72 ‰bIJ25-/6V+.)
(7+.@G-/: (7: ” '.n) (L6f
[ <
N,OIJ256H*6 (7@ @G2+)>KC (L:2VK>25@GIJ25:H*D (7@*),0hDO29+.)61‰>:H-/)>6DO),@*IJ25*: (L-/6q+.) 35)>-: (76K,25D
@ C
I.C;") G8(7&6 >
+.- &K 'C/++ (7+)0.2 '.6<2T+)X
[ <
N,O9),6HD V+0 ( ˜ (7Cc6D (9+.)I.:H2K,)>6H6<2566H-/6NDO)>@ LD<-/K>276d+I (L*: (VK,250.6NDO-: '-/: 276
@G2+.),C/256+.)VI.:<) 3B-/*6 bL2 4yQ- > A) >X7 ),6<K>27C$+Ž (GK>25:H:<)>K 6D (E+256+I (L: 7@G),D<:<256++ (G:<)>+) @"7g)80.2 ˜ (7K,D<2E++ (L69
[ < NnO
˜ '.0.K,-/2590 (7:<),@ K,25@G2 )K (7- G8(7680.) F5*: (L&6 7 +0 bL2 6<)bIJ2+)>0.+.2mDO-/-: (7:X-/KC ( &HB)>
6 ( +I (7:NDO-/:X+.2 K,250'Ž.),K>-;@*),0MD<2
+ (A-6 '+(()>6NDO-: '*D '.-: (8> (7*: (((K,25@GIg) DO- &b72A+.) 28(70h6D ( + U‰ 7 A:<) ˜ ),:<-;++ ((),@P)>I BF5-: ( ˜ U) 7e256X:<),-6 '.Cc6D (7+.276
+
I (7:H)>K,)>@ K>270MD<*: (7+-;D 37:<-/27&6 7IJ25-/
+
6 (L6S
[ <J=ROE2D<-;37)>*: (L@F2569@G)>C$Ž25:<),6)G276XI-/25:H)>6:<),-6 '.Cc6D (7+25&6 7‘),3B^- C
+.),0.K>B- (70.+.2 ” ')l‰(I.:<),K>-;6<2 '@K>)>:NDO2`&K '.-;++ (7+.2 ” '9(70.+.2`6<$
) ( '.6H*D (7@ [ <
N,O K,25@G2`@G2+)>C/276S+.)
I.:H),3B-/-6 b792 >
?)>0hD<:<2(+.)>6NDO)SK>270MD<"
) GBDO82 7‘9I (7*: (Q),6H6D (QD<)>6<) ˜ 27- +.),K>-/+-/+..
2 (7+25I6D (Lf: ((7: ” '.-cDO),K,*D '*: (Q++ ( [ <=
DO27Ig25C;52 F5B- (G+ (76H)H‰q+.) 0-/++ (IJ25R: '.
@ (:<)>+)K,[email protected]/) 6D (7@G)>0hDO) -/0hDO),:<C/X- F (7++ (I7¡K>25@ (7IJ)>+0 (76 '.
@ ()K (L@ (79+ (
-/0hD<)>:<@;‰>+K- (87K>25@UK>250.k) GIH),6+.
) OX
) ( 6D (7C)Ž.25&6 7++ (7+.2 ” '.)9)>6NDO)>E6 (7K,:<),6<K>),0h6D (7
@ '.
@ (SK>25@GIJ250.)>0hD<)
C/-;0.)) (L: (721@*2B+.),C/2 4 + B- F5'.-: (-,8> @"> ˜ '.0 )b721C/U2 F /6NDO-/&K (K‰ (7I.C;-/)K (L++ (T0.2560.2B+.256-/0hD<)>:<@;‰>+-/256 7+I (7-: (
<L
~
(**
V
+
ŽH
V
~
‹
|
} (**
I
+
N
N|
T
T
l$
!
!
J
(**
#
(*
J
+
]+
T
Y
(__
_
N
|
X
&
0
ŽJx (**
+
|
(
T
!
N|
H
p
O
WY
Ž|
}|
H
N
X
T
K|
)O
(_
WO

!" *
&)! * # !"
## # # Camada de
Entrada
*
Camada
Intermédia
Camada de
Saída
wi,0
wi,j
j
i
@ (Z
[ <J=FK>[email protected];),D6(L@*),0MD<) -;0MD<)>:HC/-BF5(7++(87dK>25@
+ X- F5'.*: ( ,8> 0 -/0hD<)>:<@;‰>+-/25678'.@W02+.2G+.)96*( /++(87K>250)"GIH),6+) OX) (LD*(7C$Ž256&>
(_
0.2B+.256Q+) )>0hDO:-(7++(87
]
V
02+.276
]
N
IJ)>:<@G-;D<-/:4'.@( (7I.:<),0.+.- )(UF5),@ 0+b72VC/-/0))(7:> 2V0.2B+.2V+)6*( /++(87P‰W'DO-;C/- &(7++(f( ˜ '.0 )bL28C/-;0.))(L:&7hI+(7:-(
)>6H)K (7C;25+0 (7:256++(7+.276\+.)S6*( /++(87g3-;6HD<2 ” ')D( ˜ '.0 )bL2(C;25F ;6HDO-;K)(SDO),@ '.@ K>250hDO:-(7+.25@ /0-/2EC;-/@G-;D*(7+.2
4 z @k> 6H*D (\)>6NDO*: ( D3&‰ F7K- (D<)>@ (A3 (70h6D (UF5),@ +.)),3B-cD6(7:R2n'.6<2+) D3‰,K>0.-;K)(76 +) CcDO:*(AF5)>@7 ” '.)IJ2B+.)>@
C/) A3 (7
: (i'.@ (SIJ)>:H++ (S+.)9-/0 ˜ 25:H@ ( )b72 4 U) > F9>X7)>6<&K (7C/27+0 (7@G)>0hDO2 @k>
@ ( ;3
6O 3
+.) 0.
) '@oK>250 '0MD<2*+)X+)>6<C;2&K (7@G)>0hDO256D<)>@GIg2AC
“ :*(L-/689I (76<-6 (7+.256 4 "| 7q+.) 0.-;+.25i
6 ( +I (L:HDO-;:8+.2 D<)>@GIg2 4 + B- FU'.*: ( ,8> @"7 6H)>0.+2:H)>I.:H)>6H)>0h6D (79+ (IJ)>BC (
6<) ” ' >0.K,K- (
z ¡z z 5Œ 7+I (7-: ( '.
@ (
K,25@ 2TK>27@*I.:H-/@G)>0hDO2 > ‘25: k) G),@*IC/92 7I(
€
(7I.C;-/&
K ( )b72f++ (
€ 5z a'6 ,:<-;) 5z Bz z .z I:<2B9+ ' >-;:<B- (W(76R6<) ” ' >0.K,K- (76 5z Z) Bz Xz
I+(7-: (S256-/0.6N6D (70hDO),6 € G) €
21)K (L6<2G++ (SI.:<) 3-;*6 b721+.)9K '.:HD<2GI*: ( ,92 7.210.2B+.21+.)9*6 ( ;++ (T++ (E
[ <= \DO:H)>-;+0 (7+.21+I (7-: (T) ˜ ),K,*D '9(7:
K>27:<:<),6<IJ250.+ ,0.K>B- (76 ),0hDO:<)f256A3 (7C/25:H)>6+I (76H*6 (7+25&6 7 F5)>-: (7+.25m6 (V9I (7:HD<-/:q++ ( 3 7hK>25@ 2XA3 (7C/25:qI:<)>6H)>0hDOA) >
6H6<-;$
@ 7.21@G2+)>C/i
2 F7)>*: (LC ˜ 25:<0)>K>-;+.21Ig),KC (E
[ <= 9++ (7+2GIJ25: 0
Œ
Œ
5ˆ
w … ~‰ˆ ‹ ƒ ‹ | ‹
4 ,I> @
~e€
Rƒ … ~‰ˆ
ƒ …Œ
‡†
‹H†
˜†
@d)
2S0 .@*),:<21+.)0.2B+.256 +.)
)>@ ” '.) +.),0.27*D (12S02+.2S+)*6 ( ;++ (87 ( ˜ '.0 &b721C/52 F /6HD<-/&K ( 4
)>0hD<*: (7++ ( 4 €
@">
0
Y
N
N
K
T
K

G
N
V
K~
B
(
p
((
B
:` c
2
y
2
"
A
d0d'd #$
FB
&%
*
'
#
)(
X
!
2
K
*
~
#$
'
)(+
d
Y
,%
K~
O
,%
0
-
a
a
/.1032 4
y
5
`
a
65879.1032 y
`
;:^`=<>
K
y
65?79.
`
`:
<A>
E
2y
`
v
/
@.
2 4
B
.1032
DC
e
GFIHJF
Série Temporal x1 x2 ...
Deslocamento
+
-XF5'.:*(
xt-12
... xt-2 xt-1 xt
...
12
,8> (( 0@?)>6HC/2BK)(7@G)>0hD<256+.)'.@
2
1
S6 >:<-;)\DO),@*IJ25:*(LCS>
(
?%
*
!" # %$&'(! # ) *! # _
q
k
#%
T&.#%"f
IJ)>6-(7:E+9( 6-'+( '35),0MD-'.+.)A7,(
I.:H2+9' >-B' '.@ K>250 '.0hDO2 3A(7:H-K(7+.2`+.)mD >K,0.-/K&(76 ” '.) 6H)
DO27:<0+(7:-(7@ I9(7:HD<-/K&'CK(7:H@*),0MD<) DO),-/6I+(7:-(SI.:<2C/)>@(76+.)X25ID<-/@G- &( )b7287 ” '.),:0 '.@ >:H-/K)( ” '.),:K,25@DC
.-;+
0 (LD 37:<K- (I> 2)>0.+2 (76H6<-/
@ 7 6-':<I.:H)>)>0+.)>0hDO) K>250.6ND6(LD*(7: ” '.) ( (7I.C;-/K&( )b72 +)>6HD*(76AD >K,0.-/K&(76(0.2
+.25@ /0-/2E9+ (QI.:<) 3-;*6 b72b6H) -(Q6D bL2b)>6<&K (76<6H92 >T?) ˜ (7K,D<92 7R(QI.:H),3B-/-6 b72b3-B(J( (7IJ)>0+(L66-'.:F5-B' 0.276
(70.276f02"37)>0h6
D (I7J6H)>0.+2*2G0 .@*),:<21+.) (7I.C;-/&K ( &HB)>6+-/@G-/0 'DO2S)9K,25@WIJ52 '.K>21+.),6HD*( ” '.)U>
D<*: (9(7C .2*)>@ &K '.:H6<2b+I (L6<*6 (QIJ)>BC (*25IDO-/@G- &( )bL2*+.)8+I (7: L@*) DO:<276+.)V@*2B+.)>C;256fK>250h35),0.K>-;25+0 (7-;6
+.)9I.:H),3B-/-6 b792 7+'D<-/C/- )(70+.2T:<),I.:<),6<),0M*D ( &HB)>6 .-/0 7:<B- (7&6 7K>25@G2S6<)X-/XC '.6HD<*: (T0.
2 '.)X6<)96<) F5'.) 0
O
P
=
|
&%
T BC
%
%
)%
=
DC
T 0
f2)>6ND*'.+2+.)
+.!
) " $#&% p K|
LI.-/)) WF (7I.-;)
7 ˜ 25:-(7@ 'D<-/C;- )(L+.256N! @OI9(7:*(25ID<-/@G- )(L:2@G2+)>C/2
'6O"72DO),0.+.2AC6<)9:<),6-'.CcD6(7+.276f),0.K>27:*( -(7+25:<),6fI9(7:*(S6 ,:<-;)>6f6*( ,250+(7-;6K&'.:ND6(76>
O,F
Y
H
(
(**
O
q
+
T
=
T
&%
@G)>6<@G2VD<-/IJ2V+)N! @O\D6(L@! ,@)( 25- 'DO-/C;- &(7+.29K>25@ 6'.K>),6<6<21I+(L:*(8I.:H),3B-/6H),6 +0 (L0.K>),-/:*(L6
4 U) > F9>X7+)>I 356<-cDO256*+(70K 7:H-/256 @IJ25:E\+.-;:*(7I,+(7+-+(L0+( '.Ce),DW(7CQ>
7250.+.).( 25:*(L@
>K 2B+.- K)( C
+.276f276fK,2) K>-;)>0hDO),6+.2*@G2B+.)>C;D
2 N\W[ >
=
T
A%
|
(**
J
q
+
L-)(6H)&'.6GK>27CK(J25:*(L+.25:<),6
7d27IDO-;@*- )(7:-(7@
2561I+(7: L@*) DO:<276S+.)A@*2B+.)>C;256PN[f^Nf7
+.)( )>0.+)>0.+.2 '.)256@N! @OfK,250.6<)F5'.),@&@G)>C25:<),6 6<25CX' &HB)>6 +.2/ '.)
(76 D ,K>0.-;K)(76 )>6HD*(LD ;6HD<-/K)(L6
K,250h35)>0K>-/27+0 (7-/6 4 U) > F9>X7@ /0-/@G2506 '+(L+.*: (7+256 @k>
\++(
Z ( **
+
q
0
H
=
K
)%
250hD*'+.297f:<)>K,)>0hDO),6A+.)>6H)>0h3525Cc3B-/@G)>0hDO256b09(1 32K,25@*2 6<) -(L@ 2o'.6H2 +.)cN! @O K,25@ [ 4' #
O
576 6O
98 ' 6O1[
BO
[ 8 [ O (-/;K +(7C;) -;K U7
:
)J(c/+' <j ' 5=< ?> A@ Q/B
(70 C+(7( ) E
D (7SC >^7 . (7C;D<)>-: (7*: (7@ ),6HD<)\+I (70.27*: (7
@ (87 (7KC (L:-F (70+.2 ( (7I.C/-;K)(-/C/-;++(7+.) ++(D 'VI.:<)kC
3B-/-6 b792 > R25:R") G)>@GI.C/82 7Uh(J52 '.++ (L0
(7IC/-/K,5
2 '(/B02MK>27@ '@ (LCE( (J),D<2+.)6 ;@!J25C/256rD<)>:<@G-/09(7-/6
IJ)>:HD<)>0.K,)>0.+J
2 (721K>270 '.0hDOG
2 F ƒ Iz HVz JBLz KQz› NM Lz OIP&Q ;z R RzLOIS Uz TCV7OW 7I+(7:-(D(/2143 >
(7: (\)>6N6D (D<)>6<A) 7( 25-B+.)>K,-/+.-;+.f2 (7+.27I6D (7:‘9+ '+(L46 (7I.:H2 G-;@ ( H),6R9I (7*: (n(I.:<) 3-;*6 b782 7 (7!
@ +(LX6 +(76H)) (79+ (76
)>@ N! 2OmK,25@ :[ 8
[ O"7d++ (7+.2 )>6NDO),6*6H)m:H),35),6HD<-/:<),@+..
) '.@ ),0.25:<@G)bIJ27DO),0.K>B- (7SC 7)>@ :<)>BC ( )bL2`'L6
:<),I.:<),6<),0M*D ( &HB)>Y
6 .-/0 L:<K- (L&6 7rP
) (7-/0++ ((IJ25: 7(L+I (7:<),0hDO)>@G)>0hD<U) 7 90 b72mk) G-/6HD<-/:H)>@FD<*: (+(LC .2560)>6H*D ( 7:H)) (8>
,(SI.:H-/@G)>-;*
: ( (LI.:<)2 G-/
@ ( )bL92 7 'D<-/C;- )(L+.2 '.
@ (TK>27!
@ .-/90 ( )b728C/-/0)) (7:+)\U3 (LC/25:H)>6+I (L6<*6 (L+.256 4y@G2+)>C/2
N
[ @"> ),6HD<)XK,)>0 L:<-/82 7.25
6 F5)>0)>6+.
) '.@WK,:<25@G256<6H25
@ (TK>2B+.- &K (7@ 276fIJ)>6H256Ig),C/256 '+(L-/6256A3 (7C/27:<)>6
I (76H*6 (7+256R-6 b72fT
+
@ '.C;D<-/I.C;-/&K (7+.256 > ,(6<) F5'.0.9+ (,(7I.:H)2 G-;@ ( )b792 7g(L!
@ g276r256‘A3 (7C;25:<),6r))>:<:H256e+I (76H*6 (7+.276R-6 b72
K>270.6<-;+.)>-: (7+.256 76H&) F5'.-;0.+.2 '.
@ (9),6HD<*: (LD &F5-;)K (96<-/@G-/BC (7: (L2X@G2B+.)>C;2 N[.
^ Nf7M250.+.)f25@6 F5),0.)>6K>2B+.- )K (7@
256GK>2B) K,-/),0MD<)>6*+.2`@G2B+.)>C;92 > ‘25:GK>250.6H&) F5'-/0hDOA) 7+I (7*: (c'.
@ (9+ (7++ ( 3 7@(76 (LI.:<)2 G-/
@ ( &HB)>61-6 b72
+.) 0.-/9+ (76Ig),C/256@G2+)>C/276+.)9I.:<) 3B-/*6 bL92 7++ (7+.276f90 (Z( 27:<
@ (10
\
=
;
\
K
;
)
(**
1
"!
&
( **
+
=
1
ˆA
@
+
(***N+
p
a
pB
X
=
D|
Y
|
Y
T
%
D|
)Y
N
&%
=
X
X
)
! # $&
76<)&(7+.2G0 ' @ S
( K>27@!.-/09( )b72SC;-/0.)&(7:tu1w r| =-S>?)U>^7
Œ
~e€ Rƒ … ~‰ˆ
‡†
C39(
E
-
4
a
`
y
y a
E
-
)
4
a
y a
`
y
250.+)
4 ,8> (_ @
6587
76<)&(7+.2G0 ' @W@*2B+.),C/2St\u9v tSw Rz r| = S- >?)U>^7
Œ
…
~r€ ƒ w ~‰ˆ ƒ
‡†
C39(
Œ7 ~‰ˆ |
y :
6587
4 ,8> (( @
6587
+.),0.27D6(S2S3A(7C/27:+.2DF5)>0)S0.21K,:<25@G256<6H25@(T+.)'.@W-/0+.-;3 /+8'.2T)
U
y
(
q
2SD6(7@(70-.2S+9(
"
3
>
." - "C–6H) '.) '.@&@G2B+.)>C;2\+.)
(7I.:H)>0.+- )(AF5)>@ Ig276<6-'-+'.@ (g2 ( j ' 5=< '+(70.+2(\K,25:<:H)>6HIg250 C
+ ,0.K>-B(T)>0hDO:H))>0hDO:-(7++(76)6*( ;++(76 \K,25:<:H)>K D6( 4y2U'bI.: 3)G-/@(V+.-;6<6H2@dI+(7:-( O
6O U7.:<) DO-/:-(7+.256
++(E@G)>6H@ (1IJ259I '.BC ( )b782 7J0 '.0K)((70hDO),6n'D<-/C/- )(7+2560+(EK,:<-K( )b72*25'mD<:<)>-;0.2E+9(E:<),+.)U> I.:<2BK>),6<6<2E+.)
(7I.:H)>0.+- )(AF5)>@
Ig2B+.)T6H)>:\3B-/6NDO2bK,25@*2 '.@FI.:H2 .C;)>
@ (*+.D
) ( '6HD6(L@*),0MD<2b+.)SK&':H3A(76\25' +)D(7I.:<2)G-^C
@( )b72*+.Y
) ( '.0 &HB)>&6 7 250.+.) (E:<),+.)8DO),0h6D (QC) ( ),K,-D '+(7n: '.
@ ( J2 (E-;0hDO)>:HIg27KC ( &b72*90 b72QC/-;0.)) (L:+.276\++(7+.276
f2 -(L&6 7
>
@G256NDO*: (VK>25@G28IJ2+)>@ 2K,25:<:H)>:d9+ '+(76 F7)>0.),*: (7C;- )( &HB)>6+.-/6NDO-/0h*D (76d9I (7*: (828@*),6<@G2
+ X- F5'.*: (&,8>
K>270 '.0hDO2 +.)A++ (7+256S+.)bDO:H)>-/092 > '.Q- 72'@ ( J2 (0F5)>0)>*: (LC/- &( )bL2 2K,25:<:H)bK>25@ ( &K '.:NU3 ( 7qK>25@
'.@P),:<:H2m@ /0.-;@*2*+
I (7-: (A276X9+ (7+.2569+.)1DO),6HDOA) > @*),6<@G2 A90 b72m6H)1-6 '.K,)>+.)*K>25
@ (bK '.:HA3 ( 7 '.)
25:HB- F5-;+0 ($'.@ )>:<:H2 @ (7-;25:X+I (7*: ( 256S&K (76<276S+.)bDO)>6NDOA) 7d-;6HDOc
2 (LIg),*6 (7:S+..
) (LI.:<),6<)>0h*D (7D
: '.@ @G)>0.25:8)>:<:H2
I+(7-: (b256++ (7+.276X+)TDO:<),-/0.82 >Tk (LXC ( )>0 37@*),0.92 7r+.),6<B- F7+0 (7+.2A+.) O ' # i O ) '+(L0.+.2
22BK>25:H:<!
'.@@G2B+.)>C;2X@G)>@G25:H- )()>@
+.),@ (76HK- (256") G),@*I.C;256+.)DO:<),-/0.82 75DO*: ( 6D (70.+A2 C–6H)f+E) '@ +.256I.:<2 .C/),@ (76
@(7-/66 >:H-/256:<),KC (7K,-/2590 (7+.256K,25@WD
2 '.6H2*+.)T
[ < NnO /28(7:<C;U) 7
>
?,'.: (70hDO)2\I.:H2K,)>6H6<29+.) (7I:<)>0+.- &(UF5)>
@ 772@*2B+.)>C;2IJ2B+.))K (LI6D (7:RK>),:H6D (L6 )K (7-: (7K,D<)>: /6HD<-/&K (7&6 75K,25@G2
2G-: ' ;+.92 7- '.)9)>6N6D b72GI.:H)>6<),0hDO)>60.256++ (7+.276f+)9D<:<),-/0.21
@ (76+0 b72G+0 (Z( '.0 )bL2G-;@*IC /K,-;*D ( (16<)>E: (7I:<)>0 C
+.-;++ (8> 6NDO)f") G)>@GI.C/29-;BC '.6NDO*: (\276+25-/6q2 H)>K,D<-;37256dK,250hDO-: (7+.-;D 35:<-;256 ++ ((7I:<)2 G-/
@ ( )b7:2 ( '0.K>-;25+0 (7QC > R27:
'.@
BC (7+.29DO)>i
@ C–6H,) (9@G-/0.-;@*- )( &b72\+.2V)>:<:H28+.)DO:H)>-;0.92 7MIg),C/2X52 'D<:<
2 (X@*-;0.-/@G- &( )b72+.28),:<:<2X+I (7-: (
(76)>0hD<*
: (7++ (L6f+)>6<K,25-0 .),K>-;++ (7&6 >
F5)>0.),*
: (7C;- &( )b72 9-;0 '.),0.K>B- (7++ (SIg27:DO: ,6 ( (7K,D<25:<),6 ,()_ M-/Z0 7
= 28(7:<C;U) 7
0
?
0
T
K~
%
0
N
T
L
(**p+
p
(]
O
T N
p
CO
T O
|
\
)
T
( **
?%
+
T

K
K
n
G
0 O
N
T @ A
¸ @¸
?
!#"%$ &('*)+
D|
~
$%
A ' 4
¸ º¸
EO;
' 4
A ')
—
,-'."0/#1"‚2„ƒ 1354 67,F“
‘’†98
T
>”
…T…T‡  ;:
I
UJ
( ***
X
T ( ***N+
rk‘:*(LD*( –C 6H)q+.)@'.@ ( (7K DO25: +.)q+.-E( ;K>-;CLK,250hDO:<27C/29>
>
q
]
!" # %$&'(! # !
#
Saída
B
A
Dados de Treino
Dados de Teste
-BF5':*(
+
,8> (] 02e)>0)>:*(LC/-T&()bL2S)iO
i
')
# O
Entrada
6)>0hDO:-(7++(76+.) 35)>@ K>250hDO),:-/0,( 25:H@ ( )b72V6-' K,-/),0MD<)9I+(7:*(SIJ)>:H@*-cDO-/:m(T2D<)>0 &b721++(766-( /++(L6
+.),6<) -(7++(76,= -S>?)U>^7rDO),@P+.)1)"G-/6NDO-;:f'.@ ( ( '.0 )b72(@ ( DO)>@ LD<-/K)(*K>25@(LCBF5'.@ F5:*(A'+)GI:<)>K,-/6-b72
'.)f:<),KC (7K,-/250.
) (L6),0hDO*: (L++ (76 K,25@ (766-( /++(L6&> ‘25:d2U'DO:H2XCB(7+.297hK,250h3 ,@ '.)f)>6ND6(/( '.0 )bL286<) -(
O i 5=hQ- > A
) >X7LIgC) '.)>+0 (L@6 (7C;D<)>*: ( &HB)>6 90 (76 )>0hD<:*(7++(L6 +.),37)>@I:<24352BK)(7: Ig)C ')>0+(76@(LC;DO),:*( H),6 0+(L6
6-( /++ (L&6 7.+I (L*: (D(G
@ (7-;25: +I (L:HDO)9+.276f&K (76<27&6 >
O
N
ˆ
K
Q
}|
WX
K
=%
N
ˆ
6 '9(9K&(7:<+-/0+(7C;-/++(L+.)d+),35)6H)>:q)>C;),3A(7++(I7hK>25@ )"G)>@GI.C;256"4y25' O ' O
0+(ED<)>:H@*-;0.25C/2UF5-K(S)>6ND6(LD /6NDO-/K&( @ ')S6<) -(L@F:<),I.:<),6<),0MD*(LDO-c35256(LK>)>:HK)(b+.2.([email protected]/),0MD<)U> `F7)>0.)kC
:-(7C/- )( &b72 16<)>@GI.:H)*) ( )>K,-D '+(7++ ($((9I (7:HD<-/:+.)1+.25-;6DO-/IJ256+.)G9+ '+(L6V6H-;*D '9( &HB)>6 0 ' 5=< ) ' 5=< 2 I.:H-/@G)>-/:H2m&K (76<82 74'.@YA3 (7C;25: E+.),D<)>:<@G-/90 (7+.M
2 ( 9I (7:HD<-/:89+ ( -/,0 ( 27:<
@ ( )b72
+.276 3A(7C/25:H)>63B- >-;-0 .256 > 6H&) F5'.0++ (T6<-c*D '+( &b728),90 F5C;2 +(V-D '.+.2T2T:H)>6NDO92 752 'Q6<) -(87.&K (76<2506 ( 25*: (X+.2
+.27@ ;0.-/2G+.256\9+ (7+.256\+)TDO:<),-/0.82 > -0 '+(70hDOG
2 '.D
) (E-;0MD<)>:HIg25BC ( )bL2EIJ2+.)86<)>:C) ( )>K *D '+(L++ (bK>25@
:H)>KC ( DO-;A3 ( (7&K '-/++ (7+U) 72V@*),6<@G2 V90 b72T6<)+I (76<-6 (TK>25@ (8k) GD<*: (7IJ25BC ( )b782 7B027DO25:HK- (7@G)>0hD<)@G)>0.276
¡37)>CS>
O:@ O O
' >
O
0 ?
FO
%
A
Y
p
O
}
A
p
!%
T
ˆ
G
|
|
j i7h@*),+.-/++(9IJ)>C/2X0 .@G)>:<28+.)I9(7: 7@G),D<:<256C/-c3B:<)>6
4 M @ '.)*K>250hD ,@Y)*Ig),CK((6-'+( K&(7I+(7K,-/++(7+)*+.)J(7I.:<),0.+.- )(UF5),@$> f@ @G2B+.)>C;2 '.)Q09b72 6<) -(
6' K>-;)>0hDO),@*),0hDO)A:<),I.:<),6<)>0hD*(LDO-c352 +.2 I.:H2 .C/),@ (m)>@ ) '+( &b72 -/: ( (7C+(L:80+(M(7I:<2)G-/@( )b72
++(!( '.0 )b72P(D(7I.:H)>0.+.),:&> R27:f2U'DO:H2GCB(7+.92 7I'.@ @G2B+.)>C;2S+.)>
@ (76<B- (7+.D
2 ( '6H6D (L+.P
2 (7256++ (7+256+.2
I.:H2.C;)>@(T)>@W)C '9( )b72G-/: G8(7:2*: ' /+92 7I.:H24352B)K (70.+.
2 O ' # i O >
A
?
4
A ')
H
DC
0
)%
V
|
X
ˆ
|
K
)
l@G)>C25:+( 25:H@ (T+.)9) 3-cD6(7: 2O ' # i O 'DO-/C;- &(7:%'.@(! '+(70hDO-;++(7+.)9),C/),3A(7+9(T+.)9K)(76H256
+.)ED<:<),-/0.29>n'+(70.+2 )>6NDO)b0 .@G)>:<2 ( 25:VIJ)>C;2 @G)>0.256 , 4 DO:H-/0hD6( @35) >)>6S6'.IJ)>:<-;25:T(L2 0 .@G)>:<2 +.)
I+(7: 7@G),DO:H25&6 77)>0h6D b72 @T'-;DO2-/@GI.:<243 ¡35),C- '.)2K,25:<:-(n'.@(Ig),:<++(+.) F7)>0.),:*(7C;- )( )b72 /28(7:HC/)A7
>
O
)
"%
T
%
_
DC
H
N|
DC
T N
(***+
!
#
,
$&
q
I.:H2.C/),@ ( '.)0.),@ 6<)>@GI.:H))"G-;6HDO),@ 6-' K>-/),0hDO)>6 K)(76H256 +.)DO:H)>-;0.2V+-/6<IJ250 c35),-/6)0+bL286<)f+.) 35)
:<),+9' ,-/:92m0 .@G)>:H2m+)*I+(L: 7@G),D<:<256+.)P'.@P@G2B+.2(7: .-cDO: 7:<-;297+.) 3-;+.2$((I.:H2.C;)>@(76+.)( (7C;D*(Q+.)
:<),I.:<),6<),0M*D (LDO-c3B-/++ (7+U) > 6<6<-;$
@ 7e++ (L+.$
2 '@ 0 @*),:<2 G2 +.)G++ (7+.276V+.)1DO:H)>-;0.2A") G-/6NDO)>@ 8+ '+(7
6 (7C;D<)>: C
0+(LD<-;A3 (76+I (7*: (*K>250hDO:H25KC (Ln: (EK,25@*IC/") G-;++ (7+.)V52 ' :<),I.:<),6<),0M*D (LDO-c3B-/++ (7+)S+.T
) '.@ @*2B+.),C/2 /28(7:HC/A) 7
0
' j i ' 5=< T
) O ;@ 5=< O
' j i ' 5=< +(L6<)>B- ( C–6H)0 '.@
K>250hD<:<25C;28+.256A3 (7C/25:H)>6d+.256 9I (7: 7@G),D<:<256d+.n) '.@ @G2+)>C/2X+I (7-: (
2D<)>: '.
@ (J2 (.F5)>0.),*: (7C;- &( )b782 7‘),0h3525Cc35)>0+.2 $
2 '6<2 +)E:<),6HD<:<- H),6VU2 ' IJ)>+0 (7C;-/++ (L+.)>696<2 .:<)G)>6NDO)>6 7
+.)(@*2B+.d
2 ( 'L
) ( :<),+.L
) (LI.:<),0.++ ( ( '.0 &HB)>6 BOJO i 6O"> \ 27@*2 ") G),@*I.C;2D<)>i
@ C–6H$
) ( ' j
;@ U78'.@W+256@ (L-/6IJ259
I '.BC (7:<),6@ ,DO2B+.256+):<&) FU'.KC (7:H- &( )b782 7250.+)256++ (7+.256+)9D<:<),-/0.2S-6 b72
+.-c3-;+.-/+256)>@o+.27-/6DO-/IJ256+.)V)K (76H256 0
' )
5=< > \6fI.:<-;@*),-/:<276*
6 b7P
2 'DO-;C/- )(7+.276+0 (
(7I.:H)>0.+- )(AF5)>@W+2*@G2+)>C/8
2 7)>,0 '9(70hDO2 '.)9256 .CcDO-;@*256 *6 b7P
2 'DO-;C/- )(7+.276 +I (7-: ((&( )>:<-;:++ ( '+(7C/-;++ (7+.)
+.),6HDO)L=MS- >?U) >^77+I (7-: ()>6NDO-;@ (7:e2\),:<:H2\+.%) F7)>0.),*: (7C;- )( )b792 >?,'.-: (70hDO) ( ( (76<)d+.) (7I:<)>0+.- &(UF5)>
@ 77&K (7C/K '.KC (gC–6<)
21)>:H:<2G+.)U3 (LC/-/9+ ( )b728+./) ( 25:<
@ (TIg),:<- 3+.-;)K (87+I (7-: (70.+.A2 C6</) '+(70+.2E),6HDO) (7@G)) ( )(D(U'.@G)>0h6D (L&: >
l:<) F5'.KC (L:<- &( )bL28+.-;@*-;0 '-g2S) ( )>-;D<2T+.) ' j ' 5=< IJ)>C;2T)>6ND ;T
@ '.C/28+0 (i(7I.:H)>0.+.- )( C
F5),@F+.Y
) ( '0 &HB)>6 O i 6O"> 2b)>0h*D (70hDO92 7R'D<-/C;- )(P'.
@ (E)>6NDO-: '*D '.-: ( G9(I7 '.)1+.),37)S6<)>:),6<IJ)>K,- &K (7++ (
)>@ (¡U3 (L0 >29IJ)>C/f2 'DO-/C;- &(7+.25: > !
@ J25-: (\6<)Ig276<*6 (f'D<-/C;- )(L: '.
@ (nF5*: (L0.+.))>6NDO: '*D '.-: (87hK>27`
@ '.@ F7*: (70.+)
0 .@G)>:<28+.)\0.2B+.256-;0hDO)>:H@ ,+.-/27&6 7B+0 (8I.: LDO-;)K (87I(825ID<-/@G- &( )b72X+.256d+I (7: 7@*) DO:H256dD<25:<+0 (gC–6<)+.)\+.- ( /K,-/C
( '.6NDOA
) 7") GX- F5-/0.+
2 '.@ F5-: (70.+.)f)>6 ( 25: ,2TK>27@*9I '6D (7K,-/25+0 (LSC > L(7-/m6 (7-;0.++ (87h),
@ F7)>*: (LSC 7M*6 b72V@ DO2B+.2536 '.)
)"GX- F5)>
@ '@W+.)>C;-/&K (7+.Z
2 +(7BC (70 ,92 7.K>270MD<:<25BC (7+.21IJ25: '.@ 4 52 'm
@ (7-;6 @d+I (L: 7@G),D<:<2 4 6 @ +.)9:<) F5'.BC (7:<- )( &b792 >
@ (E(7C;D<)>:<90 (LDO-cU3 (+-/6HD<-/0h6D (+(L6<)>B- ( C–6H)d90 (fI.:H2K '.*: (+.2) '.@l@G2+.),C/E2 (7+.C) '+(7+.92 7L)>@D<)>:<@G256e+.):<),I.:<k) C
6<),0h6D (LD<-;3B-/++ (L+.) 4yQ- > A) >X7rK,[email protected]/k) G-;++ (7+.) @"> 6H6<-;$
@ 7Z'@FI.:H2 .C/),@ ( '.)16<) -(b+.)S+E- ( /K,-/C (7I.:H)>0.+- )(AF5)>@
I+(7-: (i'.@W@G2+.),C/2SIJ2+)>: S6H)>: ( (7K>-;C/@G)>0hDOn) (7I.:<),0.+.-;+.21Ig25:U2 'DO:H92 >
(g27:<+
+ (UF7)>@F),6H*D (LD ;6HDO-;)K (Q+I (L*: (.(LO ;@ 5=< I (76<-6 ((IJ)>BC (A),6HD<-/
@ (LDO-cU3 (*+.2A)>:<:H2A+.)
O19
F5),0.)>: (7C/- )( &b72A+I (7*: (A)K (L++ ($'.@ +256V@G2B+.)>C;25&6 7e52 ' DO25IJ25C;52 F5K- (L6\+.)G:<)>+U) 7 ),6<K,25C .),0.+.A2 C6<)*2m@G2+)>C/2
'.)A@*-;0.-/@G- &(m),6<*
6 ()>6NDO-/
@ (LD<-;A3 (8> G-/6NDO),@ +.-;37)>:H6<256G@ DO2B+.256T9I (7*: ( )>6NDO-/
@ (7i
: ( &K (7+I (7K,-/++ (7+)b+.)
F5),0.)>: (7C/- )( &b72 +.
) '@ (
[ < N:2dK,25@*2 6<) -(M( 8 5=< ' i S25' 2 O ' j ( :H250
k- .6 .-/-: (70.S- 7 ,R= h2 9(43BQ- 7
7 ')S*
6 b72A+.) 35)>-: (769") GB- F7)>0hDO),6)>@ D<)>:H@*256K>25@G9I '*D (7K>-;25+0 (7-;&6 >
@ ((7CcDO)>:H+0 (LD<-;A3 (*-: ( >2 ¡37)>C S++ (L++ (QIg),KC (ED<)>25:HK- (E++ (Q-;,0 ( 25:H@ ( &b792 7J250.+.)S2b),:<:H2(+i
) F5)>0.),*: (7C;- &( )b72
X)>6HD<-/
@ (7+.P
2 (1+I (7:HD<-/:+.)X)>6N6D (LD /6NDO-/&K (766<-;@*I.C;)>6 7- '.) (LK>:<),6<K,)>0h6D (7@ '.
@ (SIg),+0 (7C/-;++ (7+./) '.)V+.)>IJ)>0+.)
++(SK>27@*I.C;") G-/9+ (7+.)+.21@G2+.),C/92 70.25@G)) (79+ (7@*),0hDO) 0
' >' ] ' 5=< N U7"K>25,0 .)>K,-/+.2IJ25: Nf7] &7,6<&) FU'.0.+.2f2K>BC (U'.-6 'KC (7+.2 (7- 7A) 7
B%
K
K
H
DC
|
O
6C
(**
x
)
O
;
)
}
"
H
T
K
"A
Q
J
xA
)
T %
T
Q
<
0
0
1C
T N
T
O
+
T N
T A
K
Q
K
Y
0
T
T
T
G
DC
|
%
T H
@!
%
K
H
0 V
O
T
|
O
;
+
0 T
G
%
0 (**
#
(**
V
|
AA
G
+
%
T %
(*
, + 0
q
E
[O
t
€ w {
5
€&"%'3&&(#"0$¸&'3)³¸, '3"%/#1"‚2„ƒ#6 Œ “ŽŠ"N‰‹Š[‡'
 '3"%/1‚ 2‘"! ‰‹‡#! ‘ ™ˆ$ “Ž†&%‰Ž…T‡'“Ž('†ˆ‡ …R‘’†ˆ‡'“Ž:
‰‹…0‡'“‹:
H
|ƒ
'
M
J
0J
4 ,8> (] @
q
' > ' /2K;&
L: U7
(
(]
(*
q
'5=< C
E
!" # %$&'(! # f+.)>6H-BF509(7+.2 +.) d ]&Q25'
!
#
d) ++(7+.2 0+( ( 72 :<@(
6
O 7
1 7
. +0
4 ,8> , @
€ w { | ƒ M w | ƒ M
250+.) { +.)>0.2LD6(`26<27@ (LD 35:<-;2 +.2 '9(7+.:*(L+.2 +.276*),:<:<276GI9(7:*( DO2B+.256G2561)"G)>@GI.C;2561+.)
D<:<)>-;0.297 2X0 .@G)>:<2V+.))kG)>@GI.C/256+.)DO:H)>-/028) M 280 .@G)>:H28+.)I+(7: 7@*) DO:H256C/-;3B:H)>6&7M:H)>6<IJ)>KkC
D<-;3A(7@G)>0hDO)A> (7:-(1276f@G2B+.)>C;256I.:H25Ig276HDO27&6 7.D ,D
@ C6<)/ '.) 0
w ƒ "| ƒ
M(€
ƒ
4 ,8> @
M
€ ƒ
M
€
ƒ
250.+) +.)>0.2L6D (12G0 .@G)>:H21+.)90.2+256-/0hDO),:<@ >+.-;256++ (1:<),+.U) >
5
5
(
H
H
DC
X
~
E
`
'
DC
y
'
y
(
c
y
H
DC
%
P"
#
P
& L: SDO)>6ND6(7:fK)(L++('.@ +.256f@ DO2B+.256+.)XI.:<) 3-;6*b72G:<)( )>:H-/+.256f)>@o),I BF7:*(7( )A7,( 25-r+.),6<)>0h3725C;3B-/+9( '.@(
(7I.C;-/K&( )b72()>@
+2dK;+(7@(7++( :! 7 '.) ( ( J((-/0hDO)F5:*( &b72 ++(mK>CK(L6<6<)#"%$ K>25@
256 (7@!.-;)>0hDO),6
+.)I.:H52 F5-: (7@ ( )b72 4QNn/
[ < N ) Nn/[N! &@"> lK>CK(L6<6<)&"'$ ( 25-g+.)>6H)>0h3525Cc3B-/++(SI+(7:-(T@ (L0.-/I9'CK(7:6 ,:<-/),6
DO),@*IJ25-: (7-/6 7K>270MD<)>0.+2E)>0hD<:<)952 'D<:<256 0
D<2+.27625E6 (LDO:H- 9'D<256++ (S6 ,:<-;)9D<)>@GIg27*: (7QC 7+.) 0.-;+.256Ig27: '.@ 35),K,D<25:+)X:H)) (7-;6>=
+.-c35),:<*6 (L6\)>6N6D (LD /6HD<-/&K (7&6 7K,25@G2E2bK LC/&K 'C/2E+)8A3 (7C/25:H)>6@ G-;@*256 7 @ ;0.-/@G256i
) (7f6 (A'DO2BK>25:H:<),KC ( C
H),6>=)
@ ,D<2+.276+.)9I.:<) 3-;*6 b7216H-/@GI.C/),&
6 4yU) > F9>^7 OEN ) N[.
^ N"@">
(L*
: (bDO2B+.2562569@ ,DO2B+.256 7 ( 25- +.),K>-/+-/+.2A+.-c3-;+.-/:2569)>C;)>@G)>0hDO2569+.)1&K (7++ (A6 >:H-/)SDO),@*IJ25-: (7C ),@P+.25-;6
DO-;Ig276 +.)K,250 '.0hD<256 0 O 4' j i7 K>270MD<)>0.+2X276 I.:H-/@G)>-/:H256 )( +.256 A3 (7C;25:<),6 ++ (\6 >:H-/U) 7
) O
6O "7 K>25@o256:H)>6H*
D (70hDO),6 )( 7 '.)X6<)>-: b72 'DO-/C;- &(7+.2569I (7*: (1@*),+.-/:2*+.)>6H)>@GIg),-0 .2*+0 (
I.:H),3B-/-6 b72*+)X&K (7++ (S@ ,DO2B+.92 >
( *(
X
K
%
N
=
O
&%
&%
|
|
}
%
X
=
%
&%
p
A
*_
(_
?%
T
%
+*-, . N$B0/21436587:98;121< k (7g),CK( ,8> +)>6<K,:<) 35)8276f@G2B+.)>C;256+.) N I+(L:*(D(S6 >:H-/),6++( 2),K &b72 ,8> >/,8> \6I+(7: L@*) DO:<276+.2
@G2+.),C/2 4 7 ) @ ( 25:*(7@ )>6HK>25CE.-/+256 (TI+(L:HDO-;: +.),'.@ (TI:<2BK&'.:-(8K>25@ '.@( F5:<),C+(>=@?+.) > 7+.2
A  ž
B DC –• \™ &%
'
EHE¸
GF-H º¸ JI % LK
•M ON O• >”GP
QSR<
e” ‰• +NUTVP
(
O
-
&(6 #"%'3,
2 '3/#"
'3"%/1‚ 2
{=
4
&%
)%
'."%/1‚ 2
#56 (47'.6 #) 5)+'3"%/#1"‚2
‹†ˆ‡'‹Œ
H
_
6
4 '36 )+
(
‘ ‰‹†
‰
‘ ˆ‡'‰‹
‡ <‘

“Ž† ‰Ž…T‡'“Ž
‘ †ˆ‡'‘
“Ž†”‘
K†ˆ‡ … ‘’†ˆ‡'“Ž
‰ ˆ…T‡ 
:
_(
q
@G)>0.25:\3A(7C;25:+.)1)>:H:<2 u9v { ~!#" 7e6<),0.+.20(L6X),6HD<-/@(LDO-c3U(L6\6*(%$,250+(7-;6K)(7C;K&'.CB(7++(76IJ)>CB(769) '+(%&H),6
' >(I7 ' > ) ' > I7q250.+)Q2 0 .@*),:<2 @ G-/@G2 +.)E)>6HD*(%&&HB)>6!( 27- )>6ND6(J)>C;)>K,-/+.2 ),@
€*) > f2 K)(76H2
++(76f6 ,:<-;)>690 b72*-6 (%$>27+0 (7-/+
6 -, € " 7[(7Ig),0+(76 ( 25:*(7@ 25IDO-;@*-.$)(7+9(76
(76fK>250.6ND6(70hD<)>6+)T(7C;-/6*(L@*),0MD<21)
DO),0.+ ,0.K>B- (/10 ) 2 " >43 C;DO-;@ (1K>27BC '.+0 (I7ru9v { 657 7+)>0.27D*(Q2b)>:H:<2b+.)SI.:H),3B-/6-b72b+.)SK'.:HD<2bI.:*(%$,2
I (7-: (S256 .C;D<-/@G256 KU+.256),C/)>@G)>0hD<256++ (S6 >:H-/A) >
+
H
"q
}|
DC
z
Y
&%
K~
C
1C
H
&%
k(J)>CK(
' 9> 8:6;m2B+.),C/256+.)N=<
$?>A@CB1D
I+(76<6-(UF5),-/:<276
I+(7IJ)>C
@*25:NDO),6
@*),C J25:<0.)
'HG/@G-/)
K(
I.:<#) &>256
@ (70;K +(76
J72 J)
'9(7+.: DO-/&
K(
.)>0.270
0
>
]
_
>
]
_
>
_
>
_
>
_
_
>
_
_
>
__
_
_
>
__
_
]
'
'
>
F >_ '
_
'
8
>
_
8
_
>
_
>988
8
8
_
_
>
__
C
_
_
_
>
F C
_
85> __
>
_]
C
_
_
>
__
C
_
_
>
__
C
_
C
_
>
_
_
>
_
_
>
_]
_
'
_
>rq%
]
]
8
H
8 >(
F >]
8 ' ]
8
__
85>
|
?%
2
%F
_
I+(7:*(D(766 >:<-;)>6DO),@*IJ25:-(7-/6>
E
,
u9v { 657
>"q
]
_
]
' qI>(
]%I > '
' 8 FF
_ > ' _ >"q '
_
>
+*
3N `27 !d21# 1$
\ 25@G2 6H)D<:*(LD*(a+);'.@( D ,K>0.-;K)( +),35),:*(76m6<2%K.6HDO-;K)(7+9(87:( 25-+.),K>-/+-/+.2Y'D<-/C/-.$)(7: '.@ ( (7I.C;-/K&(%&)b72
K>27@*),:<K>-B(7C+)fI:<),3B-;6*b72L V ' ;@ ONMZ/+' " I+(7:-((92DO),0O&)b72X+.256@G2+)>C/276QP5ID<-/@G2564N[^.NRyk(J)>CB(
' >(S "TVU _BK>:H2 ( )D 7W8 FF 'CX >
Y 6@G2B+.)>C;25X
6 ( 25-: (7@2 D<-/+.276 'DO-;C/.- $)(70.+2256q@*),6<@G256 FZ)( +.256q3A(7C/25:H)>6q-;0.-/K,-K(7-;6 ++(6 ,:<-;)U7M6<),0.+.2
(QDO: (70.6 ( 27:<
@ (%&)b72bC;52 F (7[: G;D<@*-;)K (P(7I.C/-;)K (79+ (Q'7696 ,:<-/),4
6 \]^]O_`DB1@ba Gd
) cfeg1hB1i]Z>kj(7*: ((76K>27BC '.+0 (L6
tml )1v ‹ ( 25- ),6<K>27C .-;++ (J(E0.2L6D (%&&b72Q+.)T6H) 'On,0.K>B- ( oqp z osr sz t9t;z o Œ 270.+.) o lq+.),0.27*D (J(QK>2506H6D (L0MD<)
K>27:<:<),6<IJ250.+.),0hDO) (72S+.),6<C/2B)K (L@*),0MD<Z
2 S->j‘25:") G)>@GI.C;92 79(T6 >:<-;u) \@bDva \@*2B+.),KC (7++ (VIg),KC (8C) '9(%&)b7H2 :
w ~e€ w ~‰x
ˆ p H t L ~‰xˆ p >
)%
)
&%
&%
-
?%
B%
3'
+*y r$y 1$>9\{z$ 1}| 3~mzW 3@Yg256R256 @G2+)>C/276RI.:H25IJ256HD<256 ( (%$,)>@ '.6<2+) '.@( 3 77 '.) +.)#K0) '9(7C9(-;0,( 25:H@ (%&&b72 ')6<),:€
( 25:H0.)>K,-/+
+ (E(W'.@ ++(L+.2@G2B+.)>C;297"25'86H)ƒ‚-(87L2K>270C‚'.0hDO2+.) +.),6<C;2K&(7@*),0hDO256‘+.)DO)>@GIJ2W'D<-/C;-„$)(L+.256rI+(7:-(
K>270.6HD<-: '.-;: '.
@ (I.:<) 3B-/*6 bL92 >Qj(7*: (f(7C >@ +.-/6H6<92 7LDO25:H+0 ( C–6H) D6(L@! ,@ 0)>K>),6<6…€7:<-;2+.)#K0-/: '.@ @G2+.),C/2+.)
(7I.:H)>0.+„- $)(AF5)>
@ (7+) '+(7+.82 7 52 'm6<ƒ) ‚-(I7gK,25
@ '.@ (G:<),I.:<),6<)>0h*D (LDO-c3-;++ (7+.†
) y52 'mK>[email protected];") G-/++ (L+.) " +.) 35)>-: (76
%
A%
A k(J)>CB(
t
‚
$?>A@CB1D
I+(76&>
I+(7ZI >
@*25: >
@*),SC >
Z > Z Z
Z > ZZ
Z > ZZ
Z > ZZ
Z >' Z
Z > ZZ
89> S
' Z ' I
Z > I
Z > S
'HGS>
I.:<)A>
@ (7a0 >
J72 Z>
'9(8>
.)>0Z>
' > S :6;m2+)>C/276,N[^.N
l
pz
p1r zIH
zp p1r Iz H
p z p1r zIH
p z p1r Iz H
t p
!
!
!
p
H
H
H
H
zIH t
zIH t
r
r
zIH
H
t# p
z
t '=' p
t p t *
p t
p z
z
z
u9v {
8
z
t' r
zIH
8!
t ( r
zIH
t )
t(
I
657
H
85> Z
Z >F 8
Z >' > S
IS >
I S
Z >' Z > '
>
zH
t p
zIH
t
p
t * )p
t 3' p t ) ' 1p r
t p1r
t p1r
t
p1r
zIH
t p
t )%)p
zIH
t #=* p
p
&%
H
p
t #
p
t 6 p
p
!
I9(7:*(D(766 ,:<-;)>6DO),@*IJ25:*(L-/6&>
v ‹
p
6 = ƒ6 .6ND6(7+9( (72 DO-;Ig2 +.)AI.:H2.C/),@ (c( DO:-(LD6(7:> 36<6<-;@$7m( '9(7C/-;++(7+.)A+.)'.@@G2+.),C/2 +.)(I.:H),3B-/6-b72
+.),Ig),0.+.)>:…€*+.),6HD<)>6f+.25-/6 ( (LK,DO27:<)>6#:2(=‚-(L0.)>CB(8DO)>@GIJ25:*(7C )(SK,25@*IC/)"G-;++(7+.)+.21@G2+)>C/28>
n'+(7]C (@*),C .27: 3 I+(7:*(f'.@(\++(7+9(X6 >:<-;)DO),@*IJ25:*(LC@(6‚-(70.),CK(\K>27@ (7C;D*(\K)(7:H+.-/09(7C/-;++(7+.)
IJ2+.) (U'.@G)>0h6D (7: (\K>[email protected];") G-/++ (L+.)d+) '.@ 6H-/6NDO)>
@ (87L+..- KK '.C;*D (70.+.n2 (n(7I.:H)>0.+..- $)(UF7)>@ +.) '.@ @*2B+.)>C;297
)>,0 '9(70hDO2 'L
) ‚-(70.)>BC (76Q+.) +(L^- G8( )K (L:<+.-;+0 (7C/-;++ (7+.)mIg2B+.),@ K>270MD<)>:b-;0.-6 'HK.K>-/),0hDO) -/0 ( 25:<
@ (%&)bL92 >R3
6<),C/),^K &)bL2Q+.256+.)>6HC/2B)K (7@G)>0hDO276DO),@*IJ25-: (7-/6:<),C/) U3 (L0MD<)>6\IJ2B+.)8@G)>EC .25*: (LW: (GI.:<) 3B-/*6 bL92 >=j‘25:k) G)>@GI.C/92 7
256S@G2+)>C/27T
6 N[]›
^ N K>256N*D '.
@ (7@ 'DO-;C/„- $&(7:X256T+.),6<C/2B)K (L@*),0MD<256 57 ) +I (7-: ( 6 >:H-/),6S*6 (%$,25+0 (7-;6
K>27@WIg),:<-;2+.-;K>-;++ (7+.)@*),0.*6 (7Cr)9K,25@ DO),0.O+ n,0.K>B- (8>
@ ((7I.:H2 G-;@ (%&&b72b)>@GOI G;:<-/&K (J(Q)>6NDO)1I.:H2 .C/),@ (Q9I (76<-6 (AIJ25:6HP
) 'DO-/C;„- $&(7:-;,0 ( 25:H@ (%&&b72 +(L6<)) (L++ (
0+(.(7x0 €LC/-/6H)S++ (b6 ,:<-/)SD<)>@GIg25-: (7SC >+jR25:9K,250.6<) F5'.-;0MD<U) 7 '+(LD<:<
2 .&) '.[: G/6NDO-/&K (766<),*: b7
2 'D<-/C/.- $)(79+ (76+I (L*: (.(
6<),C/),^K &)bL2*++ (m‚-(70)>KC (TD<)>@GIg25-: (7SC 7 +(76H)) (79+ (760256U3 (LC/25:H)>6+.) (U'D<2K,25:<:H)>BC (%&)b782 70.25@G)) (L++ (7@G)>0hDOq) :
CZ'.
@ ( 3 K,[email protected]/) 6D (87LK>25@lDO2B+.256R256 +)>6<C;2&K (7@G)>0hDO256‘+.),6<+.) %(LD m'.@ L
@ € G-/@G2 : €
5z sz t9t.tcz Q( ( 25+- ( DO:<E- 9'OG;+.2\2A3 (7C/25:R+.) ƒ € 87 '@ A3 (7C/27: K>2506<-/+)>*: (L+.29-6 'HKK,-/),0MD<)
I (L*: (S)>90 F7C/2 +(L:256C) ( ),-;DO276f+)X6 >:H-/)>6K,25@WIJ)>:<-;2+-/K>-;++ (7+.)@*),0.*6 (LCr)9D<)>0.H+ n>0.K,K- ( " =
+
C'@ ( 3 K>25@ DO2B+.256q256+.),6<C;2&K (7@*),0hDO256qK 'C‚-(7@6 (U'D<2K,25:<:H)>BC (%&&HB)>6q-6 b729-6 '.IJ)>:H-/25:H)>26 (n'.@++ (L+.2
3 (7C;25:C/-;@*-cDO+
A
) Q( '.U) 70.276D<)>:H@*256I:<)>6H)>0hDO),&6 7 (LDO:H- 9'OG;+.2S2SA3 (7C/25: +.) t " =
C '@ ( 3 K,25@F27:6 '+(LDO:H2b+.)>6HC/2B)K (7@G)>0hD<256\K>27:<:<),6<IJ250.+.),0hDO)>6V'7f6 (A'DO2BK>25:H:<),KC (%&H),6K>27@ '.@
3 (7C;25: A
@ (7-/6 ),C/) U3 (L+.†
2 0.29)K (76H2V9+ (766 >:H-/),6d-6 (%$>2590 (7-/6qK,25@&DO),0.O+ n,0.K>B- (87M)>6H*D (76 ( 25*: (7@ )K (7C;&K '.BC (7++ (76
(7I P5@
6 '.
@ ( ' ?@ 5=< = =67M++ (L+.Y
2 '.)f256C) ( )>-cDO256+.)DO),0.O+ n,0.K>B- (XDO),0.+.),@ (96<2 .:<),Ig25: C–6H,) (7276
+ (S-6 (%$>2590 (7C/-;++ (7+.) " =.)
+
Q+Q ¸
! ¼¸ " H¸ "# º¸ %$ '&"Ÿ(#¸
‘¸ ¸ ¢¸*) "# ,+ ¼¸.-
02/ 1 - 043 - 06587 P
(b‚'
?%
13'
;#
&%
&%
B
'
B3'
)%
;#
?%
%
'
&%
67 & 272
2 '3,
%1 2
)
6
1.'3,'."
6
%,
4 "0) "0&('
&("02 '32 4
,
)
0"%'36
0,
5"%
2 67'
2 .6<2G+.)9-/0 ( 52 :<@(%&)bL2T+.)9+.)>K,25@GIg256H-„&&b72.=.-Q> )A>X7
C D'
€
6-(%$>2509(7C
,
6H) A
( 6 ,:<-/)Z( 25:96-(%$>2509(7C)*0+bL2m),6HD6(LK>-/270x€7:<-B( y K>27@j'.@
IJ)>:…G;2+2
&%
5z, s6<)(16 >:H-/):( 25:6-(%$>2509(7C
=.)
€
€
"
5z, z7, ƒ
" =
3lk(g),CK(76 ' > ' ) '
++(),K^)& bL2 ' >985> ' >
>
?%
) $
€
5z s6<)(S6 >:H-/):( 25:09b72*),6HD*(7K>-;250x€7:H-K(8>
'$
S@*276HDO:-(7@(L6‚-(70.)>CB(76&7+.)#K.0.-/++(L6f6H)&F5'0.+.2G)>6HD*(76*.)&':…G/6NDO-;K)(767.I+(7:-(i(766 ,:<-/),6
&%
k(g),CK(
' > ' :)'.:…G;6HD<-/K)(L6I+(7:*(D(766?%>:<-;)>66*(q$>250+(L-/6&>
$f>A@qB D
iB ] " D
I+(L6<6*(AF5)>-;:<256 -/@
D D &%
De @ba ]xB@
I+(LIg),C
-/@
@G25:HD<)>6
,b72
@G)>CEg25:H0.)
,b72
! "B B @bDiiB a#
"
34857(SI7^>X>^>^7.8 '
\45
8 79858 798bI
S 798 ' ?45
8 798bI
S 798 ' 3458 7(I
S 7^>X>^>^7.8 ' 458 7 ' 7 F 7.8%58 7.8 IS 7.8 '
\45
8 79858 798bI
S 798 ' ?45
8 798bI
S 798 ' 3458 7(I
S 7^>X>^>^7.8 ' 458 7 S 7.8 Z 7.8U8 7.8bS 7.8 '
\45
8 79858 798bI
S 798 ' ?45
8 798bS 3458 7(I
S 7^>X>^>^7.8 ' U8 7 IS 798 Z 79858 798bIS 798 ' \45
8 79858 798bI
S 798 ' ?45
8 798bS ]OB+
L: (¡3A(7C;-K(7:@( '9(7C/-;++(7+.)+.)K)(7++(X@*2B+.),C/297( 25:-(7@DO),6HD*(7++(76d+.-;37)>:<6-(76f[
<J=RO"7K>25@ 2V0 .@*),:<2V+.)
0.2B+.256d-/0hDO),:<@ >+.-;2562(X3A(7:<-B(7:)>0hDO:H) Z ) 8 ' 7B+.)@G2B+.2 (X)"GI.C;25:*(7:DO2B++(76%(763.)&'.:[G/6NDO-/K&(76 +)‚-(70.),CK(76
DO),@*IJ25-: (7-/6 > Y 6IJ)>6<276-/0.-;K>-K(L-/6 ( 25:*(L@ (LC/))( DO25:H-K(7@G)>0hDO)EF5),:*(7+.276+.)>0hD<:<2S+.2S+.27@LG;0.-/2 ˆr z r Q7I+(7:-(
'[email protected]+.2*K>25@
A)>0hDO-: (7++ (7k
6 35),: ),K^&&b72 SI>985> " > ?n(7+.2 '.)X+.- ( )>:<),0hDO)>6f3A(7C/25:H)>6f+.)XIg),6<256-/0.-;K>-K(L-/6
IJ2+.),@ K,250.9+ 'H$>-/: (+.- ( )>:<),0hDO)>6 I.:<) 3-;-6 HB)>6 75DO:<-;0h6D (,(LI.:<),0.+.„- $&(UF5),0.6 -/0+.)>IJ)>0.+)>0hDO),6 ( 25*: (7@ (7IC/-/&K (7+.256
(S)
K (79+ (G@G2+)>C/82 7IJ25: ( 25:<
@ (i(iF (7-: (70hDO-/: 6<B- F70..- K%K $70.K,K- (T)>6N6D (L…D G/6NDO-/&K (8>
j
( *(
DC
%
5
5
A I
k(J)>CB(
6 = ƒ6 ' > O:f)&'.:[G/6NDO-/K&(76I+(7:-(D(766&%>:H-/),6f09b7216*(%$,250+(7-;6&>
iB ] "
34857(SI7^>X>^>^7.8 '
-/@
\4857(SI7 ' 7 ?4
8 ) 4 857(S 34
857(SI7^>X>^>^7.8 '
-/@
\4
857(SI7 ' 7 ?4
8 ) 4 857(S 34
857(SI7^>X>^>^7.8 '
,b72
4 857(SI7 F 7.8 Z 7.8%857.8 S \4
857(SI7.8 Z 7.8%8 ,b72
34
857(SI7^>X>^>^7.8 '
\4 857(I7 7.8 Z ,b72
34
857(SI7^>X>^>^7.8 '
\ I 7 F 7.8 Z 7.8%8 ,b72
34
857(SI7^>X>^>^7.8 '
\m SI7 97 I 7 F $f>@CB D
" D
/@G-/K&(
'OG
I.:H)^&>276
@(70.K;+(76
J72g)
7+.:…€LDO-;K)(
'+(
.),0.250
7C 525:<-cDO@G2a[
/[ / ( 25-n(7+.25ID*(7+.2aI+(7:-(Z2ZDO:H)>-;0.297+9(7+.2 ')`IJ)>:H@*-cDO) ),@ F5)>:-(7Cf'.@(
K>270M37)>:Fn>0.K,K- (S
@ (7-/6: €7I-/++(87B6<),0.+.2SD6(L@! ,@ @ (7-;6 ),6HD7€¡37)>C),@UDO),:<@G256 +2D(b‚'.6HD*(7@G)>0hDO2T+2566<)'.6
I+(7: $7@G),DO:H25m6 ( 25-: (7`
@ 'D<-/C;„- $)(L+.256 256qA3 (7C;25:<),6m(LK>250.6H)>CE+(7+.256I+(7:-(X),6HD<)>6 I9(7: $7@G),D<:<2567MK>25@ € t
)
€ t T U -/),+.@G-/C/C;)>: 7 8 FF X " > Y DO:<),-/0.2V++ (V:H)>+.) 9+ (7+.28K,25@G
2 K0+.!
2 '+(70.+2T2VI:<25F5:H)>6H6<2
0.2 D<:<),-/0.2 +)>)K (Lu- € m
) € t " 52 '9 '+(70.+2 6<
) (LD<-/90 F7)E2 0 .@G)>:H2 @ €gG-;@*2(+.)Q-cDO),*: (%&H),6
€
"T jq:<)>;K )>C;&D 7W8 FFI X >
+ (@G),DO2B+.25C;52 F5B- (%'DO-;C/.- $)(7++ (I74-/: C6<k) Cƒ€") GI.C;-/sK €gC–KC (),@l+.),*D (7C )9I (7*: (E(6 >:<-;6) h] i ]
@DO)>:H@*276R+
y
k (J)>BC ( ' >( " >3 'S- 79(LIg),+0 (76dD<…: n,6 ‚-(70.),KC (7=6 y+.- ( )>:H)>0hDO),6 " -6 b7T
2 'D<-/C/.- $)(79+ (7&6 7h++ (L+.!
2 '.)\6H)DO-: (L6D (V9+ '.
@ (
6 ,:<-;)V),6H6D (LK>-/27x0 €7:<B- (yk (g),KC ( ' > " > j (7-: (*6<-;@*IC/.- K.)K (7: (G") GI.C;-/)K (q&)b792 7](LIg),+0 (76f6<)>-: b72*3B-;…6 G;37)>-;,6 (7XC F5'.0.6
+.256:<),-6 '.Cc6D (7+.276:H)>C/) A3 (70hDO)>6 > Y 6f:<),-6 '.Cc6D (7+2569+ (76 .CcDO-;@ (76 '+( DO:<2*K>25XC '.+0 (76f*6 bL2E++ (7+256),@WDO)>:H@*276
+.0
) '@ ( @ >+K- ( 6H2 .:<) 256 ' Z DO:<-;0h6D ( " DO:<),-/0.27&6 > Y 6Q-/0hD<)>:HA3 (7C;256E+) K>250 K](7O0 &&(879I (7*: ( '@ O0 Gc35)>C
+.) 6HB- F50.9- KK $L0.K>B- ( +.) K76D (L!
@ ,@ -6 b72Z") G- -/+.256E+I (7*: ( 276Q)>:H:<256b+.) I:<),3B-;*6 b72 3I n>0.+.-;K>) 3 "
T C/k) G),&: 7W8 F%F X >
Y @G)>0.27:)>:H:<2+.) DO:H)>-;0.
2 u9v { !~ | @(LDO-;90 F5-;+.2+I (7-: ( (‚-(70.)>BC (!0
7¡K,25@ 8bS 02+.276r-/0hDO),:<@ >+.-;25&6 >
@ '.@&0 @*),:<29+.)>
@ (76HK- (7+.2)>C/) A3 (7+.29+.)+I (7: $7@G),DO:H25&6 7h.
2 '.)C/) A3 (f('@ (\IJ)>:H++ (
6HD<)f@G2B+.)>C;2\K>250hD >`
+.E) F5)>0)>*: (LC/„- $&(%&)bL92 > ?) ( (7K DO92 7M
2 (U'.@G)>0hDO2X+.2X0 .@*),:<2V+.)02+.276-;0hDO)>:H@ ,+.-/276qI.:<24352B)K ( '.@ @G)>0.25:
)>:H:<2m+.)*D<:<)>-;0.92 >\ 250h-D '.+.92 7 '+(L0.+.2 *D (72C (7K>250hD<)>K>A) 7 2 +)>6<),@*IJ)>,0 .2 +.2 @G2B+.)>C;2AD<)>0.+J
) (mI-/25-: (7&: 7
+.) 3-;+.d
2 (0'.
@ ( )>6<IJ)>K,K- (7C;„- $&(%&)b72 ++ ( :<)>+U) > Y @*2B+.),C/2 6 '9F5)>:H-/+.2 IJ)>C;2568A3 (7C/27:<)>68+.)bt FK,250hD >@
Y
( XF
A%
4
*
%
DC
<
==
?%
&%
C
%
*
A%
H
&%
A%
%
6C
DC
%
)%
F
7-;0.++(c'.@0 .@*),:<2)>C;),3A(7+.2`+.)mI9(7: $7@G),D<:<2561)A7Ig27:G2U'DO:H2`CB(7+.297D6(7@Y ,@I.:<2B+9'O$'.@6<2.:<)kC
(b‚'.6N6
D (7@G)>0hD<29> Y @G)>6H@*2 0+bL2`6'.K>),+.) I+(L:*( 2`K,:<-;D >:H-/2 P70 '.)( '0.K>-;250+( 0.25'D<:<256SDO),:<@G256&7
6<),C/),K>K>-;25+0 (70+.0
2 '.
@ ( :<),+.) '.) ( 27:<0.),K>
) '.
@ (m++ (L6T@*),C .27:<)>6VI.:<) 3B-/-6 HB)>68+.)Q&K ':HDO2 I.:*(%$,2 yK,25CB'.09(
u9v { 657N" > k‘2B++ (¡3B- (87 2@G)>C 25:S:<),-6 '.Cc6D (7+.2+.)AI.:H),3B-/-6 b792 7K,25:<:H)>6<IJ250.+)>0hDOL
) (72 @*),0.25:1)>:H:<2+.)
I.:H),3B-/-6 b792 7+I (7:H)>K,)X-;+0 (LD<-/90 FGc35),SC >
(
DC
A%
&%
H
k(J)>CB(
)>6'.C;D*(7+.256+9(76\[E<J=ZO8I9(7:*(D(P(g27:<++(UF7)>@ ),@*IHG/:<-;K)(T'16 ,:<-;)4h] 3
M
u9v { ~! t u9v { 57
' > : U
&%
Z
3
8!
8 Z
Z
\
I
8 '
8
F
888
88
'
8 I
S 8b
8 ' F
8 8 8
8 ' F
8!
8!9> I
858 >(
8 ' 8 ' Z S
8 ' S I
8 ' %S
8 ' S F
>
8bI>98
8!9>98
8 Z >
Z
Z >'
Z >
Z >I
Z >Z
Z >'
Z >
>
Z >I
8
Z .> 8
8 F >Z 8 I >98
8 >I 8 F > H
8 I >(S
S Z >(
S Z >(S 8 >I 8 Z
8 ' %
8!O8 F
8 F
8bS
Z
H
8!9>
858 > i ]U>
7: 7+ A)T\++(LD[K)>C;+ T 8 FFI X :<),K>25@G)>0++(7:*(L@o2EK>:H-;D >:<-;2 I+(7:-('.@(*K,25@GI+(7:*(q&)b72G)>0hDO:H)
+.- ( )>:<),0hDO)>6fDO25IJ25C;25F5-K(L6+.)G[
< NnO"7g)>@!J25:*((7IJ)>0+(76DO),6HD*(76<6H)>@ '@ ( .0.-/K&(*6 >:<-;)† \] !^]O_`DB1@ba " >
@nDO),6HD<)T@ (L-/6f+.),*D (7C +(L+.92 7 6H2.:H)T2Q+.),6<)>@GIJ)>0-.2A+.)8K)(7++(*K>:<-cD ,:<-/2*+.)T6H)>C/),K^&&b72b+.)T@G2+)>C/276&7
( 25:H0.)>K,-/+.2G+
0 (*k (J)>BC ( ' > > 3>i 4 V+.)X)K (L++ ((^ 1 ;@;@ 4 $
^ 1 6<),: €G@*),+.-/++ (1)>@
DO),:<@G256 +B) '+b72T+-/6H*D (70hDO))>6HD €87),@ D<)>:H@*256IJ)>:<K,)>0h*D '9(7-/6 7.)>@ :<),KC (%&&b7T
2 (L2T@*),C .27:@G2B+.)>C;2V2 DO-/+2
S " 76<)>0+.2E++ (L++ (SIg),KC (S") GI.:H)>6<-6 b7O2 :
( *( 9( _
&%
C
?%
)%
6
6
%
u9v {
5
H
w v| H u9v { 657 w S |
u9v { 657 w S |
' >98b "
H
H
6 :<),6-'.CcD6(7+256SK>250K:<@(7@ '.)( @*),+.-/+9( +.)Au9v { ~! 25:H-BF5-;0+($'@Y6H2.:<)kC(b‚'6HD6(L@*),0MD<2 K>25@
T
(76T[
<=ZO">d369IJ25'.K)(L6X)kGK>)>I &&HB)>6V2K,25:<:H)>@PK,25@(766 >:H-/)>6X0+b72A),6HD6(LK>-/270x€7:<-B(76&7r),@!J25:*(b6<){‚-(b+.)
6<)8)>6<IJ)>-: (7B: '.) F5)>:H) '.
@ (*IJ)>:H++(E+.)TF7)>0.),:*(7C;-„$)(q&)b72GI+(7:-(E:<),+.)>6\K,25@'.@n0 .@*),:<2Q@(7-;6f),C/) 3U(L+.2
+.)T02+.27&6 >u3Y
@ g256256\K,:<-;D >:H-/256ft ) U6 '9F5)>:H)>@ @*2B+.)>C;256f-/O+ n,0MD<-/K,256+I (L*: (J(E
@ (7-;25:<B- (G++ (L6
6 ,:<-;)>&6 >k‘29+ (43BB- (87, '+(70+.21K>250.6H-/+.),*: (79+ (P(T@ >+K- (TF5C;2 +(7QC 7I(S),6H6D ( D G/6NDO-;)K ( ( 27:<0.),K>f) '.@U@*),C .25:
+.),6<)>@GIJ)>-0 .82 7‘6H)>0.+2 '.P
) (b+.E- ( ),:<),O0 &)(b-6 '-: F5)1)>@ @*2B+.),C/256\90 b72AC/-/0)) (7:H)>d
6 1h] i ].69) D a# " 7
)>@ ') (S+.-;6<K>:H)>I $L0.K>B- ( 9+.) Ht 4 KJ7.),@W@ >+.B- (87.+I (7-: (S2G@G)>EC .25:+256@*2B+.)>C;25&6 >
36V@*),C .25:H)>6T
[ <=ZO"7RD<)>0.+2 )>@ K,250h6D ((2 K>:H-;D >:<-;2 P7R*6 b7$
2 (7I.:H)>6<),0h6D (7++ (L6T+0 (Ak (J)>BC ( ' > >
\ 25@G2S)>6HIg),*
: (7+.82 72GK,:<-cD >:H-/2T6 '9F5),:<) (T'DO-;C/.- $)(%&&b72T+.) ‚-(70)>KC (L6+.)9IgC) '.)>+0 (1)K (L:<+.-;+0 (7C/-;++ (7+.A) 7 ( (¡3725:<k) C
Y
H
?%
DC
&%
&%
%
+%
#
#
%
&%
)%
A IZ
k(g),CK(
'
>
6 = ƒ6 :@?),6<)>@GIJ)>0-.2*+.256K>:H-;D&%>:<-;256+.)96H)>C/),K^&&b72*+)X@G2B+.)>C;256I+(7:-(D(76\[E<J=ZO">
u9v { ~! t
$?>A@CB1D
I+(76<6-(UF5),-/:<276
I+(7IJ)>C
@*25:NDO),6
@*),C J25:<0.)
'HG/@G-/)
K(
I.:<#) &>256
@ (70;K +(76
J72 J)
'9(7+.
: € DO-/&K (
.)>0.270
8 ' > (
H
8!8> (
9> ZZ)(
8U8 > (
(
(
8 I > (
8bS > )I (
S >' (
8 F >' (
8bS > ' (
> B1]
>
(
(
(
F 8 (
(
(
(
(
(
8bI>98 (
(
(
8!9> AS (
(
(
S Z >I (
I> I)(
(
(
(
(
(
K>),0.+.2 (76 ),6HD<:*(LD &F5-B(76 ) 75(76H6<-/@ K>27@*2256 @*2B+.)>C;256‘C/-/0))(7:H)>6&77K>25@ l € 0.2B+.256 -/0hDO),:<@ >+.-;256&7
I+(7-: (\DO2B++(76@(766 ,:<-;)C/-/0))(7:H)>6&>j (7:-((766 >:H-/),609b729C/-/0))(7:H)>6&7 (),6HD6( DG/6NDO-;K)( I.:H-;3B-/C;)&F5-B(‚-(70.),CK(76
+.)b
@ (7-/27:X&K (7:<+-/+0 (7C;-/++ (L+.U) 7 K,250hDO),0.+.2 )>0hDO:H) (8 ' ),0MD<:*(7+9(76&> \ 250hD*'.+297K>250hDO-;0 '+(M( ( (¡3525:H)>K>),:
DO27Ig25C;52 F5B- (76+.):<),+.)+.),37)>-: (766<-/@GI.C;)>u6 K>25@ $>),:<2S52 ''[email protected]+.256-;0MD<)>:H@ ,+.-/256 " I+(L:*(i(766 >:H-/)>609b72
C/-;0.)) (L:<)>6 1h] i ]d) `a D " >Qj‘25:Rk) G)>@GI.C/92 7A(76‘@*),C .27:<)>6eI.:H),3B-/6 H),6 +I (L*: (E(6 ,:<-;) h] i ] U77-6 b72
2 D<-/++ (L6K>25@ '.@ (T:H)>+..
) '.)9K>270MD >@ T0.2B+.256-;0hDO)>:H@ ,+.-/27&6 7),!
@ J25*: (TDO),0.+.21K>27@*21K>270.6<C) 'Hn>0.K,K- (
'.@W
@ (7-;25:dA3 (7C;25:+.) D7+.),3B-/+2 (7210 .@G)>:H2G),C/) U3 (L+.21+.)9K>250.k) GIH),k
6 k (J)>BC ( ' > " >
&%
&%
%
&%
%
?%
&%
&%
%
DC
k (J)>CB(
$f>A@CB1D
I9(76<6-(UF5)>-;:<256
I9(7Ig),C
@G25:NDO)>6
@G)>EC g27:<0.)
'OG;@*-;)
K(
I:<^) &,256
@(70.;K 9(76
JL2 J)
'+(L+.
: €LD<-/&K (
)>0.250
'
[
<=ZOTK,25@W21@G)>0.25:3A(7C;25:+.)
:
>
3
l
485798bSI798 '
?485798bSI798 '
\4857.8%857.8 SI7.8 '
\4
857.8%857.8 SI7.8 '
?4
857(S ?4
8
4 857(SI7 F 7.8 Z 7.88U7.8bS 34
857(SI7^>X>^>X798 '
34
857(SI7^>X>^>X798 '
34
857(SI7^>X>^>X798 '
Z
?
u9vs{
M
Z
Z
Z
Z
'
Z
8
F
Z
S
D>
S
88
8!
8! F
8 I > Z
85> Z
8 ' 8
Z > FZ Z
Z > Z Z
> F Z
8 >I Z
% Z >Z Z
Z > ' Z
57
>(S
>(S
H
Z S
>
Z 8
> ZZ
>'
>
Z S
>
>
Z _
I 8
a1e iB1a#
O@CB1a Y ! " ( ( "# ( %$&'( &&H )(*(* ( &+)(*# ( +,
- <=ZO"7 ' ‚-(H:
' (*( $)( './ ( ( ' G !(*$ ( 0 ( (( ‚-( ' ( 1!&23 ( (*&45
# ( ( $)( ' ' Z !(' ( " ( ' (q&&H 6 ( ( $ ( ( 2&* 7 .2 ( ( # FU' ( ' ( &* C
7 $ '$&( ( # ( G #(*$ (I7 &'8 ' ( ( #&' ( 9:!&8 ( ( ( 1&3$&( 7 ('; 7 ( *15)$&' K]( ' &)( ' ( #<5 F ( " >
=0 ( $&' K+FU' (%&&b > N! <m7+( 03 ' (%&&H ?(*'($( ( (* ( ( F & ( ( ( * ( !#( ( ' 7
$ 7 ( &3 !&'$&' ( (*'!& 7 ( * H @ S>3 $ ( #(*' ( *(* ( > ( 3 ' (%&&b ( (A K '( (
( ( 7 ( *B BC=D >+3 ( ' ' &)b ( 5!( b ( ( E!&#F G/
H$ ( H!#(' M SJILK VMDONMPOQ 0!R #" > YS5$#M&*$ &)b ( *( $)( ( ! ( 7 6 ' (
@ UT '*O < G
V ' ' 5=< $ &&b S > SI> " > j( ( 5$#W5 ( 2 ! (UF 7 ( ( ' (*( $)( ((
$'($ ( ONM$'YX 6ONM @Z ONM A@ @ O\[ "ONM M][ 5=< #! ! P' !(*( $&( ( ( $ C
$(' ( 6 Z)(<B(*'( 7 G ' ' G b ^ ( '!(6' ( 3 ' (%&)b 7 $& ( G $& &)b F22& (*'5( 7 G ' 7 ' #^# ( '; `_ D " > Ya&# ( '! bD ) K " (*'5( 7 G ' . b F & ( 7 ( (P( *($ (%&&b GH3 ( # F &' (*$ >
j ( ( 6$ 'O$)( ' 7&( ($& (*6B& ( ' M >NM A@ &$ &&b SI>(SI> " 7 #'#' € 7 &
3 (iF & (%&&b M(*1 & 6H&$&'&'; 7 ' '+( ';cH## ( '!&'!6 b >$#( ( 7 ( (M' ( a[ M 5=< 7 5 K '( (d( ! ( 7 ' ( (#( 8' ( &&b F (U' #( ( ' ( $ ' ( ( ( $ #
( > >X7 & F ( 7 # b F & ( ( B3 ' +(%&&H B$ ' 7 ( 0& 'O$ (* " >j d!(2 7 36e ( 5$& K ' ( P fD
F (%&&H >
3 G ' *a& ' $&(* ( ( 7 7 H& ' d ( B# b c&$#(B&g'0 ( (P( ( h] i ]
i
h ( ( ' > I " > 3 ' ( 7 ( j>$(d (* ( #&' ( $< #1# ' ( 7-( ( 7 C
$&' (u‚-( '& ( !&23 ( 7 ' ‚…€ !(' +(P( $';$&(*2 7 ( ( '!M$ ( - <J=RO;2 & ' &*$&$(' ( >> 1/&*aM# 7 (* b >
#!k$23# ( '!W$ ' ( ( $'(#!&'!k$l! ( ( a ' ! ( #(* 7 $&
3/0#A$2# 7 ( M& (h (7 & ( ' > F 7 '5 ( (2&(* ( (/ '+( (* ( 1A$&( #(*9H#*&$ &&b H/&*8 ( ( N! <@O">4? H# ( #(* ' HM$#( ( NMPmQ 0!R ! ' n&3' ) ' &(*
( o (*p ( (c( - <J=RO"7 7 (*5 ( ( ( $&!o ( ' (? G (* !(* ' ( 'a( ( &' &)( '!#
/&* 7 &%!#2' 2&W ( $ & > ' ( ' 7 q$&(d #(* ( &&'; (0' (
( (T( (*'5 ( 7 ( ( 9( ' ( &' ( 1& Z > )(r ( ( (*'($ ( sa ?/5* >
'+( (* ( 5
j K 7+(G
h ( ( ' >98 ZG# ( H & N! <@O"7 $#&3'&' ( 0'# 7 ( *
P>ut s ( &&( ' s2v&$ ( ( (W( (w*(' ( #x b B&m ' B( n '(*$
a`@CB bha †
D > bB1ia D
%
!
G*
%
%
H
>
6
%
6
%
>
%
%
%
H
%
E
%
%
C
%
=
%
%
%
%
%
%
%
H
%
C
%
%
A I S
h( & (
' ( 0
' >I : U
3
3
N!
e8
eS
e8
\
h ( (
' > F :@?
eS
e8
eS
<
6 = ƒ6 ( (P(P( (UF = G # (*$ ( +a #(*
NMPOQ 0R! MN POQ 57
N! @
< O
M
S
8!
88
8 '
8
%
89>
8 I
>
H
>
8!O8 S
8 ' F
8 ' 8!
8 ' I I
8 ' F
8 ' %Z
8 ' %F
8 I>
8 I
>
8 F >F 8 F > S
8 I > S Z >.8 8! 8
h]
>
Z
Z >(
Z >98
>
Z >Z
8 I > I Z >98
8! ZZ
%
H
i ]A>
H
Z
#&' c 5H$(d (*1M&*$ &)b M/&*? ( ( $f>@CB D
NMPmQ 0R! ( # (UF (*# (
(
(
( 3
(
(
(
#
(
(
(
#' (
(
(
'OG (*$ (
(
(
(
# & SI> I 8 (
(
' > I%I)(
( '$ +( > ' I)(
8bSI>(S (
(
J (
(
(
'+( € !($ (
(
' > (
' >( (
Z >' 8 (
Z >' 8 (
&''
(
SI> %Z)(
SI> I)(
(
> B ]
N! @
< O">
m O
0 ! (0 - <J=ZO"7 $ G $& &)b (* cfeg1hB1i]Z>4? ( $\! 7 2&
'& 7 ' b G (* !S( ( &&' & 9&'! - <J= &b' ('!# (*81/5*
( ( #' & #&' # 7 '(*$ 2&'! (*3 5 #'5( $ F +7 3 (**( $ 5 >uh $# 2&'; ‚…€ ' b a# U&$& 1 (0' b .*(*'5 # 7 '5 '& 0#$$&(*' H ‚ <# '! 7 H2&*1&$& (0 b ( ( &' >
‚
3
F (
&
#
#'
G 2($
# & '$ J 5 € (*$
&''
%
N!
ed8
4857.8 SI7.8 '
?4857.8 SI7.8 '
\8U7.88U7.8bS 7.8 '
\
8U7.88U7.8bS 7.8 '
?4
8
?4
8
\
8U7 SI7 F 798 Z 34
857(SI7X>^>^>X798 '
34
857(SI7X>^>^>X798 '
34
857(SI7X>^>^>X798 '
?
$<>2&' 7 * 1
' 9> 8 Z :2N! <@O
$f>A@qB D
h & %
%
‚
I '
J 6
<
ed8
ed8
e
S
'
ed8
S
ed8
e
S
e
S
e
S
S
NMPmQ
H57
S 85> F d8U> S
Z >(S
S >S
8 ' I
> F 85>
Z > F Z > Z S
Z > ' Z > ZZ
> F Z >Z 8
8 >F Z >Z
Z ' Z >' Z >Z 8
Z > I Z >Z 8
M
ed8
P>
S
S
!+"#$
' € * (*#M &(1!&23 (* ( '&$! <$&' ‚ '2('($ /!(0 ' \T #
< >'
V &' $&2 $&#( & >6$''!&B $ ' (*H)M!'5 n '$&(
$ K $(*&'! ! J$#& & MB &(*$ sB&# j 7 *( & ?95 7 ( #*&$$&(*' 6( 7 6 #(*&H ( # (0 !( K $( (* $&g( ( &&';6$ $& G ( !($ 0M#( '5 0M G '5(* (* !(*'
##' 5B6 &/50$' 7 '$&(*' (*6M 7 ( ' 2&';
g (*
&! ( 5
#(* $22/&*H.
xM < V
?@ 7 (* q('( 5M' # $ #'q $\ * 7 ' '!k# W ! ##!a(*.2.5k5 7 ( #'oo#(*(*# o' p# '
' ###' & 7 &B# ( 3 36#/5*6&# K '(*
< $
$#.$& V xM $#'5 j$' ‚ '!G5#*$
'!H !(1 x2G *( $ 7 (* #'( $ j 3 7 ((' & 5 '5
=1# $
*( $ & G$ '5 g/&* #' & #( ( $ '52$ $&!& G #!($ 3
&%
- /.
/*10
2+3* -4 *65
. 879+ -6:
<=
<
;
IH
CZ
;
:` P?79FK* [7
4 *65
;
:
A=
` &B
;
>
U;
B $WYX
;
=
; ?>
B
9>
T
V
.J\87 ^]* - D+[_,79F G* /
: ` 2=
TV :
."HMOQP*6F J+RF -6: :
` ` (N
;
: MV
"S
:
:
@;
* ,+
MB
;
:
(%
.JFK*6F 6+L7
()
>
:
D+ - 795E*6F G.
;
?>
&%
'
;
(%
;
B C
:
%
aB
=
:
A I
6 = ƒ6 !($ & $^^ G 6G 7 (d B 3 &' *( $ & #
3 ( '( #'!&021 a$ ? $>$ !( !( 7 2&2 '& ( $ & j .&#(* 0 !.3 # 5 H# G #(*$ (25* M&' ( $ $/(* < $&2a6$&(d #(* j (* (; 5 # #$ & 8/&* 7 (* (*'#(* ' $ &( (* 5#' '!&('! 3 ( K '(* G !(*$ ' ' € *(a &(*&!&23 (* $' ! & F .c5&23
' ^6/&*05.# 7 (* ‚ '& 0 (* YS&# ^3(M$'$& (
##!13'5M( $\!#1#(*'$&(* (* : ‚ '& L $ /(* .2
&*> #'5( $ ; ( (*' $ & a'!#)5( #'!&H$(d &(*0&*$ & 7 &* G #(*$ ( (*' 2& '5 *( $ & &H &
<
- *
*
.
/*15E. /*
'
: S
:
"B
` B
` CZ
- >
B
: >
;
<>
: S
` :
=
%
@;
;
` =
:
&%
>
;
;
S :
B
MV
: V ">
&%
@; ^>
Y
;
V
[S
B
S
. -6:
:?` ^>
:
@;
%
:U` <=
S
@;
B
@;
WYX -
` :
!#"$
%'& 7)(+*-,/./01(324(+576 01598 .#21(&7:6;57(+5=<+. *>57(?5@. <BAC6D.)0 6;EF(?2 AF< 0 6D0 ( 6D5>A76D0
5>6;A AC6;./015G6;0HA7.JI1*7( (+*7*>(+2./01(+5 LK
M@N PO Q 6DE9./0 SRUT/V/T
B
S
?
>
>
S
B
B
B
>
>
:
W ?XY [Z
\Z [Z ]Z ^X_
#Z @X
`Xa:_
X
bYca dZ eX )f+Y gX h_ gZ +Z BY X [Z
)_ia bj Z
BX P_ [Z X kX _ )_mlon Z pX a [qsr
$a tZ
Z pu 7Z Ba pvxw bYca y 9Z ez B_ Y{n |_
}lB_ vxw
Yca y j Z 9f _ _'l
BXY [Z X
^X_
3Z $_
X
q ~€Yc_ Ujl )Y [Z ea `X
P_ Z ‚ P_ +Z BY
\Z [Z
)fiƒ _ Z _\a4Z Uj „_
Z FZ `X 4… Uj
Z _ `X Z `Xa:_ )q
† .‡<‰ˆŠI1‹;A7Œ1D.gˆ)0[A7(+*76;./*Ž*7( (+*>6DŒ 57( Œ1(J.21(?57(?EFI(+0 .21(JŒ1EE9.:21(+;.$21(JI1*7(B€6;5 .‡21(?IS(?0121(921(
21./6;5 ˆ)<BAC./*>(+5$I1*>6D01<?6DIPˆ)6;5+‘’ˆ‡“7ˆ)01(?”ˆ•AC(?EFI./*7ˆ)(]ˆt<?./E9I1D( 6;2Pˆ)21(21.EF.:21(+;. —– ./6ACˆ)E E
21(?EF./045>AC*7ˆ)21. Œ1(˜ˆJ(?5>ACˆŠAC‹;5>AC6;<‰ˆJ™eš:› Œ1E ./Eœ<+*76A *76D.žI1ˆ)*CˆJˆJ57(+;(+<?Ÿ .921(+5-AC(?5 ˆ)<BAC./*>( q
† .@(?0[A^ˆ)0[AC. ./6 6 ŒPˆ)DE9(+0[A7(¡*>(?)(+”ˆŠ21. Œ1(pI1ˆ)*CˆFˆ)5 u j (?5>AC(e<+*76A *76D.JAC(?0121(eˆ ˆ‰/./*>(+<+(?*
E9.€21(?D./5¢576;EFI4D(+5 E9(+5>EF.£I1ˆ)*Cˆ`5 *>6D(+5¤0 .£;6D01(+ˆ)*7(?5 ¢¥ ˆ)€57Œ1<?(+21(¦I./* Œ4(G.€<?./*7*>(GŒ1E§576 016;¨1<‰ˆŠA76;/.
ˆ)Œ1E9(+0[A7.’01.d0 E9(+*7.’21(gIPˆ)*7©)EF(BAC*>./5J2Pˆd*>(+21( ŒPˆ)0124.•57(ˆ)<?*7(+5><+(?0HACˆ)E 01.€24./5J6D0[AC(?*7E 216;./5
21(B€6;21.Fª9ˆŠ21./IŸ .J21(«Œ1EFˆpAC./I./D. 6”ˆ¡21(«*7(+24(¡<?./E9I1D(BA^ˆ)E9(+0[AC(Ž6;0[AC(+*>D6 ˆ)2Pˆ
¬ ˆ)6;5xˆŠ6D012Pˆ ˆ)5 (+Œ1*>‹D5-AC6D<+ˆ)5­IPˆ)*7ˆ˜ˆŠ5“7ˆŠ01(+Dˆ)5­21(+5>D6;®‰ˆ)0[AC(?5 ./*Cˆ)E21(+5>(+0[/./:6D2Pˆ)5¯<+.)E ˆ)5>(01.)5
Šˆ)D.)*7(+5`21(9ˆ)Œ4AC.:<+.)*7*7(?”ˆ)Ÿ . e° *Cˆ (?5>AC(?5eˆŠIS(?0Pˆ)5ŽE9(+21(?E6D0[AC(?*Cˆ)<?Ÿ+±:(+5Ž;6D01(+ˆ)*7(?5 Œ1(J0 .g5 .ˆŠ5
²[³
*8H
D+
7
7
\ * - .
7
\* - *6F 37
7 -
7
7
.
/*
7 -
* /* -
)
. -
*65(7 -
\2+RF
- *6F /.
* - - . -
G*65
\ .
7 /*
.J\
.J5
S
.
+R5+[_,7
^79\ L+R\
* - L\&7
9+L7 -
* - Q7 -
.
Q7
.
7
/*
=
/*
*
/*
\.
. -
+RF -
U5(7
* -
\.
* - - . -
D+
7
7 -
^79\87
*6\25E. -
*6O - *
/*
7
\*. -
/* - *65
/\*&_,7
/5(7
Z
.
+3.JF 79+ -
7
W
/.J\2+ L5E. -
.J5 ^79\87 .*6F
/. *65
Q7
F 7
.J\2FK*
* Q79O C
7
.J5
+R\&7 /. -
/\&7
/. -
F+ 7 -
\*&7 D+[_,7
@*
.
/*5E. /*
+3.JF 9\2+L7 -
7 -
L+R5E.
/*
7
.
795
.J5E.T.
/*
+ ^79+ -
* /\.JF 79+ -
W
.JF - + /*6\87 /. -
/. -
* - - +
7 -
+3.JF 9\2+3. -
\.
FK*
*6F
+R5+[_,7
.
: S
V
B
%
'
. -
.J5E.
>
V %
S
;
-
%
WYX -
;
379+ -
>
%
`
:
/*
7 - - +R5
%
.JO
;
S
`
*
5E. /*
`
\2+ .
. -
9+ @*6\*6F G* -
*6F .
- *6F /.
/* -
+
^79\87
S
B
`
%
:`
B
:
;
B
>
;
S
>
:
V
: `
;
;
:
²V
!"#
#$%&')($
650
600
550
x(t)
500
450
400
350
300
300
350
400
450
500
550
600
650
x(t-1)
– 6 Œ1*Cˆ+* R ‘-,m0HA7(+*7ˆ)<+Ÿ?±€(?5`(+0[A7*7(«./5 21(+5>D.:<‰ˆ)E9(+0[A7./5/.10%2¡( .GI1ˆ)*CˆJˆJ5 *>6D()346587:9<;
EFˆ)6D5¤ˆ)21( ŒPˆŠ2Pˆ)5 IPˆ)*7ˆ£5 *>6D(?5­<+./E9I1D( ˆ)5 = ./*­( (?EFI4D. ˆŽˆŠŒ4AC.:<+./*>*7(?”ˆ)Ÿ .£21(¦21(?57;.€<+ˆ)EF(?0[AC.ŽŒ1E
IPˆ)*7ˆgˆg5 *>6D(>34?57:9<;pAC(?EŒ1EŠˆ);./*£I1*A@ 6;EF.$24(9Œ4ECBED?FGIHKJML:LON E9(+216;0121.$<+.)*7*7(?<?ACˆ)EF(?0[AC(9ˆ
(+;(?Šˆ)2Pˆ˜*7(+Dˆ)Ÿ .pD6;01(‰ˆ)*x( 6D5-AC(?0HA7(PB – 6 Œ1*7ˆ+* R N ­¥ .:2Pˆ‰€6Dˆ .eEF(?57E9.p0 .ž5>(Ž57Œ1<?(+21(«IPˆ)*7ˆpˆp5 *76;(
Q eSRUT 4?V8W6XZY R ./0121(@.)ˆŠD./*¡21($ˆ)Œ€AC.:<+./*>*7(+Dˆ)Ÿ .\[ ŒPˆ)5>($0HŒ1D.]B^D_F`GaH8JbH:c:N ˆ)I(+57ˆ)*p21(=( 6D5-AC6D*
Œ1EFˆ ./*>A7(Ž6D0[AC(?*Cˆ)<?Ÿ .J0 .J;6D01(+ˆ)* €6;57‹/(+01ˆ ./*>E=ˆp24(¡Œ4E=ˆžIPˆ)*ed ./”ˆfB – 6 Œ1*Cˆ`* bg N
O .t6D0[h [+5=24(57(Œ4AC6;D6;®‰ˆ)* (?Œ1*7‹;5>A76D<‰ˆŠ5 .’6D21(+ˆ) 57(+*>6”ˆdˆ•ˆ)24./ISŸ .•24(PE [?AC.:21./5Fˆ)Œ4A7./iE dŠAC6;<+./5
IPˆ)*7ˆ=ˆ=I4*7.:<+Œ1*7ˆF2Pˆ=E9(+ ./*¤“7ˆ)01(?”ˆJAC(+E9I./*Cˆ) (˜EF.:21(+;.J21(pI1*>(?:6D5 . O 575>6DE (+5>A7(p<‰ˆŠI1‹;A7Œ1D.96De* d
ˆ ./*721ˆ)*`ˆ9./I4A76DE96D®‰ˆŠŸ .9ˆ)Œ4A7./iE dŠAC6;<‰ˆ 5>. ˆ .)*7EFˆ921(˜Œ1E v IPˆŠ*Cˆ=.F21(+5>(+0 .$24(e<‰ˆŠ2Pˆ=Œ1E
21./5 E9.€24(+D.)5G6D015>I16D*7ˆ)21./5¦01ˆ † ˆŠACŒ4*7(+®+ˆ
B
>
%
%
`
>
;
B
:
>
>
;
:
S
;
:
%
;
;
`
;
V
B
;
:
>
>
;
:
V
:
V
%
;
:
S
:
>
S
CZ
>
:
:
>
jfkl
monqpsr1t)pSuvwtnyxfz|{}r~i€‚frt
& 6D5>A7(+E 216„ƒ (?*7(?0HA7(+5pA76DI./5e21(=(+5>A7*CˆŠAe[…/6Dˆ)5e24(@I1*7.:<+Œ4*CˆIPˆŠ*CˆEid Œ16D01ˆ)5e21(@ˆ)I1*7(?01216;®‰ˆh…/(?E†¤IS._‡
21(?0121.9(+5>ACˆ)5 57(+* <?”ˆ)5>576;¨1<‰ˆ)2PˆŠ5¦57(…)Œ10121.9AC*eˆ?5 <+”ˆŠ5757(?5 I1*76;01<+6;IPˆ)6D5Š‰Œ‹Gˆ)01® ˆ_ƒ (?Aˆ)Ž† RUT)T ²_ ‘
‘ 4?9qY e 4 R’ 5”“ R ‡ † (?5>A^ˆ9(+5-AC*Cˆb•A […)6”Kˆ † .=(?57IPˆŠŸ+.=24(e57.)DŒ1Ÿ?±€(?'
5 [¡—( –€I1;./*Cˆ)24.=57(?E 57(+*6D0K˜1Œ1(+01<?6”ˆ)24.
&
I(+;./5Ž*7(?57Œ1A^ˆ)21.)5Ž21(JI1*7.:<+Œ1*7ˆ)5¡ˆ)0[AC(?*76D.)*7(+™5  š
E …/(+*7ˆ)Ž †ˆ$I1*>.€<?Œ1*CˆgŒ4A76DD6;®‰ˆ=Œ4E=ˆ@(?5>AC*>Œ4ACŒ4*Cˆ
(?›
E dŠ*>/.)*7h( † ./0121(F<‰ˆ)21ˆ01.:21.‡<+./0[•A [?E Œ4E=ˆg57./;Œ1Ÿ œŠ.<+ˆ)01216;2PˆŠA^8ˆ Ÿž./EF.‡—( –€(?EFI1;./5¡21(+5-A^ˆ
`
²
: $S&## $ & )& 1
0.9
0.8
0.7
x(t)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x(t-1)
– 6„…/Œ1*Cˆ`*K g ‘-,m0[A7(+*CˆŠ<+Ÿ+±:(+5 (+0[A7*7(¡./5 21(+5>D.:<‰ˆ)E9(+0[AC.)5/.10%2«().GIPˆŠ*CˆJˆž5e[+*>6D( Q eSRUT 4?V8W6XZY R 
Y on)a ( X
X '‚ha Z \Z [Z 
(?5>AC*7ˆŠ•A [™…/6”ˆ«AC(?E ‡ 57(ˆ)5I1*>.€<?Œ1*CˆŠ521( X
‡ O Œ46 [«Œ4A76D;6D®‰ˆŠ21.pŒ1E 4016D<?.FI./0[AC.J21(¡I1*7.:<+Œ4*CˆK†P<?*76”ˆŠ0121.JŒ1EFˆJ04. ŠˆJ57./;Œ1ŸœŠ.
ˆ$IPˆ)*-AC6;*Ž2PˆˆŠ0HA7(+*>6D./™* †57(+0421\. …/(?*Cˆ);EF(?0[AC(ž(+5-A^ˆˆ‡ˆŠ21./I4ACˆ)2Pˆ B\01.g<‰ˆŠ57.24(95>(+*¡EF(? 1.)* Œ1(
ˆ‡ˆ)0[AC(?*76D.)* N— † (+0 :Œ4E *>( …/6;5>A7. [9E=ˆŠ0HA76D21.g5>. 1*7(F.<+ˆ)E96D0 1.‡I(+*7<?./*7*>6D21K.  )dŠ*76”ˆŠ5¡e5 œ). ˆŠ5
eA [+<+046D<‰ˆŠ5 Œ1(«Œ4A76D;6D®‰ˆŠEœ(?5>A^ˆJ(+5-AC*7ˆŠ•A [™…/6”Kˆ †457(+0421.F24(¡*>™( ƒ (?*76D*?‘
ža:Y )_ 7Z )Y :n ‡ ¥ *7ˆŠA^6ˆ ‡m57(F21(9Œ1EiE [BAC.:21. …)(+0 [?*76D<?.21(FI1*7.:<+Œ4*CKˆ † Œ4(FAC(?E ˆ‡/(?*
<?./E ƒ (+0 @)EF(?01./5 Œ4(e.:<+./*>*7(+E<?./E.=I4*7.:<+(+5>57.@24(eˆ)*>*7—( ƒ (+<+6;EF(?0[AC.921(eE9(?ACˆ)6D™5  O I1*7.:<+Œ1*7ˆ
(?0H)./;)(’.Œ15>.21(]5Cˆ)AC./5$ˆŠD(‰ˆb•A @/*>6D./5$ˆtI1ˆ)*>A76D*@21(]Œ1E IS./0[A7. †`ˆŠ21./I4ACˆ)0121_. ‡ 57(dˆ#57./;Œ1Ÿ œŠ.
ˆ)AC(?*Cˆ)2Pˆ921(žˆ)<?./*724.@<+./E Œ1E IPˆ)*7©)E9(?AC*>.=21(˜AC(+E9I(+*CˆbACŒ1*7Kˆ † Œ1(ž24(+<+*>(+5><+h( † ªFEF(?216D2Pˆ Œ1(
.JI1*>.€<?(+575>.=21(?<+./*>*7_( 
`Y{n |_ eZ h_ ‡ `(?57(+0[)./;:6D24./5£(+5>IS(?<+6¨P<‰ˆ)E9(+0[A7(eIPˆ)*7ˆF./I€AC6DE96D®+ˆ)* ŒPˆ)6;5 Œ1(+* AC6;IS./5
21(pA7./I./D:. …)6”ˆ)5 IPˆ)*7ˆ u † ˆ$IPˆŠ*>AC6;*`2Pˆ$*>(+E9.€Ÿ œ).@21(J01.:21./5Ž(ž<?./01—( –€±:(+5«21(?5701(?<+(+5>•5 d)*>6”ˆ)™5 †
5>( …/Œ10421.F.JI1*>6D01<?‹DI16;.p21( U… Ž6 {h( †4A7(+0[A^?ˆ ‡ 57(«. 4A7(+* ˆž*7(?21(«E=ˆŠ6D5G5>6DE9I1D(?5 Œ1(«EF(? 1./*
!#"#"$&%"'#(*)+#,.-
0/
21
/
43
53
76
3
98
/
:<;
/
= ?>@ABC D
/
/
:
>
E
FHG
9IJE #
/
/
LK
NM
/
>OG
QP
IJR 5ST
/
76
43
UVXWY[ZE\]=^`_[ab\dce^fYEghjikmlWnpodqsrutvJwyx{z}|qu~#w€
‚
W0^jY[gƒhfiCk„vr…wyx{z}|†qu~#w4
H
‡dˆ?^fhjhj^jac‰WŠ‹Œ]u{ZEac*ŽC‘’“[”^jhj•ƒksWŠyWL\ŒŠyn–aƒ_H\ŒŠyn–aYE]=^`ks]aY[Wb^jY[ghjik—E]=WƒY[Z[\C]=^`_HW˜l\dh`a0_H\dŠy\k–ab_Ea0al[hj^j]a™ W˜_Ea
H
UH
OH
n–\dgnuam\]dWY[•ƒcL^j]a›šmœs\WhjWg^`a[[žF\dYœs^`_[aƒ_H\kY WŸk W›c˜ [hfœs^jl[hf^`]daƒ_[aklEanua.ahf¡c!_[a.Y[\]d\k–kF^`_[a_[\#¢#—dœ W›Šyn–\£ [\Yƒœ–\dcL\dYœ–\
Hœ–^fhj^f¤Ca_[aL£ [\„ks\ŒœsWn–Y[Wƒ ŠacbWksab]=WƒcLWLa@¥7tJ¦JtJ§ xEt¨vƒr©.ªu«xEtJ¬b
²/²
!"#
#$%&')($
5>(˜ˆŠ2Pˆ)I4A7(˜ªž*>(+57.)DŒ1Ÿœ).J21(«Œ1E 2Pˆ)24.FI1*>. 1;(+EFˆK O 5 I1*>6D01<?6DIPˆŠ6D5 ƒ Œ401Ÿ+±:(+5 21(«Œ1Eˆ)„…/./*>6;ACE9.
21(=<+./*-AC(=I1ˆ)5757ˆ)E I(+Dˆ(+5><+./ Pˆ2Pˆ B\5 N¡Œ1016D21ˆ)21(OB 5 Neˆ57(+*e<+./*-A^ˆ)2Pˆ B\5 N † ŒPˆ)0124.3(™ƒ (+<BACŒPˆŠ*p.
<?./*>A7(¡( ŒPˆ)0421.FI1ˆ)*Cˆ)*¦.žA7*7(+6;01.J2Pˆž*7(?21(P‰ ¥ 16;EFE – 6;(+57;(+*™† RUT/T 6 
`Y{n |_
B_ ha:_ w ‡, …/ŒPˆ);EF(?0HA7(J21(+5>(+0[/./:6D21./5˜IPˆ)*7ˆ./I4A76DE96D®+ˆ)* ŒPˆ)6;5 Œ1(+*¡AC6;IS./5
21(£A7./I./D:. …)6”ˆ)5¯IPˆ)*7ˆ u ^j *7(?<+./*>*7(?EˆpŒ1EFˆp(+5>A7*CˆŠeA […/6Dˆžˆ) …).p21„6 ƒ (?*7(?0HA7h( †P<?./EF(?Ÿ‰ˆ)0421.J<+./E
Œ1EFˆ=*>(+21(ž5>6DE9I1D(?5 †ª ŒPˆŠ •5 œ).gˆŠ<+*7(?57<?(+0[A^ˆ)24./5«01.€24./5Ž(p<+.)01—( –€±:(+5 †¢ˆŠeA [ Œ1(žŒ1EFˆ@57./;Œ1Ÿ œŠ.
57ˆŠAC6;A5 ƒ\ˆŠeA @/*76Dˆe57(m“7ˆ9(?01<+./0[A7*Cˆ)2PŸˆ ‰ 8x. ¯(?Œ10 … † RUT)T/T  
‘ 4?9qY e 4 R 3-9 4
S5Xs5‡ & 5-AC( AC6DI.«21( I1*7.:<+Œ4*CˆŽIPˆ)5>5Cˆ˜I./*­Œ1E<+./E9I1*7.)EF6;5757.Ž(?0[AC*7( Œ1EFˆŽI1*7.:<+Œ1*7ˆ
( –1ˆŠŒ15>A76;Šˆ=21.@(?57IPˆŠŸ+.@21(e57./;Œ1Ÿ+±:(+5(e. … |Y|Y BY 9f :n †P5>(+0121.$EFˆ)0[AC6;2PˆFŒ4E=ˆ9IS./I4Œ1”ˆ)Ÿ œ).921(
I./0[AC./5¢21(xI1*7.:<+Œ1*7Kˆ  & E—<+ˆ)2PˆI./0[AC'. [xŒ€AC6D;6D®+ˆ)21. Œ1EFˆ PE [?A7*76D<+ˆ I1ˆ)*Cˆ 57(+;(+<?<+6D.)0Pˆ)* ./5¤I./0[AC.)5
I1*>./E96D575>./*7(?5 †Š57(+0421.Ž./5¤*>(+5-A^ˆ)0[AC(?5 21(?57<‰ˆŠ*>A^ˆŠ21./5 -ž./EF.—( –€(+E9I1;./5 eA ˆ+>E ‡m57(¯AC.:2Pˆ)5 ˆ)5¤eA [+<+046D<‰ˆŠ5
2Pˆ v †1A^ˆŠ6D5¦<+.)EF.J./5 v ./Œˆ /
& E I1*>6D01<?‹DI16;. † ˆ X Ba on —( –€6 …)($ˆ <+./04576D24(+*CˆŠŸ œ).321(FAC.:2Pˆ)5žˆ)5e57./;Œ1Ÿ+±:(+5žI./575>‹;)(+6D™5 †­57(?0121.
I./*¦6D5>57.9ˆ)I(+0Pˆ)5 ˆ)I4D6D< d‰/(+ Œ1ˆ)0121.F.9(?57IPˆŠŸ+.921(«I1*7.:<+Œ1*7>ˆ [¡246DE96D0HŒ4ACK. †4. Œ1(˜0 œ).J57(Ž/(?*76;¨1<‰ˆJ0Pˆ
EFˆ)6D./*>6”ˆ24./5 I4*7. 1;(+EFˆ)521(xˆ)I1*>(+01216;®‰hˆ …)(+ŸE  N d Šˆ)*>6”ˆ)0[AC(?5 Œ4(U0 œ). —( –€„6 …/(+E Œ1(x57( AC./E9( (+E ;6D0 Pˆ
21( <+./0[ACˆ˜AC.:2Pˆ)5¯ˆ)5¯57./;Œ1Ÿ+±:(+™5 †4ˆŠ<?ACŒ1ˆ)0121.eˆŠAC*7ˆUh [+5x21(`Œ1E <?./E9I1*7./E96D5>57.¡(+0[AC*>(.¡AC(?EFI.˜( .e(?57IPˆŠŸ+.
21(pI4*7.:<+Œ1*7ˆ B\h( Œ… †}•A [?<+016;<‰ˆ)5Ž24( BX '‚ha Z P_ «X 7n w ‰./* ƒ † RUT ²[³  N  † .$(?0HACˆ)0[AC. †ACˆ)6D5
Šˆ)*76Dˆ)0[AC(?5xˆŠIS(?0Pˆ)5 I1*7.:<+Œ4*Cˆ)E57./;Œ1Ÿ+±:(+5 IPˆ)*7ˆ¡.«I1*>. 1;(+EFˆ£0:Œ4E 57Œ 8‡ <+./0 “>Œ10[AC.¡21(?)(+*CˆŠ5*7(?5>A7*76;A7.«21.
(+5>IPˆ)Ÿ?.F21(«5>./DŒ1Ÿ?±€(?5 
= ./*.)Œ4AC*>. Dˆ)21. †U.)5i
E [BAC.:21./521( … |Y|Y BY 9f :n †‰<+./E9.¦./5ˆŠ …/./*>6;A7EF./521(­<?./*>A7(­./Œ«<+./015-AC*>Œ4AC6/./™5 †
•5 œŠ.‡5>Œ157<?(+I4A7‹;)(+6D5¡ˆ).)5£EF‹;016DE9./5 D.:<‰ˆ)6;5 ‰ O 0 …/(?D6D04(e(?A¡ˆŠŽ † RUT/T *   ¬ ˆ)6;5Žˆ)6D042PKˆ †U0 œŠ.$*Cˆ)*7ˆ)5£/(?®+(+™5 †
(+5-AC(?5ePE [?AC.:21./5£A7(+0124(+E6 …/Œ1ˆ)DE9(+0[AC(pˆ ƒ\ˆ)®?(+*«6D04<+6D246D*Žˆg57ŒPˆ‡ˆŠA7(+01Ÿ œ). ˆ)I(+01ˆ)5«0:Œ4E57Œ <+./0 “>Œ10[AC.
*7(?5>A7*76;A7.J21.J(+57I1ˆ)Ÿ+.F21(«I1*7.:<+Œ1*7Kˆ 
† (?5>AC(AC*Cˆ Pˆ) 4.¡6;* ‡ 57—( ‡ d˜ˆŠ21./I4ACˆ)*ˆ 1AC6DEFˆŽ(+5-AC*Cˆb•A […)6”Kˆ †:ˆ X Ba `X ¢‚ † Œ1(57(`6;•* d«E=ˆbAC—( ‡
*76Dˆ)D6;®‰ˆ)*GˆŠAC*7ˆUh [+5£24./5 v  & 5>AC(?5£Œ4A76DD6;®‰ˆ)EœŒ1EFˆ9I1*>.€<?Œ1*CPˆ …/D. Pˆ)EpŒ1AC6 ‡mI./0[AC. †121ˆ)0121.@.)*76 …)(+E
ˆž57./;Œ1Ÿ+±:(+5 21(«(?D(?Šˆ)21ˆ ŒPˆŠD6D21ˆ)21h( † Œ4(¡(?57<+ˆ)IPˆ)E ˆžE9‹D016;EF./5xD.:<‰ˆ)6;)5 ‰Œ‹*Cˆ)0 )h( † R‰T/T 6³  
76
/
€3
/
:
>
3
E
FHG?IJE5G s
s
/
HG
>OG
NM
/
/
>
JHI /
CI D
G
IJ /
/
/
76
#
J JGJG
76
CI D
/
3
6
6
&6
43
HI 1
>
G
AE
{
/
6
/
/
fpSw! w!"t$#&% ~ xf~ ' ~Pxfz(—~ )šz# r~
* +t (
,.-0/&-21 53 476478:9;47<>=?A@>BDC28:EGFD?DHI<JKC2?D@>LD=CIBA8
jfk
O +< .)E 16D01ˆ)Ÿœ).ž24(¡I1ˆ)*Cˆ)246 …/EFˆ)5†HA^ˆŠ6D5¦<+.)EF.ž.J<+.)01(—–€6D.)016D5-A^ˆp(«.J(?/.)DŒ1<?6D./0UdŠ*76D.eIPˆ)*Cˆžˆž*>(+57.)DŒ1Ÿœ).
21(xI1*7. 4D(+EFˆ)5™†bA7(+E—<+./E9.'ƒ .)*>AC(¯6D0457I16;*Cˆ)Ÿœ).`ˆŠ5ƒ ./*>E=ˆ)5¢21(x(?/.)DŒ1Ÿœ). Œ1(G.:<+.)*7*7(?E 01./5 57(+*>(+5¤:6/./5™†
6
MON 2P
RQ SQ
76
nua_[ E™ Wbaƒ_HWlHœua_[ablEan–a˜Wbœs\nscLW
TQ VU
Dw'rdqstw D¦Jr˜vƒrur'…Er=¥ D¥ 
/
²T
(+5-A^ˆ)0421.£ˆ 57(?* . H“>(+<?A7.`21(xˆŠA7(+01Ÿœ).I./*¢ˆ Œ1(?D(+5 Œ1(¯57(¯21(+216;<‰ˆ)E ª`ˆ)0UdŠD6D5>(h†U(?57I(+<+6¨P<‰ˆŠŸœ).(x21(?57(?08‡
/.);:6DE9(+0[AC.˜21(`5>6D5-AC(+EFˆ)5¯<+./E9I1Œ4ACˆ)<+6;./0Pˆ)6;5 21(£ˆ)AC.˜21(+5>(+E9IS(?0 1.  & E IPˆ)*-AC6D<?Œ1”ˆŠ*†:ˆ˜<?./E 16;0Pˆ)Ÿ œŠ.
vxw bYca y u v Uj I.€21( ‡m5>(
21( u <?./E v †}2Pˆ)0121.=./*76„…/(+E ª)5 u 7Z Ba
I1*>.€<?(+5757ˆ)* 21(«216;)(+*>5Cˆ)5#ƒ ./*7EFˆ)5™†Pˆ) …)Œ1E=ˆŠ52Pˆ)5 ŒPˆ)6;5 5•œ).J6D04216D<+ˆ)2Pˆ)5 ˆž57(™…/Œ16;* ‰ 16AC;(?:, † RUT/T ³  ‘
01. _ †¯IPˆ)*7ˆd24(?AC(?*7E96D0PˆŠ*ž./5ž)ˆŠD./*>(+5ž21./59I(+57.)59I1ˆ)*Cˆ3AC./I./;.:…/6”ˆŠ5e21(‡*7(?21($K¨ –4ˆ)2Pˆ)5Fª
I1*>6D./*>6
01. Z 4… JZ w £_ ^X bY 7n †HIPˆ)*Cˆp(B/./;Œ16D* AC.)IS./;:. …/6Dˆ)5 21(£*7(?21h( †4(+E AC(+*>EF.)521(£04.€21.)5
6;0HA7(+*>iE [?216D./5(¡<?./01( –4±:(+5 (
0Pˆ BY Z =Z [Z £X _ †¢(+EA7(+*>EF./5¡21(9Œ1EFˆ‡*>(+21Œ1Ÿ œ).21ˆ<‰ˆŠ*7216;0Pˆ)D6;2Pˆ)21(e21.
<?./0b“>Œ10[AC.921./5¦Šˆ);./*7(?5¦21(«(+0[AC*7ˆ)2PˆJ./Œg57(+;(+<?Ÿ œ).921(«<‰ˆ)5>./5 21(ŽAC*>(+6D04. 
O ˆŠAC(?01Ÿ œ).’6De* dd5>(+*J€6;*Cˆ)21ˆdIPˆŠ*Cˆ•ˆŠ5 1AC6;E=ˆ)5ž24ŒPˆ)5JA^ˆ)*>™( ƒ\ˆ)™5 †G21( ƒ .)*7EFˆdˆd*7(?57.//(+*Fˆ)5 Œ1(+5-AC±:(+5
D(BŠˆ)0[A^ˆ)2PˆŠ5¤01.£<+ˆ)I1‹ACŒ1;.£ˆ)0[AC(?*76;./* †Š./Œp57(m“7Kˆ † ŒPˆ)8 [¦ˆ`E9(+ 1./*4“7ˆ)01(?”ˆA7(+E9IS./*7ˆ)H(E9(+ 1./* AC./I./Dh. …/6”ˆ
2Pˆ u IPˆ)*CˆgŒ1EFˆ‡21ˆ)2PˆA5 [+*>6D(žAC(?EFI./*CˆŠŽ  & 5-A^ˆ)5 Œ1(+5-AC±:(+5˜eA ˆ+E:6D0421. ˆg57(?*e*7(?57./:6D2Pˆ)5«I(+Dˆ
<+.)E 16D01ˆ)Ÿ œ).«21( 1(?Œ1*7‹;5>A76D<‰ˆŠ5¯<?./E I1*>.€<?(+575>./5¯21( _ P_ )_ w †[<+./E9. ƒ ./61:6D5>A7.¡ˆ)0[AC(+*>6D./*>EF(?0[ACh( †
EFˆ)5 Œ4(¡A7(+0121(?E ˆ9U0 œŠ.F5>(+*ˆ)5EFˆ)6;5¦(?¨P<+ˆ)®+(?5`57.)DŒ1Ÿ?±€(?5IPˆŠ*CˆJ.FI1*>. 1;(+EFKˆ † ŒPˆ)0124.=.9(+57I1ˆ)Ÿ+.F21(
I1*>.€<?Œ1*Cˆž(+0[)./;:6D24i. [«57Œ 15>ACˆ)01<+6Dˆ)Ž 
O 5 u v <?./E9(+Ÿ‰ˆŠ*Cˆ)E—ˆ 57(+*¢Œ4A76DD6;®‰ˆ)21ˆ)501.¨10Pˆ)H21./5 ˆ)01./5¢./6AC(+0[ACKˆ †Š<?./E .A7*Cˆ 1ˆ) 1. 21( ¬ 6D;D(?* †
¥ .€212J( N (+2 …/( ‰ RUT ² T   E ˆŠ01.«E=ˆ)6;5 ACˆ)*721_( † 16;A7D(?,˜(¦57(?Œ15 <+./Dˆ ./*Cˆ)24./*7(?5 21(+E9./015-AC*7ˆ)*Cˆ)E Œ1(
./5 v IS.:21(?E 5>(+*˜Œ4AC6;D6D®+ˆ)21./5«IPˆŠ*Cˆ(?01<+.)0HA7*Cˆ)*e01.U)ˆŠ5˜AC.)IS./;:. …/6Dˆ)5Ž21(=*>(+21(=<+./E/(?D.:<+6;2Pˆ)21(?5
21(=ˆ)I1*7(?01216;®‰hˆ …/(?E57Œ1I(+*>6D./*>(+5pªŠ5e2Pˆ)5˜*7(?21(+5p<?./E9I1D(BA^ˆ)E9(+0[AC(96D0[A7(+*7;6 …[ˆŠ2Pˆ)5 †¢U0 œ).57(@24(+57<?Œ1*CˆŠ0121.
A^ˆŠE [?E ˆJI1*7(?57e5 œ).FI1ˆ)*CˆJˆJ57(+;(+<?Ÿ œ).921(«*7(?21(+5 21( Pˆ)6 –1ˆž<+ˆ)*7216;0Pˆ);6D2Pˆ)24h(  (+5724(e(+0[•A œ). †P.J<‰ˆ)E9I.
AC(?Eœ<?*7(?57<+6;21.p(£246;/(?*75>./5AC6;IS.)5x21( u v •A ˆ?Eœ5>6D21.eˆ)I1*>(+57(?0[A^ˆ)21.)5 †P216;5>AC6;0 …/Œ16;0121_. ‡ 57( I(+D.˜AC6DI.¡21(
*7(?I1*7(?57(?0HACˆ)Ÿ œŠ. † 2Pˆ)0121.$<?./*7I.gˆ@21ŒPˆŠ5£€6;57±:(+5Ž5>. 1*7(e.@AC(+EFˆ4‘`ˆ ‚ B_ (Jˆ ‚ ‰M‹*7ˆ)0 Šh( † RUT/T ³  
† ˆFI1*76;EF(?6D*C8ˆ †(e(+EA7(+*>EF./521(p<?.€216¨P<‰ˆŠŸ œ). †<ƒ (+6A^ˆ=ˆŠ. Pˆ)6 –4.=01‹;)(+Ž †S<‰ˆ)21ˆ …/(+01(e<+.:216;¨P<+ˆ=216;*7(+<BA^?ˆ ‡
E9(+0[AC(=ˆ—( –€6;5>•A ˆ?01<+6Dˆ21(FŒ1E01.€24../Œt<?./01( – œŠ.  † ../Œ€AC*7.—( –:AC*>(+E9.AC(?E ‡ 57(Fˆ:6De5 œ). ‚ Kˆ †¢21(
ˆ)AC. 01‹/(?Ž †­./0124($—( –€6D5-AC(+E *7™( …/*Cˆ)5eIPˆ)*Cˆ3ˆ <?./015-AC*7Œ4Ÿ œ).]2Pˆ3*7(?21( B\_( M…K„† Z w bY w P_ BYca€Y
‰ «*>ŒPˆ)Œ
16ACD(B:, † RUT/T  N 
EFˆ32Pˆ)5J21(+5-Šˆ)0[A^hˆ …/(?01592Pˆd<?.€246;¨P<+ˆ)Ÿ œ).]216;*7(?<?A^ˆ3(?5>A d]01.’ˆ)Œ1E9(+0[AC.]( –4I4D./5>6;/.]21.d<+.)EFI1*>6 ‡
E9(+0[AC.’21.’<?*7./E9./5>57./EFKˆ †Gª]E9(+216;2Pˆ Œ1(ˆ’<+ˆ)*7216;0Pˆ);6D2Pˆ)24(@2Pˆ’*>(+21(ˆ)Œ1E9(+0[A^8ˆ †. Œ1(_ˆ ƒ (?<?A^ˆ’ˆ
57Œ1ˆ (+57<+ˆ)”ˆ 16D;6D2Pˆ)24h(  O 57576;E †-[=*7(+<?./E9(+012PˆŠ2Pˆ]ˆ)IS(?0Pˆ)5pI1ˆ)*Cˆ *>(+21(?5ž21($IS( Œ1(+0Pˆ3<+ˆ)*7216;0Pˆ);6D2Pˆ)24h( †
57(?0121.](+5-A^ˆ I1*>(?:6”ˆŠEF(?0HA7(@21(B¨P016D21ˆ IS(?D. Œ4A76D;6D®‰ˆŠ21./*  & 5>A7($I1*7.:<+(?216DE9(+0[AC.AC(+E ˆŠˆ)0[A^hˆ …)(+E 21(
6DE9I(+216;* Œ1(JŒ1EFˆ@*7(+24(ž<+*7(?57Ÿ+ˆ(+E21(+EFˆ)5>6”ˆ@h( †<?./E6;5757K. † Œ1(ž/(+0 Pˆˆ$I(+*>21(+*«<‰ˆŠIPˆ)<+6;2Pˆ)21(e21(
…/(?01(+*7ˆ)D6;®‰ˆ)Ÿ œ). 
K}}> &)
/
76
/
3
NM
>OG
>
G
JG
E
4G
M
6
AI
–E
FEG NM
/
G
3
FJ
B
:
T
JGH
:
A
OB
EG
# A 4 FEG
T
GH 4JI
:
HG
HG
5
FJ
B
/
91
/
€3
€3
/
M
6
#
N3
– s
C C
/
/
76
56
G
M
6
>
3
43
/
6
G
6
6
K
G
M
{E #
76
IC
6
I
JGH
3
/
/
/
/
&6
/
53
#
IJ
T
!"#
#$%&')($
/. *`./Œ4AC*>.@”ˆŠ21. †}01ˆ=<+.:216;¨1<‰ˆ)Ÿœ).@6D04216D*>(+<?ACˆK†}04(+E AC.:2Pˆ)5£ˆŠ5£(+5-AC*7Œ€ACŒ1*7ˆ)5Ž5•œ).$6„…/ŒPˆ);EF(?0[AC(¡I1*7._‡
_d‰/(+6;5†¯57(?0121. ƒ\ˆ‰/./*>(+<+6;2Pˆ)59ˆ)5ž(?5>AC*>Œ4ACŒ4*Cˆ)5ž*>(…/Œ1Dˆ)*7(?5 & E S./*7ˆA^ˆ)xIS.)575Cˆ]57(?* 4AC6;IPˆŠ*Cˆ <+(?*>ACˆ)5
ˆ)I1;6D<+ˆ)Ÿ+±:(+5™†SA^ˆŠE [?E <+./*>*7(—‡ 57(ž.$*>6D57<?.@21(p(?D6;EF6;0Pˆ)* ˆ)5£5>./DŒ1Ÿ?±€(?5£I./*>)(+0[ACŒ1*7ˆ$E=ˆ)6;5£ˆ)24( ŒPˆ)2PˆŠ5Ž(
Œ1(ž(+5><‰ˆ)I(+Eªg6;0[ACŒ16;Ÿ œ). HŒ1EFˆ)0P8ˆ  21(ž*7—( ƒ (+*>6D*Žˆ)6;012Pˆ Œ1(9ˆ@<?.€216¨P<‰ˆŠŸ œ).$6;01216D*>(+<BA^ˆ=( –46„…/(žŒ1E
EFˆ)6D./*x(+5 ƒ ./*7Ÿ?.F<?./EFI4Œ4A^ˆ)<?6D./01ˆ)Ž †€21(?:6D24.FˆŠ.9I4*7.:<+(+5>57.F21(«21(+5><+.:216;¨P<+ˆ)Ÿ œŠ.921ˆ)5 57./;Œ1Ÿ+±:(+™5 
=
6
1
/
6
/
/
3
,.-0/&- /
?647HI? = ? ?D8
?
O „…/Œ1015¢(+5-ACŒ124./5¤5>. 1*7( u ˆŠI1D6;<‰ˆ)2PˆŠ5 ª I1*7(B:6D5•œŠ.*>(+<+.)*7*7(?E§ˆ 1(?Œ1*7‹;5>AC6;<‰ˆ)5¢IPˆ)*7ˆˆ 21(?¨1016DŸœ).`2PˆŠ5
AC.)IS./;.:…/6Dˆ)5­2Pˆe*>(+21(>‰Mž./*-AC(+®«(BA`ˆŠŽ† RUT/T ³6 †4(+E S./*7ˆeˆeEFˆ)6;./*76Dˆ£Œ4AC6;D6D®?( ˆe6D0[ACŒ46DŸœŠ.˜./Œ=Ei[BAC.:21./5¯21(
_ P_ )_ w ‰ ¥ ˆŠ0 … – 6D5 [8 6D< † RUT/T – ˆ)*7ˆ)2Pˆ‰, ž 1ˆŠA7¨P(?D2q† RUT/T ²_  O 5 u v <+./*>IS.)*76D®+ˆ)E
Œ1EFˆ3ˆ);A7(+*>0PˆŠAC6ŠˆI1*7.)EF6;5757.)*Cˆ IPˆ)*7ˆ]ˆ)Œ4AC.)E=ˆŠA76D®+ˆ)*e(?5>AC(gI1*>.€<?(+5>57. †x(+D6;EF6;0Pˆ)0124..]I1*7.:<+(?216DE9(+0[A7.
ƒ\ˆ)5-AC6D246D./5>.ž21( _ P_ )_ w 
O …/*CˆŠ0121(ŽEFˆ)6D./*>6”ˆ«21./5GA7*Cˆ PˆŠ 1./557. 1*>( u v ˆ)I1;6D<‰ˆŠ2Pˆ)5GªpI4*7(?:6;•5 œ).J./I4ACˆpIS.)*GŒ1EFˆp<+.:216;K¨ ‡
<‰ˆŠŸ œ).ž216;*7(?<?A^8ˆ †457(?0121.J*7(?I1*7(?57(?0HACˆ)21./5 01.e<+*7.)EF./5>57./EFˆeŒ1EFˆeIPˆŠ0 @/I1;6”ˆ˜24(£IPˆ)*7©)EF(BAC*>./5A^ˆŠ6D5<?./E9.
.g0 1EF(?*7.‡21(J01.:21./5Ž21(J(+0[A7*Cˆ)2Pˆg(J6D0[AC(?*7PE [+216;./5 †}./5«IS(?57./5¡6D016;<+6Dˆ)6D™5 †}ˆ))5 ƒ Œ104Ÿ+±:(+5«21(9ˆ)<?A76;Šˆ)Ÿ œ).g(
A^6ˆ –1ˆŠ5¦21(¡ˆ)I1*7(?01216;®‰hˆ …/(?E ‰Mž./*>A7(+®«(?A ˆŠŽ † RUT/T)V – ˆ);<+.ž(?A ˆŠŽ † RUT/T ² ž 1(?0 qŒ † RUT/T)T   & E ./*7ˆ
<‰ˆŠ2Pˆ`Œ1E§21(+5-AC(?5­IPˆ)*C©ŠEF(BAC*7.)5 I./5757ˆ`6D80 ˜PŒ1(+04<+6”ˆŠ*¤.£E9.€24(+D. ¨P0PˆŠ€21(I1*7(B€6;•5 œ)K. †[ª;Œ1®21.`(+57I4‹D*76AC.21.
<+*>6;eA [+*76;.p™eš:›—(£2Pˆ)5—( –€IS(?*7„6 ˆ+01<?6”ˆ)5G*>(+DˆŠA^ˆ)21ˆ)501.ž<+ˆ)I1‹ACŒ1;.eˆ)0[A7(+*76;./* †€IPˆ)*>(+<+(`57(+*E=ˆ)6;56;EFI./*>ACˆ)0[AC(
Œ1E ˆ “>Œ15-A^ˆ)E9(+0[A7.=<+.)*7*7(?<?A7.=2Pˆ£“7ˆ)01(+DˆJA7(+E9IS.)*Cˆ)(˜2PˆF*>(+I1*>(+57(?0[A^ˆŠA76;:6D2PˆŠ21(e./Œ<+./E9I1;—( –€6D2PˆŠ21(«21.
E9.€21(?D. †4(+EAC(?*7E9./5 21.=0 1E9(+*>.FAC.ŠA^ˆ)21(¡<+.)01—( –€±:(+5  † .FAC*7ˆ Pˆ) 1.J21( ( ‹Gˆ)*>./0 ‰ RUT/T 6³  †ˆ)I(+0PˆŠ5
(+5-A^ˆ 1;A76DEFˆeIPˆ)*-AC( ƒ ./6<+./04576D24(+*CˆŠ2PKˆ †P57(?0121.@( –€I1D./*7ˆ)21.J.9(+57I1ˆ)Ÿ+.@24(¡I4*7.:<+Œ1*7ˆF21(«<+.)01—( –€±:(+5 †IPˆ)*7ˆ
Œ1E§“7ˆŠ01(+DˆeK¨ –4Kˆ †PIPˆ)*7ˆ9I1*>(?)(+*ˆJA5 [+*>6D(«<‰hˆ @ŠAC6D<+ˆ 5S9
° *CKˆ † 01(+5-A^ˆtAC(?57( [3I1*>./I./5>A7.#(+5>A7(3EF.:21(?D. † ./0124( 57(dˆ)21.)I4A^ˆ•Œ4E v 16;U0 d)*76;. †¦(+E Œ1(
<‰ˆŠ2Pˆ¡6;01216€‹;21Œ1.Ž21(?01.)ACˆ¡Œ1EFˆŽ01.UŠˆ«A7./IS.)D:. …/6DˆIPˆŠ*Cˆ«Œ1E=ˆ u †[5>(+0121.˜Œ4AC6;D6;®‰ˆ)2Pˆ<+./E9.ŽAC./I./Dh. …/6”ˆ
Pˆ)5>( ˆd21(+5><+*76A^ˆ•01ˆ Q (?<+Ÿ œŠ.   – .)6 24(+<+6;216D24.’Œ4A76D;6D®‰ˆŠ*žŒ1E=ˆd<+.:216;¨1<‰ˆ)Ÿ œ).•216;*7(?<?A^8ˆ †G2Pˆ)21. Œ1(
ˆ)5p( –€IS(?*76 ˆ?01<+6Dˆ)5žˆ)0[A7(+*76;./*7(?5e21(?EF.)015>A7*Cˆ)*7ˆ)E Œ1(=57($<+.)0157™( …/Œ1(+E S.)015p*7(?57Œ1A^ˆ)24./5p(+E I1*>(?:6De5 œ).
<+.)E *7(?21(+5921( Pˆ)6 –1ˆ3<+ˆ)*7216;0Pˆ);6D2Pˆ)24h(  Q (g.]Šˆ)D./*e21(gŒ1E 2Pˆ)21. …/(?01( ƒ ./* R †¯(+0[A œ).’ˆ3<+./04—( –Kœ).
<+.)*7*7(?57I./0121(?0[AC(£( –46;5>A76D•* d8†:<+ˆ)57.˜<+./0[A7•* d)*>6D.¡U0 œ). [ <+.)01576;21(+*7ˆ)2PKˆ  O —( –€<?(+IŸ œ).p.:<+.)*7*7( 0Pˆ)5x<+./04—( –€±€(?5
(+0[A7*7(J./5Ž01.:21./5Ž6;0HA7(+*>iE [?216D./5(J.$01.€24.$21(J5Cˆ)‹;2PKˆ †Œ1EFˆ@<+.)015>ACˆ)0[AC(J21.gEF.:21(?D.$ˆ)24./I4A^ˆŠ21. †2PˆŠ21.
Œ1(¡(+5>ACˆ9(?5>A7*CˆŠeA […/6Dˆ ƒ\ˆU)./*7(?<+(˜>ˆ …/(+*7ˆ)Ÿ œ).921(«*7(?21(+5¦_ d);6D2Pˆ)™5 
O <?./015>A7*7Œ1Ÿ œ).Ž2PˆA7./I./D:. …)6”ˆ¦21(*>(+21‚( [*7(+ˆ)D6;®‰ˆ)21ˆ :6”ˆŒ1E=ˆ E=ˆbAC*76;® 21(GI(+57.)5 †/(?5>A^ˆŠ0121.Ž./5 …/(+01(?5
./A* …[ˆ)016;®‰ˆ)21.)5`57™( …/Œ10124.gˆ)5£D6;0 Pˆ)52Pˆ=EFˆŠAC*>6D_® † Œ1(ž21(?01.)ACˆ)E„ˆŠ5£D„6 …[ˆ)Ÿ+±:(+5 Œ1(ž(+0[A7*Cˆ)E 0HŒ1E„2PˆŠ21.
01.:21". B – „6 …/Œ1*Cfˆ *  N  `(9*7—( ƒ (+*>6D* Œ1(F(?5>A7(FAC6;IS.g21(9<+.:216¨P<‰ˆ)Ÿ œ).$AC(?EˆgŠˆ)0[A^_ˆ …/(+E21( ƒ\ˆ)<?6DD6A^ˆ)*`ˆ
“>Œ101Ÿ œ).Ž21(G04.€21.)5 21(G216 ƒ (+*>(+0[AC(?5 *7(?21(+™5 †H:6Dˆ`.£./I(+*7ˆ)21./* 21(¦<+*>Œ1®‰ˆ)E9(+0[A7. £ŒPˆ)0[A7.«ª`<‰ˆ)*>216D01ˆ)D6;2Pˆ)21(
>@G
NM
76
¨3
6
#
u F
C CJ
=
3
– s
T
NM
b3
G
C C
6
43
76
NM
G
+1
T
+1
T
6
b3
6
€3
1
>
/
6
NM
6
/
/
6
6
/
/
3
K
/
/
K}}> &)
T4R
21.J<+*>./E9./575>./E=ˆ8†1(+5-A^ˆJ57(+*ed921ˆ)2PˆžIS(?”ˆž(—–€I1*>(+5>5•œ).1‘
2
R
2
BE*K N
I1ˆ)*CˆžŒ1EFˆp*7(?21(˜<?./E 01.:21./5 21(«(?0HA7*Cˆ)21ˆ9( 01.:21./5¦6;0[AC(+*>Ei[?216D.)5
Camada de
Entrada
Camada
Intermédia
Camada de
Saída
+1
w i,j
+1
3
1
MP
1
2
3
4
5
3
5
j
4
4
2
0
5
i
Nodo
Cromossoma
3
4
5
1 1 1 0 0 1 1 0 1
– 6 …/Œ1*7ˆ *  ‘ & 5 Œ1(+EFˆJ21(«<+.:216;¨P<+ˆ)ŸœŠ.924(¡Œ4E=ˆ u 
`(+0[A7*7.e24(+5>A7(<?(+0UdŠ*76DK. †[.€<?./*7*>(+*•dŽŒ1E<+./*-AC( 0HŒ1E 01.:21.¡6D0[AC(?*7EP[+216;. † ŒPˆ)0124.˜(?5>AC( 0Uœ).«*>(+<+( S(?*
<+.)01(—–€±:(+5ˆpIPˆ)*>A76D*G21ˆ)5 (+0[AC*7ˆ)2Pˆ)+5 B – 6 …/Œ1*7ˆ * Œ*”N— (¡Œ4E EF.:21.p5>6DE96DDˆ)*†H.:<+./*>*7(+*edžŒ1E <+.)*>AC(Ž0HŒ1E
01.:21.•24((?0HA7*Cˆ)21ˆK†G(ACˆ)E <[+E 04.•<+.)*7*7(?57I./0121(?0[AC( 21(?57;.€<+ˆ)EF(?0[AC.]AC(+E9I./*Cˆ)Z† ŒPˆŠ0121.t.d01.:21.
0Uœ).@A76;)(+*£<?./01—( –€±:(+5«21(ž57ˆ)‹D2Pˆ B – „6 …/Œ1*Ciˆ *  ³ N— & 5>A^ˆ$(?5>AC*7ˆŠ•A [™…/6”ˆ@I(+*>EF6AC(˜—( –€I1D.)*Cˆ)*£Œ4E(?57IPˆ)Ÿ?.g21(
I1*>.€<?Œ1*Cˆ Œ1(G<?./0[•A [?E.ŽI1;(+01.£21ˆ)5 AC./I./;:. …/6”ˆŠ5¢24(G*7(?21h( †[21(?5721( ˆ`5>6DE9I1D(?57E9(+0[AC(xD6;01(‰ˆ)™* †)5>(+E04.€21.)5
6D0[A7(+*7PE [+246D./™5 † ˆŠ•A [$ª3<?./EFI4D(?ACˆ)E9(+0[AC(F6D0[AC(?*7D„6 …[ˆ)2P8ˆ †­ˆ)575>6DE <+./E9. ƒ\ˆ)®$ˆ3( –4I4D./*7ˆ)Ÿ œ).324( Œ1ˆ) Œ1(?*
57Œ S<?./0b“>Œ10[AC.921(¡21(+5>D.:<‰ˆ)E9(+0[A7./5GAC(?EFI./*CˆŠ6D5 
/
NM
/
K
ƒ6
„K
/
6
/
/
/
56
– 6 …)Œ1*Cˆ`* Œ*1‘ž./*-AC(«0HŒ1E01.:21.J6D0[AC(?*7EP[+216;. 
O ƒ Œ101ŸœŠ.’21(‡ˆ)I€AC6D2 œ). [‡. 4AC6;2Pˆ3ˆŠAC*7ˆ‰: [+5921(‡Œ1EFˆ]24(+57<?.€246;¨P<+ˆ)Ÿ œ).d21.]<+*>./E9./575>./E=ˆ3IPˆŠ*Cˆ]ˆ
u † Œ1(˜I./*¦5>ŒPˆJ)(+®[¡A7*7(?6D0Pˆ)21Kˆ †157(?0121.J¨P0Pˆ);EF(?0[AC(«<‰ˆ);<+Œ1Dˆ)21.ž.957(?ŒŠˆ)D.)*G21(¡™eš:P›  O 57576;E †
6
NM
/
Tg
!"#
#$%&')($
– 6 …/Œ1*7ˆ`*  ³ ‘ž./*>A7(«0:Œ4E 01.:21.J21(«(+0[AC*7ˆ)2PˆK
.=. :“>(+<BAC6;).=21. v †SI1ˆ)5757ˆFI(+”ˆ9ˆJI1*7.:<+Œ1*7ˆF2PˆJAC./I./;.:…/6”ˆ˜(¦“7ˆ)04(+”ˆžAC(?EFI./*7ˆ) Œ1(eE96D016;EF6;®‰ˆ)E
(+5-AC($Šˆ)D.)* O ˆ)21./IŸœ).324.d<?*76•A [+*>6D.3™˜š€›„ˆ)I1*7(?57(?0HACˆ]A7e* ˆ?5p)ˆŠ0HAChˆ …/(?01>5 ƒ Œ1012Pˆ)E9(+0[ACˆ)6D5p5>. 1*>(ˆŠ5
21(?E=ˆ)6;5B\(_M… † )Y \Z ha [Z N`‘
( –46„…/(ŽŒ1E <d)D<?Œ1D.e576DE9I1;(+5 †€57(?0121. Pˆ)5>ACˆ)0[AC(«E9(+01./5¦( –€6 …/(?0HA7(«(+E A7(+*7E9./5¦<?./EFI4Œ4A^ˆ)<?6D./01ˆ)6D5
21. Œ1(¡./Œ4A7*7./5¦(?5>AC6;E=ˆŠ21./*7(?5¦21./5 IPˆ)*7©)E9(?AC*>./5¦21( …/(?01(+*7ˆ)D6;®‰ˆ)Ÿ œ).ž2PˆJ*7(+24(
[dŒ1E ./E (+5-AC6;E=ˆ)24./*$2P]
ˆ …/(+01(?*Cˆ);6D®+ˆ)Ÿ œ).2Pˆ*7(?21h( †Ž<?./K0 ƒ ./*>EF(]. Œ1( ƒ .)6Ž21(+E9./015-AC*CˆŠ21.
Q
ˆ)0[A7(+*76;./*7E9(+0[A7P( B (?<+Ÿ œŠ.  V  N (
ˆ)Œ4EF(?0HACˆžˆpI1*7(?57e5 œ).JIPˆ)*Cˆžˆp5>(+;(+<+Ÿ œ).J21(`A7./IS.)D:. …/6Dˆ)5¯21(Ž*7(?21(Ž21(?)(+*7ˆ)5 576DE9I1;(+5 †€ˆ)<?(+D(?*Cˆ)0421.
.JI1*>.€<?(+575>.=21(«<?./0[/(+A* …:ˆ+04<+6”ˆJ21. v 
° ƒ Œ401<+6;./0Pˆ)E9(+0[AC. …/;. Pˆ)S21(+5-AC(¡576;5>AC(?E=`ˆ [«21(?57<?*76;A7.F01ˆ – 6 …/Œ1*7`ˆ *  V  O .J01‹;)(+2PˆJI1*7h. …/*Cˆ)EFˆ)Ÿ œ). †
ƒ ./*7ˆ)Eˆ)24./I4A^ˆŠ21./5«./5¡ˆ)E 16;(+0[AC(?5«21(FI4*7:. …/*7ˆ)EFˆ)Ÿ œ). v ( u
†¢<+./Eˆg6;0[AC(+*7ˆ)<+Ÿ œ).‡21.
v <+./Eˆ u ˆJ57(?*21(B¨P016;2Pˆ904.FPE @€24Œ1D.ž21(¡ˆ‰Šˆ)D6Dˆ)Ÿ œŠ. †45>(+0121.F(+5-AC(¡576D5-AC(?E=ˆJ6D0[AC™( …/*CˆŠ21.J0Pˆ
ˆ)I1;6D<+ˆ)Ÿ œ)`. W ;•
/
>
6
76
D
H :
6
/
:
T
/
6
T
:
>
76
>
6
>
NM
>
>
NM
>
,.-0/&- E 4 =C
7@>J CIBD8
† (?5>A7(`<‰ˆŠ57. †:. v 6D*ed¡<?./E9IS./*-A^ˆ)* ‡m5>(¦<+./E9.˜Œ4E I1*7.:<+(?216DE9(+0[AC.¡21( 57(™…/Œ1012Pˆ˜./*721(?E†HI(+;. Œ1(ˆ
(+5><+./ Pˆ«21./5 57(?Œ15xI1ˆ)*C©)E9(?A7*7./5­0 œ).+[¦A•œ).«<+*7‹AC6;<‰ˆK†[(?E *7(?”ˆ)Ÿœ).¡ˆ).«EF.:21(+;.Ž21( v I1ˆ)*CˆŽI1*>(?:6D5eœ).
/
>
Q (+<+Ÿœ).  V  N— O 575>6DEŸ†€(2Pˆ)21.¡AC*7ˆŠA^ˆ)* ‡m5>(21(Œ1EFˆ˜*7(?I1*7(?57(?0HACˆ)ŸœŠ. 16D0UdŠ*76”ˆ8†”ƒ .)624(+<+6;216D24.eˆ)24./I4A^ˆŠ*
.JEF.:21(?D.ž./*>6 …/6;0Pˆ)21( N ./;”ˆ)012 B – 6 …)Œ1*Cˆ g  V N †1IS.)*¦Œ1E=ˆ Œ1(?5>A œŠ.F21(«5>6DE9I1D6;<+6D21ˆ)21(h
O I./I1Œ4”ˆ)Ÿ œ).F6;016D<?6”ˆ)[+…/(?*Cˆ)21ˆF21(ƒ ./*7EFˆJˆ)D(+ˆŠA•@/*>6”ˆK†4<+./E.9)ˆŠD./* 21./5 …/(?01(+5`ˆFI(+*>A7(+01<?(+*`ˆ).
ˆ) ƒ\ˆ S(BAC. † R  ° 0 1E9(+*7.eE d?–€6;EF.¡21(`04.€21.)5G21(£(?0HA7*Cˆ)21ˆfB Nx(`6;0HA7(+*>Ei[?216D./5B Nƒ .)6}ˆ “>Œ45>A^ˆŠ21.
ˆ)./5¡Šˆ)D./*>(+5 R ( V † 2Pˆ)21. Œ4($ˆ)5e( –€IS(?*76 ˆ?01<+6Dˆ)5pˆŠ0HA7(+*>6D./*>(+5pˆŠIS./0[ACˆ)EIPˆ)*Cˆ. Œ157.21(@*7(?21(+5e21(
Pˆ)6 –4ˆe<‰ˆ)*>216D01ˆ)D6;2Pˆ)21_(  EFˆe./Œ€AC*Cˆ˜IS./;‹;A76D<‰ˆŽ6;*76”ˆ˜ˆ)Œ1E9(+0[A^ˆŠ*.ž(+5>IPˆ)Ÿ?.ž21(£I1*>.€<?Œ1*Cˆp5>(+E (+04™( ƒ ‹D<?6D./5
>
€3
B
6
/
6
+1
/
6
6
K}}> &)
T
População Inicial
Avaliação
Nova População
Geração de
RNUs
Mutação
Cruzamento
Treino
RPROP
Recombinação
Genética
BIC
Selecção de Progenitores
– 6 …)Œ1*Cˆ *K V ‘ & 5 Œ4(+EFˆF21()ƒ Œ101<?6D./01ˆ)EF(?0[AC.ž21.9576;5>AC(?E=ˆž21(«./I€AC6DE96D®+ˆ)ŸœŠ.p01(+Œ4*7./0PˆŠŽ
/
ˆ)<?*7(+5><+6;21./5 = ./*˜<+./015>(…/Œ46D0[AC(_†­. <+*>./EF.)5757.)E=ˆgAC(+E Œ1E<+.)EFI1*>6DE9(+0[AC.21( 2 GyL…/(+01(?5
B\( ŒPˆ)Ÿ œŠi
. *  R N †1. Œ4(eˆ)I./0[A^ˆžIPˆŠ*CˆžŒ1E (?57IPˆ)Ÿ?.=21(«I1*>.€<?Œ1*Cˆž21(
57.)DŒ1Ÿ?±€(?5 246D5>A76D0[A^ˆŠ5
O <‰ˆ)*>216D0PˆŠD6D21ˆ)21(21ˆ«I./I1Œ4”ˆ)Ÿœ). ƒ ./64¨K–4ˆ)21ˆ«(?EG2H:HK – ./64Œ4AC6;D6D®+ˆ)21.Œ1E <+*>Œ1®‰ˆŠEF(?0HA7.«21(
21./6;5 I./0[AC.)5 †/*>(+57I./01e5 d‰/(+4IS(?”ˆ<?*76Dˆ)Ÿœ).21( ² 21./5¤04. )./5 6;01216;:‹;21Œ1./5™†Š5>(+0121.«ˆEpŒ4A^ˆŠŸœ). 16D0UdŠ*76”ˆ
*7(?57I./01e5 dU)(+1I(+Dˆ`<+*>6”ˆ)Ÿ œ).`24./5¤*>(+5>ACˆ)0[AC(?5­(+D(?EF(?0[AC./5™ ° I1*7.:<+(?575>.Ž21(5>(+D(?<+Ÿœ).)[*>(‰ˆ);6D®‰ˆŠ21.£ˆŠA7*Cˆ‰:[?5
2Pˆ«Œ4AC6;D6;®‰ˆ)Ÿ œ).Ž21.˜Šˆ);./*­21(ˆ)I4A76DU2 œ).«I./-* ƒ ./*7EFˆ«ˆ¡5>(+*>6”ˆ)*¯ˆ)5 57.)DŒ1Ÿ?±€(?5 B <+./0[/(?*7e5 œ).pI./* ./*721(?0Pˆ)Ÿ œ)”. N—†
57(?0121.t24(+I./6D5Fˆ)I1;6D<‰ˆŠ2PˆdŒ4E=ˆdˆ)E9./5>A7*Chˆ …/(?E (+5-AC.:< d)5-AC6D<+ˆ’<?./E 57Œ 15-AC6ACŒ16;Ÿ œ). † Œ1( …[ˆ)*7ˆ)0[AC(‡Œ1EFˆ
57Œ4I1*7(?E=ˆ)<?6”ˆž(+5-AC.:< d)5-AC6;<‰ˆž21./5 EFˆ)6D5¦ˆŠI4AC./™5 
O 6;0H).€<+ˆ)Ÿ œŠ.e21. v [`21ˆ)2Pˆe<?./EF.«¨P0121ˆ ŒPˆ)0121. GhHhH+…/(?*Cˆ)Ÿ?±€(?5 †:2Pˆ)21. Œ1(./5E9(+ 1_. ‡
*7(?5˜6;01216€‹;21Œ1./)5 ƒ ./*7ˆ)E5>(+E9I1*7(9(+01<?./0[AC*7ˆ)21./5˜(+š
E …/(?*Cˆ)Ÿ?±€(?5pˆ)0[AC(?*76;./*7(?5  = ./* 4;AC6;EFK. †ˆ).‡EF(? 1./*
6D04216;:‹D24Œ1.«(+01<?./0[AC*CˆŠ21.pI(+D. v j •5 œŠ.pˆ)I1;6D<+ˆ)21./5­AC*>6D0[A^iˆ B N¤AC*7(?6D01.)5x6;0121(+I(+0421(+0[AC(?5 †1I1ˆ)*Cˆ¡I1*7_. ‡
:6D21(?01<+6Dˆ)*žŒ1EFˆ E=ˆŠ6D./*˜*7(+;(?Š©)01<?6”ˆ (?5>A^ˆbAC‹D5-AC6;<‰Kˆ  `(g*7™( ƒ (?*76;*Jˆ)6D0121ˆ Œ4h( †¯IPˆ)*Cˆ]ˆ)5 u ^j ƒ .)*Cˆ)E
<+.)01576;21(+*7ˆ)21./5¦AC.:21./5¦.)5 I1ˆ)*C©)E9(?A7*7./5¦<?./015-A^ˆ)0[AC(?521ˆ ¥ ˆ (+”`ˆ *K R 
O 5žE9(+ 1./*7(?5˜A7./IS.)D:. …/6Dˆ)5«IPˆ)*7ˆ3ˆ)5 u ^j . 4AC6;2Pˆ)5žˆI1ˆ)*>A76D* u v ^j •5 œŠ.]ˆ)I1*7(?57(?0HACˆ)2Pˆ)5J0PˆŠ5
– „6 …/Œ1*CˆŠP5 *K ( *  ²  (+*76¨P<‰6ˆ ‡m57( Œ1((?E A7.€2PˆŠ5=ˆ)5F*7(?21(+5@( –€6D5>A7(+E D„6 …[ˆ)Ÿ?±€(?59246D*7(?<?ACˆ)5=(?0HA7*7(3ˆŠ5
(+0[A7*Cˆ)2PˆŠ5£(e57ˆ)‹D2PˆŠ`5 B\ˆŠA^ˆ) 1./•5 N—† . Œ1(pˆbAC(+5-A^ˆ@ˆFŒ4AC6;D6D21ˆ)21(Ž21(?5>A^ˆŠ5  ° E9(+5>EF.FU0 œ).=5>Œ1<+(?21(ž<+.)EˆŠ5
<+.)01—( –€±:(+5G21( f †€(?5>ACˆ)0121.p(?5>ACˆ)5¦ˆ)I(+0PˆŠ5I1*>(+57(?0[AC(+5¦(?E Œ1ˆŠAC*>.pe5 [?*76D(?)5 B^3 R 3-5 † 9-5 † Q eSRUT 46V
W6XEY R ( 5S9 N— = ./*¦57ŒPˆž/(?h® †P./5 01.:21./5¦6;0[AC(+*>i
E [?216D.)5AC(?0121(+E ˆJ*>(+<?( (+* Œ1E 0 1E9(+*>.9246DE96D0HŒ4AC.
21(«<+.)01—( –€±:(+5ˆJI1ˆ)*>A76D*¦2Pˆ)5¦(?0[AC*CˆŠ2Pˆ)5 B\(+0[A7*7( R )( *ON—
O ¥ ˆ S(?”ˆ *  g 21(+5><+*7(B/(9./5ŽE9(+ 4./*7(?5£EF.:21(?D./5£24( u (?01<+.)0HA7*Cˆ)24./5«IS(?D. v 16;U0 d)*76;. †
IPˆ)*7ˆ£AC.:2Pˆ)5¯ˆ)5 e5 [?*76D(?5x21ˆ Q (?<+Ÿ œ).  R  j ./5 Œ1ˆ)6D5 •5 œŠ.˜21(B¨P016;21./5 (+E A7(+*7E9./5­2Pˆ«57Œ1ˆG“7ˆ)04(+”ˆ£A7(+E9IS_. ‡
/
/
¨6
/
6
/
>
/
€3
1
>
43
/
*K
NM
G
6
NM
€3
G
G
NM
6
/
8
/
€3
/
FEG
6
&6
M
43
/
G
+1
>
6
T*
!"#
#$%&')($
¥ ˆ S(?”ˆ>*  R ‘ ¯ˆ);./*7(?5¦21./5 IPˆ)*7©)EF(BAC*>./5¦21.J576;5>AC(?E=ˆž21(«./I€AC6DE96D®+ˆ)ŸœŠ.p01(+Œ4*7./0PˆŠŽ
6
8
’+R 4 R YhW 5”4 g ;—W6XZY R ;
;™W4 e W e 4 R
‘ R 4 h 5”W4?9<;
XEYOX R ZX R 7 9
34?5 T X R “ 5 h
!
5”4 h 9
XZ;—W 5 h"R T 5 >3W6X h X R 7 9
>
6
Ud
GŠ2H:H
T²
v 16;0 )*76;.
9
O D (‰ˆbA•@/*>6”ˆ † R
O  …/./*>6;A7EF.p24( N ./DDˆ)012
ž*>Œ1®‰ˆ)E9(+0[A7.F21( g IS.)0HA7./5B ² ¬ Œ€A^ˆ)Ÿ œ). 46DU0 d)*>6”ˆfB g N
oG
hH:H
96
u
NM
0
2
e@
0!2
O ;(‰ˆŠA /*76Dˆ 2 O „ …/./*>6;ACE9. u u N
T 5^9
/G HKJ„2
GhHKJMH
<" .1G $# GoHKJ„2
% GŠ2 H:HhH
P
1
12
12
13
1
1
2
2
3
6
11
10
11
12
12
13
13
1
2
1
7
7
12
13
– 6„…/Œ1*Cˆ/*K ‘ ¥ /. I./;.:…/6”ˆŠ5}21( *7(?21( . 4A76D2Pˆ)5}IPˆ)*Cˆ ˆ)5 5A[+*76;(+557ˆ)®+./01ˆ)6D5( <+.)E AC(?012 ˆ+04<+6”ˆ3 R ;; R “<5X^469 ;_†
3 R 3-5† h 9 4 W 5;h† h 5 -9 4 5 † Q eg1h XEY R ( 34657:9 ;_
13
76
K}}> &)
T³
1
2
3
4
5
6
7
9
10
11
12
13
1
2
3
8
11
12
13
1
1
2
2
4
3
6
4
7
5
8
8
9
9
11
12
12
– 6„…/Œ1*Cˆ *  ² ‘ ¥ ./I./D.:…)6”ˆ)5¦21(¡*7(?21(p. €AC6D21ˆ)5 IPˆ)*CˆFˆ)5`5A[+*>6D(+50Uœ).FD6D04(‰ˆ)*>(+5
T 4?V8W6XZY R ( S5 S9
13
13
76
h"R Y R ;h† 9 5 † Q eR
/T V
!"#
#$%&')($
*CˆŠqB <+./;Œ10Pˆ N—†b0 4EF(?*7.Ž21(x01.€24./5 6D0[A7(+*7EP[+246D./5‚B\<?./DŒ101ˆ N (0 1E9(+*>.`AC.ŠA^ˆ):21(G<?./01(—–€±:(+5#B<N—
O <+./;Œ10Pˆ œ24(+01.)ACˆ‡. ƒ\ˆ)<BAC./*Ž21(J*>(+21Œ1Ÿœ).21ˆ$A7./I./D.:…)6”ˆ B (+EI(+*><+(+0[ACˆh…/(+E N—† ŒPˆ)0124.5>(F<?./E ‡
IPˆ)*7ˆpˆeAC.)IS./;:. …/6Dˆ«. 4AC6;2Pˆ˜I(+;.p576;5>AC(?E=ˆ˜21( u v <?./EœˆeAC./I./D.h…/6”ˆŽ<+.)EFI1;(?ACˆ)EF(?0[AC(`6;0[AC(+*>D6„…[ˆ)2Pˆ
( Œ16Šˆ)D(?0HA7h( †P./Œg5>('“7ˆ4‘
1
+1
/
G
NM
6
/
BE*K g N
}G20 ./0124(
21(?01.)ACˆ . 0 1EF(?*7. AC.)ACˆ)/21( <?./01(—–€±:(+5 2Pˆ A7./I./D.:…)6”ˆx24(x*>(+21(¯<+./E9I1;(?A^ˆŠEF(?0HA7( 6D0[A7(+*7;6 …[ˆŠ2PˆK
= .)*¤—( –€(?EFI1;. †/IPˆŠ*Cˆ`ˆ5e[+*>6D( h"R Y R ;AC(?E ‡ 57( Œ4(}G 2<0 2 hc G2  = ./* 1AC6DE9. †bˆ`<?./DŒ101ˆ
£ˆ)I1*7(?57(?0HACˆ@.=(?*7*7.=21(eI1*>(?:6D5eœ).=I1ˆ)*Cˆ9<‰ˆ)2PˆFEF.:21(+;. †P(+EA7(+*7E9./5 2Pˆ=EP[+216Dˆ924./5A7*76D0[ACˆ
AC*>(+6;01./5 †4<+./E Œ4E …/*CˆŠŒ‡24(¡5>6 …/046;¨P<+©)01<+6Dˆp21(L 
¥ ˆ (+D>ˆ *  g ‘ žGˆ)*Cˆ)<BAC(?*7‹D5-AC6;<‰ˆ)5¦21.)5 E9.:21(+;./5G21(«I1*>(?:6De5 œ).F. 4AC6;21./5:6”ˆJˆJ./I4A76DE96D®‰ˆŠŸœ).˜01(+Œ1*>./0Pˆ)Z
+1
/
1
6
6
4?XE5
I1ˆ)5757ˆh…/(+6;*7./5
I1ˆ)IS(?
E9./*-AC(+5
E9(+ S.)*701(
Œ1‹;EF6;<‰ˆ
I4*7(+Ÿ?./5
EFˆ)01< 1ˆ)5
Š. (
ŒPˆŠ21•* dŠA76D<+ˆ
4(+01./0
€6
/
J3
76
/
3
R †R g †R !
Rg
R † g † R/R † R g † R #
R † g † † V † R † R/R † R g † R !
R †g † †R g †R !
R † †R #
R † g † † ² † R/R † R g † R !
R † g † †Œ* † ³ † V † † T † R † R/R † R g † R !
R † g †M* † V † † ² † T † R g † R #
R † g † †Œ* † ³ † ² † T † R/R † R g † R #
R
³
g
g
*
R V ³*
R V³
g
V R * ³³ V R R
R V/³/T³ V g* V4R *
R³ ²g  g³ "" 

V
R ² g" " R g


"
 )V  4R
M* T "  4R
R ²Œ* " " ²  ³
*T
 €R "  g * "  g
7
& E …/(?*Cˆ)Z†ˆ=6;01<+6;2 ˆ+01<?6”ˆ=24. ƒ\ˆ)<?A7./*`21(e*7(+24Œ1Ÿœ). B$ N57. 4*7(žˆ)5AC./I./D.h…/6”ˆ)5 21(p*>(+21(ŸB . …[ˆ)0 1.
(+EIS(?*7<?(+0[A^ˆh…)(+E0Pˆ$*>(+21Œ1Ÿœ).g2Pˆ)5Ž;6 …[ˆ)Ÿ?±€(?5`(?0HA7*7(ž01.:21./5•N`.€<?./*7*>(p<+.)EŠˆ)D.)*7(+5`(+0[AC*>(ž./5 hH% (
hH% BiˆJ—( –€<+(?ISŸ œ).=.:<+./*>*7(«0Pˆ)5¦A7./IS.)D:
. …/6Dˆ)5G21(¡*7(?21(«21(¡EF(?01./* <‰ˆ)*>216D01ˆ)D6;2Pˆ)21_( †4<+.)EF.J01.9<‰ˆ)5>.=2PˆŠ5
¥
R
R
R
5e[?*76;(+/5 3 ;; “<5X^469 ;£'( 3 3-5ZN— ˆ) ƒ\ˆ)<?A7.e21(?EF.)015>A7*Cˆ Œ1(£'. &)(<+.)0157™( …/Œ1(Ž™( ƒ (?<?A7ŒPˆ)*Œ4Eœ<?./*>A7(
57Œ 15>ACˆ)01<+6Dˆ)01.e0 1E9(+*>.˜AC.ŠA^ˆ)P21(<+./04—( –€±€(?5I./575>‹;)(+6D™5 †€. Œ1(`*>(+57Œ4;A^ˆ¡(+E E9.€21(?D./5­EFˆ)6;5¯5>6DE9I1D(?5 
ž./E9IPˆ)*CˆŠ0121.3(+5-AC(?59*>(+5>Œ1;ACˆ)21./5ž<?./E .)5ž. 4AC6;21./5pI(+Dˆ)5 1(?Œ1*7‹;5>A76D<‰ˆŠ5pŒ4AC6;D6;®‰ˆ)2PˆŠ5˜01.]<+ˆ)I1‹;A7Œ1D.
ˆ)0[AC(?*76;./* B ¥ ˆ (+”ˆ  N †1<+.)01<+;Œ16 ‡ 57( Œ1()‘
( –46;5>A7(=Œ1EFˆ216 ƒ (+*>(+01Ÿ+ˆˆ).01‹;)(+¯2Pˆ)5 “7ˆŠ01(+Dˆ)5ŽAC(+E9I./*Cˆ)6;5«57(+;(+<?<+6D.)0Pˆ)2Pˆ)™5 † <+.)E ˆ‡—( –€<+(?ISŸ œ).
2PˆžI1*>6DE9(+6;*CˆeA5 [+*76;h( †U3 R ;; R “<5X^469 ;
.576D5-AC(?E=ˆ 21(x.)I4AC6;EF6;®‰ˆ)Ÿ œ). 01(+Œ1*>./0Pˆ)HAC(?0121(ˆ(+5><+./ 1(+*¤ˆ)5 ˆ)* Œ16AC(+<BACŒ1*7ˆ)5¤EFˆ)6;5¢5>6DE9I1D(?5 † Œ1(
<?./0[•A ˆ+EŒ1E E9(+01./*¤0 4EF(?*7.«21( <+./04—( –€±€(?5 †€ˆ)I(+5CˆŠ*­21( IS./5>57Œ1‹;*7(?EEFˆ)6D5 04.€21.)5­6D0[AC(?*7PE [+216;./5
(
76
53
/
56
/
+1
76
6
3
/
:
T
:
€3
1
/
/
T
T
.p5>6D5-AC(+EFˆpˆ)<BACŒPˆŠˆ)I1*>(+5>(+0[A^ˆžE9(+ 4./*7(?5I1*>(?:6D5>±€(?5†1(?57I(+<+6Dˆ)DE9(+0[A7(£IPˆ)*7ˆpˆ)5G5A[+*76;(+5G0 œ).žD6;01(—‡
ˆ)*>(+5+Biˆž( –4<?(+IŸœ).F.€<?./*7*>(Ž<+./E ˆJ5A[+*>6D( 3 R 3-54_N 
K}}> &)
:
43
O 1Œ 6Ž† ˆŸ˜1(—–€6 16;D6;2Pˆ)21(p24. v IS(?*7E96;AC(ž5>(+;(+<+<?6D./01ˆ)*«EF.:21(+;./5Ž<+.)EEF(?01./*7(?5¡Šˆ);./*7(?5«21(=™˜š€›
IPˆ)*7ˆ=AC./I./;.:…/6”ˆŠ521(ž*>(+21(ž<?./E„EFˆ)6;5`01.:21./5£6;0[AC(+*>Ei[?216D.)5`(žE9(+01./5`IPˆ)*C©ŠEF(BAC*7.)5†*>(+57Œ4;A^ˆŠ0121.$(+E
E9(+ 4./*7(?5¦I1*7(B€6;57±:(+5™
ž./0[: [?E *7—( ƒ (+*76;*ˆŠ6D012Pˆ Œ1(Žˆ)5A7./I./D:. …)6”ˆ)5­21(`*7(+24(£(+5><+./ 16D2PˆŠ5IPˆ)*>(+<?(+E A^ˆ)E <[+E (?5>A^ˆŠ*¦ˆ “>Œ15 ‡
A^ˆŠ2Pˆ)5 ˆ). …/*CˆŠŒ21(«<?./EFI4D—( –€6;2Pˆ)21(Ž2PˆžA5 [+*76;h(  = ˆ)*7ˆFˆŠ5 A5 [+*>6D(+5 ;6D01(+ˆ)*7(?5 †1(?5>AC(?5`<?./0[•A ˆ+E(?0[AC*7( ˆ R
<+.)01—( –€±:(+5 †PŒ4E Šˆ)D./* Œ1(¡ˆ)Œ1E9(+0[A^ˆžIPˆ)*7ˆ R IPˆ)*7ˆžˆ)5¦e5 [?*76D(?5 U0 œ).žD6;01(‰ˆŠ*7(+™5 †1(+;(?Šˆ)0124_. ‡m5>(ŽˆŠ•A [«ªŠ5 g
( *J<+./04—( –€±€(?5I1ˆ)*CˆJˆ)5 e5 [?*76;(+5 21.žAC6;IS.ž<+hˆ @)AC6;<+. 
O A7‹;ACŒ4D.921(+E9./015-AC*CˆbAC6;). †ˆ – 6„…/Œ1*7ˆP*  T ˆŠI1*7(?57(+0[ACˆ@./5 1AC6;EF./5 R 21./5`(?D(?EF(?0HA7./5 2Pˆ=5e[?*76;(
h"R Y R ;_† (+E<+./E9.gˆ)5«*7(?57I(+<BAC6;Šˆ)5ŽI4*7(?:6;57±:(+)
5 ƒ ./*704(+<+6;2Pˆ)5ŽI(+;.$576D5-AC(?E=ˆ@21( u v †<?./015>6D21( ‡
*CˆŠ0121. ˆ‡iE [?216”ˆ$2PˆŠ5˜AC*>6D0[A^ˆ‡ˆ)I1*>(+01246D®‰_ˆ …/(+01™5 Ÿž./E9.5>(=I.€21(J/(?*76¨P<‰ˆ)™* †¤./5«Šˆ)D.)*7(+5«21(F5Cˆ)‹;2Pˆg2Pˆ
u (+04<+./0[AC*7ˆ)>E ‡m57(¡I1A* @ –€6;EF./5 2PˆŠ5. 457(+*-Šˆ)Ÿ+±:(+5*7(‰ˆŠ6D5 †P*>(?)(+”ˆŠ0121.=Œ4E=ˆ S./Pˆ …/(?01(+*7ˆ)D6;®‰ˆ)Ÿ œ).JIS.)*
IPˆ)*-AC(«21.JE9.€21(?D. 
0/
>
46
43
/
€3
6
/
@1
NM
Ÿ6
NM
76
6
160
manchas
RNU
140
120
100
80
60
40
20
0
265
270
275
280
– 6„…/Œ1*7ˆ`*  T ‘ = >* (?:6D5>±€(?5¦€6Dˆž576D5-AC(?E=ˆž21( u v IPˆ)*7ˆJˆ95A[+*76;(
NM
G
285
h"R Y R ;h
G
T²
!"#
#$%&')($
fpSw! w!"t$#&% ~ xf~ ' ~Pxfz(—~ m `~$(™Ÿ€ w™~ * rw™~
,.- 2- 1 4 B 5H D? = C ?D8 47@ CIJK?A8 4 EGFD?DHI<JKC2?D@>LD=CI?A8
° 21(+5>(+E9IS(?0 1.«21./5 v (?EI1*>. 1;(+EFˆ)5 24(¦./I4AC6;EF6;®‰ˆ)Ÿœ). [¦ˆ_ƒ (+<BA^ˆ)24.ŽIS./* Œ1E<?(+*-AC.Ž0 1E9(+*7.`21(
ƒ\ˆ)<BAC./*>(+5 O „…/Œ1015¢21(+5-AC(?5ƒ\ˆ)<?A7./*7(?5¤5eœ).`21(BAC(?*7E96D0Pˆ)24./5 IS(?D.`I4*7. 1;(+EFˆ ˆ*7(?57.//(?*†/5>(+0121.`0Uœ).`*7ˆ)*CˆŠ5
/(?®+(?5¤6D04<+./0[AC*>./ d‰)(+6D5™ ° Œ€AC*7.)55•œ).ƒ\ˆ)<BAC./*>(+5 Œ1( 21(?A7(+*7E96D01ˆ)E . I1*A@/I1*76;./ƒ Œ101<?6D./0PˆŠEF(?0HA7.¦21. v †
I.€21(?0121.957(?*`ˆ “>Œ45>A^ˆŠ21./5 IPˆ)*7ˆ9E9(+ 1./*CˆŠ*¦ˆ9(B¨P<dŠ<+6”ˆJ21. v  & 5-AC(?5`IPˆ)*7©)E9(?AC*>./5¦6D04<+DŒ4(+EŸ†1(+0[AC*>(
jfk
>
3
G
76
+1
76
/
>
>
./Œ4A7*7./5™†1ˆe<+ˆ)*7246D0Pˆ);6D2PˆŠ21( 2PˆpIS.)I1Œ1”ˆŠŸœ). †:ˆ)5xA^ˆ?–4ˆ)5G24(Žˆ)I1;6D<‰ˆŠŸœ).¡21./5G.)IS(?*Cˆ)21.)*7(+521(£<+*>Œ1®‰ˆŠEF(?0HA7.
(«EpŒ4ACˆ)Ÿ œ)K. †PˆpA^?ˆ –4ˆž21(¡*7(+04. Šˆ)Ÿœ).J2PˆJIS./I4Œ1”ˆ)Ÿœ). †€.9I4*7.:<+(+5>57.F21(«57(+;(+<?Ÿœ). 
O 6;K0 ˜PŒ ˆ?01<+6Dˆ•21(+5-AC(?5 ƒ\ˆ)<?A7./*7(?5=01.t24(+57(?EFI(+0 1.#21( Œ1E v 0 œ).tI.€21(57(?*=21(?57<+*>6;ACˆ•IS.)*
Œ1E I4*7.:<+(+5>57.’ˆ)0Pˆ);‹;A76D<+K. †¤2Pˆ)24. Œ1(gŒ1E v [gI./*p21(B¨P016;Ÿ œ).]Œ1E E9.:21(+;. (+5-AC.:< d)5-AC6D<?.  ,m5>A7.
57„6 …/016¨P<‰ˆ Œ1( ./5 iE [BAC.:21./5<?./0[/(+04<+6D.)0Pˆ)6D5 2Pˆ ŽZ P_ bY ./Œ¡21( 21(?)(+*7ˆ)5 <?./EpŒ1045¢eA [+<+046D<‰ˆŠ5
21(@.)I4AC6;EF6;®‰ˆ)Ÿ œ). †¢U0 œ). e5 œ). ./5pEFˆ)6;5˜(B¨P<‰ˆ)®?(+5žIPˆŠ*Cˆ.A7*CˆŠACˆ)E9(+0[AC.21(+5-AC(+`5 ƒ\ˆŠ<?AC.)*7(+™5  O 5>576DŸE † 01.)5
1AC6DE9./5 ˆ)01./5 ˆ)575>6D5>A76D8Œ ‡ 57(ˆ).Ž21(+5>(+0[/.);:6DE9(+0[AC.Ž24(¦01.U)ˆŠ5¤•A [?<+016;<‰ˆ)5 I1ˆ)*CˆŽˆ`.)I4AC6;EF6;®‰ˆ)Ÿ œ).24( v †
ˆŠA7*Cˆ‰: [?5=21(‡21ŒPˆ)59<+.)*7*7(?0[AC(+5 j Œ1(‡Œ4A76DD6;®‰ˆ)E ./Œ Œ1E >ƒha B_ P_ [Z BX_ )_ w .)Œ z B_ v
‰ = (?A7*7.U:O5 H6 ¬ < žGˆ)DZ † RUT/T  
° 5xPE [?A7.€21.)5­21(`ˆU“>Œ15>ACˆ)EF(?0[AC.˜ˆ)2Pˆ)I4ACˆŠAC6/.¡21(?A7(+*>EF6;0Pˆ)E.)5¯Šˆ);./*7(?5­21./5¯IPˆ)*C©ŠEF(BAC*7.)5¯24. v
21(GŒ4E=#ˆ ƒ ./*7EFˆ 246D0P©)E96D<+Kˆ †b21Œ1*CˆŠ0HA7(Gˆ`5>ŒPˆ£—( –€(?<+Œ1Ÿ œ). †HˆŠA7*Cˆ‰: [?5 21h( †)IS./* —( –€(+E9I1;. †)I1*>.€<?(+5>57./5 24( … |Y|Y BY 9f :n  & E ./*7ˆ˜57(m“7ˆ)E IS.)A7(+01<?6”ˆ);EF(?0[AC( I1*7.)EF6;5757.)*7(+™5 †4(?5>AC(?5GPE [?AC.:21./5xˆ)I1*>(+5>(+0[A^ˆ)EœŒ1EFˆ˜e5 [?*76;(
21(G24(+5>Šˆ)0[AChˆ …/(+045  & E§I1*76;EF(?6D*7. DKŒ …[ˆ)* †Š.Žˆ)Œ4A7_. ‡'ˆU“>Œ15>ACˆ)EF(?0[AC.`A5 @)[Gˆ)I4D6D< d‰/(+€ˆ)./5 ƒ\ˆ)<?A7./*7(?5­ˆ)<BAC6;)./5 †
<+.)EF.9ˆpA^?ˆ –4ˆJ21(«EpŒ4ACˆ)Ÿ œ)K.  O 246;¨P<?Œ1D2PˆŠ21(«57Œ1A* …/(«<+./E .)#5 ƒ\ˆŠ<?AC.)*7(+5 Œ1(¡U0 œ).J(+5-A œ).9216;*7(+<BA^ˆ)E9(+0[A7(
(+0[)./;:6D24./5 0Pˆ9I4*7.:21Œ1Ÿ œŠ.F21(¡01.UŠˆ)5 57./;Œ1Ÿ+±:(++5 B h( Œ… „†ˆJ<‰ˆ)*>216D01ˆ)D6;2Pˆ)21(£21ˆJI./I1Œ4”ˆ)Ÿ œ)”. N— = ./* ./Œ4AC*>.
”ˆŠ21. †[ˆŽI1A* @/I1*76DˆŽˆŠ¨P0PˆŠŸ œ).«21./5­PE [?A7.€24./5­21( ˆ “>Œ15-A^ˆ)E9(+0[A7.¡24(+I(+0121( 2PˆŽ6D0[A7Œ16DŸ œ).Ž21.«I1*7h. …/*Cˆ)EFˆ)21.)* †
216¨P<+Œ1A^ˆ)0421.žŒ1EFˆ9ˆŠU0 d)D6;57(£. :“>(+<BAC6;ŠˆJ21.J21(+5>(+E9IS(?0 1.921. v 
O ˆ)AC(+*>0PˆŠA76;ŠˆeªpŒ4A76D;6D®‰ˆŠŸ œ).¡21./5GPE [?A7.€24./521(«ˆU“>Œ15>ACˆ)EF(?0[AC.žIPˆ)5>5CˆpI(+DˆeŒ4AC6;D6;®‰ˆ)Ÿ œ).e21.)5 z B_ v †£I4*7./I./5>A7./5gIS.)* «*>™( ƒ (+045>AC(BA7A7( ‰ RUT ² V   ° 5 z B_ v Œ€AC6D;6D®+ˆ)E v ˆ#Œ1E 01‹/(+
E9(?A^ˆJIPˆ)*7ˆ924(?AC(?*7E96D0PˆŠ*G)ˆŠD./*>(+5¦K¨ –€./5 21(˜I1ˆ)*C©)E9(?A7*7./5 21. v ˆ).F04‹;/(?. :“>(?<?ACK.  «*>™( ƒ (?015>A7(?A7A7(
21(?EF./045>AC*>./Œ(?EFI16;*76;<‰ˆ)E9(+0[AC( Œ1( .)5 z B_ v <?./0157™( …/Œ1(?E Œ1E E9(+ 4./*J21(+5>(+E9IS(?0 1. † (+E
*7(?”ˆ)Ÿ œ).9ªJˆ)I1D6;<‰ˆ)Ÿ œ).p21(«*>( …/*7ˆ)5 [Z9… † ŒPˆ)0121.957(ŽA7*CˆŠACˆJ24( v 16;U0 d)*76;./5 
° 5 z B_ v •5 œ).=ˆŠAC*7ˆ)<?A76;)./5 57. .FI./0[AC.F21(¡:6;5>A^ˆJ2Pˆ9./I4AC6;EF6;®‰ˆ)Ÿ œ).ž21( v 21(B:6D21.Fˆ
21./6;5 ƒ\ˆ)<?A7./*7(?5+‘«I(+*7E96;A7(+E—( –€I1D.)*Cˆ)*ŽŒ1E„(+D(BŠˆ)21.g0 1EF(?*7.‡21(JIPˆ)*7©)EF(BAC*>./5 †6;0121(+I(+0421(+0[AC(?EF(?0[AC(
2Pˆ]<‰ˆ)*>216D01ˆ)D6;2Pˆ)21(@24.’(?57IPˆ)Ÿ?.•21(‡I1*>.€<?Œ1*Cˆ (gI./*J./Œ4A7*7.d”ˆ)21.]I./* Œ1(g*>(‰ˆ);6D®‰ˆŠE Œ1EFˆ3I1*7.:<+Œ1*7ˆ
ˆ)Œ4A7./iE dŠAC6;<‰ˆ0 œ). AC(?0121(+04<+6D.)5CKˆ  ¥ .:2Pˆ‰:6”Kˆ † eA ˆ+E ˆ 21(+5-Šˆ)0[A^hˆ …/(?E 21(@( –€6 …/6;*eŒ1E (+D(BŠˆ)21.3(+5 ƒ ./*7Ÿ?.
€3
>
53
/
>
/
JE
F
E
F 4
>
1
/
+G –
#
u F
G
u F>
G
>
I D
6
/
6
>
3
>
–
G
– F>
G
>
>
/
u F>
u F>
G
G
/
AHI
76
G
>
T
TQ VU
D¦JrH¥ D¥ 
3
6
+1
SQ
43
>
76
VXWY[ZE\]=^`_HWL\dce^fYEghjikmlWnvt–…7w
G
/
G
}}> (
‚—
T/T
&#—
<+.)EFI1Œ€A^ˆ)<?6D./0PˆŠŽ
,.- - /
?647HI? = ? ?D8
?
° ¦5 I1*7.)EF6;5757.)*7(+5x*7(?57Œ1A^ˆ)21.)5¦2Pˆp./I4A76DE96D®‰ˆŠŸœ).¡21(Ž576;5>A7(+EFˆ)5G<+.)EFI1Œ€A^ˆ)<?6D./0PˆŠ6D5 Pˆ)57(+ˆ)21./5¦(?E u
5•œŠ.’Œ1E S./E 6D01216;<‰ˆ)24./*p21( Œ1(gA^ˆ)E <[+E IS.:21(?*•œ).](—–€6;5>AC6;* S(?01(™ƒ ‹;<+6D.)5ž0:Œ4E=ˆ3./I4A76DE96D®+ˆ)Ÿœ).21.
E9.€21(?D.@(B/./;Œ1<+6;./0Ud)*>6D.  `(J01.)ACˆ)* Œ1(9ˆŸ…[ˆŠE=ˆ=24./5«EF.:21(+;./5£21( v ^j A7(+5-A^ˆ)21.)5¡04.<+ˆ)I1‹;A7Œ1D.
ˆ)0[AC(?*76;./* † [«I./*>)(+0[ACŒ4*CˆJ*7(+24Œ4AC./*7Kˆ †Še“ d Œ1(«(+0[/.//(˜ˆ)I(+0Pˆ)5 ˆ)5 4(+Œ1*>‹D5>A76D<+ˆ)5 21(“7ˆ)01(+Dˆ)5GAC(?EFI./*7ˆ)6D5
(p./5`EF.:21(+;./5 $( q † œ). ƒ ./*7ˆ)EAC(+5-A^ˆ)21ˆ)5Ž01(+E 216 ƒ (+*7(?0[AC(+5`<+./E 46D0Pˆ)Ÿ?±€(?5`21( “7ˆ)01(+Dˆ)5 †S01(+E
./5 E9.€21(?D./5 &) & —†P(+E Œ4( G P
° *CKˆ † IPˆ)*7ˆ•<+.)DEFˆŠA^ˆ)*9(+5-A^ˆ)5=D6DE96;ACˆ)Ÿ+±:(+™5 †‚[ I4*7./I./5>A7.tŒ1E z B_ v 16;U0 d)*76;. † Œ1(]ˆŠ.t6D80 ‡
:[?5e21(J./I€AC6DE96D®+ˆ)*£./5«I1A* @/I1*>6D./5«IPˆ)*7©)E9(?AC*>./5Ž21. v ˆŠ.‡04‹;/(? . :“>(+<BAC. †¢6De* d$<+.:216;¨P<+ˆ)*ŽE9.€21(?D./5
&) & —†¤ˆ5>(+*7(?E./I4AC6;EF6;®‰ˆ)24./5£:6”ˆ v <+.)E*7(+<?Œ1*75>.3ˆ*>(+I1*>(+5>(+0[A^ˆ)Ÿ?±€(?5p0Pˆ Pˆ)57( R 
O 5>576;E † .9<+*7.)EF./5>57./EFˆ Œ4(e<+.:216¨P<‰ˆJIS.)5757‹/(?6D5 57./;Œ1Ÿ+±:(+5 IPˆ)*7ˆ9.FI1*7. 4D(+EFˆJˆ)I1*>(+57(?0[A^ˆ=Œ1EFˆJ<‰ˆ)* ‡
216;0Pˆ)D6;2Pˆ)21`( B\Œ1EFˆžEF(?216D21ˆp21./5 57(?Œ1'5 …)(+01(?5 N¦2Pˆ)2PˆžI./*+‘
/
6
6
6
/
K
>
/
>OG
NM
p6
G
03
6
/
– F>
>
76
>
/
6
G
Q6
/
76
2
BE*K N
( Œ4(Ž<+./*>*7(+5>IS.)0121(¡ªž(—–€6D5-A•ˆ+04<+6”ˆ B ./Œg0Uœ).”N¯21./5¦<+.:(?¨1<+6D(?0[AC(+5 21.JE9.€24(+D.K† 1†!& ( 6†1(Ž(+E 1Œ (
J( F24(+01.)ACˆ)E .@D6;EF6AC(«57Œ1I(+*>6D./*21./5£<?.€(B¨P<+6;(+0[AC(?5«ˆ)21E96;A76D21./5 IPˆŠ*Cˆ@./5£E9.:21(+;./5 & (
& B – 6 …/Œ1*7`
ˆ *  R N—
/
Pmax
µ
Cromossoma
A1 A2
/
Qmax
... A i M1 M2
... Mj
– 6„…/Œ1*Cˆ`*K R ‘ & 5 Œ1(+EFˆ924(¡<?.€246;¨P<+ˆ)Ÿœ).J21. z B_ v 
Q ( Šˆ)D.)*F21(3Œ4E 2PˆŠ21. …/(+04(\ƒ ./* R † (?0HA•œ).#.#<+.:(?¨1<+6D(?0[AC( <?./*7*>(+57I./0124(+0[AC(]57(?*•d#<+.:216¨P<‰ˆ)24.
ˆ).t04‹;/(?24.t<+*>./EF.)5757.)E=Kˆ †¦5>(+0124.#21(+5><‰ˆ)*-A^ˆ)21.#04.t<‰ˆ)5>.t<+.)0HA7*•d)*>6D.  † .t<+ˆ)I1‹ACŒ1;.•ˆ)0[A7(+*76;./*† ˆŠ5
“7ˆ)01(?”ˆ)5­A7(+E9IS./*7ˆ)6D5 &)s( & <+./6;01<+6;216”ˆŠE†ŠIS(?D. Œ1(`5>( A7./*70Pˆ‰Šˆ«ˆ)I(+0Pˆ)5¯01(?<+(+5>5•d)*>6D.˜21(?¨P046D* Œ1EFˆ
21(?”ˆ)5™ † .]I1*7(?57(?0HA7(<?./0[AC—( –:A7. †xACˆ)GU0 œ).]5>(+•* ddˆ3576ACŒPˆ)Ÿ œ).3<+.)EpŒ1ŸE †x0Pˆ3E9(+216;2Pˆ (+E Œ4(‡EeŒ16;A7.
ƒ *7( Œ1(+0[AC(?EF(?0[AC(‡57(@AC(?•* d G †¯IS(?D. Œ1(g57(?•* d3<+.)0H)(+016;(+0[AC(‡216 ƒ (+*7(?01<+6Dˆ)*pˆŠ5“7ˆ)01(+Dˆ)5  Q (?0121.
ˆ)5>576DŸE †”[I./5>57‹;)(+hˆ …/.)*Cˆ¡ˆ)I1*7(?57(?0HACˆ)*.¡I1*>.€<?(+216;EF(?0HA7.˜24(21(?57<?.€216¨P<‰ˆŠŸ œ).˜21(Œ4E <?*7./E9./5>57./EFˆŽ21.
z B_ v B – 6 …/Œ1*7`ˆ *  R/R N—
° 5 I1ˆ)*C©)E9(?A7*7./5 21.JE9.€24(+D.ž24(?¨P016;21.9IS(?D. z B_ v •5 œ).JI./5>A7(+*76;./*7E9(+0[A7(¡(?5>A76DEFˆ)21./5¦I(+;.
v 24( Pˆ)6 –4.˜01‹;)(+1 B\./Œ@04‹;/(?S. :“>(+<BAC”. N † Œ1(£<?.€216¨P<‰ˆeˆ)55>./DŒ1Ÿ?±€(?50Pˆ Pˆ)57( R †:<+./E <‰ˆŠ2Pˆ …/(?01(
/
u F>
/
/
/
/
u F>
>
– F>
O6
6
/
6
R
!"#
#$%&')($
Pmax
Nível Meta
Q max
1 0 1 0 1 0 0 1 0 1 0 0 0
µ
Nível Objecto
A 2 A 4 M1 M3
– 6 …/Œ4*Cˆ`*  R/R ‘ `(?57<?.€216¨P<‰ˆŠŸœ).921(«Œ1E 6;01216;:‹;21Œ1.ž21. z B_ v
AR < 2,4 > MA < 1,3 >
Janelas

u F>
„K
$ˆ *7(—ƒ (+*76;*‡ 57(JˆgŒ1E„<?.€(B¨P<+6;(+0[AC(921.gEF.:21(?D. &) & †¢(+E Œ1( [J<+./04576D24(+*CˆŠ2Pˆ$Œ1E=ˆ$<?./04¨U…/Œ4*Cˆ)Ÿœ).
(+EœACŒ121.Fˆ)0UdŠD.:…[ˆeª9Œ4A76D;6D®‰ˆŠ2Pˆe0Pˆ Q (?<+ŸœŠ.  V  
= ./*‡57Œ1ˆ)(+h® †«]
. ƒ Œ101<?6D./0PˆŠEF(?0HA7.21.5>6D5-AC(+EFˆ#21. z B_ v [](?E ACŒ121. 57(?EF(? PˆŠ0HA7(dˆ).
21.dI1*7.:<+(?575>.t57Œ H“7ˆ)<+(?0HA7( ª]./I4A76DE96D®‰ˆŠŸ œ).301(?Œ1*7.)0Pˆ)+ B – 6„…/Œ1*7ˆ *  V N— O ˆ)I€AC6D2 œ).]21(<+ˆ)2Pˆ]EF(BA^ˆ?‡
6D04216;:‹D24Œ1. [(?0H•A œ).p. €AC6D21ˆ¡ˆŠI @/5xˆ˜24(+57<?.€246;¨P<+ˆ)Ÿ œ).˜21.e5>(+Œ@<?*7./E9./5>57./EFˆ¡04. v 21( 1ˆ)6–€.¡01‹;)(+Ž†
6D0[).€<+ˆ)0121_. ‡ 57( .«*7(+5>IS(?<?A76;/.˜I1*7.:<+(?575>.p21( ˆ)I1*>(+01216;®‰hˆ …)(+E h( †[¨P01ˆ)DE9(+0[AC_( †H<‰ˆ);<+Œ1Dˆ)0121._‡ 57(¦.«Šˆ)D./*¤21(
™eš:›21.9E9.€21(?D.ž./I€AC6DE96D®+ˆ)21. 
/
– F>
43
6
>
76
¨6
População Inicial
Avaliação
Nova População
Geração de
AGEs
Mutação
Aprendizagem
AGE
Cruzamento
Recombinação
Genética
BIC
Selecção de Progenitores
– 6 …)Œ1*Cˆ`*  R g ‘ & 5 Œ4(+EFˆ921()ƒ Œ104<+6D.)0Pˆ)E9(+0[AC.J21.J576;5>A7(+EFˆJ24(¡.)I4AC6;EF6;®‰ˆ)Ÿœ).p(?)./DŒ4<+6D.)0Ud)*76DˆK
/
& E A7(+*>EF./5¯21(I1*7.:…)*Cˆ)EFˆ)ŸœŠ. †[(+5-AC(£5>Œ 8‡m5>6D5-AC(+EFˆƒ .)6SˆŠ216D<?6D./0PˆŠ21.¡ªeˆ)I1;6D<+ˆ)Ÿœ). W6;e†€0Pˆ¡EF(?216D21ˆ
(+E Œ1(gˆ 6D0[A7(+*CˆŠ<+ŸœŠ. 21. z B_ v <?./E . v ˆ). 01‹/(+x. :“>(?<?AC. [=ACˆ)E <[+E21(B¨P016D21ˆ 01.
EP@€21Œ4D.p21(˜ˆ‰Šˆ)D6Dˆ)Ÿœ).e21.JI1*76;EF(?6D*7.K
6
/
u F>
>
76
6
}}> (
‚—
,.- - E 4 =C
7@>J CIBD8
R 4R
&#—
75 (?EF(? PˆŠ01Ÿ‰ˆ$21.‡576;5>AC(?E=ˆ@24( u v †¢(?5>A7( z B_ v 46D0Ud)*>6D. ƒ Œ401<+6;./0Pˆ)*ed@6 …/ŒPˆŠDE9(+0[AC(p<?./E9.
Œ1E„ˆ) …/.)*76;A7EF.J21(ž.)I4AC6;EF6;®‰ˆ)Ÿœ).=21(ž5>(…/Œ4012Pˆ$./*724(+EŸ†IS(?D. Œ1(9ˆ@(?57<+.) Pˆ@21.)5Ž57(+Œ45¡I1ˆ)*C©)E9(?A7*7./5
0Uœ). [g21(?)(+*7ˆ)5=<?*7Œ1<?6”ˆ)Z = ./*9Œ1E=ˆ Œ1(?5>A œŠ.•21(‡576;EFI1;6D<?6D2Pˆ)24(=(‡21(g<+./E9IPˆ)*7ˆ)Ÿœ).K†ƒ ./6¦24(+<+6;216D24.
ˆ)21.)I4A^ˆ)*¦.)5E9(+5>EF./5¦I1ˆ)*C©)E9(?A7*7./5¦24. v ˆ)0[AC(?*76D.)*7E9(+0[AC(ŽŒ4A76D;6D®‰ˆŠ21.pIPˆ)*7ˆ9.)I4AC6;EF6;®‰ˆ)*x.FE9.€24(+D.
01(?Œ1*7./01ˆ)Ž †1.)Œ‡5>('“7Kˆ † ƒ .)6<+./015>6D21(?*Cˆ)24. BiOˆ N
. v 16D0 d)*76;.žI1*7./I./5-AC.JIS.)* N ./;”ˆ)012
ˆžI./I1Œ1Dˆ)Ÿ œ).ž6;016D<?6”ˆ) [)…/(+*7ˆ)2PˆJ21)( ƒ ./*7EFˆžˆ);(‰ˆŠeA @/*76DKˆ †:A7./EFˆ)0121.pŠˆ);./*7(?5¦21.F<?./0b“>Œ10[A7. † R ˆž<‰ˆŠ*7216;0Pˆ)D6;2Pˆ)21(`2PˆžIS./I4Œ1”ˆ)Ÿ œ)>. [¡ˆ “>Œ15-A^ˆ)2PˆJIPˆ)*7ˆž.96;0[AC(+6;*7f. 2 HhH
Œ1EFˆž*7(?<+./E 46D0Pˆ)Ÿ œ)>. …/(?0 [?A76D<‰ˆp:6”ˆž<?*7Œ1®+ˆ)EF(?0[AC.921(«21./6D5¦I./0[AC.)5 («EpŒ€A^ˆ)Ÿ œ). 16DU0 dŠ*76”ˆ
Œ1EF`ˆ ƒ Œ101Ÿ œ).J21(¡ˆ)I4AC6;U2 œ).ž21(B¨P016;2Pˆ9I(+;.pŠˆ)D./*¦24(˜™˜š€›
Œ1EFˆž57(?D(+<?Ÿ œ). Pˆ)5>(‰ˆ)21ˆ90Pˆž./*>21(+E (˜ˆŠEF./5-AC*7hˆ …/(+Eœ(+5-AC.:< d)5-AC6D<+ˆž<+./E 5>Œ 15-AC6;A7Œ16DŸ œ). (
Œ1E z B_ ‡ v <+Œb“7ˆJ6D0[/.:<‰ˆŠŸ œ). [«2Pˆ)2Pˆž<?./EF.ž¨P042PˆFˆŠ.J¨1E 21( G_H:H>…/(+*7ˆ)Ÿ+±:(+™5 
Q ™( …/Œ16D0421.’.d(+5 Œ1(+EFˆ’E9(+0[A^ˆŠ ˆ)21./I4ACˆ)21.dˆ)0[AC(?*76;./*7E9(+0[AC_( †Gˆ)E S./5ž.)5F;6DE96;AC(?5e21(‡./*>21(+|
E ƒ .)*Cˆ)E
21(B¨P016D24./5J01.dŠˆ);./*p21( G G 2 cK†¯. Œ4(U2 d]./*>6 …/(?E ˆ3Œ1E <+*>./E9./575>./E=ˆ <?./E Œ1E
<+.)EFI1*>6DE9(+0[AC.ž24( >…)(+01(?`5 B 2¡I1ˆ)*CˆJˆž<+./045>A^ˆŠ0HA7(˜( 2 cžIPˆŠ*Cˆž./5 <+.:(?¨P<?6D(?0HA7(+5 &)—( &)N 
= ˆ)*7ˆ. v ˆ).01‹;)(+H. :“>(?<?A7. †hƒ ./*7ˆ)E Œ4A76DD6;®‰ˆ)24./5./5 )ˆŠD./*>(+5 IPˆ)21e* œ).`21ˆ Q (?<+Ÿ œŠ.  V  B ¥ ˆ (+Dˆ
*  N—
O ¥ ˆ (+Dˆ * M*d21(?57<+*>(?)( ./5JEF(? 1.)*7(+5žE9.:21(+;./5ž21( &) & (+04<+./0[AC*7ˆ)21./59I(+D.]5>6D5>A7(+EFˆ321(
z B_ v 5 † IPˆ)*7ˆ$A7.€21ˆ)5Žˆ)5«e5 [?*76;(+5Ž2Pˆ Q (?<+Ÿ œŠ.  R  q žGˆ)2Pˆ$E9.€24(+D. [924(?¨P016;21.$I(+D.$5>(+Œd<+./0 ‡
“>Œ10[AC.ž24(£<+.:(?¨P<?6D(?0HA7(+5 & ( & †457(+0421.žA^ˆ)E <[+E ˆ)I4*7(+5>(+0[A^ˆŠ21.J.p0 1EF(?*7.pA7.)A^ˆ)21(£I1ˆ)*C©)E9(?A7*7./5
B\<?./DŒ40Pˆ <N  O . EF(? 1.)*¡E9.:21(+;.(?01<+./0[A7*Cˆ)21
. ƒ ./*Cˆ)E ˆ)I4D6D<+ˆ)2Pˆ)5ŽA7*76D0[ACˆ./I4A76DE96D®+ˆ)Ÿ+±:(+5Ž6;0121(+I(+0 ‡
21(?0HA7(+5J21. v 21( 1ˆ)6 –€.301‹/(+Z †­IPˆ)*7ˆ …[ˆ)*CˆŠ0HA76D*˜Œ1E=ˆ EFˆ)6;./*˜(B:6D2 ˆ?01<+6Dˆ](?5>ACˆŠAC‹;5>AC6;<‰Kˆ †¤57(+0421.’.)5
(+*>*7./5ž24(@I1*7(B:6D•5 œŠ.321(?¨P046D21./5ž(?E A7(+*>EF./5e2Pˆ iE [?216”8ˆ † <+./E Œ1EFˆ57„6 …/016;¨1<‰©)01<?6”ˆ‡21( L B\<?./DŒ101ˆ
—N  (=Œ1EFˆ<?./EFI1ˆ)*Cˆ)Ÿ œ).24(+5>A7(+5p*>(+5>Œ1;ACˆ)21./™5 † <+./E./5˜. 4A76D21./5˜ˆ)0[AC(?*76;./*7E9(+0[AC(9:6”ˆˆŠ5
“7ˆ)01(?”ˆ)5 4(+Œ1*>‹D5>A76D<+ˆ)5 B ¥ ˆ (+”ˆ  R N †1I.€21(«ˆb¨P*7EFˆ)* ‡ 57( Œ1(Š‘
ˆ)5 “7ˆ)01(+Dˆ)5xA7(+E9IS.)*Cˆ)6;5x5>(+D(?<+<?6D./0PˆŠ2Pˆ)5 B &) ( & N•5 œ). (+E 216 ƒ (+*7(?0[AC(+5 ˆ Œ1Z6 †4*7™( …/*C+ˆ …/(+*7ˆ)Ž †
ˆJ<‰ˆ)*>216D01ˆ)D6;2Pˆ)21(Ž2Pˆ`“7ˆ)01(?”ˆ &)[eˆ9EF(?01./* †P(¡.9EF.:21(+;. & [_†01ˆ9EFˆ)6D.)*76”ˆp24./5<+ˆ)57.)5 † .
EFˆ)6D5<+./015>6D21(?*Cˆ)24. B\ˆ Œ16Œ4A76DD6;®‰ˆ)24.p(+E e5 [?*76;(+5 N
G
NM
43
– F>
6
/
43
/
>
T
>
:
T
6
T
:
T
:
:
6
T
6
T
:
:
6
–
:
T
6
>
/
6
/
>
76
6
43
u F>
6
+1
43
>
?6
!K
03
76
6
/
:
/
6
T
T
/
6
R
g
!"#
#$%&')($
¥ ˆ S(?”ˆ *  ‘ ¯ˆ)D./*>(+5921./5FIPˆ)*C©ŠEF(BAC*7.)5=21.’576D5-AC(?E=ˆ•(?E AC(+*>EF.)5=21.’I1*7.:<+(?5757.#24( ./I4A76DE96D®‰ˆŠŸœ).
(?)./DŒ4<+6D.)0Ud)*76DˆK
6
8
XE;™W 5 h"R T 5
>
6
Ud
2 H:H
v 46D0 )*>6D.
’+R 4 R YhW54E;™W6XEY R ;
‘ <9 3 R 7K9
‘ R 4
h 5OW 469<;
3SW6X T K9
XZYOX R EX R 7 K9
3465 T X R “<5 h
g
3SW6X h X R 7 9
4_X^5
IPˆŠ575Cˆ_…/(+6;*7./5
IPˆŠIS(?
E9./*>A7(+5
E9(+ S./*>01(
Œ1‹;EF6;<‰ˆ
I1*>(+Ÿ?./5
EFˆ)01< PˆŠ5
Š. S(
ŒPˆ)24•* dŠA76D<‰ˆ
1(?01./0
€6
/
J3
76
3
/
T 5^9
v <+./E u u
G
O ;(‰ˆŠAe@/*76Dˆ 0+2 2 O „ …/./*>6;ACE9. Ž(+04(+*CˆŠD6D5-A^ˆ
GŠ2h† G
:H
O *>6;A7iE [BAC6D<?Ÿ. B V N
«ˆ)Œ1575>6”ˆ)01ˆB N
hHhH
¥ ˆ S(?”ˆ>* Œ*1‘žGˆ)*7ˆ)<?A7(+*7‹;5>A76D<‰ˆŠ5¦21./5 EF.:21(?D./5
6
K
oG
>
hH
O™eDš:(+› ˆŠA•@)*76”ˆ † R
O  …)./*76ACE9.e21( N .)D”ˆŠ012
GHK† G 2 H:H%
`./6D5¦I./0[ACg .)5 B ² N
‹6DU0 dŠ*76”ˆ B N
’ 4 Rxh 5 W 9
sW R 7 9
! 54 h X R 7 9
9
oG
2 H:H:H
& &—. 4A76D21./5G:6DˆJ.)I4AC6;EF6;®‰ˆ)Ÿœ).p(?)./DŒ4<+6D.)0Ud)*76DˆK
&)
&
g
g
g
R
R
R † † †T †R
 g"  g
g
³ g ³ " R
Rg
g
"g
R
R † R/R † R
R!
*
R † † R/R † R g
*
T "  *
R †g
R † g † †Œ* † † R/R ²
 * " 
R
R
Œ* ² " 
² R V " g
R †g † †T †R !
R † T#
g
g
g *T " R
R
R † † † †² †T †R # R † †³ †V †R
³  ³" 
†R #
* †³
#
V ³ " 
g †!
R †² †R #
76
7
R
. z B_ v AC(?0121(¯ˆ¦(+5><+./ 1(+* ./5E9.€24(+D.)5E=ˆŠ6D55>6DE9I1D(?5B\6Z (_„† <+.)E E9(+01./*<+ˆ)*7246D0Pˆ);6D2PˆŠ21( N
IPˆŠ*CˆJˆ)5 5e[?*76D(?5 0Uœ).JD6;01(‰ˆ)*>(+5B\ˆJ( –€<+(+IŸœŠ.=.:<+./*>*7(Ž<+.)Eˆž5e[+*>6D( h"R Y R ;N (
ˆ9./I4AC6;EF6;®‰ˆ)Ÿœ).J(?)./DŒ1<?6D./0 d)*76DˆJ5>(+;(+<+<?6D./01ˆ v Œ1(p;(?Šˆ)EªŠ5`E9(+ 4./*7(?5I1*>(?:6D5>±€(?5 †S<+./E
ˆž(—–€<?(+IŸœ).F2Pˆž5e[+*>6D( h 9 4 W 5;h
= .)*«¨1E†5>(+*•dgˆ)I4*7(+5>(+0[A^ˆŠ21.Œ1E—( –€(+E9I1;.‡24(9I4*7(?:6;•5 œ).gIPˆ)*7ˆ$.‡5>6D5-AC(+EFˆ@21( z B_ v † 57(?0121.
(+5><+./ 16D21ˆdˆ3A5 [+*76;( 9 -5  O – „6 …/Œ1*Cˆ *K R ( –€6 (‡.)5p)ˆŠD./*>(+5žPE [+216;./5p2Pˆ)5JI1*>(?:6D5>±€(?5J*7(‰ˆŠD6D®+ˆ)2Pˆ)5
:6”ˆ$. v IPˆ)*Cˆg./5 1AC6DE9./5 g B :6D0[AC( N£(+D(?EF(?0[AC./5«21(?5>A^ˆge5 [?*76;\( B Ž6 {h( †./5«(+;(+E9(+0[AC./5«21(žA7(+5>A7( N 
† (?5>A7(ž<‰ˆ)5>. †ˆ)E 1ˆ)5£ˆ)5`<+Œ1*-)ˆŠ5£57(p(?01<+.)0HA7*Cˆ)EI1e* @–€6DEFˆ)™5 †}*7(B/(?”ˆ)0124.$Œ1E ./E ˆ “>Œ15-AC(žI./*`I1ˆ)*>A7(
21.JE9.€21(?D.ž(?57<+.) 16;21. 
}#\< &#}
& ! $
u F>
:
€3
T
>
:
G
/
43
u F>
€3
>
G
46
1
6
6
43
10000
kobe
AGE
8000
6000
4000
2000
0
-2000
-4000
182
184
186
188
190
192
194
196
198
– 6„…/Œ1*Cˆ`*K R ‘ = >* (?:6D5>±€(?5¦€6Dˆž.9E9.:21(+;.>@/I4AC6;EF. u z I1ˆ)*CˆJˆJ5e[+*>6D(
>
t)rt #&% ~ z *>psrz '
,.- ,.-21 EJ LDJ CIB64 = 4 FCI8D?
jfk j
~
>
200
9 -5

(
~ixfz —~ n
EFˆe/(?® Œ4(Ž57(ŽI1*>.€<?(+21(?ŒˆpŒ1EFˆp./I4A76DE96D®+ˆ)Ÿœ).¡21./5¦E9.:21(+;./56;0157I16;*Cˆ)24./5G0Pˆ † ˆŠACŒ1*>(+®+ˆK†P(+6;5 Œ1(
57(< 1(…)./Œ$ˆ).˜IS./0[A7.e6D24(‰ˆ)PIPˆŠ*Cˆ˜5>(`(—ƒ (+<?A7ŒPˆ)*xŒ1E=ˆ«<+.)EFIPˆŠ*Cˆ)Ÿœ).˜<?./E ./5¯EF.:21(+;./5 21(+5>6 …/01ˆ)21./5¯IS.)*
<+.)0H)(+01<?6D./01ˆ)6D5™
/
J3
/
R
!"#
#$%&')($
*
† ˆ ¥ ˆ S(?”ˆ *  ³ [‡ˆ)I1*7(?57(?0HACˆ)21.d.]21(+5>(+E9IS(?0 1.d21(g<‰ˆ)2Pˆ3E9.€24(+D.IPˆ)*Cˆ A7.€2PˆŠ5Jˆ)5ž5e[?*76D(?5J2Pˆ
Q (?<+ŸœŠ.  R  † (+E AC(+*>EF.)521( 21ŒPˆ)5EP[?A7*76D<+ˆ)5IPˆŠ*Cˆ ˆ ˆUŠˆ);6”ˆ)Ÿœ).G21. (?*7*7.4‘. (­. B\(?EœI1ˆ)e* ˆ?0HA7(+5>6D5 N  & 5>A^ˆ 1;A76DEFˆ¡E9(+216;2Pˆƒ .)66;01<+;Œ1‹D21ˆ¡IPˆŠ*Cˆ+ƒ\ˆ)<?6D;6;A^ˆŠ*­ˆe<+.)EFIPˆŠ*Cˆ)Ÿœ).e(?0HA7*7(£5A[+*>6D(+5(
E9.€21(?D./521„6 ƒ (?*7(+0[A7(+5
¥ ˆ (+Dˆ *K ³ ‘ ž.)EFIPˆŠ*Cˆ)Ÿ œ).ž(+0[AC*>(˜.)5¦21„6 ƒ (?*7(+0[A7(+5 iE [BAC.:21./5¦21(«I1*>(?:6De5 œ). 
4?X^5
;
5OW R g
²
²
²
²
IPˆ)5>5Chˆ …)(+6D*>./5 B  N R  B  ² R N ³R g  ³ B ³  * N ³R g  g³ B ³  /³ N
IPˆ)I(+
³ BE*KM* N V4R  B V g  N  B  N
 B  N
R B g ³ N R *:*ŸB^* ³ N ² B /V ² N R B ² N
E9./*>A7(+5
E9(+ ./*>01( ³ B ³  N R  B ³  V N  B ³  N  T B^*  ² N
Œ1‹DE96D<+ˆ
 B R N
 /V B N
 /V B * N
B^* ² N
I1*>(+Ÿ+.)5
 ³ *B  )T N
 g B Œ* R N Œ* T B  ² N "
B  N
g
g
g
²
³
R Œ*B N B R N R  V B R * N
EFˆ)01< Pˆ)5
 B N
€RUT/² T B R ³ N ³)² g ³ B  ³ N * T ² B g  V N " ³ B g  ³ N
). S(
ŒPˆ)21e* dŠAC6;<‰ˆ  B R 4Rg N  B ²R €R N \B  N  ³ B R N
1(?01./0
 B R/R N
 V B N
B R N  B V N
6
3
1
6
46
/
J3
6
/
3
7
O PI ˆ)*>A76D*G24./5 2Pˆ)21./5 I1*>(+5>(+0[AC(?5`01(?5>A^ˆ ¥ ˆ S(?”ˆžI.€21( ‡m5>(¡<?./01<?DŒ16;* Œ1()‘
° EP[?A7.€21. 21( `Y P_ v ?X
)Y B\<+.)DŒ10Pˆ v N¢ˆŠI1*7(?57(+0[ACˆ`Œ1E—EF(? 1.)*21(+5>(+E9IS(?0 1.
IPˆŠ*Cˆžˆ)5¦A5 [+*76;(+5¦57ˆ)®+./01ˆ)6D5¦(Ž<?./EœA7(+012 ˆ?01<+6DˆŸB\5e[?*76;(+53 R ;; R “ 5X^4?9<;«()3 R 3-5ZN— ¥ ˆ)ƒ\ˆŠ<?AC.ž0 œ).
[F57Œ1*>I1*7(?(+0121(?0[ACh( † 2PˆŠ21. Œ1(@(?5>AC(Fi
E [BAC.:21. ƒ .)6¯(?57I(+<?6;¨P<+ˆ)EF(?0[AC(@21(?57(?0H)./;:6;21.3IPˆ)*7ˆD6;2Pˆ)*
°
<?./E (?5>A7(AC6;IS.’21( e5 [?*76;(+5  5>Œ1<+(?5757. 21. v [ 24(?:6D21.tˆtŒ1E ˆU“>Œ15>ACˆ)EF(?0[AC.t5>Œ1<+(?57576/.
2PˆŠ5(?5>AC6;E=ˆbAC6;Šˆ)5 57ˆ)®+./01ˆ)6D5 (˜24(˜AC(?012 ˆ?01<+6DKˆ †S0 œ).=21(?IS(?0121(?0121.$21(¡IS(?57./5 K¨ –€./5  = ./*`./Œ€AC*CˆŠ5
IPˆŠ”ˆ‰:*Cˆ)™5 †}. v Œ4A76DD6;®‰ˆžŒ1EFˆ=E9(+PE @/*76Dˆ921(eD./0 …).FI1*7ˆ)®+K. † (+E 57Œ1I(+*>6D./*`iª ƒ ./*704(+<+6;2Pˆ=I(+Dˆ
“7ˆ)04(+”ˆA7(+E9IS.)*Cˆ) Œ1( [gˆ)I1D6;<‰ˆ)21ˆ01./5ž./Œ€AC*7.)5žiE [BAC.:21./5  ¥ ˆŠE [?E <?./0[: [?E *7(‰ˆŠDŸ‰ˆŠ* Œ1(
. z B_ v <+./015>( …/Œ4(=57Œ4IS(?*Cˆ)™* † (?EAC(+*>EF.)5¡24(F21(?57(?EFI(+0 4. †¤ˆgE9(?AC.:21./;:. …/6Dˆ=21( !
B\<?./DŒ40Pˆ
N †­EF(?57E9.]ˆ)IS(?5Cˆ)*J21(?5>ACˆdŒ4A76D;6D®‰ˆŠ*eŒ1EFˆAC*7ˆ)01A5 ƒ .)*7EFˆ)Ÿ œ).3;:. …[ˆ)*>‹;A7EF6;<‰ˆ
IPˆŠ*CˆJˆže5 [+*>6D( 3 R ;; R “ 5X^4?9<;h† Œ1(¡ 4)( [ ƒ\ˆ‰)./•* d‰/(?Ž 
ž./0[A7Œ121. †¢(F24P
( ƒ ./*>E=ˆgˆ)„ …/.$6D04(+57I(+*7ˆ)2PKˆ † ˆ$)ˆŠ0HAChˆ …/(?E21. v e“ dg0 œ). [JA œŠ.‡:6D5>‹;)(+­IPˆ)*7ˆ
ˆ)5gA5 [+*76;(+5g5CˆŠ®+./0PˆŠ6D5$E9(+0157ˆ)6D5 B e5 [+*>6D(?5 h 9<4 W 5;3( h 5 -9 4 S5KN  `( ƒ\ˆ)<?A7. †`.E9.€24(+D.•21(
./I€AC6DE96D®+ˆ)Ÿ œŠ.$01(+Œ1*>./0Pˆ)­< 4( …[ˆˆˆ)I4*7(+5>(+0[A^ˆŠ*eE9(+ 4./*7(?5¡*>(+5>Œ1;ACˆ)21./5«IPˆ)*7ˆˆge5 [?*76;( h 9 4 W 5;h†
6;01216D<+ˆ)0121. Œ1(ˆdE9(+PE @/*>6”ˆ21(‡D.)0 …/.3I1*7ˆ)®+.dU0 œ).d57(?•* dd•A œ).]<+*>Œ1<+6Dˆ)Ž † ŒPˆ)0121.d57(‡*7(BAC6;*Cˆ]ˆ
<?./EFI./01(?0[AC(«21(ŽAC(?012 ˆ+04<+6”ˆ9ª)5¦A5 [+*76;(+5 5CˆŠ®+./0PˆŠ6D5 
/
6
>
:
D
4G
=
AEBBI
F
>
43
3
/
>
>
B6
/
/
6
– F>
3
5RE
5G
/
43
>
:
K
J3
/
43
/
}#\< &#}
R ³
& ! $
ˆ)*Cˆ¡ˆ)5 5e[?*76D(?5 <+./E ƒ .)*>AC(¦A7(+012 ˆ?01<+6Dˆ B 5e[?*76D(?5 Q h XEY R (#34657:9<; N—†:ˆ«EF(BAC.:21./D.h…/6”ˆ 21( !
ˆ)I4*7(+5>(+0[A^ˆ3./5eI16D./*>(+5˜*7(+5>Œ1;ACˆ)21./5™† <+.)E . EP[?A7.€24.21( v (@.576D5-AC(?E=ˆ‡21(
u v <?./E (?*7*>./5¦21(«I1*7(B:6D5•œŠ.ž(+E A7Œ121.J57(?EF(? Pˆ)0[A7(+5†4(Ž<+./Eœ. z B_ v ˆ9ˆŠI1*7(?57(+0[ACˆ)*
.JE9(+ 4./*G21(?57(+E9I(+0 1.K
ž./E9.(?57I(+*7ˆ)21. †­.EF.:21(+;.21( v 0Uœ).(?5>A•d3ˆ)I4AC.IPˆ)*7ˆD6;2Pˆ)*«<+./E5A[+*76;(+5p0 œ). D6;01(‰ˆŠ*7(+5
B e5 [+*>6D(?5 h"R Y R ;$( 9-58N—† I1*7.:21Œ1®?6D0124. ./5pI16;./*7(?5p*7(?57Œ1A^ˆ)24./5  O E9(?A7.€21.)D:. …/6Dˆ$21( <?./0157™( …/Œ1(žE9(+ 1./*7(?5£I1*>(?:6D5>±€(?5 †EFˆ)5 [p5>Œ1I1”ˆŠ0HACˆ)2PKˆ †}IS./*`Œ1E=ˆFE=ˆ)A* …/(+E <+.)01576;21(+e* dU)(+Z†IS.)*
ˆ)E S./5¦.)5 PE [?A7.€24./5¦6D015>I16D*7ˆ)21./50Pˆ † ˆŠACŒ4*7(+®+Kˆ † Œ1(Ž•A ˆ?E Œ1E 21(?57(?EFI(+0 4.=576;EF6;”ˆ)™* 
° EF.:21(+;. &) &#A7./*70P6ˆ ‡m57(­6;01(?¨1<‰ˆ)® 0Pˆ¦I1*>(?:6De5 œ).21ˆ)5 e5 [+*>6D(?5¢<+hˆ @)A76D<‰ˆŠ5 B\A5 [+*76;( Q R T 46VKW6XEY R (
S59N—†/I(+;. Œ1(04(+EˆE9(?AC.:21./;:. …/6DˆG21( †b01(+E—.576D5-AC(?E=ˆ 21( z B_ v j <?./0157™( …/Œ1(?E
I1*>(?:6D5>±€(?5E9(+ 1./*>(+5g21. Œ1(•ˆ)5‡. 4AC6;2Pˆ)5‡ˆŠA7*Cˆ‰: [?52Pˆ D(?6;ACŒ4*Cˆ#21.Šˆ);./*$PE [+216;. 21ˆe5 [?*76;(
B <+./K0 ƒ .)*7E9(¯6;01216;<‰ˆ)21. I(+D. Šˆ)D.)*21
( † Œ1(x(+5-A dI4e* @–€6DE9.21.)5 R N— † .`(?0[A^ˆ)0[ACK. †
.t5>6D5-AC(+EFˆ•21(3.)I4AC6;EF6;®‰ˆ)Ÿ œ).’04(+Œ1*>./0Pˆ)<‰ˆ)I4ACˆ•I(+A* ƒ (?6;ACˆ)EF(?0[AC( (?5>AC(?5$™( ƒ (?6;AC.)5=U0 œ).#;6D01(+ˆ)*7(?5 †
I1*>.€24Œ1®+6;0121.JI1*7(B:6D57±:(+5 21(«*7ˆ)*Cˆ ŒPˆ);6D2Pˆ)24h( 
,.- ,.- / 4 ?D8:64 ? R< B D?
O A•[£ˆ Œ1Ž6 †€ˆ)I(+0Pˆ)557(£<?./01576;21(+*>./Œ@.p24(+57(?EFI(+0 1.ž21./5GE9.:21(+;./5x24(£I1*7(B:6D•5 œŠ. †€E9(+246D21.˜(+E AC(+*>EF.)5
2Pˆž57Œ1ˆ9(B¨P< d)<?6”Kˆ †1ˆŠAC*7ˆUh [+5 21.J*7(?<+Œ1*>57.FˆJPE [?A7*76;<‰ˆ)5G24(¡(?*7*>.  Q (+0421.=ˆŠ57576;E †4. Œ1(«5>(¡I.:21(«ˆŠ¨P*>E=ˆ)*
(+E AC(?*7E9./5¦21(Ž(+5 ƒ ./*7Ÿ?.J<+./E9I1Œ4ACˆ)<+6;./0Pˆ) = (+”ˆž21(?57<?*76DŸ œ).J21./5¦E9.€24(+D.)56D0457I16;*Cˆ)21.)5G0Pˆ † ˆŠA7Œ1*7(?®‰Kˆ †
IPˆ)*>(+<?(¡5>(+* @ [:6D. Œ1(«—( –€6 …/(?E Œ1E I.:21(+*¦21(«<?./EFI4Œ4A^ˆ)Ÿ œ).J57„6 …/016;¨1<‰ˆŠA76;Šˆ)E9(+0[AC(£5>Œ1I(+*76;./* 
= ˆ)*7ˆt57( A7(+*@Œ1EFˆt6D24(+6”ˆd2Pˆ ŒPˆ)0[AC6¨P<‰ˆŠŸ œ).#21.)5@<+Œ15-AC./5$24(3<+./E9I1Œ4ACˆ)Ÿ œ).•21(3<‰ˆ)21ˆtEF.:21(+;. †
57(?•* dpŒ4A76D;6D®‰ˆŠ2Pˆ˜<?./EF.e—( –€(+E9I1D.pˆpe5 [+*>6D(£E9(+045Cˆ) 3 R ;; R “ 5XE469<;h†P<+.)E R *h*p(+;(+E9(+0[AC./™5 †421.)5 Œ1ˆ)6D5G.)5
1AC6DE9./5 R *Ž•5 œ).ŽŒ€AC6D;6D®+ˆ)21./5 IPˆ)*CˆŽˆŽI1*>(?:6De5 œ).  O ¥ ˆ (+Dˆ *  V 24(+57<?*7(B/( ./5 AC(?EFI./5 21( <?./EFI4Œ4A^ˆ)Ÿ œ). †
(+E 5>( …/Œ40121./™5 †¡<+ˆ)D<?Œ1”ˆŠ21./5$I(+”ˆ ˆ)I1;6D<+ˆ)Ÿ œ). W ;•†£IPˆŠ*CˆŒ1E I1*7.:<+(?5757ˆ)21./* P_ BY P_ |a ˆ
* ³ ¬ N _® 
O ./IS(?*Cˆ)Ÿ œ).21( 34?5S XE; 9 <+./015>6D5-AC(](+E (?5>A76DEFˆ)*@.#Šˆ)D./*=21(3<‰ˆŠA7./*7®?( B R *”N=.)IS(?*Cˆ)Ÿ?±€(?5$21(
<dŠD<+Œ4D>. B <‰ˆ)5>./5­21(GA7(+5>A7( N †[57(+0421.«IS./* 6D5>57.ŽŒ1EFˆ`./I(+*7ˆ)Ÿ œ).`21(?)(+*CˆŠ5¯e* d)I16;2PKˆ †)5>('“7ˆ ŒPˆ)8 ƒ ./*¤.ŽE9.€24(+D.
<+.)01576;21(+*7ˆ)21. 
& E57™( …/Œ16;2PKˆ †)5>Œ1e* …)(+E.)5¤AC(?EFI./5¤24( R 34?5 T X R “ 5 h †[ˆ)I4D6D< d‰/(+6;5 ˆ)I(+01ˆ)5­ˆ)./5 EF.:21(?D./5¢6D015>I16 ‡
*CˆŠ21./5¦0Pˆ † ˆbACŒ1*>(+®‰8ˆ †121(?¨1016D2Pˆž<?./EF.ž.JˆU“>Œ15>ACˆ)EF(?0[AC.J21./5 IPˆ)*7©)E9(?AC*>./5G21(ŽE9.:21(+;./5K¨ –€./™5  – ./*7ˆ)E
Œ4A76DD6;®‰ˆ)24./5˜.)5pEF.:21(?D./5¡E=ˆŠ6D5e<?./E9I1D( –4.)5eIPˆ)*7ˆ3ˆJ“7ˆ)01(?”ˆA7(+E9IS.)*Cˆ) R † g †„† R ! † 21(?¨1016D21.)5
I(+”ˆ¡AC./I./Dh. …/6”ˆŽ<+.)EFI1;(?ACˆ)EF(?0[AC( 6D0[AC(?*7D„6 …[ˆ)2Pˆ R ‡ R ‡ R IPˆ)*7ˆe.pE9.€24(+D.¡01(?Œ1*7./01ˆ)}(£.eIS(?D.pE9.€24(+D.
‡IPˆ)*Cˆž. v 
=
:
5RE
5G
>
G
NM
43
43
– F>
/
3
3
>
:
€3
6
:
/
u F>
/
€3
76
/
/
/
53
/
76
/
/
/
1
6
#
/
>
s
R /V
!"#
#$%&')($
° 5 )ˆŠD./*>(+5¤. 4AC6;21./5¤<?./04¨P*>E=ˆŠE Œ1( ˆŽˆ)I4*7(+04216D®+ˆh…/(+E§(?)./DŒ4<+6D.)0Ud)*76Dˆ'[GEFˆ)6;5¤(—–€6„…/(+0[AC(¦(?E§A7(+* ‡
E9./5G<+.)EFI1Œ€A^ˆ)<?6D./0PˆŠ6D5†H*>( Œ1(+*>(+0124.=ˆ)I4*7.–€6DEFˆ)2Pˆ)E9(+0[AC(.ž21. 1*>.ž21.pAC(?EFI. † ŒPˆ)0121.J<?./EFI1ˆ)*Cˆ)24.
<+.)E .ŽAC*7(?6D01. u u  † .¡(?0[A^ˆ)0[ACK. †:<?./0[: [?E *7(‰ˆŠDŸ‰ˆŠ* Œ4(ˆ«ˆ)I4*7(+04216D®+hˆ …/(+E01(+Œ4*7./0PˆŠPŒ4AC6;D6D®+ˆ`Œ1E
<+*>6;eA [+*76;.g—( –:AC*7ˆ21(FIPˆ)*C_ˆ …/(+ŸE †¢ˆ ƒ\ˆ)A^ˆ$21(FI1*7:. …)*7(+5>57.01.A7*7(+6;01. † Œ1( [Fˆ)<BAC6;Šˆ)24.0PˆgEFˆ)6D./*ŽI1ˆ)*>A7(
2Pˆ)5 5>6;ACŒ1ˆ)Ÿ+±:(+™5 
= ./* 1;A76DE9. †5>Œ1e* …/( ˆ•./I(+*CˆŠŸ œ).t24( 9 3W6X h X R 7 9S† Œ1(<+./015>6D5-AC( 0PˆtI4*7.:<+Œ1*7ˆ•21.tE9.€24(+D.
@/I4A76DE9.321(gI1*7(B:6D•5 œŠ.  † œ). [‡ˆ)I1*>(+57(?0[A^ˆ)21.d.])ˆŠD./*pI1ˆ)*Cˆ]ˆ]EF(BAC.:21./Dh. …/6”ˆ‡21( † 2Pˆ)21. Œ1(g.
r
B
_
E9.€21(?D‚. ƒ .)6)./I4A76DE96D®+ˆ)21.GˆbAC*Cˆ‰h [+5 2Pˆ ˆ)I1;6D<‰ˆŠŸ œ).G<?./E9(+*7<?6”ˆ)
†bI1ˆ)*CˆG. 576;5>A7(+EFˆG./IS(?*CˆŠA76;).
Z +q ° A7(+E9IS.˜21(+5><+*>6;AC.˜IPˆ)*7ˆ˜.¡iE [BAC.:21.e21( v <+.)*7*7(?57I./0121(`ˆ).eŒ457.e24(`Œ1EFˆ¡I4*7.:<+Œ1*7ˆ˜(+E
…/*>(+ 1ˆg24(  4R  = ˆ)*Cˆg./5«i
E [BAC.:21./5«6D0457I16;*Cˆ)21.)5Ž0Pˆ † ˆŠACŒ4*7(+®+Kˆ †sƒ ./*CˆŠE(+5><+./ 16D21.)5¡.)5«A7(+E9IS.)5Ž21(
. 4A7(+01Ÿ œ).ž21.žE9(+ 1./*¯EF.:21(+;. †:<+./*>*7(+5>IS.)0121(+0421.9`ª …/(+*7ˆ)Ÿ œ). RUT 21.ž5>6D5-AC(+EFˆe21( u v ( …/(?*Cˆ)Ÿ œ).
* ³ 21. z B_ v B ¥ ˆ (+”`
ˆ *K V N 
01(+5-AC( AC6;IS. 21( ./I(+*7ˆ)Ÿ œ). Œ1(xˆ)5 21„6 ƒ (?*7(+04Ÿ‰ˆ)5¢21(¯<+./E9I1Œ4ACˆ)Ÿ œ). (?0HA7*7(¯./5 EF.:21(?D./55>(ˆ)<?(+0[ACŒ1ˆ)
E 
``( ƒ\ˆ)<BAC. †}.$576D5-AC(?E=ˆ=24( u v AC(?E„Œ1E<+Œ15-AC.$<?./EFI4Œ4A^ˆ)<?6D./01ˆ) 24(ž<+(+*><‰ˆ$21( )V /(+®?(+5«57Œ4IS(?*76D.)*
ˆ).J—( –€„6 …/6D21.žI(+;.JiE [BAC.:21.J21( v <ž./E9.J57(+*>6”ˆž21(«(+5>IS(?*Cˆ)™* †P.F5>6D5-AC(+EFˆp21( z B_ v ˆ)I1*>(+57(?0[A^ˆ
./5«EFˆ)6D./*>(+5Ž*>( Œ16D5>6;A7./5«<+./E9I1Œ4ACˆ)<+6;./0Pˆ)6;5 † ˆ)I1*>. –46;E=ˆŠ2Pˆ)E9(+0[AC( g:g /(?®+(?5e57Œ4IS(?*76D.)*˜ªg—( –€„6 …/6D2Pˆ$I(+;.
576;5>A7(+EFˆ@21( u v  ¥ *7ˆŠA^?ˆ ‡ 57(ž21(žŒ4E A76DI.$21(p<+.)EFI./*>ACˆ)E9(+0[AC. Œ1( [ž<?./EpŒ1E 0Pˆ@*7(?57./;Œ1Ÿ œŠ.$21(
I1*>. 1D(?E=ˆŠ5 `XY B_ 
¥ ˆ (+D>ˆ *  V ‘ žŒ15>A7.F<?./EFI4Œ4A^ˆ)<?6D./01ˆ)}21(«<+ˆ)2PˆJEF.:21(+;.žIPˆ)*7ˆ9ˆžA5 [+*76;( 3 R ;; R “ 5XE469<;h
3-5”4 R 7 9
34?5S XE; 9
H
H
H
H
g
R 3465 T X R “ 5 h
‡
‡
*
g* ‡
R R ² * /³
9 3W X h X R 7 9
/
6
/
/
76
/
P
/
/
1
/
ŸEJJICEG
ŒG
>
43
€3
76
€3
u F>
G
NM
6
/
G
M
K
>
– F>
/
NM
M
76
/
G
CIJE
4 #HG
6
jfk
%
wnS€/ nSn ~
z
* € ™( 
~
n
z#n
& 5>A7(x<+ˆ)I1‹;A7Œ1D.¦<?(+0[AC*>./Œ8‡ 57(¯0PˆˆŠŒ4AC./EFˆŠA76D®‰ˆŠŸœ).G24.I1*>.€<?(+5>57.`24(¯I4*7.:<+Œ1*7ˆK†Š24./5 21./6D5sƒ\ˆ)<BAC./*>(+5 <+*>Œ1<+6Dˆ)6D5
IPˆ)*7ˆ#ˆ#I1*7(B€6;5•œ).#24./5$EF.:21(?D./5F21(3I1*7(B:6D5•œŠ. 6;0157I46D*CˆŠ21./5@0Pˆ † ˆŠACŒ4*7(+®+ˆ4‘#ˆ“7ˆ)01(?”ˆ’A7(+E9IS.)*Cˆ)(
<+.)EFI1;—( –€6D21ˆ)21(Ž21.JE9.€21(?D. 
Q œ).]ˆ)I4*7(+5>(+0[A^ˆŠ2Pˆ)59ˆ)5pI1*>6D01<?6DIPˆŠ6D5¡(+5>A7*CˆŠeA […/6Dˆ)5p21(=I1*7.:<+Œ1*7Kˆ †­<+.)EF.3ˆ X Ba
‚ † Œ1(
EFˆ)0[•A [+E Œ1E=ˆžI./I1Œ1Dˆ)Ÿ œŠ.924(˜I./0[AC./5 21(¡I1*>.€<?Œ1*CKˆ  ° 5 v e5 œ).FŒ4EI1*7.:21Œ4A7.9A7‹DI16;<+.ž21(?5>A^ˆ9(+5 ‡
AC*7ˆŠ•A [™…/6”8ˆ †b5>(+0124.£<+./04576D24(+*CˆŠ21./5¤24(?:6D21.`ˆ)./5 ˆ) …)./*76ACE9./521(¯I1*7.:<+Œ4*Cˆ Œ1(x6DE9I1D(?EF(?0[A^ˆ)ŸE †U. Œ1(x 1(?5
>
HI {
/
G
/
/
43
R
I(+*7E96;A7(«D.:<‰ˆ);6D®‰ˆŠ*G*Cˆ)I46D2Pˆ)E9(+0[A7(˜5>./DŒ1Ÿ?±€(?524(e(+;(?Šˆ)2Pˆ ŒPˆ);6D2Pˆ)24(h† (+5-A^ˆ)0124.$ˆ)575>6DE ).€<+ˆ)<+6;./0Pˆ)21.)5
IPˆ)*7ˆžI1*7. 4D(+EFˆ)5¦21(«0PˆbACŒ1*>(+®‰ˆJ<+.)E 16D01ˆŠA•@/*>6”ˆK
O <+./E 16D0PˆŠŸœ).$21( v ( u [žE9.)AC6)ˆŠ2Pˆ=I(+D.)5£I1*7.:<+(?575>./5«21(ž57(?D(+<?Ÿœ).‡I1*A@/I1*76;./5£21.)5
57(?*7(?5˜:6;)./5† ./0121(Fˆ w bYca .:<+./*>*7(9ˆ).04‹;/(? 2Pˆ)5¡IS./I4Œ1”ˆ)Ÿ?±€(?5†¢21(?A7(+*>EF6;0Pˆ)0121.ˆ)5¡(+5-AC*7Œ€ACŒ1*7ˆ)5
Ud)5>6D<+ˆ)5 21./5­.)*e…[ˆ)046D57E9./5™†)57(?0121.¡ˆ£ˆ)I4*7(+04216D®+ˆh…/(+E*7(?57I./015•d‰)(+PI(+”ˆ`ˆ)2Pˆ)I4ACˆ)ŸœŠ.Ž21(GŒ1E6D01216:‹D21Œ1.
ˆ).9ˆ)E 46D(+0[A7( Œ4(˜.J*7.:21(?6”ˆK
`( ƒ\ˆ)<BAC. † ˆ<+./E 16D0PˆŠŸœ).21($ˆ)E ./5¡./5pIPˆŠ*Cˆ)216„…/EFˆ)5†¢<+./0 1(+<?6D2PˆI(+;./5e5>6D5-AC(+EFˆ)5˜21( u 7Z
Ba
vw bYca y u v †¦AC(+E …[ˆ)0 4.#Œ1E=ˆ•ˆŠAC(?01Ÿœ).#<?*7(?57<+(?0[AC(]IS(?”ˆ•<?./EpŒ1046D2Pˆ)24(
<+6;(+0[AC‹¨P<‰ˆ8†G(+E IPˆ)*-AC6D<?Œ1”ˆŠ*9I1ˆ)*Cˆd.t21(+5>(+0 4.#21(A7./IS.)D.:…/6Dˆ)5ž21( u  † (?5>A7( 21./E9‹D016;. †¯((+E
AC(?*7E9./5g21(•*>(+I1*>(+5>(+0[A^ˆ)Ÿœ).21.<+./0 1(+<?6DE9(+0[AC. 216D5>IS.)01‹;)(+¡ˆ). 01‹;)(+«21. Œ4016;)(+*75>. 21(d216;57<+Œ4*757K. †
I./576;<+6D.)0Pˆ)E>‡m57(=21ŒPˆ)5J:6D57±:(+5J<?./E :6D5-A^ˆdªd5>./DŒ1Ÿ œ).]21.dEF(?57E9.dI4*7. 1;(+EFˆ4‘$Œ1EFˆ ‚ B_ †.)0121Ÿ( [
Œ4A76DD6;®‰ˆ)21ˆpŒ1E=ˆJ<+.:216¨P<‰ˆ)Ÿœ).J216D*>(+<BA^ˆJIPˆ)*Cˆ9./5 01.:21./5 (˜<?./01—( –€±:(+52Pˆ9*>(+21_( †S.)Œ4AC*7ˆ ‚ †P./0124(˜e5 œ).
21(B¨P016D21ˆ)5 *7(…)*Cˆ)5 IPˆ)*7ˆJˆJ<?./015-AC*7Œ4Ÿ œ).92PˆJ*7(+24h( 
– ./6 ™( ƒ (+<BACŒPˆŠ21.=Œ1E 1*>(?)(eD(BŠˆ)0[A^ˆ)E9(+0[AC.F21.=(?5>ACˆ)21.=21ˆ=ˆ)*-ACh( † 5>. 1*7(eˆ=ˆ)I4D6D<+ˆ)Ÿ œŠ.924( u v ª
I1*>(?:6De5 œ). †[57(?0121.¡I1*7.)IS./5-AC.«Œ1E E9.:21(+;.£21( <+.:216;¨1<‰ˆ)Ÿ œ).Ž216D*>(+<BA^ˆŽ21„6 ƒ (?*7(?0HA7( 21.«Œ157ŒPˆŠŽ †[I./*­IS(?*7E96;A76D*
21(B¨P016D*«Œ1EFˆ ŒPˆ) Œ4(+*ŽAC./I./;:. …/6”ˆF21(J*7(+24(9(`“7ˆ)04(+”ˆ@A7(+E9IS./*7ˆ)Ž  ° 576;5>A7(+EFˆg24( u v I4*7./I./5>A7.
ƒ ./6 ˆ)I1;6D<+ˆ)21.dª)5=A5 [+*>6D(+59AC(?EFI./*CˆŠ6D5ž. :“>(?<?A7.t21((?5>A7Œ121. †¦5>(+0121.•<+./E9IPˆ)*7ˆ)21.d<+./E .•5>6D5-AC(+EFˆ]21(
_ P_ )_ w 21(+5><+*76AC.’01.’<+ˆ)I1‹ACŒ1;.’ˆŠ0HA7(+*>6D./™*  `(?5>A^ˆd<+./E9IPˆ)*7ˆ)Ÿ œŠ.’<?./01<+;Œ16 ‡ 57( Œ1(ˆ’./I4A76 ‡
E96D®‰ˆŠŸ œ).01(+Œ1*>./0Pˆ)xˆ)I1*>(+5>(+0[A^ˆ3Œ1E EF(? 1.)*˜21(?57(?EFI(+0 4. †­57(?D(+<?<+6;./0Pˆ)0124. EF.:21(?D./5˜ˆ “>Œ15-A^ˆ)21.)5žª
<+.)EFI1;—( –€6D21ˆ)21(Ž2Pˆže5 [?*76;(«A7(+E9IS.)*Cˆ)Z 
° 5 S.)015`*>(+57Œ4;A^ˆŠ21./5`. 4AC6;21./5`6;01216;<+6”ˆŠE Œ1(eA^ˆŠE [?E 21(?)(+E„( –€6D5>A76D* S(?01™( ƒ ‹;<+6;./5`0HŒ1EFˆ=./I4A76 ‡
E96D®‰ˆŠŸ œ).g21.‡EF.:21(?D.$(?)./DŒ4<+6D.)U0 d)*76;.  ° 5 z B_ v Œ4AC6;D6;®‰ˆ)E v 0HŒ1E04‹;/(? EF(BA^Kˆ † IPˆ)*7ˆ
ˆ.)I4AC6;EF6;®‰ˆ)Ÿ œ).g21./5eI1ˆ)*C©)E9(?A7*7./5¡21( v 21.04‹;/(?x6;K0 ƒ (+*>6D./™*  & 5>A^ˆ<+./E 46D0Pˆ)Ÿ œ). S(?01(?¨P<?6”ˆ‡21(
Œ1EFˆF( –4I4D./*7ˆ)Ÿ œ).@ˆ)Œ4AC.)E dŠA76D<+Kˆ † U0 œ).=A7(+0121(?01<+6;./5C8ˆ †}21(pŒ4E0 1E9(+*>.@(+;(?Šˆ)21.F21(pIPˆ)*7©)E9(?AC*>./5  O 5 ‡
576;E †1ƒ .)6GI1*7.)IS./5-AC.3Œ1E 576;5>AC(?E=ˆ 24( z B_ v IPˆ)*Cˆ]ˆ I1*>.€<?Œ1*Cˆ321.)5žEF.:21(+;./5e(B/./;Œ1<+6;./U0 d)*>6D./5
<+.)01576;21(+*7ˆ)21./#5 @/I4A76DE9./5 † Œ1(˜24(+Œ‡./*7„6 …/(+Eœˆ9E9(+ 1./*>(+5¦E9.€21(?D./521(«I1*7(B€6;•5 œ)K. 
– 6D01ˆ)DE9(+0[AC_( †Uƒ ./6 —( ƒ (+<BACŒPˆ)21ˆ@Œ1E=ˆF<+./E9IPˆ)*7ˆ)Ÿ œ).F(+0[AC*>(p./5£E9.:21(+;./5<?./0[/(?01<+6;./0Pˆ)6;5`(p./56D015>I16 ‡
*CˆŠ21./5p0Pˆ † ˆŠACŒ4*7(+®+Kˆ  ° 5pI1*76;EF(?6D*>./5 †­ˆŠIS(?0Pˆ)5p*>(?/(?”ˆ)*7ˆ)E EF(? 1./*>(+5p*>(+5>Œ1;ACˆ)21./5p01ˆI1*7(B:6D•5 œŠ.321(
e5 [?*76;(+595Cˆ)®?./0Pˆ)6;5 †GˆbAC*Cˆ‰h [+5921.’P
E [?A7.€24.d24( v  O IS(?5Cˆ)*J21(‡Œ4A76DD6;®‰ˆ)*˜.’E9(+5>EF.dE9.€21(?D. & &
57Œ :“7ˆ)<+(?0[ACh( † .g576D5-AC(?E=ˆ z B_ v . 4A7(?)(FŒ1E21(+5>(+E9IS(?0 1.57Œ1I(+*>6D./*«ª$E9(?AC.:21./;:. …/6Dˆ (+E
AC.:2Pˆ)5Gˆ)5¦e5 [?*76D(?5 †1*>(?)(+”ˆŠ0121.J—( –€<+(?D(?0HA7(+5 I1*>(?:6D5>±€(?5 I1ˆ)*Cˆžˆ)5e5 [+*>6D(?5¦<+./E AC(+042 ˆ+01<?6”ˆž(ŽU0 œ).ž;6D01(+ˆ)*7(?5 
= ./* 5>ŒPˆ9)(+h® † («21( ƒ ./*7EFˆžˆ)„ …/.ž57Œ1*>I1*7(?(+0124(+0[AC_( †}.9576D5-AC(?E=ˆž21(«./I4A76DE96D®+ˆ)Ÿ œ).e01(+Œ1*>./0Pˆ) . €AC(?)(
./015¦*7(?57Œ1A^ˆ)24./5G0PˆžI1*>(?:6De5 œ).ž2Pˆ)5¦A5 [+*76;(+5¦57ˆ)®+./01ˆ)6D5G5>(+E A7(+01K2 ˆ+01<?6”Kˆ †124(+E9./015>A7*Cˆ)0421.pA^ˆ)E [?E Œ1E
—( –€<?(+D(?0[AC(`24(+57(?EFI(+0 1.˜01ˆ¡I1*>(?:6De5 œ).¡2Pˆ)5¯e5 [+*>6D(?5¯0 œ).˜;6D01(+ˆ)*7(?5 †[(?57I(+<+6Dˆ)DE9(+0[A7(¦IPˆ)*Cˆ¡ˆ)5 e5 [?*76;(+5¯<+./E
<+.)EFI./*>ACˆ)E9(+0[AC./5<‰hˆ @)A76D<?. †45>(+0121.921(Ž*>(‰ˆ);Ÿ‰ˆ)* Œ1(«IPˆŠ*Cˆp(+5-A^ˆ)5 1AC6;E=ˆ)5¯AC.:21./5G.)5 .)Œ4AC*>./5GE9.€21(?D./5
” '$q)$ $} `1
$ $
/
76
6
>
6
G
>OG
NM
6
/
6
K
M
6
E
4G
AI
–E
6
FEG
M
JG
53
G
3
>@G
M
3
53
{E #
76
IC
6
/
NM
76
/
G
NM
76
#
u F
C CJ
/
K
43
O6
3
/
6
6
u F>
>
6
G
>
G
G
6
Q6
+1
– F>
/
€3
43
>
u F>
56
76
3
76
6
6
53
/
N1
G
R ²
!"#
#$%&')($
57(«*>(?/(?”ˆ)*7ˆ)E 6;01(?¨P<+ˆ)®+(?5
¥ .:2Pˆ‰:6”Kˆ †¯. S.)E 21(+5>(+E9IS(?0 1.d. 4A76D21./5žI(+;./5žE9.€21(?D./5e6D015>I16D*7ˆ)21./5ž0Pˆ † ˆbACŒ1*>(+®‰ˆ A7(+E Œ1E
57(?U0 œ). † Œ1(¡57(«EFˆ)016ƒ (+5>ACˆp01.957(+Œˆ)<?*7(+5><+6;21.F<?Œ15>A7.F<?./E9I1Œ4A^ˆŠ<+6D.)0Pˆ)Ž
/
6
3
76
!‡" % ¥ 1(+*>(p6D501.)A 46D0 …F*7(+EFˆ)* Šˆ 1D(eˆ S.)Œ4A`6A O D ./01( Pˆ)5`A7.@21.@6;5 16A`A 4(p*76„… [AŠ(?,:5
ˆŠA¦A 1(«*76„… [A¦AC6DE9(Žˆ)042‡A 1(Ž6D015-AC*>Œ1EF(?0[AI4”ˆ‰,:5 6AC5>(+„ƒ  K
M . Pˆ)010 Q ( Pˆ)5>A76”ˆ)0 ‹Gˆ)< 
3
3
C3
&6
73
6
3
@3
3
73
3
C3
ƒ6
J3
3Z \Z $Z ‚ P_ 9… P_ =_ `X ¡X FX ]Z ¡X w Uj
BYca Z
‡X h_ Ba:Y 3Z X w
_ `X )Yq W BX P_ [Z ta
+a |_ B_\a £X B_ «Z xX w
_ `X )Ykj Z ‚ B_ia [Z ea ƒha P_ =Z ?X ˜Z ‚ P_ +Z BY ˜Z BX Z Un 9q
ž./E9. ƒ ./6G21(?EF./045>AC*7ˆ)21.’ˆ)0[AC(?*76D.)*7E9(+0[AC(_†x./5JE9.€24(+D.)5p21(gI1*7(B:6D5•œŠ.’6;0157I16;*Cˆ)24./5ž(+E|ƒ (?0 @/E9(+01.)5
0PˆŠA7Œ1*CˆŠ6D5 ˆ)575>Œ1E9(+>E ‡m57(¡<+.)EF.9Œ1EFˆ9ˆŠ;AC(?*70PˆbAC6;Šˆž(?¨1<‰ˆ)®eˆ)./5 iE [BAC.:21./5 <+.)0H)(+01<?6D./01ˆ)6D521(˜I4*7(?:6;•5 œ). †
I1*>6D01<?6DIPˆ);EF(?0[AC( ŒPˆ)0421.FŒ4E=ˆž2Pˆ)21ˆJA5 [+*>6D(ŽAC(?EFI./*CˆŠˆ)I1*>(+5>(+0[A^ˆ9<+./E9IS.)01(+0[AC(?5 U0 œ).JD6;01(‰ˆ)*>(+™5 
ž./0[ACŒ124. †S(?5>A7(e21(?57(+E9I(+0 1i
. [˜. 4AC6;21.9ªF<+Œ45>A^ˆ921(¡Œ1E ˆ)Œ1E9(+0[AC.92Pˆ9<+./E9I1D( –€6D2Pˆ)24(Ž21./5 EF_. ‡
21(?D./5£24(žI1*7(B€6;•5 œ)K. †./Œ357(m“7Kˆ †—( –€6D5-AC(žŒ1EE=ˆŠ6D./*0 4EF(?*7.$21(žIPˆŠ*C©)E9(?A7*7./5 Œ1(J01(?<+(?57576A^ˆ)E21(ž57(?*
ˆ “>Œ15-A^ˆ)24./5  & 5>A^ˆJ<+.)EFI1;—( –€6D21ˆ)21(Ž*7—( ˜P(+<BAC( ‡m57(¡0HŒ1E ˆ)Œ1E9(+0[A7.924.F<?Œ15>A7.F<?./EFI4Œ4A^ˆ)<?6D./01ˆ)Ž  = ˆ)*CˆJŒ1E
:Œ1 …/ˆ)* <+.)EFI1Œ€A^ˆ)21.)*­IS(?5757./ˆ)Ž †[.«I1*>.€<?(+575>.˜24(ˆŠI1*7(?01216D®+hˆ …/(?E —( –€6 …)(¦Œ1E I.€21(?*­21(¦<+.)EFI1Œ€A^ˆ)Ÿ œ).«0Pˆ
./*>21(+E 21ˆ)5­21(+®?(+0PˆŠ5x21(¦5>( …/Œ40121./™5 †€(?0 ŒPˆ)0[AC. Œ1( .¡I4*7.:<+(+5>57.¡21( ./I4A76DE96D®‰ˆŠŸ œ).<+./0[•A [?E *7( Œ16D5>6;AC.)5
ˆ)6;012Pˆp57Œ4IS(?*76D.)*7(+™5 †P0PˆJ./*721(?E 21./5 E96D Pˆ)*7(?5G21(«57™( …/Œ10124./5 
& E S.)*Cˆg(+5>A7(FA7(+E9IS.‡21(=<?./E9I1Œ4A^ˆŠŸ œ).‡U0 œ).‡57(m“7ˆŒ1š
E ƒ\ˆ)<BAC./*«*7(?D(B)ˆŠ0HA7h( † 0PˆI1*>(+5>(+01Ÿ+ˆ21(9IS( ‡
*7‹;.€24./5A7(+E9IS./*7ˆ)6D5 D.)0 …/./5 B\_( M… †}A7*76DE9(+5-AC*7ˆ)6D5 ./Œ3E9(+0157ˆ)6D•5 N—†}.=EF(?57E9.¡e“ d@U0 œ).@5>Œ1<+(?21( ŒPˆ)0121.gˆŠ5
57( Œ ˆ+01<?6”ˆ)5GA7(+E9IS.)*Cˆ)6;5¯e5 œ).p<?Œ1*>ACˆ)5 B\_( M…K„†€EF6;0:Œ€AC./5¯./Œ@5>( …/Œ10421./5 N  O 575>6DE 57(?0121. †€57(+e* d Œ1( [`I./5 ‡
57‹/(? ˆ)I1;6D<+ˆ)* ./5`E9.€24(+D.)56;0157I16;*Cˆ)24./501ˆ † ˆŠA7Œ1*7(?®‰ˆ@IPˆŠ*Cˆ@ˆ9I1*7(B€6;•5 œ).=21(pe5 [?*76;(+5£(?E A7(+E9IS.F*7(‰ˆŠ R /T
;
BI
„A
HG
=JI
=
HG
eICEGH
5C
{
5 s
–I
=JG
G
4G #EG
A
BI
FEG
IJE
AE
EE
=JG
J
HG
{
#
AEC
4G
4G ‰
4G =JG
=
5
HIJJGJGH
JGH
u #
A
C
A
C
GH
{JI
H 4HG
5 4G IJE
/
3
6
1
/
/
/
/
€3
6
/
/
/
R/R
-
” & )($8
\ }&'- & 5>A7(=<‰ˆŠI1‹;A7Œ1D.gI1*>.€<?Œ1*Cˆ)*ed‡*>(+5>IS./0421(+*eˆ‡(?5>A^ˆ Œ4(+5>A•œ). †¤ˆŠAC*7ˆUh[+5˜2PˆI1*>./I./5>ACˆ‡21(9Œ1EFˆˆŠ* Œ16;A7(+< ‡
ACŒ4*CˆpIPˆ)*7ˆžˆžI1*7(B€6;5•œ).ž(?EœA7(+E9IS.ž*>(‰ˆ)Z† Œ1(ŽI(+*7E96;A7(Žˆ)21.)I4A^ˆ)*EF.:21(+;./56;0157I46D*CˆŠ21./501ˆ † ˆŠACŒ4*7(+®+ˆ
ˆž(+5-A^ˆ)5 576ACŒPˆ)Ÿ?±€(?5 
/
/
/
" * pSz#n
kl
š~ rw /~
z
~rtw™n
`(9Œ1EFˆfƒ .)*7EFˆ …/(+*7ˆ)Ž†(?E576D5-AC(?E=ˆ)5Ž24(i…/(?5>A•œ).g(F<?./0[AC*7.)D.$2PˆgI1*7.:21Œ1Ÿœ). †¢ˆgI1*7(B€6;5•œ).‡I.)AC(?01<+6Dˆ
Œ1EFˆFE9(+ 1./*76Dˆž21./5`I4*7.:<+(+5>57./5`21(e<?./0[AC*7.)D.  ° I(+*7‹;.€24.F21(¡AC(?EFI.=21Œ4*Cˆ)0[AC(˜. ŒPˆ)¢57(eI1*7(BAC(+0421(
Œ1(dI1*7(B)ˆŠD(+Ÿ+ˆ Œ4E=ˆ2Pˆ)2Pˆ#AC.)E=ˆ)21ˆ24(’21(?<+6;5•œ). †`21(+5>6 …/0PˆŠ21.I./* … P_ _ `X )Y †Žˆ?ƒ (+<?ACˆ
0PˆŠA7Œ1*CˆŠDE9(+0[AC(Ž.JI1*>.€<?(+575>.F24(¡5>(+;(+<+Ÿ œ).921.FPE [?A7.€24.ž21(«I1*7(B€6;•5 œ)K. 
O 5˜I1*7(B€6;57±:(+5¡IS.:21(?E57(+*¡<+Dˆ)575>6;¨P<+ˆ)2Pˆ)5¡(+E ŒPˆbAC*7.‡<‰ˆbAC( …)./*76Dˆ)5«I1*76;01<+6;IPˆ)6D5™† 21(+I(+0124(+0121.2Pˆ
*7(?”ˆ)Ÿ œ).9—( –€6D5-AC(+0[A7(p(+0[AC*>(p.=I(+*>‹D.:21.JAC(+E9I./*Cˆ)24.=576;5>A7(+EFˆ Œ1(p 1(˜(?5>•A d=57Œ H“7ˆ)<+(?0HA7(p(e21ˆF(+5><‰ˆ)Dˆ
21(«AC(?EFI.F<?./015>6D21(?*Cˆ)2Pˆ9IPˆ)*7ˆ=ˆJI1*7(B€6;•5 œ)K.  O 575>6DŸE †P(˜I1ˆ)*Cˆ9Œ1E2Pˆ)21.F<+./0[A7—( –:AC. B Ž6 {h( †P5>6;ACŒ1ˆ)Ÿ œ).9(+E
Œ1(e5>(e21(?57(?0H)./;)(p.=I4*7. 1;(+EFˆ9(?E( ŒPˆ)Ÿ œ)”. N †}ˆ)557™( …/Œ16D0[A7(+5`<+ˆŠAC™( …/./*>6”ˆ)5 21(¡I1*7(B:6D•5 œŠ.=21(B/(+E 57(?*
<+.)01576;21(+*7ˆ)2Pˆ)™5 †1AC(+0421.F(?E <+.)0HACˆ924„6 ƒ (+*>(+0[AC(?5 1./*76;®+./0[A7(+5¦AC(?EFI./*CˆŠ6D)5 ‰ `6DK0 …9(BAˆ)Ž † RUT/T 6³  ‘
w «Z :n †€<+./*>*7(+5>IS.)0121(+0421. †PI./*( –4(?EFI4D. †4ˆp(?/.)DŒ1Ÿ?±€(?5 ˆ)0HŒPˆ)6D521(Žˆ)I1;6 ‡
<+ˆ)Ÿ+±:(+5¦¨P0PˆŠ01<+(?6D*CˆŠ5 †P01(?<+(+5>•5 d)*>6”ˆ)5 IPˆ)*7ˆž.9I4”ˆ)01(+ˆ)E9(+0[AC.J21(«6D0[)(+5>A76DE9(+0[AC.)5
w £Z z l7Z Hj AC6;I16D<+ˆ)EF(?0[AC( ™( ƒ (?<?ACŒ1ˆ)2Pˆ)5GI1ˆ)*Cˆ¡IS(?*7‹D.:21./5¯E9(+0157ˆ)6D™5 †€21(EF.:21.˜ˆ
ˆ)Œ –46;D6Dˆ)*.JI1Dˆ)01(‰ˆŠEF(?0HA7.J21(«*7(+<?Œ1*75>./5
w xZ a h_ :j 01./*>E=ˆ);EF(?0[AC( ˆŠ5757.:<+6Dˆ)2Pˆ)5 ˆG5>( Œ ˆ?01<+6Dˆ)5AC(+E9I./*Cˆ)6;5 Œ1(­Šˆ)*76Dˆ)E
(?0HA7*7( 216Dˆ)5 ./Œ 1./*7ˆ)5  ¥ *7ˆŠA^ˆ)>E ‡m5>(G21( I1*>(?:6D5>±€(?5¯(?575>(+01<?6”ˆ)6;5­IPˆ)*CˆŽŒ1E<+./0[A7*7./;). @/I4AC6;EFK. †)IPˆ)*7ˆ
21(?<+6;57±:(+5 (+E 5>6;A7ŒPˆ)Ÿ+±:(+5 <?*7‹;A76D<+ˆ)5G./Œ‡IPˆ)*7ˆ9ˆž21(BAC(?<+Ÿ œŠ.=21(«576ACŒPˆŠŸ+±:(+5 ˆ)01.)*7EFˆ)6D5 (
w
`X u )Yoj Œ4(d;6D2Pˆ’<+./E ˆŠEF./5-AC*7ˆ)5=AC(?EFI./*7ˆ)6D5 Œ4h( †£(?E i
E [?216”8ˆ † 0 œ).
( –4<?(+21(?E .EF6;0:Œ€AC.  † (+5-A^ˆ576ACŒPˆ)Ÿ œ). † .576D5-AC(?E=ˆ#21(3I1*>(?:6De5 œ).21(?)(’.)IS(?*Cˆ)*$21( ƒ .)*7EFˆ
ˆ)Œ€AC./iE dŠAC6;<‰Kˆ †:57(?0121.=ˆJ5>( …/Œ4*Cˆ)01Ÿ+ˆ9Œ4E ƒ\ˆ)<?A7./*¦<+*>‹;A76D<+K. 
ž./0[: [?Eœ*>™( ƒ (?*76D*xˆ)6;012Pˆ Œ1((+E ./*7ˆ˜(+5-A^ˆ¡<+”ˆŠ57576¨P<‰ˆŠŸ œ).˜57(`EFˆ)0[AC(?0 Pˆ˜_ d);6D2PˆŽIPˆŠ*Cˆ˜Œ4E=ˆ¡21„6 ƒ (?*7(+0[A7(
…[ˆ)EFˆ24(¦ˆ)E 16;(+0[AC(?5 †[.£E9(+5>EF.`IS.:21(+e* d`U0 œ).`57Œ1<?(+21(?*­<+./E§*7(?57I(+6;A7.«ˆ)./5 IS(?*7‹D.:21./5¢AC(?EFI./*CˆŠ6D5  = .)*
(—–€(?EFI1;. † Œ1E 1./*>6D®?./0[AC(FA7(+E9IS.)*Cˆ) 21(=A7e* ˆ?5 1./*7ˆ)5e(?E ˆ‰Šˆ)01Ÿ?. [@<+./04576D24(+*CˆŠ21. <+.)EF.21(@PE [+216;.
I1*7ˆ)®+. †}0Pˆ@I1*7(B:6D•5 œŠ.$21(pI1*>(+<+6;I16;ACˆ)Ÿ œŠ.@I1DŒ€€6;./PE [?AC*>6D<+Kˆ †}ˆbAC*Cˆ‰h [+5Ž2Pˆ$ˆ)0 d)D6;57(¡21(ž6DEFhˆ …/(?015`21(e*Cˆ)2PˆŠ*
‰ `(+01.:(+Œ – 6D®‰ˆŠ01q2 † RUT)T ?³  
K
/
€3
/
AE
EE
=
=
AE
/
/
/
€3
6
/
76
N3
:
4G HJG
ŸE K
C E
T
:
4G HJG
–
E
T
:
4G HJG
=
/
E
/
3
T
:
4G e
/
A
C
/
6
/
6
3
K
3
3
” K%$&# $ \ &#$
k
Pu/rw™z#n
z
\ }&'- ~rtw™n z
z
~
R)R/R
+(
z#t
ˆ Cˆ¡ˆUŠˆ)”ˆ‰ˆPˆ«Œ
+B•œ †OƒCˆ
/ Pˆ4ŒPˆe[!
"Cˆ#
Œ
Fˆ$PˆPˆ$‰ˆ ˆ%”ˆ&'
()7ˆ)#B – …/Œ7ˆ ³ +*6N—†,DŒ%Pˆ-Pˆž.„ˆ%”ˆ/Pˆ )~4Z bY 7n bj Œ 0% Œ 01…/Œ 0eˆ %2Cˆ
‘
9-5e4 ¥ C
ˆ Cˆ?‡34ŽŒ F5ˆ —–%eœ96ª e[ 9-5@ˆ %2CˆP7ˆ %PžGˆ 1+‹ CŒ1 †4hˆ …75ˆ Œ ^ˆ)8
 9* g ? %2\‰;:<%
=ˆ %† g *  >=?e[@D@® )+'tª F 7ŒCˆ Œ P@:…7_ˆ ƒ †A
B'
-P$
ˆ 7Œ1ˆˆ + CˆŠŸ œ$ ‰ˆŠŽ †C1Œ 7ˆ %2'9Œ B7ˆ '$%P$ˆ Pˆ “7ˆ )%CDˆ $E )h=FG -)ˆŠŸ+± #ƒCˆ H…CˆPˆ G)+DˆJŒ %; Pˆ /Pˆ ¥ ˆ =© %”Kˆ †
=
Œ •d) ”Kˆ †
I*KJ7 ˆ %L*KMM ³ †N
Œ O"7‹ PD…/Œ1Dˆ 8¡Œ O™…/Œ %  £ŒPˆ %
ˆ %Pˆ) CˆFˆ e[Q ŒPˆ %-8Pˆ R'QPˆ CˆŽFˆ >ŒP-ˆ ()DŸ œ †Šh ˆ—‡3 Œ 8R^ˆ«ˆ %2^ˆ
-
(-
"%%2'-P$
ˆ e[ 9-5 †C/SŒ '“78ˆ †,Cˆ Cˆ?‡37žŒ F&ˆ e[7Cˆ%Ud”Kˆ †
%Uœ9 %+
ˆ 
Y:9 4 R 7 9UT#Cˆ5e[%Ve[
Œ Fˆ ƒR'G'% ˆ%”8ˆ †—ƒ%?‡3ˆ g * … PWˆ '
%2
+
ˆ 1‹Dˆ K† F1Œ Cˆ %V8-%-GŒ Pˆ %2'.% Cˆ) /‹.%q† ¬ ˆ Cˆ :Œ '
‰ 9 …%
- %8ƒ+ †C*KMMh*  X=E( >Šˆ)Ÿ+
± (™…/Œ >‡3Sˆ ‰ˆ Pˆ  ³ …)Œ %™† ˆ
P
ˆ 'QPˆJ CŒC5ˆ 1ˆ G%Cˆ%2'«Œ Y? 'P+ˆ :…7ˆ FKˆ 
FD—ƒ Œ 9ˆ 1ˆ 4R^ˆ/A[«ˆ %2^ˆ
ID”ˆŠŸ+± Žˆ $ % …Z$'
)  † $
(
‰
ˆ †VBP ¡ˆ /7Œ A…
%20/Cˆ '-_†V%1…/Œ %0‰ˆ †V? ˜ˆ !Cˆ! ˆ %Dˆ
DP
ˆ %Vh
= 7 –P
1 † ˆ – …/Œ 7ˆ ³  g ('7ˆ ˆ Jˆ)PŒ '+Dˆ)Ÿ+± 1Pˆ 7[
ˆ 5"7‹ 1$ -)6ˆ ‡
Ÿœ †,„ƒ%2†\PLˆ e[ 9-5•4”† ˆ )-
]* -)ˆŠŸ+± =F0ƒ%1Ÿ‰ˆ 0%%VCˆ 1ˆ "? P
ˆ ˆ ˆ) 7ˆ)Ÿ+± Œ /7ˆ H%(
()R^ˆ
%2'71ˆ Ge[
=
€3
;
/
J 4 F
/
76
76
/
/
@6
76
3
3
/
K
J3
6
6
76
6
/
43
k
76
Pw™nqpSz
t
xfz|{}rz
%
w™n ~
z
z
~
+(
z#t
B
+ˆ):ˆ>Œ
—‡3
E7Œ”ˆ)Z†W
`PˆR'?Œ1”ˆ†a% Œ.;®"'ˆGR' ‡
Fˆ,.%2') \T#
"[ˆ¦Pˆ.)P
>‡3!™ƒ,\
=ˆŠˆDˆ,—–P
(1 Œx_œ
ˆ>…R œD
H'
()7+ˆ)A G+ˆ)ŒPˆ88?ŒGdh…/ŒPˆf‰ ¬ ˆ ”ˆ8b ˆ)Ž†A*KMM ²_ †Pˆ7)/DŒ;Ÿœ
(#e…' Œ Pˆ %'‰ /%K… F%+Œ –†\*KMMJ  †1ˆ …•œ1G%2') /P/ˆ 1Œ1Ÿ œ
‰Mž Pˆ7¨+†C*KM ² M  /@
Œ >ƒ%
(%VD/%e…DDˆ ? ['+Ÿˆ ‰Mž Pˆ R<V'%;Œ G ž %q† g  
=^ P•œ
_
"
/
/
6
C3
6
b3
Rc
P
ed
2P
U { Eksl&\YEk Wbœs\cblWn n–^`a˜_[abn–\ksl[^jn–aƒ™ W&
K
b3
b3
**
g
-
” & )($8
\ }&'- 15000
10000
5000
0
-5000
-10000
-15000
0
200
400
600
800
1000
1200
95
90
85
80
75
70
65
60
55
0
500
1000
1500
2000
– „…/Œ7ˆ ³ +*/‘8[G
"CˆQ
H
"D‰ˆ)B <9-5e46Y:9<4 R 7K9N 
” %$$S %&')($} \ }&'-
**
1
10000
0.5
rk
5000
0
0
-0.5
-5000
-1
0
10
20
30
40
50
60
70
80
90
5
100
10
15
20
15
20
k
1
10000
0.5
rk
5000
0
0
-0.5
-5000
-1
0
1000
1020
1040
1060
1080
1100
5
10
k
!#"$
&%$(')**+,!-"./(%!#%01!2*43656789
:,
**
!"#
$% %% '&eœ4
'
()F %)( "
+*3-, ( /. % C
10' Q'&eœ4.
,R'- % .32
/
,!54 % %6&%% % 7)8:938;2 >#< =, % (b' ( )9 % ?>=,#% % % %@% A,'. % 8
B %2C,32ED-,
% & % %2 % 9
U%",F.
10P / ,.%/9 % _FD' % \%G
%)HI % % R'
% 2
, %)( / , %3
%2KJ0L8ŒK %NM / , ;&RC,.O& ( 9
K,
QPSRUT#VXW:YF%Z9$ %)( 8O2 *KMM6[\ B-] % <V'%/,3^ _ B-] %`2?a \cb % %2ca *
dL2AFG%%fe,
R % %
9),
P (g% # (/%)H
h % I ( % % '2
(0
A, %)H
h %ji
% 22
% % /
( ( FD % 8 % % O+'G)8
k0b' % % %)(/M '
8
=_;G% H% %2' % F& I 7
'
)5 %)( % 4',6 % . % %2 % G % % % l
6R'
% 4F& I 6'
m
F % ,'
% /. % 32VE
( % en,-4%O9 % % o,
%
% (
)R % H
"D )
\ L
P ( &'& I $'
BD/R'
% $
m
% ( 2 (
pen,D %)( ( ( /e,
"L )
,
% " % %', ()% ] 38
q
&
e,@
( ( % L%6& ( &
%2' r,
%f% Ae,bC, % % %s% '& I L
'
()^ %N( 24%3e, % %2'X^'9=,%X't%u,
( '
() %)( 2E3, % %V9ve, %)( P ( (3,P % % %N( % % 7 % %w% '& I 7F&/ % 4x,R % Z8#=F
wy)Q'G
e,+' I 8' % % 8
Ob %)( ] -% % G H'h E
9=,%2''8
z|{
{}
5=
3~|"€ Zƒ‚ "„3…‡†‰ˆŠ„3`‹U€5Œ Ž  K‘’ƒ…“
” O
R'
% % %k% F& I (
Y'
)( %)( F&C•Z%&
ž – žn V ˜ VF¡5¢¤£ ˜¦§¥  FV 2 %©¨¤–)ª ˜«ž – ™œ›n1Ÿ­¬ƒ¤— £ ŸAž)—™œ›nržn V ž – žn VF2 %
% Ÿx± ¡L£ – °j ª;– ™œ›n – ° – £E¡ ˜ £ žnŸ V§V Ÿ²¯Q
žnŸ ª  W;: % %Z^_ G
(
& e, % 'Zb % % l % – —n˜ V ˜š™œ›nkžnŸ
¥§¤® VF¡L£ —™œ›n1žnK¯Q
žnŸ ª r
 žnŸo° £ Ÿ ¨ ˜ V I 32
] 2C* M=³M¤dL8
=Y
% b % % FDP/9Q,
% , (g% 0
, % % %Š( C, % 6 % 6 =y ( % e, %NHI 32EŠG
%´% '& % H'h 8 =I % % '9=,%2)2 ¨¤–)ª ˜«ž –6HI 32G%R' b'
(% % # % ! ( '& % %2' % %% ( , H
I /5=y ( % 'en, %)HI Z8 $ R'
(%2')2
&
% ¥§¤® VF¡«£ —™œ›nµžnŠ¯Q
žnŸ ª ¶žnŸ° £ Ÿ ¨ ˜ V I Z2en,@%6& ( &s,
% 4x, % (%2' 7 % % ,
· ( '
%
P ( 32,kG
%X% (
(%
/. % 4 38 ” % &'.&FtN%[ P ( Z2\
9=,F*3 % 3
% % 2NED' % " /( % Q
% % " M P|Gš,C,
8
B ¸y % /%R'/P32j0/"R % ,
%r% Ae,+'C, %r% , % Y
% Q
/'& I U'
()4 %)( e,8%6& ( &8 "%%2'Gš,%% % \ % % ,
()Ci% % L7 ¹O9=, % [8»º6>Fl
D
k¼3, ( 7 ° £C½F¾ ° £ ¿¥§Ÿ V§V – ¯QŸF® ¡  /
1¼3, ( 7 ° £ Ÿ ¨ ˜ V ›n 8
q
1¼P3, ( -Gx0F*3 % %25%V
(g% ,
'
% ¨¤–)ª ˜«ž – ™œ›n .
('8=
R'
% – —˜ V ˜š™œ›n % !S,
5*
% en, HI 14 % .)A•1Q
% ' N
% ( / . % %% % &=0QN2
n
ncX
"n!o
**œ[
!"
Sistema
Módulo de Pré-processamento
Dados
Problema
Aquisição em
Tempo Real
Dados
Digitais
Validação em
Tempo Real
Série
Temporal
Módulo de Previsão
Agente de
Decisão
Previsão
Previsão em
Tempo Real
Modelo
Construção
do Modelo
% (8
¹/9), % [8»ºZl#=EAe,bC, % /'& I H
"7 )
)GFDP
( Z2j,
O%E=,f,
O%6& % % %)( ¼)9N*3O9 %)( 2%Z)G=yn4b';& % % C, %
% E % E(=y ( % 8QT#
O'9=, % 2 % 9 % E I ZP % F) ( %
#& %)( %)H
I 32
,¤4D=y4O&10#t ( ' % Q % % .% % % %ZG
%)HI 1 ( '& % %2)2PZ,3.%r,
%
A01'
() %)( t ( ' % 9
,
b'
(% % (" M P'9=, /( % w
7)8:938;2 ,
?
% % (' % 9
O=,
/A, M >F8
@ '7 % y %N( ] 32"R'D
k¼3, ( &% I $A•L% % Z2C"F % -%2
% (%2'5)%%2'
@)y ( %f% 0 ( ,% % u7)8:938;2 %f% HI @
)%%20) M tN5s – £ ž – £ Ÿ
(s,
% ( %)H
I &0 % #G
k¼)9 % G6>F2A % '%N*e7L% M ©e, %f% en, HI $+& )
%)( O. % % G
% % 8
@ Še,((
9),)2 % y" % 5*3E* I % 1
3, % ·3( % - % % 1
P ( ['& I 32Se, %6& ( & % ' tN% HI % %O. % 9 I
%
%
'& 'Q
(
38
$ 3
· ( 32& %)( F&# I 4
%6& % % ,
–
ŸF®
% -%V ( 6=,$
% %2' ( O9 %2'N2e, % b';& % C•Z2
% H
h G ( '& % %2 % %r% ( , HI (=y ( % Y'en,
z|{S{
†“5
P3l % %R'x, H I R' % (8
'
() )
2 %
¡ ŸSžnŸžnŸ§¥F˜ V ›n 2Nen,Q"C•F,
% 7­4 % %A•323,
%¤4x,%V
%)HI Z8
†"!ˆŠ„3`‹|€Œ
@ 5 % M C, ( % %2
2
e, % %=,*e47P74'& I 7
x0.
" % % % ,
O % (
( 32­4 % 5D'"D%&%% %)( =, % I 32N'%rtN % Z
(%' % 1e,1
' % % ,
7EDP"38 q % 2R'G % 5%3,3.)2% en,4%% % 0P7
3,*
% % %)( F'& I 32e,4E%V45
% !G H 6FDP ( ,;& % (%2'F% % G % E4%A, H
I 32P
**KJ
!"#
% I D% % A, % ) %)HI 38
$ 0=, g( % Z2\
wy) %f% '
(O. %)H
I $0
( ( -% % /% %
£ ˜ ¡ ¯Q V ŸF® ½F¡ ˜¦¥§ V PZ,3. % P ( F % %s% '& I LDA0/
" %
7 G ¿& % % %2
%2¿>F2V' % % *3",
7
% % @"% C,
. % & % T ª  ¾
FF& % 0'tN%2
( %Vp7% % ( ] % 5'9=,%§>E % % en,5) % , ( O . % ?PEFP41F& I Z
)
%
(
$
%
/
(
%
(
)
%
H
I
(
'
()S 8
%
9=,%2')2. *3F*­•S)
,' /.
[@
( 6x0F*e'tN%'8 T#R %
I 6)
(+'
( OtN % !6323,3.%5Q'e,'.
(3,P % % % % 6P
% %/. % 9 YG
( ( Q/'& I 3
8
% & % 2N
(re, % %Z1% %k% "
% % G(( % %/. % 9
YG
P ( % % % % @"% C,
. % 2 % FDP/9% % D
(3,P % % % 7 I 9 % % '.% % &@E*
9=,%
2 X
e,)PC•L%tj9=, % ,
'
)@
% % ( %3932C % % 1)-A0
'
() % '8.T#
9 %)( 2NP& % %O. % 9
O%&x95,
% G
% A• % % % E;*
% - %)H
h /
% 2?J$
( % e,L'
)@ % % 2 % ( %2 % D% %X% %, HI Z
38
$% %
FDP
( ( O tN % 0
kG%3¼
%32GG % , % K, (g%)H
I 32?,' ( O. % %f,
% ® ¡ Ÿ ª FŸ ® ¡ ˜ —n¯ p% [
:".)2)(Z % %
%
k
%
%
%/. 9
O x0)8 q ·3( '
!" c& %)( C % A 0G % !
,
% % &=04w,
% PSR$#?2"% % G
% ¿
* º¤*'*¿º¤* )
* 88=
432&%('*),+.-0/G4&%('1)+324/2 % % R %
( /. % C % %"% '& I 3
2% % A0
( (g% %
¹O9=, % [8:Zj•¤*e% % '
& ( , H
I & % 43, % E
,& % w, (g%)H
I 32V%F%7 D5 % % y" % .
+*3E
'
()32
7
Y'9=,%
8
T# % FDP)5% % % % e,@ '
()S % %/. % 9
]"LD
%, M 32#
e,
] % 4 % ,
% ]
%
%
)
%
H
I
(
I
9 %&'9 [
I'
5[
"% S[
ZF&P 7L¹O9=, %
% (
[8 [=>F8"YFKG % 'Z2 % ktN
w
&
9=,%
2 k& %)( EZ&1F&P I Q06+a*=876n2 ,
& )
% I w,+'7 % %2'/+& %)( .D*KMZ8 [23e,00)y' % "[7'9=,%
8
q ,' % ) ()R % %2'1 % %f% %A, H
I @L
( ( $7'& I @
% &0
%
'& ( , HI 6 % A¼ % A0E'
() %)( 8YFG % b'32 % .x0.
%2'% % 8=,&
( ] % !4=y5*
& %)H
h '2A% I $ % % &'. % %2 % ) % (%2'E%ji
('2"=, 54 % 2CEDP
% h % ( ' % e,D )
% % P HI p
[ 8 a6
)
%
M
Y
e,)2 e,
% (
%39&$
"$F& % %98j,% % -FD'17
©G %R' % % %r% A0:;<>=?N>E8
% %(5 % % % %1% F&P I Y
" %)( 2"A•
% 8't % .0Q,
% %V
%2'
% G%V'2 % ' % =
& 0FK,
% 4 % % (/% " %)( ( O. % %2)2 % Z%&)0E
E% % % ' %)( % 8 % A0)8 q =yn4O& e,FF)
9=, % % &=0. % ,' ( / . %)HI -R %
4 % % (g% " %)( 2 % & % %2'GO9% % % )@ – ® Ÿ ª;– žnŸ ¨ ˜ V ˜ A
˜ ª ˜«ž – žnŸ 2 % % "#'tN%en, % # I - % % M &0%,
% L
%2'& % %p%p% %/. % 9
+,
?
( ( &7'& I 32
% OG%VL % 4 % % (/% '
() %N( FG % %D % M A, ( % %2''2!
e,LLFtN%
n
ncX
"n!o
**6
!"
500
tr
pr
450
400
350
RMQE
300
250
200
150
100
50
0
0
5
10
15
20
25
30
35
40
45
50
tempo (segundos)
¹ /9=, % [8:3l $ =9 %r% %O. % 9
Y % %r% x0 !)8
500
tr
pr
450
400
350
RMQE
300
250
200
150
100
50
0
0
1
2
3
4
5
tempo (segundos)
¹/9=, % [8 [l
%R % %2'E% % .P( % %/. % 9
Y % %1% x0()8
**¿³
!"#
e, % 8 I % G%2' % % G % % (
(Z8
q
,7#,
% 4 % % (/% &/y ( % GF&'E*3043, % |& % %2 % 9% % % % '2en, % ( F*
% H % %/. % 9
fl
m
3,3./% · (D/ % G/'% % % %8
Y % % % % %2')\N
m
)
(+'Ke,D$
P ( Z
% %2% ] % ,
% 1¼ % 2 )F
B % % % % %2'76
"Z2 %
% % G % G-'%D% I DA•D)G %)( %)HI Z8
PF
CJ
DJ
HT
Tempo
t−CJ
t
Passado
t+PF
Presente
Futuro
% (8
¹/9=, % [8 JZl $ (%3i
(60'& I H
"7 )
q , ' % "'9
"R % %2&'
% &Z
%
% H
I 6,
% 4 % % (g% &/y ( % 7«e,--
% $
( ( (7F&P I ZwtZDP7
?
% % % ( / . %)HI Z2.=,
% % % @f9% )
( %+% ( %3955'
()>
()e,,
'
% % E)F % h '2A'&+ % %N*3
YR'DD=yF* % 4x, % %2'38
T# % % A0
9 % % %/. % 9
00FtN% % °j £ –)ª
L% · (@ £ Ÿ ¨ ˜ V Ÿ V FŸ ¯
£ ŸF® ¡ Ÿ ¤¯° £ ˜ ¯QŸF® ¡ rž – Z– ® Ÿ ª;–
 £ ˜¤¤® ¡ Ÿ
– ® Ÿ ª;– ¡ fž –Z
(GG % b''l.
ŸF¯ ¾
Ÿ V ª ¿¥ – ¯QŸF®
D
2A
7«¹/9), % [n8 J6>E8
q 'UG % 8 I 't%8" ( 8
e,GD=y ( % [% · [&'& h 6­4
)% % [" M P '9=, (g% 1
% A0N2 %2'[ ( % %2' % 4 % % (g% " %)( ¶$ 6%
9),%2'N2 % %
54 % 2 %
5*
% [
r*
% 2P%
% % 7
% H
I P
tN% )
"%& %N( #
2=e,UG#
w,'-x,) % .32V)PC•-;tN
, ( % % % % % 8
% %/. % 9
&
( (1F& I 32"%3e, % %2'pe,K,
& %N( % % )
e,%$"A•
G% % 1%A,tN%2'/%G
%)HI 38
n
#S
z|{$#{}
**KM
rZ
"!
'&)(+*"„Z…, 
%
†.-|€5Œ0/21
$%43C%65798 ;
, : %<3>=@?A=CBEDF=C398C%<BG5HI8J= :
%<?3N5A79?A5H08C% : = J %4D3( O ?%)H
I<=KR AS², Bk%
&PO 7CI<=@5BQ8J5ABEDF=6395%)( 2?G = O
%<7
H;? %<7
5A7N?3 8§%<7THj%U795A?
H
I<=©%4H08N5A3 =C3
:
O
:
O
O
\MO¦8 5 8;2ZG = O % : =CD *
8§%
%X% y;OOy ( O =<8J5?%VR $ W YXLZ[: %f( O H 9), % 9 5B : 5ED;3N= 9 3C%<Bk%)H
<
I =
% B __^O 8N? ] O 5 2a`cb=³=³œd¦2
:
W]\ 53NH OO9 ] <
% BQ<
% H O D , (/%)H4
I = : @
% ?=f=C3 : 5AH3% : @
% 8J5BGDF=C3C%N( 8
e, 5 O H;?'( ,;O, Bd?A=CH x4 , H08N= : 5eD;3N=P?A5 :;O BE5AHI8N=C7UDj%<3A% @
ghBiDj%<3j8 ?
(/%<3 2 % Gš, H3H<
I =
R $W re, 5 : 5 & =)( & 5=U8J5BGDF= : =
7 O 7j8J5BQ% 2 BG5 :;Ok: =U5Bl7N5 9=, H : =<7 7nmœ>F8
O ,
o
%48N5AH
8
y %<7%47)7 0
B
J
53
:
*
9CO
7j8J=
7
3N5
B
& %N(k=C395A7
J
5AB
:
H
%ƒ7 0
:
%
5>D
%DF5A3AML=
:
7395
O
G
5A3
B
(
=C7KBE=
:
5 L=C7
:
=
=C7
2
=
5
§%
2
%<DM3N5A795AHI8§%
5A7j8
B
%„?% , Q
: ;G
:;O
q
=C3 <B’5A79?A=
% y
5A3N5HI8J5A7
m
=
BE=
m
=
BE=
m
=
BE=
T <
G
=
§%
=C3
'( +(
=
BE=
'( +%4D;3N5H
5 k=
:
%1%Dj%<398
:
O
%
5…395
:
9CO
(
3
O
798N=C7
Q%47 O %
5B
:
S%4H08N5A3
5"‘U„5 L5ABE5AHI8J=C7
:
5
%E?% e, +
: =
:
H;?
%
O
:;O
798
=†3
:
•
D
%
Ok:
&PO C7 I<= 0K:
5KDM3N5
:
5
, %4H
5K=Dt53AMk=
:
=C395A7
O
M‡“ˆCm
2
G
5
2nG
=C3NH;5?
—
DfO
=CH
7N5AH
O
'(
==C7T?=f5
§% jI<=r(
7j8 UH
'( , M : =rDj%<3C%r7N53 &PO
, %u%<D3( O ?%)H
I<=„5AB
H;?
:
0
=
Dt5 k=UB
OL:
:
j%<3C%p%VDM3N5 P
& O 7CI<=u5AB–8J5BGDF=e3N5
%)( 2 e,
=GBE5A79BG=UDM3N=
y L( 5ABk% l
HI8J=C7pD
O
3
O
t
?
%
H;5 <3
8J=
=
:
5A?€8
=
:
0
=
7
,
C%
DF=C398
G
=CH
H;5?A5A797
O:
=CH
5?
•
3
O
:
k%
B
O
:
O
=G=
OL:;Ok:
twp~xž
=
,
79=
D ( ? %
D 3
O
:
:
5BG=
5
(g%47 PR$#`VF8
5V?A=<BGD
D %43C%‰=<7BE=
&PO %4BG5H08N5 2 j
5'(k=C7TD;3
% H :
0F*œ: 5 t H Ok: =C7 8 gh798§4
=†D;395
:
&PO % T < V6\
=C7
j%43C%)H
I<=6?=CB˜=C7KB 0 8N= : =C7>H3I<=@?A=<H & 5AH;? O =CH3%
8J5ABEDF=ƒ3N5
%)(
5
:
G«• ? O ( O BED3k( 5BG5H08C%)HI4= 8 |3A%48§%4H : = * 7N5
:
'(
5 k=C7
=
:
*
7
O
2
7N5H
:
=
0 3 O 57
7
Dj%<3
i BG5€8J3N=<7G™š5r› 2-en, 5 : 5H;=<8C%<B 2
H;? %
%
7 0 3 O 5+8J5BGDF=C3A%)( 2en, 5795A3A<
I =
:
O
:
O
H;7ND
O
C%
3
:
j%GD;395A795AH3H
%
7N5H
3%´@%48 ,
=C7GH
:
57
0
3
O
:
567
. % 2 8N=C3NH3% * 795
57”HjI<=E7C%
. =CHj% O 7 2
3N5
B
%
?%43 :;O Hj%)( OL: % : 5”B •¤DfO BQ% : 5
, O ( OO . %<3 , BQ% 4 %<H;5'(g% : 5A7x( OO. %<HI8J5?A=<B , Q
Ÿ Œ Ÿ ‡¡‡L‡¡Ÿ! ¢">E2 Dj%<3A%1%4B y =<7T=C7BG= : 5
(L=C7 : 5"D;395 P
<
& O 7AI<=E5ABi?=CH;7 OL: 5A3A%)HI4= 8
8
§%
5AH;=48 <B
:
=
DF5
7
=C39BG565
5
T < \
5
5AHI8J57p5798
O
2
:
2 %<Dt5Hj%<7G7N5u8J=C39Hj%‰H;5?A57N7 • 3 O =‰5A7j8 O Bk%<3 : = O
3N57NDF5A?€8
%<BE5AHI8N5 2 =C7T?=f5 t ? O 5AHI8J57 : 5%)( O 7A<
% BG5HI8J=5 : 5•8N5AH
OO&
=
% D3<
% 398 O 3 : 5 , Bk
% D;3N=P? , 3C
% 5AB 9 395
( ] % 8
y 8 Ok: =<7S
B
j%
%('
'(
(
5 k=<7
:
j%<3C%r%U7N=)( , H I<=
5 k=U?=CH;5
:
7•BE=
5H;7D
%
'(
=C7”8J3
H;5 <3
O
5 k=U—
:
%†7
y 0 B
HjI<=‰7C%
.
Ok:
% 9
:
5 k=
:
OO
8 4B
7
H;?
06O H G 5A3 O =C3r%<=„BE5AH;=C3 : =C7E8N5ABEDt=<7 : % : =†DF5
(/% Gš, H3HI4=‰R $W ’
7 zmœ>F8
=GBG=
5
(L=C7
5D;3N5
:
:
&fO 7CI<=G7N58J5AH ] %=CDM8C% : =EDt=<3pBk%<HI8J53 , Bk%
?% : H;? O %
& %Nk( =C395A7 l vrwŠx zm=22{ ‹xŒV5E~6ŽxŒ 8 gh7j8J5A7 & %)k( =<3N5A7 G % . 5AB?A=CB
:
:
O
:
=( ]
C%
¹
G
5GDM3N5
zm=8
5
:
=
:
Ok:
3, %<7+D;395 &PO x7 hf57 2a: %
=
:
% ,
& %)( 5
f‡ˆCm
j%<3C%E=5798 M
, :
5
% 8N3C% &=0 7
e,;O;& %)(k5H08N5 2 4
% 7N5 9), H :
e, 5 2 5Bi?% : U
5AB’?
3
œ>E2-e,
=C7
:
:
8
?A=
9),
7N5
5?
%47pHj%Gqf5?
HI4= [ 8 a+G =<3C%<Bi?=CH;7 Ok: 53C% : %47 2 8J5H : =5B &PO 798C%
5
?
:
, 398N=rDM3C% . =r5Bs8N5ABEDt=u3N5
%)( 8 o 797 O B 2 Dj%43C%s%VD;3 O BG5 O 3A%7 0 3 O 5 2 :;<>=2
5Gv6wyx
% ?% : H;? O %6Hj%8 , 3A%)( : =
zm=2|{>} x 5V~rx =2e, 5G3N5 8 5A?€8J5AB u
:
9 3 N
• t
7NBE=
O
, %<HI8J=
7 H3%„=C3
Y %)M e,
C%
5A7)8J5BGDF=C3
O
&fO C7 I<=
D;3N5
7N5E=C7
‚
3
%
…
`
Dt=C7
O
H'hf57
œa
`
$%<3A%% %
%<75 D
5
DF5A3
H;?
O
2)G
=
)( ]
57N?A=
O
%<7%<HI8J53
O
=C3N57
O
%"%8J=CDF==(L= C
% ?=CBED3(k5€8§%<BE5AHI8J5
9 O
5BG=<H;798N3C<
% 3A<
% B e , 5 y =CH;7|3N57 , (¡8§%
% 5A79?A==( ] % : 5 ,
+12 =CDf8J= ,* 7N5'Dt5'(gT
OL:
:
0A:MO =C7 8 @)=”?
%<7N= : =p—
?%43C%<?€8J5A3xk
M 7j8 O ?
%<7 2 % : =<DM8§%<H : = * 795Q%47N7 O B , BQBE= : 5'(k=u— %('
Bk<
% HI8J5A3 =C7TBG57NBE=C7Dj4
% 3 i BE58N3N=C7 : 5²%<D;3N5H :;OO. % 9 5B , 8 O ( O/. %
%)( 9 =C3 O 8JBE= P P
D3<
% 3C%r%1<
% D;3N5H :;OO. % 9 5B : % PSR #>F8
HI8N5A3NB
O
B
HI8J5A3
% 3ML8 , (k=C7
=C7'H;=C7T? 4D
:
D;3N5?A5
7 5 :8 938O2
5AHI8J57
:
% ‰HjI<=
e , 5 %UBG5€8J= : ==(L= C
9 O% : 5
G = O % y =C3 : % : % : 5 &POL: =1% :3, %<73C% . hf57
D;3 H;? Dj%
7
ghBD;3 BE5 3N=©(
% 3 2 DF=C3 e, 5r%e7 , % , 8 O ( O/. %)HI<=G5 DfO/9 5r%VD;3N57N5AHZH% : 5 , BDF5A3 O 8N=e= ,
O
O
O 8
O
O
,39 <
7 798N5ABk%pDF5A3 ? %)(
O
O O
7 ?A=<BG=p= G =C3NHM5A? OL: =+DF5
L( =”D;39= 9 3C%4BQ%  £ Ÿ§¥ – VF¡ £  >F2 795AH : =²%”7 , %% , 8J=<BQ%48 O/. %)HI<=
5
ML? O ( 5 D 5? , H
<
I =ƒ5AB 8N5ABEDt= 3N5
%)( 7 = 8J5BGDF= ( O B O 8N5 0 zmœ>F8 ghB 7N5 9=, H : =u( ,Z9 %<3 2 DF=C3 e, 5X%
:
:;OOG
&=0
=CH
G
B’395
53
O
S%
!"#
x( OO9 % : % : 5 )2C: % : = e, 5
=<77A<
I =”= y 8 OL: =C72?A=CBšDF= , ?=C7|HM= : =<7
:
B
BE=
5
L
( = e, 5 O H;?'( , ML7N795o%47BE5A79BQ%47
:
$ =<3 3
· (¡8 O BG= 2`G = O': 5A? OL:;Ok: =
!MŸ! E8 |
O
—
3
O
H
:
=(L= 9CO %
BE58J=
=
:
, (¡8§%
3N57
BE58J=
=C7
:
5
:
e,
=
:
8
5…=<7=
=(L= C
9 O % 2 =E— %('
5'(g4
% 8 OO& %<BE5AHI8J5©%<=
=
:
,
—
O
( OO . %
B
%Ž5A7j8 O Bk%)H
I<=ŽDt=<3eBkMLH
, k
% =C7 T < VF8 B =CHI8 ,;:
y 8 Ok: =<7 &PO ‰
% 3N5D;3N57N5H08C% : =GH;=
BG=
2 ?=CHI8 O H , C%
2#e, 5¶(L5 & = , %ŽD O =C3N57
=
% ?5AHI8J5¶% 5A7j8§%
2 =†BE= : 5'(k= y %<795…7 ,3yn4 <
5
(L=U5
% 8 O;& = 8
:
& ==( , ? O =CH • 3 O =+%)L( 8N5A39Hj4
=¶%
% 31% 4 <
% H;5'(g% : 5 &PO 7 O/y;O ( Ok: % : 5k%<=
4x, 7j8§<
3
:
=C7
:
2 G = OT: 5A? Ok:;OL:
& %)(k=<3 : 5r‘U x !>Z2, B & %)(L=C3K3A% . = •¿& 5
(TDj%43C%Dt53NB O 8 O 3 en, 5r= BE= : 5
(k=…?A=CH;7 O/9 % , BQ%@3 • D Ok: %
%<D;395AH :MO/. % 9 5ABl?=CBl3N5? , 397N=p% , Bl?A=CH 4x, HI8J= : 5KDj% : 3AP
h 5A7 : 5>8N3N5 O H;= : 5 & 5A3C%47”7 OO9 H O;t ?%48 OO& = 7 5 8:938O2
Dj%<3A%
%
, B DM3N=P?A5A797C% : =C31$|5AHI8 O/, B
[
".)2 5798J5 & %)(L=C3w(L5 & % % e , 5u5AB ?
% : %7N5 9=, H : =„795
5
% D;39= DfO BQ% : <
% BG5HI8J5 b>UO 8N5A3A%)H
P
h 5A7 : =k%)( 9 =C3 O 8JBE= P P
š5 º6[: =k%)( 9 =C3 O 8JBE=K5 & ==( , ? O;*
D 5? , 8N5AB <
^
D;3N=P?A57N7N=
:;O
H
B
O
?A=
F> 8
¹O H3%)(kBE5AHI8J5 2 H;= e, 5 :;OO. 395A7NDF5 O 8J= %<=K395 9CO 798N= : =<7 & %)(L=C3N57 : 5pD;395 &PO 7AI<= 2G = O : 5? Ok:MOk: =?A=CHI8C% y;O;*
( OO. %<3 5A798N5A7"<
% DF5AHj%<7%<= t B : 5>Π>Im=2 Dj%43C% 9 %<3A%<HI8 O 3 en, 5 ] % 4 %U8N5ABEDt=
7 ,Zt ? O 5AHI8J5Dj%<3A%r%1% t Hj%)H
I<=
H
? %)(
5u?%
% , B : =C7UBE= : 5
(L=C7 e, 5u5A7j8 • %@7N53E= yn4 5A?€8J= : 5e5A7j8 ,;: = 8 o 797 O B 2 = Dt53AML= : = : %
O
O O
:
:
=CH
•
i
e, %
BE=C7
O
3
O
=
% & %)( O %)HI<=
`
>
DM3N5
%VD;395 P
& O 7AI<=e5AB’8J5ABEDF=V3N5
%)(DF5A3 :3, 3C%s%<=p(L=CH 9
h 5A7Dj%<3A%1%U7 0 3 O 5 :;<>= 5 a>> Dj%<3A%r%
7 0 3 O
& O 7AP
P
5
:
C%
=C7•395A798 <HI8J57
c8
!>>Im=2
H
,
C%)(
B’8J=<8
:
5
‘’ƒŒn“œ/…†"Œ
z|{$#{
q
=
:
I =KBE5AH;? O =CH3% : =C75AB 5D3M 9 3A% G 5 G =C3C%4B_8J5798§% : =C7 H3%>D;395 &PO 7AI<= : %47 :3, %<7
& O 7A<
P
7
0 3 O 5A7 5BŠ8J5BGDF=K395%)( 8 $%43C%>?
% : %BG= : 5
(L= O H;79D O 3A% : =Hj%K@"%48 , 395 . % 2nG =<3C%<B 5 en, %<? O =CHj% : =<7'8N3 O HI8C%
h 5A7 >F2 D3<
% 3C%r%<797N5 9), 3C%<3 , Bk%UBQ% O =C3395
(L5 &Ni H;? O %5A7j8§%48AMk7j8 O ?
% 8
7Lº6> ?%<79=C7Dj%<3A%
5798 ,;: = 7 O¦8 5 8;2 7 O B , (/%)H
P
7'8N3
7
BE=
:
'(
5 k=C7
:
5”D;395
CM , L( = : 5ABE=CH;798N3C%48 OO& = 2 , BQ%w%8J5AHZHI<=U57NDF5A? O %)(F7N5A3 •: 5 & =<8§% : % J 7 0 3 O 5 :;<>=2 %48N3C% &=0 7 : %
%<H • ( O 795 : <
% 7+·Z(L8 O BQ%47K? O H e, 5AHI8C% 7L[6> D;395 &PO 7xhf57U5AB 8N5ABEDt=395%)( 2 ?A=CH;7 Ok: 53C%<H : = =C7U3N57 , (¡8§% : =<7
=
% 7
y 8 Ok: =<7+Dt=<3•BG5 O = : 5 , BD;3N=P?A57N7C% : =C3 ŸF® ¡ ˜ —n¯ Š%
[
".f7šG =<3C%<B , 8 O ( OO. % : %47#%<DF5AHj%47 4
·3¡( 8 O Bk<
% 7 ? O H en, 5AHI8§% 7¦[6> D;3N5 &fO 7AP
h 5A7)Dj<
% 3A% G 4
% ? O ( O 8C<
% 3-%+L( 5 O 8 , 3C% : =C7 : % : =C7 >F8
o
8 ¡8
ghByDM3
O
BE5
O
( ,39 %<3 2
3N=
AI
7N5A3 <=K5
DfO/y;OL:
=C7'=C7
395A7
, (L8C%
:
j%<3A%=>B 0
=C7'D
8J=
:
=
:
5
T <
7«¹O/9), 3C% [ 8 6=>F8 Y %
¿a
` f`
10000
kobe-r
AE
8000
6000
4000
2000
0
-2000
-4000
-6000
-8000
950
955
960
965
¹O/9), 3C% [ 8 6l %)(L=C3N57T3N5
%
tj9=, C3 %
:
5AD;395A5H
:
5
0 8J= : = : 5 T < ,
q 3C% 2 8§%N(%4?A=CHI8J5?A5
B
j%<3A%UD;3N5 &fO C7 I<=
D
:
*
7N5
8
O
en, 5G5 M
D O 798N5 ,
( OO. %K= & %)k( =<3 : =
e,
Dt=C3
§%
5798 7
0
5
3
795
5
O
980
&PO x7 hf57 &PO % T <
985
990
j%<3A%1%U7 0
D
3
O
995
1000
:;<>=n8
5
% 7C%<BE5AHI8J=65AHI8J3951%<B y %<7%<7"? , 3 & %<7 2 = ,
G4
H;7j8§%<HI8N5•Dj%<7N7A%
=EDj%<3A%D;3N5
% (k=C3 7N5 9),;O HI8J5 l:
& 5A3)= & )
5
% 3 e, 5 7N5 8N=C3NH3p
% H O 8 Ok: %<BG5HI8J5 O H3% :
, BšB 0 8J= : =( O HM5<
H
O
A% §%
975
7T5"D;395
O
3ML8
B
8J3 48
970
:
Ok:
=
:
5A7
7N5
4 % 2
=
-F8
x
5
e, %
=
:
8
jI<=6?A=CH & 5AH;? O =CHj% O 7 2 ?=CBE=
DF=
5
795A3
:
& 53 OOt ?% : =6Hj%<7 ¹OO9=, 3C%47 [8 ³ 5 [8 bZ8 o en,MO¦2 =CDM8N= , * 795
Dt=C3"57N?A=)( ] 53= & %)(k=<3+B 0 :;O = : %47
8J3 HI8§%
% B y <
% 7<
% 7h7 O 8 , %NH
hP5A7 2 •
% ? , 3 & %
O
7Ǽ>6> 7 O B , (/%)H
hP5A7 2 Dj%<3A%²%"395AD;395A795AHI8§%)H
I<= : %<7D;3N5 &PO 7AhP5A7 8 ghBŽ<
5DM3N5
% 7 0 3 O 5 2 3N5 & 5
(/<
% H : = , BQ% y =6%Q% : <
% DM8C%)HI4=
:
&PO 7CI<=V5H;?A=<H08N3C% * 7N5UD;3 ¼DMO BQ% : =C7 & %N(k=C395A7”395% O 7 : G
gh798J5G8
j%<3j8J5
DF=C3TD
DF=
O
:
:
C%
H I<=…=f?=C3N395?A=<B
4A• j
5?A=<BGDF=C398 <BE5AHI8J=
=C7BE=
'(
5 k=C7
:
5"D;3N5
:
:
'(
5 k=C7H
&fO C7 I<=
5B.8J5BGDF=
3N5%N( 8
% 7BQ% O 7 G %<? O (LBG5H08N5”Hj% ¹OO9=, 3C%
& O 7CI4=E7AI<= P
P
& O 7 , %)( OO. % : 4
% BE= : 5
(k=„?A=<H08N5ABED3(g% : = 8‰Y 5
[8¡` Z2Ue, 5 : 5A7N?3N5 & 5 =C753N39=C7 : 5…D;3N5 f
& O 7CI<=´% y 7N=)( , 8N=C7 2 Dj%43C%†?
% : †
G %<?€8J= 2 %U? , 3 & % e, 5 : 57N?A395 & 5K=C75A393N=C7)= y 8 Ok: =<7 &fO % T < ?A=<H08 0 B , Bk%r%<BED3( O 8 ,;: 5”?A=CB , B & %)(k=C3
5
(L5
% D;395 &PO 7A<
I =VDF5A3 G 5 O 8C% >F8 ghBs?=CBGD3%<3C%)H
I<= 2
& % : = 2 y 5AB :;O 7j8§%<HI8J5 : =V5 O;D = . 53N= 7šen, 5 : 5AH;=48§% , Bk
=C7 BG=
5
L
( =C7 O H;79D O 3A% : =C7'Hj%K@"4
% 8 , 3N5 . %+<
% D;395A7N5HI8§<
% B & %)k( =C395A7 : 5+53N3N=K7 O/9 H OOt ?
4
% 8 O;& <
% BG5HI8J5BG5H;=C395A7 8
:
o
7
;G
:;O
3H%47)5HI8J3N5"=C7TB 0
=<7KBE=
5A3N5H
8N=
?
$%<3A%s% & 5A3 O/9=, %43•7N5U=C7•395A7 , (L8§%
=V3N5
%)(
%<3)8J= : =e=u?A=CH 4x, H08N=
OL:;Ok:
OO.
H;=r8
O
DF=
:
C%
5D;39=f?5A797
:
=<3
2
795AH
:
=C7
:
5"D;3N5
:
, §8 %4? O =<Hj%)( :;O 79Dt=CHZM & 5'( 2 G =
5U7 B
:
O
, (g%NH
hP5A7+5Bs8J3 7•?=CBGD , §8 % : =C3N57 2ƒe, 51%<DF5AHj%<7 :MOOG
=…=@D;3 BG5 39=
% º6[ ".N2 Dj<
% 3A% %)( 0 B : 5
O
O
, B $|5AHI8 O/, B
:
=C7
:
5Dt5H
:
5AB
:
=uDt=
:
5A3•?=CBED
*
5
O:
5A395AB
:
=
O
7
œa=a
`
10000
kobe-r
AGE
8000
6000
4000
2000
0
-2000
-4000
-6000
-8000
950
955
960
¹O
[ ³l 965
3
k=C395A7T395
O
970
7T5DM3N5
O
975
980
Ah
7 P5A7
O
U=
T 985
990
995
! "
D
<3
U7 3
:;<>=?#
5
O
1000
10000
kobe-r
RNU
8000
6000
4000
2000
0
-2000
-4000
-6000
-8000
950
¹O
3
955
$[ Zl %
960
“b
965
&
k=C395A7T3N5
O
970
7T5"D;395
O
975
xh
!
7 f57
O
980
PSR$#
985
990
' ! "
D
<3
U7 3
O
995
5
1000
:;<>=?#
¿a)º
`
8000
RNU
AGE
AE
6000
4000
2000
0
-2000
-4000
-6000
950
[ ¹O
3
|5HI8
O
B
Zl ¡`
L=C3N57
955
960
5
:
5A393N=”D
[ y
965
<3
<7
xM
,
|5H08
3N5
5
5A395 795
395ADF=C398 e=
„B
5?5A398N=C7+?
H
O
?
:;O
<=
<3j8
m
O
?
<3
4D;3N=
:
L=C3N57
O
8
B
3 <=
<7TB
|£ žnŸF®
?
O
O
O
? L=C7”7 <=V5 M5?
O
=C78N5A798N5A7ED
D
€8J3
ƒ79=
:
5
:
8N3
:
HI8J5
O
3N=<7
:
O
B
O
&
? <7
O
=C7
:
B
]
=
B
995
1000
' "
xh
7 f575AB
O
990
8J5BGDF=”395
0D
43
p7 A3
:;<>=#
5
O
C5 k=P?
7j8J5AB
=
OL:
:;O
5A395AHI8J57)?=CBED
º6[>
] [>
] ] b=º=º>
8
=C3N57
:
,
Z
[P`œa<\²b
[P`œ<
a \²b
a)!
[ C\²b
&  ¤¯+˜ °
•)e# ' (' ˜ ®j—)± e#
-
" j• ' 0 &
;<1 ŽW /2 3 a> Fd 5E?
:
=C39H;5A?
B
:
‰=<Dt53 48
=C7•DF5 L=D;39=f?5A797
3N5
57N5ABEDF5AH
5
:
:
=
:
H
;O
C=
=CHI8
D;39=f?5A797
5798 VB
o
=<3
:
D;3N=
=
M:
3 <B
797
O
o
47
56BG5
=<3
=C7UDF5 L=
Ok:
O
<7•B
:
=
Z
H
5
:
€8J3
B
?=
C5 k=P?
O
?
O+:
=
Ok:MOk:
C53
5r?A=CB
:
<DF5AH
:
5?
Ok:
47
B
=CDM8 43
:
M`
7
'5e5AB
? <7
O
– ™œ›n R —¯ ½F£ ˜¦¥ –
O
8
|5H08
@DF5 L=‰7
:
985
¡`
! O
O
5A7N5BGDF5AH
:
|5H08
y & [ a
#" %$
" & &
& *) ,+ &
e#
&!./) /+ y ]
' *)
'
" & l
o
43 <?€8J5A3 k7j8
L`
980
5A395AHI8J57D;395
5
b
& $[ =l 5
:;O
975
y & [ =º=º 5
970
\
oR e#
5>BE5
:
5
C5 k=P?
OL:
:
5
:
5"D;39=f?5A7N7 <BE5AHI8J=
4 8
O
O
<H
:
=
%5"
œa
`
y
& [ alY
5
m
P ŸAžnŸ R ŸF— £ ¤® –)ª
gh798N5A7
H
O
£ ˜¦Ÿ £
&
B
•
7p3
O
q
D
OL:
5
H
L8
5
<3
HI8J5A7
:
5
8J53NBE=C7
D;3N=P?
Y
7
<3
M‡
<3
UB
O
<75
BGD
O
5K395
%
53
O
a
³ 7 6)a
& 8
O
8
O
4H
O
H
5
:
5AHM=<8 <B
:;O
D
B
:;O
5A395AHI8J57pBE=
] 3N5
F=<H
H
\
:
'
=<7UD
:
5
<3
:;O
i
BG5€8J3N=<7
7N?A3958
4
O
./)<=
:
0
Cb
`
X
=
"
T
5
8
¡`
=C3 <B
48N3
7
5
Ok:
5
:
H;79D
7
O
B
=
5
<5
B
3
=C7)H
48
5
5
:
%('1),+32 /
=
:
H
M=CH
' !.'h O
5A7
;O
5
:
8
5•=
3N5
I8J395
O
HM=
& )
7 4=E5B.8J5BGDF=
3N5
:
j`!
X
O
<7
:
5
f57
:
P 5
:
5KD;3N=P?A57N7
:
<BE5AHI8J5
O
5
5”?=CBGD
:
[4b>Lº [6=a ¦
a »³ L
a ` =³0 ` ` =³0 ` »º
8
\
7
' y & [ º
O
O
8JBE=
=C7H
Lº> O
:
U:
& "
O
=C7
:
6 j`¿º
`C`
<5 L=
OL:
:
j`¿º
bM`
B
O
Ok:
5"D;3N5
º Lº
»³6
`
./)<=
:
6)º 0¦[$ &
=C3
f5AB8N5A39BG=C7
HI8
O
7
<?
C5 L=f?
B
8N=
B
& "
5T8J3
:
"795+3N57
5 k=<7
:
5
O
O
5 "
&
"
/+
& #e ! •)e# :
B
<3 =C7”B
º6a!<b $b=º º6>
a 6N³ $b=º º6a)!
³
$b=º
` b=0
º j`¿º76 ` b=0
º j`¿
º 76 ` b=0
º j`¿
º 76 5
:
7 <=
5ABy8J5BGDF=U3N5
•)e#;O
O
<7
k=<3N5A7T395
==
5p? <D
:
%
=
:
:
<D;39=
<7T5H;?A=<H08N3 <B
:
O
5A395AH
H
;O
)
e$ ! " B
<H
O
8J53NBE=C7
:MO
=u5A7j8 e?A53N?
:
3
:
O
5
<7
@5798
=C7+DF5
:
5•DM3N5
L=C3N57
:
=C3N57
:
4 k5A7
<BE5AHI8N=C7 f5AB
5?8
:
3 G5B
' D
H;=
7
O
º )
³ º
º=³6=[
6)³=³
³ =ºCb
B.8N3N5
8
PR
5DM3N=P?A5A797 <BE5AHI8N=
:
?
O
F7N5H
H;?
H
4=E5HI8J3N5"=C7
:
H
l
m
5
:
<=C7
' !./)
=CBED
:;<=
<3
`
5A7
:
O
=C7T5A393N=C7
:
O
O
C=<7
F7
,+
[ ȼZl
=C3
k=C395A7
5
' B
O
k5HI8J5A7
;O
5
D
57
OL:
5+=C7
<75 MDF5A3
:
'
5B–D
PR$# ghB
e$
MO
VB
y
<5 k=P?
<B
:
%
=C7
:
<7
B
:
=
53 <B=C7
'
?=
3NB
C5 kBE5AHI8J5U5
Ok:
t
D;3N=P?A57N7
:
),+32 / O
:
7T3N5A7
7N5•?=CH;7
'
5+?
:
&
5
PSR =C395A7'?A=CH
:
./)4= *7 )<=V7N5H;7
BE5AHI8J=
œ[
`cb=³
¿³ :
`
`
5A395AHI8J57p?=CBED
oR
¤¯+˜ ° V
>>
5BE5
:MO
e#
3
& .&
$e % Ot & e# •)e# "
e$ !
•)e# ' º> ?
:;O
e$
=<7
:
b
?¤—

=
º6[
m
]
57N5BGDF5AH
<7>8N3
L`
7U?=CH
<BE=C798N3 <7?A=<B
t'
.'h
!
'
3
BlD
f57
<797N=
m
M‡ Iˆ
m
M‡
e#
=
•)e#;O
H
' !
•)e#;O
H
<3
D
B
<3
O
=CHI8
' !
D
5p?A3
B
' .
By57ND
=C73N57
=
M:
A=
'
'
=C7
:
¿a=[
`
\
5
5pD;3N=P?
:
¡8
>fŸ>>
3 >?=CB
e#
5ABE=CH;798N3 <B
:
5G=
>>
5
.'hf57
7N=
BE5AHI8N=
!.
' =65A7ND
:
798
:;O
A=
HI8 <7 03N5A79Dt5?8
O
5D;39=f?
:
%
:;O
|5
8
.
53N5AH
<H
<=
;=
D;395
5798 ED
:
5AH
:
H
8
;:
H
=C7=
:
5AB
=
8
FHM=GD;3
M‡
5
k5AHI8
t=
x
Œ
5
O
H
D
BG5H08N=
‡
x
M‡
798J5
O
B
GBG5
5A3?A=CBED
O
:
)5A798N5
5
:
M:
>>"
5
:
5
:
=…7N5VB
:
=CH
O
AOL:
=V53N3N=
:
<H
8 <?
<5 k=
BE5AHI8N=
=C3
53
:
3N5
<=
"
& 7
O
f‡
5
:
5+?A=CBED
UB
=
:
795
:
f‡
<3
=GDF=
:
5
H
57N5BGDF5AH
:
B
53
:
;O
<=U?A=C393N57NDF=CH
a5
;O
GB
=
:
4H08
5+=DF=
?A=<B
4=
O
7 4=EH
O
œ7N5
=<7
Ok:
M‡
5"D;3N5
:
…B
:
=•?A=CB
:
7h=C7
=C7
:
H;7j8 <HI8J57
O
f57p7
O
5A3
:
8
<3
f‡
3N=U? 47N=E=
O
<3
5UDt=
O
7 A3
M:
<D
4D;3N57N5AHI8 <B
C‡
<3
<?=C3
:
?
B
5
:
=C7|5A798 <=
4798 4H08N5
5
O
5
?
D
BE5
=G? <7N=
:
OL:
k=
=C7)=
:
p=E5AHI8 <HI8N=
5•5
=…7N5VB
:
L8
<8
:
43 U=
?A=CBED;3N=
=C7p3N5A7
:
5
<H
k=C395A7TD
5
=C7
:
=C7
H
5
:
¡8
|=C3”5 f5ABED
5"H;=E7N5
x
Ok:
7 4=
O
=C7
:
=U5ABy8J53NBE=C7
OL:
=CHI8
?A=<B’=<7
‡
O
=C395A73N57
=CH
O
<3
:MO
:
<D;3N57N5H08
53
L8
5"D;3N5
5AHI8J395
8 <?
7h3N5A7
5
Œ
5AH;?
O
5
:
=C7
:
<7
<HI8J=
<D;395AH
:
:
BG5H08N=
=
7 <=
O
=C75A3N39=C7
3=C7)BG5
O
53”?=CBGD
:
C5
=C7
:
<5
:
<3 ”=+? <7N=
DF=
7N5
79Dt=<H
:;O
? 47N=
<=
H
O
D;3N=
D
<7
)<=…795G8N3
3 rH
&
) %
"
'
)+ 2 /
• ' y [ º
%5" e$
./)
& 8
e# 3
•)e# ' y
]
]
% !./)
"
' &
PSR #`V ȼ % e#
$ 5
) )
y
t • #+ ' " :;<= #+
] *)
a e#
e# •)e# ' e# e# ' ' "
& "
e$ e#
>" q
)
' ¹ [ y
" y $ ¼
)
4 •
% !.'h
T V e#
º a % e#
#+ > e$
•
4 ' &
&
)
y
"
e# l
5AB
<BE5AHI8J5
O
DF5A3
7N53+5 fD
H
O
?
O
O
=CHI8
B
53N5AHI8N5A7
BE=
C=CH
=
;:
5
`
=eDt=<3
:
3
O
7
O
=C3N57
O
?
O
=C7H
:
5
:
P5A7j8J5)?A5AH
t8
¡`
<D;395AH
+D;3N=
3
5
ˆf‡
7
O
:
<="=f?=C3N395
x
C‡
5ABsB
:MO
=H
O
)
3N57N7 4=
M‡
L5AHI8 VHM5A798N5
? 47N=
=CBED
8
B
<3 4H
œ7N5
m
==C7
:
"
=@B
8N=
%
=
:
D
43
'
H
O
),+
T7N5
?
O
+795A3
H
¼ +
D;3
:
5
:
¡8J3 <D
m
8
=C7DF5 L=C7
Ok:
BE=
O
e#
5
:
"
7 A3
]
:;O
?
5A7
O
<797
y
5AB
:
.
<7
:
5
<7GDt5
;O
5 L=C7
:
5)D;3N5
:
& 7 <=>5ABŠ8N5ABEDt=3N5
O
<7
:
O
<3
]
•)e# '
UB
3
:MO
&
.
5A395AH
<7
]
=<3
;O
BG=<7 ;795AH
5A795ABEDt5H
:
=
:
3
O
H;?
O
:
T7 3
48
O
H
O
5 +f?A5ADf8J=
,
3N5
& ] e$ BE5
?A=CHI8
5
B
F\
B
:;<>=? ?A=CB
H;5 <3
O
5"7N55A79Dt53 <3
:
"
:
=C7H
:
)<=
5H
O
<D;395A795AHI8
5h8J5AH
:
@7 A3
T
5
:
O
"
=C3
<H
7
O
=
:
<H
& Ot
H
O
? 48
O
O
4HM=)5HI8 <HI8J=
=•?=CBGD
:
<3
=
:
5
¼ +
8N=
H;7ND
O
*)
7 <=
O
?A=CBE=
7N5A3
"
=)B
5 L=C7
:
H
)
53N5H
UB
=C3 D
=C3j8J5h?A=<BGDF=CH;5H08N5
=”Dt5 k=C7BE=
:
43 …D;395
"
=C7
:
<D;395A7N5HI8 <Bl=EBG5
5A7T5798 4=GD;3
& O
:;O
' =D
:
5
O
=
Ok:
:
PSR$#ƒV
<7
7 3
:
?=CBi=
#+
" '
T
5
:
5
:
5 fD
5 fD
=C7'=
:
' " $ #+ &
' •)e# ' F\
T m
7
L8
5
L=C3
o
395A7
=
:
:
5
y
=
:
H
;=<7TBG=
& ]
5BiBE5
=<7”BE=
<D;3N5H
]
5A795ABEDt5H
:
5 k=C7
:
&
:;O
&
5B
H;7ND
:
O
5 C=
e#
=C7
:
3
:
ED;395
5 L=C7
:
=C3N57
O
=H
?
O
5=C7=
•
=CH
y
' =C7)H
5A798N5A7
*)
&
7 <=E5AB.8N5ABEDt=
3N5
O
48
<D;3N5H
8
3
=C7
O
<D;3N57N5H08N5AB
&
"
=C7TDF5 L=UB
OL:
395
&
:;O
%
5
:
GDF=
5B
:
€8J=
)
y
<B
47
L=C3N57
:
=
3
:
5
e#
T
'
53 <=G7N53 F5AB–D
:
=C7
T V
"
@B
47
5
!
<3j8J5
O
7
œa!
`
! .3)
k5HI8
4DM8
:
<=
BG5
f?A=CH =
O
5A?
:
U=C3
?
7
398 47
798N5AB
O
O
]
'
ghBlD
e#
?
O
5A?8
e#
y
5BQ7N5
57N5A35
=
#+
5?8
C=
O
L=
H
=CH
&
H
O
ȼ a$
B
B
]
& '
BG5
=<3)? <D
<?
3
O
=<7H
:
8
8J5BGDF=…395
5A7j8J5
5"7
¡8
5
:
5
:
) =
:
5
:
D;3N5
C5A397N=C78
:;O
Dt=<7
O
t8N5AB
5"D;3N5
:
!
HI8J5
;O
)
M8J5H
7 <=
O
5+7N53
:
|=<3r?=CH;795
7 4=
O
e$
3 <HI8J5+=
:
k=
<7
:
3
=
|348 5 "œ7N5
5
:
5>795>395A?A=<3N3N5
B
8
Dt=
O
DF=C798N5A3
o
O
8
3 <7
8J5BGDF=C3
O
57
H;=
:;O
=C3
7N?
:;O
3N7N=
?A=<BGD
<D
8
<795
H
5
O
BE5
O
rH
:MO
O
5
DF5 k=<7
7 <=
>H
¡8
P5A7
43
:
798
O
5E?A=<3N3N5?
:
rD;3N5
O
=
:
=<7
'
<=
=C7>D
:
65
O
O
?
?
<=G7N5
?
:
5
B
<3
5+5H
<=
<5
<75€8 <D
:
5AHI8J39=
:
5
:
=E5ABl?A=<H08
:
*)
7 <=
O
i
<3
·M8
5 C53 <7
:
BG5€8J39=C7
=@7
:
7
O
5AB
O
798N5AB
O
& rBE=
O
8N5A?8
;O
5G=
47
3
5+?=CH;798N3
:
<=
)
o
&
DF5AH
=UBE=
:
"
H;7
O
7 <=r5AB
O
5
:
5GD;3N5
:
&
5 k=<7
:
<7
5 k=
:
H;?
O
O
GD;3N=CDF=C39?
5
=uB
5798J5
<BiD;3
<DF5AH
7
O
O
BED
?
O
O
7
=
5?
O:
48J3
:
47HM=6D;39=f?5A797N=
8N=C7+8J5BGDF=C3
<7V?A=<B
O
z7N5AH
B
=
:
8
<7'7 3
:
O
47e7 A3
:
B
G=<DM8
395 C5
5VD;395
BG5
O
=
5
:
<DM3N5AH
=
OL:;Ok:
=rH
4 ./)
& 8
:
5
:
;BG53N=
B
<=
O
<3
4H;5
5
:
O
5AB
:;O
=CDM8 43
:
:
A7
:
=C7
:
5
:
<=
O
O
57 ”=<3
O
O
O
57
<7
:
<7
:
8N3
=C3 4B
=VBE=
:
H
O
7B
5
:
:
H
=<78N3
Ok:
53N5AHI8N5A7
:;O
;O
5 k=
—
:
5
—
H
47?=CB
7
BE=
H
? 4D
5 k=<7
:
C53N7N=<7
O
<?
OL:
F5KH;=<7”BE=
O
57
:
5pDM3N5
:
5
:
5
:
) 7 <=
O
5 k=C7
:
47
=<7
H;5 <3
7
395
5G395
:
FH
œ7N5
;O
8
k5B
8J5BGDF=p395
5
:
=C7H
:
H;798 <HI8J5
<3 "?
Ok:
3
O
5
:
O
=C7TDF5
8
O
:
5
:
=
=<7395
:
7 <=p5B
:
OL:
=
8J=<B
<BE=C798N3 <7T8J5BGDF=C3
7 4=…5ABQ8N5ABEDt=r3N5
O
6D;39=CDF=C798
= 795G=rD;3N=
:
<B
HI8 47
€8J=
8
O
L=C7 =
P:
H;7ND
O
:
<7u5 MDF5A3
:
:
C53
<=
2?
7T5Bi?
O
=C3NH;5?
=C3 E5798 H
D;395
5 k=C7
:
5AHI8J39=
:
D;395
H;5 <3N57
=C3
5AB
<3
<=
73N57
BE=
Ok:
5?8
=C7+H;=GB
:
<=
C5
7B
5
O
=H;5A7j8J5+8N3
:
5
:
7 <=
=<7
<HI8N5
O
79Dt=CH
=C3 <B
8
=
O
47 ?A5AHI8N3 <H
u=
:
53
O
:
=
:
Ok:
=C3D;395
<=
5
5A7j8 u7N5
8J395
?A=CH;7
O
?=CH;798N3
5E5A7j8J3
:
=
L=
5
:
=
:
5
Oh:
<?
5
:
5
D;395
:
.
h
3.3)
• y
)
e#
° £C½F¾ ° £ ¿¥§Ÿ V§V – ¯QŸF® ¡ 
3
y % ] e# # '
]
=
:
¡ ŸF¯°j £ Ÿ –)ª e$
H
O
<3 r8
5V5H
BG=
O
395
Ok:
`
5”8N5ABEDt=
:
€8J=
OL:
8J=C7
58N5A3NB
L8
8
7
B
<H
=
:
"
B
° £ Ÿ ¨ ˜ V ›npŸF¯
:
# 3 e
=
:
5A798N5? <D
:
EH;5?A57N7
O
5
:
47
:
&
] 3
O
=C7=
:
PSR$#ƒV
47
./)<=
Eqf5A?
=DF5 L=Dt53 L=
OL:
"œ7N5
5
H
7j8
O
'
=
H
OL:
Ž5A79?A=
5•5
:
<3 M8J5B
5?A=<H08N3N=
:
=
:
t
5
:
5A3
& #e ? <3
:;O
!K
=CHI8J578N5ABEDt=<3
O
5
5A?8 <H
H
O
% ° £ Ÿ ¨ ˜ V ›n
y ¼
·
.3)
*) ' Ot & " .3)
"
'
t + 3
y 4 y e#
e#
& ! ] @ – ® Ÿ ª;– žnŸ ¨ ˜ V ˜A
˜ ª ˜«ž – žnŸ e$
·
¹
,+
" 3 '
*
)
'
'
4
•)e#
" 3 &
!.3)
t
"
%('
T V y T '
& !.3)
) ! &
& PR$#`V q
e# y
& ] ' t • *) e# )
' ' y *) ;t 5 " e#
"
' "
T "
t & ]
" ) & q ]
' PSR #`V y e#
& T V
3
•)e# ' • ¼ +
D
q
4
=<3
<398
<7
B
4 !./)<=UDF=
4H
5A3N5HI8J5A7
:;O
*) 7 <=
O
"
5AB
:
=C3NBE5•3N5
2!
B
ABlDF=
s
B
"
y
8 <B
 £ ˜ ¤¤® ¡ Ÿ ¡ ŸF¯°j £ –)ª
8
<=
J
q
p=G5AHI8 <HI8N=
O
=C3
<B
5+D
7 <=
<H
O
=<H
:
€8J=
<3 K=<7
=7N5
:
=
:
<H
5
57N5BGDF5AH
BG=<7 ;H;=E? 47N=
O
:
UB
5 k=C7
H;7ND
O
3
O
D
?
DM3
43
;O
:
=G7N5?=CBED
:
H;5
O
=
:
BG5H08 …=@DF=
‚
G5798N5
:
BE=
O
HM?
H
<7
B
:
73
H
<3 4Bi=C7
O
48
5A3?=CBGD
D
8 <?
:MO
kBE5AHI8J5>D
a5AB
O
=C7
D
OL:
3N5
O
=CH
:;O
5A395AHI8J57”BE=
<3
=C3 G=C7p3N57
K=P?A=<3N3N5
e7 A3
¡8
:
O
5
79Dt=CH
&
B
C5
5 k=<7
:
:
5
:;<>= =<7+=
y
8
Ok:
=C7
! "!#!$
%
o
47N?
5AHM?A5
O
2
*( 5( 32 89 ;: :;O
7N?= <5A3
8
7
O
H;?A395 <795A7
O
7
'& )( *(
1 32 7?=CH;?5A3NHM5
O
O
O
B
:
<H
]7
O
2
8 •8 ;5h3N5
O
8 8N=E?=CHI8J39=
O
8
2
48
+(
=CH;7
O
8 >8J=D;3N5
76
)(
?€8
:;O
-4 ?
795
<H
-,
5 t5A?€8
:
8 M5p?=CH;7N5
3N5"5 <5AHI8J7
D”=
O
(
5AH;?5A7=
.(
g
<? 7N?
O
7
<?8
?
O
=CHM7
O
0/
5H08
O
<H
:
58N5A3
395AH;?5
< Ÿ –)ª ˜ – ¾>= Ÿp@?Ÿ§¥  žn ¡«£ – A –)ª ŠžnŸ = ŸF® ¨  ª ¨ ˜«žn ¯QŸAž)˜ – ® ¡ Ÿk—¯ ° £ ¿¥§Ÿ =.=  žnŸ – ®A ª ˜ = Ÿ
ŸŠž)˜ = ¥F— =.= ›nužn =f£ Ÿ = — ª ¡ – žn = A ¡ ˜«žn = ª;– ® ™ – ® žn ¾>= Ÿ – ˜ ® ž – – = A – = Ÿ = ° – £ – ¡«£ – A –)ª 
?E— ¡ — £  o
¼
D
7
*)
ƒ?=CH;?
gh798N5>795A3
DF5A3N79Dt5?8
D FE
•
5
5?8
%
<H
O
7 <=
32 0(
=E5ABi8J53NBE=C7
:
'
;=
*M
:
2
3 P5A7
7
:
=
° £ Ÿ ¨ ˜ ›n
5
' '
5AH
3
<?5AHI8J57
7TD
<3 =
8J3
8
<3
3N=
5
:
C2
C=
B
3N=
)
?A=<BGD;395A5H;7 <=
5AB
o
<5
O
:
=•795
C=
C5K=5A7j8
5eBE=
:
=
Ok:
BEDt=<398
O
M3N5 <5K7
H;?
B
:
;:
O
=CH
5
:
8
O
!
H;=CDM7N5
O
4 =<3 †395
7N?
:;O
:
K(
=C7
:
O
$ • %'
7
<H
O
795
GD;3N5
TS>6
O
8
)
7 <=
:
O
O
H
43G=
O
.(
5? ;=
=
=C73N57
:
3
?A=<7
) HM?
?A=<B’=
¡8
O
:
5A7
:
D
:
=<7
:
:
=C7
!IH)4=•3
=ŽBE5A7NBE=
8
O
H
=<7T5
COk:
C5
L2
5A79?A=
:
:
5K7
:
$"
O
7j8J5AB
:
=C7
=<7
:
:
5
B
)<=
<7p5KH
3 #"795T?A=CH 57
QP ½F£ ˜¦Ÿ =
=
<797
F5A3j8
5?8 <3U=C7
' :
£ Ÿ ¨ ˜ ›nžnŸ
L=C3N57+D
<3 <7
8J=
MO
5
:
=?=CBGDF=C3j8 <BE5AHI8J=
5
<3 @D;3N=
%
H
O
HI8
O
' BG5HI8J=
O
7 <=
e795
<?A=<H08N5A?5TDt=C3
`
3
M5A?
F4 +4 DM3N5
:
O
5
:
¼
N(
7j8
<3>5A798N5u?A=CH
O
=C39B
E79=CBG5HI8J5
<BG5HI8J=
=
& =
5
7N5U3N5?A=C393N5
LBG5
"œ7N5H
M=)?5AHI8J39=
:
8
O2 B(
ŸF¯°j £ – ˜ = P R4 % /• & P O
gh798J5
:
5A795AH
:

D;39=f?5A7N79=
<?€8
;=
2
=C7UD
:
32 B(
'%
=ƒ8N3
:
=
8J3
:
GIH
G
J
3N=CHI8
:
=
TS)³
?A=<B
7
H
O
3
;O
,+
FM
47e?A=CBED
k5 f=C7
& :
.
<7395
P5A7
!
e7
:
57N5AH
:
798J5B
O
798
:;O
`
<=
=C7pD
Ok:
=
2
8J5H
' EBG5€8J=
P
7
H;?
:
k=
CO
O
5
E5
7 E79=
O
'± ¾
L2
5
U7
;395
7
O
8J=
O
5
:
<398
4 ' =CH
Ok:
5
:
<7N5
<BED
k=
H
)5AB
'
8J=C39H
'
H
O
<5AH;?
'
=CH
O
O
3 7
O
k?
:;O
=<3 <B
HI8N5A7
;O
58N5A39B
:
<BE5AHI8J5
#+
Ž5 P8J395AB
=C7•Dt=<3+?A=CH
:
"œ7N5"=C77N5
O
'
O
=C7?A=<BGDF=CH;5H08N5A7
:
"
”7 3
:
5
O
f5
= 4 F4 B
Q2'
57N5
:
5A7
;Oh:
5A798 <? 4B
:
57N5
ŸF® ¤˜ ®
3
? 43 +=CH
=<7
:
<3
/ 34 O
3
8N=
?
O
57NDF5A?
"
C5A397N=C7"B
:;O
gB.D
O
:
4798 4H08N5"D;3N5?
œ5
±'°j¤® ŸF® ¥F˜ –)ª
=
:
<3
ª ˜ = – ¯QŸF® ¡ 
?=CBG=
5 " '
5"?
BGDF=C3j8 <H;?
O
C5
BEDt=<7N7
O
T
L5
5
5795
"
H
5"7 3
:
<BE5AHI8 E5AB–BE=
:
57T8J5ABEDF=C3
O
%('
5 k=C7T—
:
t7N5H
—
=
:
7
O
P ( 4
2
2
/
C< = = 32 0(
• ' 3
& &
3
.3)
® ¡ Ÿ ª ˜ ® ¥F˜ – £E¡ ˜ |¥F˜ –)ª ¼
% ./) ' !./)
4 ' ŸAžnŸ
ŸF— £ ¤® – ˜
.3)
£F¡ ˜ |¥F˜ – ˜ ¤¯° — ¡ – ™œ›n ŸF® ½F¡ ˜¦¥ – Ÿ ¨  ª — ¥F˜¦¤® £ ˜ – . ' "
& " &
ghB
L8N5A3NH
48
"
<=<7B
O
4
8J=
=
8N3N=C7 ?A5A3j8J=C7eBE=
5 L=C7
:
H;53 C=<7N=•?A5HI8J3
;=
H;=6D;3N=P?A57N7N=
”5 C=
4=+H
<=
:
N4
$< ŸAžnŸ = ŸF— £ ¤® – ˜ =
478 A?H
:
? <7Dt=CD
O
&
ª
=C7
5
:
B
5 C=
o
2
B
)<=
H
B(
=
;2
O
M5A7Dt53NB
kH
:
B
O
5
:
Q·M8N5
57
:
HM5 <3 T7N5AH
O
<B
:
5 k=C7
:
3N7N=
A
k5B
FM
.
O
t=V5A7j8
O
=<7EH
:
<=
<3
0/
B
:
pBE=
C=
<3
C5AB–5B
DM3N=
"
=C3N57
:
<O
5
:
<DF5AH
5AH
€8
O
L5AB
<7
5A7j8
L8
4D
O
¥ £ —
5
:
4
k=
=
Ok:
:
<3
O
O
5
5A3 43
Ok:
<BE5AHI8J5
:
&
<H
O
=‰Dt=<3
:
5
4
.
5)7N5
– ¯QŸF®
S 8
7N5…Dt=C3G?A=CHM7
=
O
798N5AB
O
= <=
7j8 ƒ=C3
4H08N5
O
=
;:
< =
=<H
B.7N5AHI8
43
?A=CBE=
=C7
DF=C39BG5H;=C3HM=
O
5AHI8J395
53N3 <BG5HI8 <7
B
•5AB
?A=C7
#+
<3
=C7eHM=Ž7N5
Ok:
BE5AHI8J=C7 ;H;=CBE5
O
&
' =<H
O
?A=<7)?=CBE=V=V7
=<DM8J=
5 L=†?A=<H;5
B
;=
:
A £ ˜¦ = = L2 ' P5A7D
<=
5798J57pBE=
:
= < #= 5A7N5H
=
C=
<7
? <Bi?
:
5A795AH
:
O
3NB
)5A7j8J5@8J3
O
C=<7
O
5KD;39=f?5A7N79=C7
:
D
;O
5@BE5AHM?
=C7e795A3N57
:
=
;:
47?=CBE=
8J=<7e5AB
O
O
¨  ª — ¥F˜¦¤®
=CDt53
5A79?A3
:
‰5 C=
4?=CHI8J3
5>795
Ÿ
8
%
)<=
5D
L8J53 <H
¡
B
?A=CH
="=
:
¯+— ¡ – ™œ›n
5
4D;3N57N5AHI8 <B
<398N5
H08N=
' ) $#
4 ' "
.
4 ' "
"
4 .
& % &
º & ' ) ' O
5p79=
:
=EDF=C3T395A?
:
t=C75A798N5A7uBE=
56D;3N=CDM3
:
H
<=
4
=
ŸF® ½F¡ ˜¦¥§
!.3)
•Dt=CD
;O
=
 £ ˜ ¡ ¯Q
Ÿ=
7
O
# ®j˜«ž)˜ £ Ÿ§¥§¥F˜¦¤® – ˜
¥§¤® Ÿx±
3
<7 M?A=CB
:
3
5>DF5A397N=CH
<7
? <B
'
=<H
<?€8J=
48
5D;39=
<395A7
O
<B
:
”5
5395A7N=
:
C5AHM?
L2
5BE=
:
=C7
?=CH
:
BG=C7
p=
5AHI8J5
:
O
B
O
k=P?
k=P?
O
L8
<3
=
:
Ok:
:
5@D;3N5
=
4=ƒ3
8J39=
433 <D
O
8 <395
H;5A7
=C3K=
8N5
<D
=
7D
O
:
=
TD
43
=C7
<BE5AHI8N5•7N=
AB
FM
8
O
:
uD;3N=P?
:
7N5
5AB
L2
4DM8 <395AB
C4
B
55 L5
:
7
5@795
:
<B
O
P5A7
o
7 4=
O
3
<?
B
OL:
5
:
kBE5AHI8J5
O
L=
<D;395AH
hB
5
O
8 <H
L8
:
ƒB
/
O
=
5AB
:MO
4
<H
;:
DF=CHI8J=
? <33N5
47
=
H;7
:
5
5
7
k=
=<3 <B
D;39=CDt=<798J=<75A7j8J5A7
=
:
7
O
BG=
:
5 L=C7
L8N5A39H
48
O
C=C7
:
5•D;3N5
O
7 <=
MH
=<3NB
5
< $ #=
=
'
H
U5798
?A=<B
O
?=CB
B
B
./)<=
B
:
FM k– ¡ –)ª  A
˜ – = < Ÿ­° £ Ÿ = ŸF® ¡ – ™œ›n©žn = ž – žn ='= Ÿ —n® žn"! –)ª  £ Ÿ = < Ÿ – ˜ = < ! < = &
/
%('
¥ – ¯ – ž – ˜ ® ¡ Ÿ £ ¯ ½ ž)˜ –!
O
.
P5A7
:
5
5
=C7?=f5
?
O
5AHI8J57
:
5BE=
:
5 L=C7—
—
M5
4 8
O
O
<3
$ |=<3'=
8J=<7
H
Ok:
3 7
O
4 "795
32 ?=
O
7
&!./)
5
<D
= ¥§¤¯° ª Ÿx±=˜«ž – žnŸžn+¯Q
žnŸ ª  H
O
:
"
8
O
<H
O
= œ7N53N5A?=C3N3
:
:
=
Ok:
"795 $
:
=
3
O
5
4 !
P "
5
:
PD;39=f?5
P
<=
4
N4 "œ7N5K5BGD
&
5 k=C7
:
MOk:
'
5BG=CHM798J39=
:
=C7TBE=
:
M8J5H
?
O
5A798N5A7'BG=
:
B
/
5
:
/
5
:
5
2
U7
@4 t=CB?A3
2
8J=CB
•
3
5
:
L8N=VH
5798
B
O
5?
:
7
O
U7 A3
:
7?
L8
I4
<77
:
O
O
=
EBG=
O
FM
5B
:
<3
=
Ot:
:
/
5
=
=
H
DF=C798N5A3
8
.3)<=
B
5A7j8J3
"
O
H
MO
8
5"7 3
:
4
5KBE=
O
O
2
5A7?A=CB.?
O
:
O
5
&
"
7h5 L5ABE5AH
O
5 k=
:
f5
5
N(
5A795AH
:
' 4 5Dt5H
=<7)BE=
:
M=
:
3
&
-M
BE=
.
5K79=
:
./)<=
>5 <=
#"
?=CBGD
O
k5
5 L=C7D;39=CDt=<798J=<7
:
=C7
<7N795AHI8 4ByH
O
<B
O
UBG5
B
43
D
O
B
;=C3
O
O
5
?
H
8J=C7 5
O
& 5 L=C7
:
K?A=CHM7
f57
k=
5p8N=CDF=
:
k=
<7
<O
"
O
L8
<D
<D
C=
"
7
:
*)
f–
<7?A=CBE=
5
./)<=
2
5
:
7N5
7
O
5
:
47N7N=P?
(
<3 <7
<5
=<7
:
F4
)7N5
O
57
8
43 08J=CH
O
=
5
¥§¤® F¡«£ —™œ›nŠžnŸ©—n¯
3
5
#"
k5
7
798J5B
O
;5AH
5•Dt=<H08
– ™œ›n
¯Q
žnŸ ª 1° – £ –¶–
5
:
"
<78N5ABEDt=
O
( S >>
4
0/
P5AB
=
O
! $O
`
5B
:
O
p¨¤–)ª ˜«ž
—˜ ˜š™œ›n
•
H
U?=CBGD
H;?
O
O
=C3NBE5AHI8J5
O
<7N5
7j8
7 <=
O
?
=
7 <=U5ABy8J5ABEDF=3N5
O
2
'
C558 4D
£ Ÿ –)ª 48N3
5+D;395
:
k=
L8
55H
3
B
5798N5A7"Dt=<798J53
:
B
5"D;395
:
O
5
:
$
*) 4 ' 2
& )<=3
A?€8J3
5H08N5A7
O
P
hH
”5
<O
?
=CH
>3N5ADM3N5A795AHI8
<3
?
5
5AHM5A3
8N5A?€8
;O
7
5
:
B
!
• 5 k=C7TD
:
= /
Ÿ ¡– ¾
=u=C7•?A=P5
:
&
8
=C7TBE=
OL:
BE5AHI8J=
O
B
H;?
=C7=
:
5
:
.3)<=
P
=
:
:
5
5
8
:
<D
H;?
O
O
:
:
?
BG=
","
D;3
&!./)
O
Ok:
=
:
:
P
47
"
O
=<7
5
5V7
4
& :
<=
O
5 k=C7
:
<HI8
3 ”DF=C7N7
O
Ok:
¡ ŸF¯°j
$ƒ?=CH;798N3
<BE5AHI8N5
O
=<D
:
:;O
:
8
4=
5KD;39=f?
:
=C39H;5A?
4 !./) =C3
& %
5
^
O
=EBG=
:
4
P‘
:
B( /
£ Ÿ ¨ ˜ = ›n²ŸF¯ ¡ ŸF¯°j £ Ÿ –)ª 34
4 "
"
*4 '
M8
H
AO
° £ Ÿ ¨ ˜ ›n¶ŸF¯
32
H
=.= – ¯QŸF® ¡  4 ° £C½F¾ ° £ ¿¥§Ÿ
=
:
5A3
:
?
O
U7N5 k5?
5
7N5AH
—
C5
=C3 <B.=
°
? 4Bi?A=CBE=
?A=CBEDF=CH;5AHI8N5A7D;3
=C72795
:
+f=H
O
P5A7
OL:
5798 4=
HI8J5
5
:
3
=
?A=<BG=GBG=<8N=C3
O
5 L=C7)—
:
5
57N5•8N3
?A=<H;7
O
5
;O
&
B
O
!.
8
=
T=C3
k=
|=<3?A=CHM7N5
5
BE=
O
398 47 H
5?=CHI8J39=
:
5A3
5
:
5
":
" ·
3 '
)
5
:
B
O
B
O
|=C3
3
O
Ok:
5
:
<5 |=CDM8
=C7
:
4 *4 ghB
+
=
8
=KD;39=f?5A797N=
:
<7
:
' !
3./)
=UD
O
5"5AHI8J3
:
G5A798 48 L798
<=
O
H
O
!.3)
&
48
"
8 3
O
5
5ADF5AH
:
E5798J3
O
P
$
HI8J=
HM5
H;5=
?A=CH
? <BE5AHI8N5
O
B
5
< ŸAžnŸ = ŸF— £ ¤® – ˜ = ¨  ª — ¥F˜¦¤®A £ ˜ – = < = 4 < $ #=
Ÿ ¡ – ¾ ª  £ ˜ ¡ ¯Q = ŸF® ½F¡ ˜¦¥§ = Ÿ ¨  ª —j¥F˜¦¤®A £ ˜¦ = &
&
%('
= K2'
4 DF=C3TBG5
5 k=C7
:
F5A3
53 <3pH
<5A3
@ – ® Ÿ ª;– ¡ ŸF¯°j £ –)ª žnŸ ª ˜ – ® ¡ Ÿ ghBy795
:
0/
=
:
<BE5AHI8
5
:
` <b
7
O
:
8J39=
+
S
=<7
4=
<7T8J5BGDF=C3
:
5
/
F4 5 k=
:
H
Ok:
=<7e3N5
=C7p5
E7N5A395AB–?A=<H;7
=C7|BE=
:
O
7?
:
&
398 <7
5 L=C7
:
5
5 C=
<HM5
:
8J=C78N5ABEDt=<3
B
5A3
OL:
O
& ,+
./)
¼
5
:
7
;O
=C7
o
:
5
7p5 fDt53
<=pD;3
D;3
O
7
O
7
O
O
=C7
O
2
O
H;?
:
=C3 <B
O
Ok:
3N5A79Dt5
:
5
=C7
:
& <7)3N5 <5
=C7795A395A7
<3 <B
O
C=C7
8
O
:
=C7eDF5
:
:
4
3
=C7
55A7j8
$pD;395
O
*)
7 <=
5
D
GD;395
.
=
FM
B
Dt=<7
8
=C7
:
3N=
O
HI8
<7T=C3
7N79=
-M
B
8JBE=C7
L8
B
O
<7
5”8N=CB
:
gBQD
=C7
O
=
53
f578
O
<7
=<7p7958N=C3NH;=
O
47N5A7”3 <?
?
O
5A?
:
<3
5•D;3N5
O
<7
:
B
8J3
7
7 <=
4
?=CB
=
Dt=
:
5A3T?=CBED
:
K7
=K= ŸF¯
2
O
'
=<H
L=f?
2
=
=<7)795
:
=
7)?
798J=<7
5
:
43NB
' 5H
4
'
5B
57N5
?
=
= =
5”5AB
8 ?AH
O
? <7
7N=
0(
DF=C798 <7TD
=•BE5
/
:MO
7j8
L5
:
=C7
O
¡8J5A39H
5A7
48
:
:
<7
O
=
5
:
5798
:
D;3N5
5
8
O
H
O
B
O
5
:
H
H;?
B.Dt53
:
7j8J5
O
5 <5A3
:
=
:
MDt=C3
H
O
& %
5ADF5AH
:
53
<7
2
O
I4
.(
kD
8J79?
O
<3
O
8J5A7
=C7
O
O
<=
5”H;=
:
<7
8N=
L2
M5H
'
05AH
žnŸ ª :
5G795
Cb `cb
4 O
O
<7N5
5
Š^
7NDF=CH
<5&
H
47
:
<3j8J5
5
:
&
? <7
O
B
8
4?8J=<7
)<=C?
Ok:
!./)
H
4=
H
O
;O
./)<=
M5
O
Ok:
H
?
:
O
=
:
<7)?A=CBE=
O
'
D
O
B
B
B
:;O
8J=CB
79?
:;O
H;5A?5A7N7
<?€8
5
:
5798J=<3'8N5AB
8 A?H
+5
3N5A?€8 K?=CB
=
H
:
HI8J5
MO
”7
:
:;O
53
5•HM=
?A=CH;795
:MO
;=<3 <BE5AHI8J=
H
O
5
5A?€8 <B
K5BD
:
"
O
7N5A3
5
:
798N=•?A=CBED
<?A57N79=
"
0(
D;3N=
'
'
5•5A79?A=
8 <?
=CH
O
47
o
k=
4H
:
C=
C5AH
5…=C7
?€8
:
=
5A3N3 <BE5AHI8 <7
P5AHI8J395”=
H;79D
<D
478
O
2
3
:
TDt=C797
LBG5HI8J5
=5€8 <D
=
O
O
O
O
?
<7
O
H;=C7TD;39=f?5A797N=C7
O
<=
8J=
:
=
"
B
5A798 <7T8 ?AH
:
O
?=CH
<=
HI8J=
? <7T5
5
O
5
:
B
7T?=CBE=
","
3
8J=
.3)
,+ 5”5 C=
:
8J3N=<7 M=>D;3
& D;39=f?5A797 <BE5AHI8J=K5
K? <3 <?€8J53
4 !./)4=
O
M5
vžnŸp¯
8N3 48 <BG5HI8J=
g
:
5”BG=
:
7
O
4H
Cb
BG5
<7N5
=C3
3
O
7j8J=C7
=
? IA
4 B4 4
DF5A797N=
=
:
`cb
B
5
5
:
<797
<7
:
5
:
<=
!.3)<=
=<3
:
7 4=
O
5
<=C7 ?=CBG=
= Ÿ ª Ÿ§¥
L4
7 <=
O
8
<HI8J57H;5A7j8J5"? 4BGDF=
4398J5
=C3NB
O
5ABE5A3
O
KD;3N5
:
O
A ª = ŸžnŸž 6žn =
)®
=K?A=<BGD
:
395
5
:
=C7795A395A7
:
=C3 =GDF=C3TD
47H
:
€8J=
Ok:
<5AHI8J=
:
BG5H08 <3'5A798N5•Dt=48J5AHM?
O
”5AHI8N3N=
D;3
?
O
<3
;=C3B
5"?A=CBED
D;3
0?A=<By=
I8
…H;=
<H
" ' ) %
"
' % + !
&
"
) #+ #+ & !.3) 3
¼
' %
! !.3)
*.
'
' =
O
M8J=
7 P5A7
O
O
:
5A?
:
=C3 O
¡ a
£ ¯ ¡ ¦¥ žnŸ ŸF® ¨  ª ¨ ¯QŸF® ¡ s
 žnŸ¯+°)® ¢ ° ª XžnŸ Ÿ E£ £ )
¯QŸF®
°jŸ £ n
¥¦¤® ª F¡ ¡ F¡ ¦¥ = ® 
® ¨ Ÿ F¡ œ›n
=
3
k=P?
N(
8
O
B.5 k5
O
?=
=C3NB
0DF5A39B
5?
:
=C39B
n¯QŸF® ¡ QŸx±'°j¤® ŸF® ¥ ª ž
®  £ ¯œ›nwž °j¤® ¨ Ÿ ª f5B
=
<=
OL:
<7N79=
<?8N=
5A7j8 <=
5
+f=C7?
O
=
Ok:
KH
=
8
O
3 œ7N5
;O
:
:
'
5
8
O
L3 <B
¾ ¥§¤® ž ¡  £ Ÿ
8 4?
?
O
M798
p5
M5A5
7
GH;5?A5A797
7 <=D
O
f57
7
<7N5e8N5AB
5•7N53T?A=
:
D;395
O
0O
k5 M=
-M *M 4
( & (
B(
;2
F5
<H
OL:
2
H
=C39B
DF=
=
Bi5 k5
3
<?8N=C3N57>?=CHI8J3
¥ £ Ÿ ¥ ¯QŸF® ¡ wž
® ž F¡L£ 1žn
=
5
:
<7T=C3
:
7)?=CBED
O
BE5AHI8N=
<7
:
B
0BG57NBE=•H;5A7j8 "7
@?A5398
7 <=
O
7
O
"5
<5
:
5A798 <=
:
HM?A5A3j8J5
O
?
=CH
O
5"7N5A38J=<B
:
A?
5
:
5
:
B
:
:
<398
:
2
5AB
:
?
H;5AHI8N5+H;=
D;3N=P?A57N79=
O
<H
H
k=P? KH;=<7TBG5
,+ '
' *) ) & !. !.3) !
& / )³ " & *) '% " ) & % ) & ' =³
=¼
=<7pH;5
:
& ! .
' r·
./)4=
MO
=
:
<BE5AHI8
:
D;3N=P?A57N7N=<7
„O
:
H
H
.3)<=D;39=f5B
:
?A=
*)
P5A7=CDF5A3 4B_H
5K=EB
7 <=
O
O
|=C3
=
C4 :;Ok:
B
s
BG5
T
2!
G
¿º>
`
:
=C7
=
= Q4 žnŸK° £ Ÿ ¨ 5r5AH
<=
<5
D;39=f?
3
:
=„BG=
:
&
5 L=
Ok:
& ' 5
D
43 =
J
zH;=)D;395A7N5HI8J5
N(
FM
N(
N(
B?=CH
BE=
=
:
32 B(
8 <?
=CH
O
pB
C5H
”?A=<BGD
5"=C7?A=CH
<5AH;?
J
32
D;395
?=CH;7
k?
O
43 L8NB
OL:
=
:
k=
O
"
' '
'
477 3
D
43
D
4398
O
0(
4
O
7N5TB
BE5AH;=<7
8
7T5
O
<=
0/
<3j8
?
O
O
3
:
=
:
F5AB
HM?
k57 8N5AB
=@5798 47K?A=<H08
:
5A7
3
BED
O
7 PDF5A3NB
O
5=
?=CBEDt=C3j8
=
57N5AH
O:
<=
&
5
B
3N5
<=
<7N=
:
/
7N=
AOL:
:
57
O
5 <5A3
:
7j8
!.3)
?
O
3N5
& 3
H;5 <3N57
O
HM?
:
O
? <BE5AHI8J55798N58
O
O
5
5
5
8J5H
0/ &
4 3
"
OL:
=e5A7NDF5A?
Ok:
5
:
=<H
5
:
48
?A=CBd7 A3
' <B
7j8J=•?=CB
=C7H
:
;O
;=
=C3
p5 fDF=CH;5H;?
3
O
(
=CH
O
=+?
:
=<3NB
8N5+?A=<H;?
O
57
:
5
H;7ND
O
5A7N5BGDF5AH
:
!4H;5A7j8J5?
<7
:
kBE5AHI8J5”7N57N5D;3N5€8J5AH
O
;=C3
B˜?A=<BGDF=CH;5H08N5A7
D
=BE5
5
:
BE5
5K8N3 <H;7
:
H;?
5 k5
:
P
O
5 k=C7
:
5A?A395A79?A5
:
?=
<797
?A=
O
5798 pH;=+795
O
BGDF=C3j8 <H;?
O
=C7?=CB_=<7BG=
OL:
<H
5?=CBGD
:
5A7)3N5
O
5
5'7N5
47)DM3N=CDF=C798N=C7
5"D;3N=P?A57N7 <BG5HI8J=E5A798 48 L798
<=
/
7N=5A7NDF5A?
798J5B
O
45AB
DF=
O
"
7N5A3=”B
<=G5"7
8N=
BED
O
?
O
5
:
Ok:
=
:
5
:
43=KBE5A79BG=>BG=
O
5
:
=7
:
798N5AB
O
57"?A=CH;7
O
5
:
<=
O
3
O
7j8J=rH
!.3)
' "
5
47
7 3
O
:
<=
O
R L2
5”DM3N=
&
L5AB
¼
5A7?
8
:
DF5A39B
O
¡8
#4
;5
=<H08
=
;:
MR B
H;5 <395A7 P=<H
O
B
ID;3
8N5AH
O
H;?
O
5AH
5
:
—
=
4
kBE5AHI8N5
OL:
="795
:
<3
k=
5
:
5 <5U7N53
:
<H
D
4=
<3
4=
=
:
=C3NB
DF=CD
48J5H
—
€8J=
8J3 <H;7
:
=C3
O
D
B
:
GB
CO
<797 <3)5A7j8J5>B
<3
O
o
<=
<7
)<=
O
L=
8
O
:
:;O
3
O
<B
O
5
=<7)5B
:
8
5
=
:
L8J3 <D
W
=
O
:
<7H
? <7
B(
8J5
O
;7j8 <HI8N5E5798
—
OL:
$>BE58J=
4?A5AHI8N5
=C7”BE=C7j8J3 4B
H;5 <3
F=CH;73N57
UW
<=
L8
2
=
<=u=
5 L=C7—
H
Y7
5
:
=
O
=
L2
5A3
5A7
5BG=
:
HM?
:
>
<3 0H
2 & Ÿ ¡ ¾ 5 L=
F5A798N5A7•395A7
<D;395A7N5HI8 <B
:
<7
:
<7T7 3
:
5
:
53
Ok:
:
5
47
"
<77 3
:
"7N5
5”8J=
:
3
H;5 <3N57
O
H
N(
O
8
5A795ABEDt5H
V:
M=CH
Z
&
57
5AHM?A=CHI8J3 <B
5”=>7N5
:
O
=C7
:
Ok:
4BG5H08N5h8
;=795
=C7
=
0(
?=CBG=
H;=G? <79=
8J39=C7B
<7
:
5A798 <?
:
' "
gB
8J=
:
=C7
<B
8J=
&
.
5A395AH
H;7ND
O
3
54
:MOk:
"
=C7rB
5A7
O
?
BE5
:;O
F=C3 @7
43
>BE=
O
O
O
<3
B
7
:
M8
L4
5
=C7)7
:
53N5H08N5
:;O
%(' #" " ' ' )
4 !./) "
"
$
! 9 1
./) "
&
'
4 ./)
%('
4 ) ! & O
5A7?A=<B.8J5H
'< =
o
3
DM3
CO
•=CDM8
7 A3
7
8
? "D
O
COL:
798N=
H
O
:
7N5H
C5
4 5
:
<7•7 3
BE58N=
B
5 C53 <7
:
k=
2
O
47
:
=C7=
7
DF=
O
5AB
:
58J5BGDF=C3
O
O
538
:
:
7 3
8JBE=
O
C5A397 <77 A3
:;O
4H
=
:
"
'
$
"
8N=
L8
t=<3
:
5=+?
:;Ok:
h5AB
8 #5 +
<3
5
5
O
Dt57 <3
<3
8J5A3?
5K7N55798J3 <H
5A3
;395?
Dt=<3 AB
5395A7
:
D
:
*)
o
7
=
7 <=
OL:
5"?
:
<=
O
:
:
O
”BG5
kBE5AHI8N5
O
"
)4=
H
=
:
B
:
4 B4
K4
32
k=
H
O CO
L2
79=
O
=
:
<7N7 <3
43
€8J=
57NDF5A?
=C3
O
=CDM8
:
;2 &0(
I4 N('
4 " 2
4
"
B
=
;:
=CH
O
O
<D;395A795AHI8 <B
5H08N5>D
O
=
D;3
<=E5
47
=CHI8
H;?=CH
O
MH
798J5B
;=
47 F?A=CBE=
Ok:
HM=CBG=
O
BE5AHI8N=
O
;5A?
8
gh798J57h7
8
º
` M`
8N3
;5?
P5A7?A=<H
D
!
$
"
% "
.
!
3
'
! ¼
)
#+ " ) "
%
#+
,
' $
!.3)
% & ' !.3)
' ' 3 "
&
3
& 3
H;5H
B
$
:
:
5
=C7u?=CH
:
5
#+ '
”?A=CBED
:
C5AHM?
O
L5
Ok:
N(
=<H
5A795ABEDt5H
5
477 3
:
7r3N5 C5
O
;=
=C7TH;=C7TD;39=f?5A797N=C7
"
"
.3)
:
:
7j8
5"5 <=
O
/
<B
O
57
BE5AHI8
795‰?
? „=
O
H
<=ED;3
C?A=CB
<3 <BG5HI8J5
<5A798
¼
DM3
O
O
O
'
H
:
F4 5
:
BE5AHI8J=‰H;=
=<7
=C77N53N5A7
7N=
:
O
=C7
:
<=C7
=<7GBE=
)5A798 [7
:
&
5 k=<7
& 3
!./) *)
)<=
?A=<BGDF=C398 <BE5AHI8J=C7H
:
O
H;5 <3N57
8
O
5…D;395
<=
O
7 <=
!
"
#%$"&('*)+,-&.$"&/%,-/0122&3,
/'+'
4&,/5/768:9*;:<''=
S
¿º
`
o
3
8
D
%
O
<=
<7
:
DF=
5A3
:
D
G
8J3
3
.
.3)<=
=<D
:
5?8
=@D;3
:
H
&
? <3D
:;O
C=C7
=C3
<B.57NDF5A?
4
<3
39=uDt5 k=
O
5U795
U?A=CHM7
48
Dt=
5A3
Ok:
B
*)
5A3 <=+795
:
7N=
LBG5H08N5
B
CO
=C3 =
<3
&
H
O
?
=CHI8
B
2
#+
47
5AB
5 fDF5A3
t=C3
D;39=
+
g
' D
47
k5
47N7
5
3N57N=
C53
5
B
:
4?
5AB
B
O
Ok:
<7D
N(
H
+7N53
œ7N5>?A=CBE=
H
395
=
8N3 <7
<D
|=C3
FM
+D;395
:
k5B
?
O
=
5
:
+4 =CH
<3
MO
8N3N=
5p=C3
:
=<3NBE5
:
O
H;? LD
5AB
7
Dt53
O
:
:
` bCb
<HI8
O
8J=‹H;=
5
OL:
5
:
B
*)
7
5A3 <3"=
L8
<D
=C7
:
N(' 4
5A3
k=
<7
=”7N5
:
?=CH;7
?=CH;7
<?
O
8
O
5
:
<=
O
53
Ok:
Dt=<7
<DM8
5B
:
:
5H08N3N=
:
5
:
=C7rBG=
& <=
8
O
O
<3
3
O
:
'
<797
C5
2
BE5AHI8J=
O
<3
BEDt=<398
O
53N57NDF5
53N=C7 <7
:
!
8
O
L2
3
53N3 4BG5H08 <7
g7j8J3
8
3 <7UDF=
8
3 <7
k=
;3N57
5B
:
47
"
O
<3
4
5>8N=CDt=
:
<7
8
5
:
O
O
5
:
k=
<7
CO
./)
4 !
+4
B
O
7N58N3 48
8 A3
O
=
O
L=
CO
4 *4
< $#=
7
8
4=
O
O
47
53
5
:
$O
3 <7
5p8N=CDt=
:
<3
O
7
O
8J5?8
MO
P‘
=”5AB
:
<3
=
:
o
^
5)8J=CDF=
:
>=CDf8
<H
=6H;=r?A3
:
CO
Dt=<7
O
./)<=
<=
<795
;=
' 5
k=
=
<7
CO
,#" 7
' =6D
:
C4 ;5A?
H
;O
BE=C7
O
!./) " 4 & O
N(
57N5H
,+
5 k=C7V?=CH;5
O
(
•7N53
8N3N=C728
=D
:
:
7>5 <=
7N5 k5A?
5"8J=CDF=
:
<3H;=C7UDM3N=P?A5A797N=C7
D
5A3 <3
OL:
·¡8
=•HM=C7
Ok:
4H08N=e5A7j8J3
5AH;53
=>=
:
53 <Bš=
:
?A=<7)D
O
4Dt=C797
kBE5AHI8N5
”?=CH;7
O
=
:
4=
O
H
O
Ok:
<R
º 5r795eDt=
O
!t5AH
7D;3N=CDF=C7j8J=
/
5
:
7 <=U5AB
O
BG5HI8J=
CO
5
8N3N=C7•8
<3
DF=<8J5H;?
<DF5AH
"7N53
O
GD
<H
< k=
5HI8J5
O
8J=CB
5
:
@8J=CDF=
% 4 !./) 4
'
./)
5AHM5A3
M=C3DF=<8J5H;?
4=•7N5
9 R R
8N=
4DM8
:
)
?
O
5?A=CH
7 <=>Dt=
@7
:
H;7
5
:
798J5B
O
:
=
Ok:
"œ7N5
B
5
5
48
<BE5AHI8J5•H;=
:
<7
;=
O
5
:
D;395
C=
5ADF=
:
:
5
5AB
:
"
B(
BE5
5
5
:
:
Ok:
5KB
:
J
F4
:
;< =
=C3Dt=
< = 4 5A79?A3
3 <7
4898J5A397N=CH
=C72B
O
<?
F=C3 "7N58J5H
! S 1
4=
F=C3
P5B
<797N5A7
8J53N57N7 4H08N5?=CH;7
=
:
(
8J5?8
7 <="5AB
O
5A3N5HI8J5A7?
:;O
7N=
P5A7
=C7BG57NBE=C7D;3
:
;2
;2
B
& '
4
:MO
Ok:
t?=CBl=
5A795AH
:
7 <=@5
O
;=C7 ;H;=CBE5
5A795AH
4?
<3
L8N5A39H
G5AB–8J53NBE=C7
? <3
:
=
;:
0/ & 4 5< =
N( N4 /
O
&
' 32
"
./)
' *)
&!. 3N5 C5 k=
<D;395AH
53p? <D
?A=C39Dt=
=rD;3N=
:
C5A3
5
:
Ok:
=?=C3N395A?8N=
:
:
GHM5A?A57N7
5B
<5&
DF=C7N7
O
5
:
UDt53
B
:
=
=<398J5BG5HI8J5
E? <D
:
3 47
:
'
B
<78N5AH
798N5
5A?8
<B
<B
O
5
:
< = 4
O
<3
:
O
#+ ! =
?=CBGD
:
HM?
5ADF5AH
:
5AH;?
OL:
O
•? <D
:
…D;395
Ok:
O
:;O
=
:
5"H;= C=<7p? <B
:
& ' 5"
& *)
' %
C5
V e|!
' ¼
47N5U7
H
5 L=C7
:
58J5AB
D
O
BEDt=<3|?=CBG=
O
4
*.
<=
'2 5
:
./)<=
5A7
H
O
O
<<
5
:
=C7=C7)3N5798 <HI8J5A7”BG=
:
=
:
8JBE=
O
R f
W 9 Z ( < =G8J=
:
5?8J58N=
BE5
O
' 798 47TD
O
8
=•395
p5798J5UBE=CBE5AHI8J=
O
4=
& "DF5 L=
Ok:
5•5A7j8 <77N5
<797 <H
8
:
= <H
=C7
:
¡8J3 <D
4 =
?A=CB
=<3NH;5?
T
2 '2+ e„
r e!
;=+5
<H;=<7 ?=CBG5
5B
5?A=CBED
J 32'0(
:;O
& ' !./) :
&
<D;3N5H
Ok:
8N5ABEDt=E3N5
:
5G795A3N5B
:
O
#+
) $
=CH
O
798 47e5
5eDM3N5
<D
O
7 <=
O
?
O
:
<7
J
7j8J5AB
3
P
:MO
5A395AHI8J57
h795A3
O
O2
u7
O
H
t53
"
® = < = ¤® = < < = =F¾ n® ¤® = < = < =.= ® 32
pBs5A7j8
7N=
;3N5
<7
C5 k=P?
2'
OL:
5B
S
5A7
:
4
:;O
3
4H08
5H;7
=
H;?
;:
O
4
=<7
<H
=C3
4
=
:
…7
7
O
@2
'
=C77N5
:
7)D
&
<7N5
k?
Dt53
C53N79=C7
5
O
"
= œ7N5
:
5H;5A3
=<3
) 5
:
:
5 '5B
:
DF5A39B
8J53NBE=C7
/
<=U=
O
8NBG=<7
U5
?
8
O
O
O
5
:
?
3
8
3 43
O
FM
!.
O
P5A7
4?8J=<3N5A7U?=CBE=
5DM3N5
:
=@D;3N=
=C3
7
qf5?
k5B
<<
&
<D;3N5H
:;O
& $
3./)
º »º & " .3) 0 4 ' '
V3
8JBE=
O
D
)
7 <=
O
5AB
:
@395 <5
43
5 C5A3 <7U3
:
>
C53
=C7
0/
?
/
:;O
DF5A3
[D'<3
?=CH
Ok:
5Bd7
4=
5AHI8J5V8N5AH
:;O
5
:
=+DF5 L=
=
OL:
32
3
:
O
=CDM8 4H
<3 4BG5€8J3N=<7
553N3N=
:
<7
& !.3)
7 4=
O
=C7UH;=
:
5e395
:
< $#=
:
:MO
DF=
O
5
:
5D;3N5
:
5
:
Bs?A=CBE=
O
8
:
=<7
:
OL:
!08J5H
8JBE=C7
O
<?
<7N7
5e?
:
5HI8J5
:
3N=CH
798 <BG5HI8J=
<7•5A7j8 <7
5 k=C7)H;5
:
4=
57N?5AH
:
:
U? 4D
<D;395A7N5HI8
5AHI8N5
' '
0
5AB
=<3 <B
:MO
4=
=CHI8
=C7+BE=
:
& !./)
> C53
<=e5AHI8J3958J=
O
5AHM7U5
<DM3N5AH
k=
=C7H;=
:
5AB.3N5
5
:
L8
4D
<795
&
5
:
:;O
<HI8
<3 48
1PW
nZ
p=
% =u?=CBGD
;:
f5
º=º
`
H;?
O
' =<H
1"
L2 u5K3N=
:
:
<DM3N5AH
O
? 4H
7
O
5A7
:
798J5
1"
5e?A=CH
:
=@D;395A79=C75AB
:
& ,+ #"
)
" ' !.3)
' ! & ' "
& .
.
& %
' & ' 1"
> &
"
'
'
!./)
3
% " ' ¾
¯ 2 4 0 !.3)
" &
" $ "
L¹ & !
4 "
& !
) )
&
' .
#+
'
4 + 3
)
#
& "
"
kH
B
BG=C7
O
=
<3
Ok:
5
:
kH
H;?
5
:
3
L=f?
5 <=
C=
:
:
A7
B
o
:
?
9
O
5H
€8J=
898JB
5AHI8J5 tD
< =
4
?A=<Bs8J=<Dt=
<3 <B
3C >D)E=#FHG
(%
5
HM?
O
<7
CO
KDF=C797
%,)+')
-.,
L=
%
9I
0(
<3 BE5
5 fDF5A3
/
8
O
H
=
:
5A?€8
*6
=
<797
B
OL:
:)+ &)+
'
=
(
<=
|=C3
B
B
:MO
5AB
:;O
<797
=CH
O
3
B
:;O
=C7
%)& %1'*) -$&-+
'2,
798
5
:
/
5AB
:;O
B
%
O
=E?A=CH
:
5AB
:MO
:MO
5AHI8N5
)(
+*
J*
/ '#/0
1%
O
=C39B
(
O
'
:
O
=.= †5
57N?5AH
(/01
,
;5A?
'2,
:
5
O
L8
O
<3
?A=CH
B
8J=
<DM3N= C5
=C7
:
8 43
O
C< =
<
=6D;3N=CDF=C7j8J=DF=C3
H08N=
O
B
DF5 k=<7
<=
B
8N=
BE5AHI8J=
8N=
5
:
=<7pDF5A79=C7
:
=C7
:
f=C7TH;= C=C7TDF5A79=C7T7 4=U?A=
HI8 <7+?=CBE=
3
=<7
:
=
:
5
:
aB
5•5A79? <D
:
H;5
O
79=
L=
EDF=CD
k=P?
<=
L2
3
57
<7 <Dt=C3
?
aH
D;39=CDF=C798N=„=
O
5BG=<H;798N3
:
¡8J3 <D
5
$O
=
? 4D
:
B
8J=@5 C=
;5A3 <H
<D;395AH
:
=
:
<3
O
<DM3N5AH
<DM3N5AH
B
O
<7”8 <=
8J=
5
:
5
8
=
53
:
UD;39=f?
5 M7N5H
:
P7N5H
B
O
B
=
M=C7
=5
:
7N7
<B
OL:
H
<D;395AH
=
?A=<BGDF=C798N=GDF5 L=
?A=CH
:
#"%$ '&
<<9+6(8;
0,
:
o
O
t=C7h=<7'D
=
<7e?A=<B
:
DF5A3 <3”=<7”B
!
')&1 :$&-5
"'
?
:;O
2
Ok:
DF=
O
=
/
:
<B
<398
<DM8
47 5ABs8 <395
<5 7
% /
O
7
O
H
O
4D
;=C3 43
47e5
=@D
:
:
=
:
@4
:
S
<=
=f?=C3N395A3
<797
5
:
)5A7j8J5>8
;DF5A39B
O
<H
=?
:
<=
H
:
5>5798J57p395
fH;=>D
`cbCb
H
O
8N=CB
<=
798 <BE5AHI8J=
`cb<b
:MO
43 U=
?A3N=<BG=C797N=CB
<?€8J=
=
:
C4
5
:
5•5 L5
t5A3)58
<H
H
O
;2
Ok:
=
:
5
:
k5
8
O
:
O
•?A=<B
F795AH
:
:
57
:
qf?
Ok:
@B
.( O,
:
:
f57
=
?
5A798 7
:
=79=
:
` bCb
+395A7
k5
5A79?A5AH
”5
3N5 C5
?
/
V?A=CBED
5
:
5
:
=C3
<=
-M
Ok:
4H
5H08N5
:
O
5e?
¡`
L8 UD
48
:
8J3
3
5AHI8N5
<7
o
MO
|O
O
:;O
57N?A5H
:
L8N5A3NH
H;?
5
P?A=CB
5HI8J5
pB
k? <H
3 4H
k5H08
O
:;O
<7
7
O
O
5AB
:;O
=<3
O
D;3N=
<BE5AHI8J5
OL:
32 32
<HI8J=uB
<D;395AH
f3 <D
C53
g
=<3
O
<3
BG=C7
O
7
O
B
D
DF=CHI8J=
B
L=f?
:
4
:
0/
5
?
:;O
;O
3
5
=<3
5
:
L2
=.=
OL:
=
7N=
=
:;O
=C7
:
5
:
5HI8J5
3
:
O
8NBG=
;395
:
5
#, .-0/2143650798:7<;143>=@?775A7
B
LK %M)N
'&-
-+
'
+
'&)+&+'=
`
T
População
Cruzamento
...
Mutação
Selecção
Codificação
Descodificação
Aprendizagem
...
...
<
<
=CDM8
O
<DM3N5AH
M
#+
;2
S
4
0
5AB
D;395AH
S LS
5 L=”H;5
:
<H
:
R
&
:;O
5AB
:
N( L2
3N=CH
2
|=C3'?A=<H;7N5
;O
p5798J5T?5AH
="?A=C39Dt=
;< =
B
+5 <=
5
:
% &
W
o
5€8
=+BE=
:
P5A7
L`
=C3j8J5
:;O
<7?=CH;5
:
4 !./)<=
B
O
5
:
3
O
" BE=
O
!P5A798
HI8N5
3
O
=
<DF=
.3)<="7
O
B
" 5798N3 48
CO
DF=
" #" #
5 +P8N5AH
53 œ7N5
:
' 5 k=UD;39=CDF=C798N=EDF=C3
:
& L8 <H;5
:
5A3
:
4 ' 795A3
:
8
+8J=CDF=
535A798
L=
CO
:
O
O
O
)
7 4=
•3N5
:
+D
:
:
55
43
=+D;39=f?5A797N=
:
=C7hDF5A79=C7
=
./)
& !
#" %$ +* "-, !. . * . )
&(')
&(') /"10'!.3) ' 1"10/.2 435. % ' 26. * .7.8292 ' *;: *6* 3 ' * * .
.
29. . %35. .(2 * "10 * & "1.80,9. ' 2<.,+/. ) : ' , &(') : ' 26, ) .80=, ' ' " .(26" & 3 ' 0' : 29." * ) ' 3' *
* "829"-. * & >,9" & * /? .A@ : .& ' . 'B)C' 35.& ' ' * . : ' 35.82 !* .82D.80529" . & "-3 'E&(')
F"10=,G. 2 ./) ' 35. 0. #. * 0) ' 1"10/.26. * . ' 2 -, ) " & * ' ,G26" ' 0 ') 8" ,G26" & * 35.I3/" .(26.(0=,G. * , " & 05" & * *9* ' "
,G2-,9.(290,G" : 2 ') " *9* ' 2 : ' 35.(2 H: *6* 2 : .& ) ) I
0 ' .S,% UTVVW & " 3' * $KJ HL <M ON &(')C' %
9P $ NRQ# A " . ,92 " * 3' ,G"1" !.3) ' 35. )C' 35.& ' * 35. : 29.
" * ) ' .(2 3 ' *C: . : - " & ./) ' 35. ' : .82 3 ' 29. *
3 ' * 35. ) * (" 26"1.`,G. ) : ' 2 % ) ,G. ) ,9" &8' * . YX%Z\[EZ8] ' _^ * ' /29.!.&- . ) .(0=, ' *: *9* ghB
<!<= (
F=C3 )7N5
J
8N5AH
<Bš=
/
FM
M8
OL:
=C7
) 4
t=<H;7395A7
L8
:
2
=C7?=CB
4
-M
A
p5798
O
B
<=
2
:
=C7|BG=
5 L=C72—
:
/
—
2
(
04
/
? T
32'0( ' ' 2 ) : .(0 * &8' 0 * "-35.(23 ' * 3 ' " * )C' 3/.& ' * 3/. : 26." *
* ' * 35.B. ' ' : 26> : 26" ' * 3 ' * * .829. * #" ' * * < = . ) 26. : 26. * .(0=, $ = ) 2 )C' 3' ) 1" B3' JI$ ' 05" * , * 5. ' * %
. * ,9.H,G2
.3)
" 5 * ,G" C
3 ' R0 ' ) ' * 0 ' * ,9. ) " * . *6* " * ,G"-3 ' ) (. 0 ' 2 ) . & 29. * & " )
3 . * , & 5" * . )
& * * * ,G.(0=, 3' * 0 B
' ) . * ) ' : 2 35" ) ) : 26,9" & 2 =5
&(') : ' ,G.(0 & " % : 2 ' : 9, " ) " ./) '`&8') 5"-0',G>29" .A0 ) "(62 " & ' 29" 053 ' *
P N A ' 0' Y. .8, TVVV & (. 0=,92 5" * .%0 '
N
. .(0=,G. *`* " ) : -. * . Y&. * ' ' 2 ) " * .F"10=,G.82 . )
) .(0=, ' 35!
P
'
, ) "* .
O " 5
P
( ' 29"
J
P
4
32 B(
=
'
: ,
' 0=,G. * ,9. )
'
=
: ' 2 "*
4 ,92 '`& *6* . *: 29"10 & " : " * 35.
.,+/" * ,9. )
. * ,
2
2 *(
=
&% '
')C' ' "/26. .829"13 ' 0 ' L )( 32
=
35" .(29.80=,G. *
2
.80, ' 5
3 . ' ,92 * , " & 05" "
0 , ' 35. ) "8, ' 3 ' *
&(' 0 3E0 ' %B3/" * & " : -"10' '
3 3 ' 3 ' 8& ') : ' 2 , 5"
&8') ' * . ) /1" .(0=,9.
. ) .(2 . ) 7"-0=,G.&-" 0 & " &(' -. & ,9"% ')C' .#+#. ) : ' 35. * ,G.B,G" : ' 3/.%. * ,G2 O, " " P ! #"`.(0/05.(3 2 $ .82 '2 /, TVV 4
' * '& % 3
3 ' * ) ' 35. ' * 8& ' 05.#+#" "
' 0=,
?
O =
) ' "-0 *9: "-2 3 ' * 0 ' *<: 2 '#& . * "
!.3) '
HL `L )(
32 0( 32
: 29. " * ) ' #,G.80535.8053 ' 7Q HL )( . ONP
A05. * ,G. ,G2 ' ' ' 263'2 ) " * . : .80' * * 3 * : 29" ) .8"12 * & ,G. ' 29" * 35. : 29." * ) ' . )
' 2 * 26. * , 0=,G. *<* . ) " ) .80,9. ,9.(" * : 2 * ' 2 0/" . . * . : 2 ' : 05. ) .(0=, '
35.!"10 . * ,9" ) .(0=, ' * ' . * , ) ' 3' : 2 ' 3 .3) ' ' 2" ) )
' * ' * ) ' 35. ' * : 2 ' : ' * , ' *: ' 35. ) * .82
3' : , 3 ' * : 29. # " * . * 35. ) "835" ' . ' 0 ' : 2 ' D.,+#" * ,9"1053 ' 3 * -,9.(260',G" % * 23'/2 , .&- 3 TVVW A. . * ' 26,9. TVVW '
2
2
( /
M
FM
2
= & 3' ) %,G29.8"10'3' : 2 &8' 2926. *6: ' 0/35.(2 : 29. " * ' 3/.E3/" .
26.(0=,G. * : .(2 ' 3 ' * . )
29.(0=,9. .
N M = ' * . ' % ' 2 : 29. " * , ' : 2 ) : .82 ' 3 ' 26.(0=,G. "
26.-" ) .(0=, 3 ' '!)C' 35. ' 35. )C' 3 ' !. * ,9. ' 2905. & .82 : 29." * ' 35.I3 ' " * : .(2 ' 3 ' *
26.(0=,G.
: 2 ' *9* . "1053 ' * .B. * ,G. : 2 '& . *6* ' . ) & * & , ,"@4 . * . ' 2/,G.80N(' ' 0 ) .82 ' 35. * . 3 ' 35.
: 26." * #
M . * . ) %0 ' 6 L ==
$
#"
)
"
$
$ )
.
O " 5
? +*-, O " P
* 03254 ' 29. * 6
: 2*9*72 3 ' * 5
29. (& ' 62 29.#" * %
. 3 ' 1
3 .98 ) 2 3 2 3 2:032 92 " ) 0 . 4:62 2 22 : 92 . 0 " * ) ' 3 '&(') : ' 2 "
, 2 ) .80, ' 35. * " * ,G. ) 2* (& ') :;4 .#+ ' * < ' 2 " ) R
.,+#" * 9, . ) * " ,78 2 . #. * . ) =85. " : 92 . .(2 0 . 4 -" 0 (
& ' 2 : ' 2 2 2
/.
>@?
M
&
BA
,) ,-+7
)
C3D
EGFIHKJMLON
=)565 3 C = =
BL5P 0=
-M
4
= UP Q# =
T
35" 0 .(2 * ' * 2 & , ' 29. *< * ,9._,G" : ' 35. : 26. 0 " *! '#" 35.80 ') "10 2 3 ' 35. M 6%$ M "'& 8/,9" 4 )" ( 2 3 ' 0=8 ) 032* , ' 4 . =85.`35.`3 ')+* 0/" ' * "#&8') ';' * 3 2 2 0 " *
N /.D2 '& . 4 4 2 .43/. ) : 4 '#" 2 . 0 ' 4 8'5 ' 3 2 &(' , 2 5 ' 35.18
" TVV10 <2 ' <
3 2
' 4-7* 2 : ' 35.82 +* .(2 ) . 4 ' 2 2 3 2 & 2* ' * .7"-0 & 4 8 2 ) , 2 )
&()' 8/,92 ' *6 2 & , ' 62 . * 0
. 7@852 ' 9. 8 ' 8 * 053/" & . * ' 41* " * , 2* <
&(') ' ' 03254 ' 2<35.`, 2 3 2* 35
! A
2
&
(
-4
2
2
N
)
2
HL =
3 , -$
.
3
'
2
2
8
3
' * " * 9, . )
2
2
2
"
&
5
'
, 2 "*
*6* " :
* :62 2 2 -" 0 (& ' 2 : ' 2 2 2`.80,92 2 3 2* 5
3 . * .80 0 ' 4 0 -" 3 ' *;: ' 5
3 .(2 ' * .(2E.;3,9.(0535"-3 ' E
3 .
) "' * ) ' 35. 4 ' * 5
: 4+2* 032 29" 0 (. " * " & 2 /
0 3 ' 2 * . 4 . & 5 ' 3 2 92 . 4 . 0 0 & " 2 35. * , 2* 2 & 2 2!< ' 3 ' %$ , /
3 .E0 * 0 . 4U* 8 : 4. =
) ;4 ,G" ;
29" ' 2 <
/
2
= =
(
35" * & " :;4 "-0 2 3/. , 4 "13 2 &8') 03254 ' 92 . * =
0 8 )+& 29" &(' * 3/. 052 29" 0 (. " * " ,G.8053 ' &(') 'F' 76. & ,9" 0 ' *
85053 2 ) 8. 0=, 2 " *12 92 . (& ' 4 2 " 2 &(') : " 4+2 5 '#" 2 2 0 34 " * .`. 2 "10=,9.(2 : 29.8, 2 5 ' 53 .E3 2 3 ' * & ((. 4 " T VV10 <
3#. ) ;: 4 ' * 3 2* 8 2 2: 4 " & 2 5 ' * 8/2!<. ) 0 ' * ) 2 " * 032 62 " 2 3 ' * 3 ')+* 0/" ' * " 0 ') . 2 3 2 ) (. 0=,G.<0 ' * . * 7, 853 ' *
35. ) .(2 & 2 3 '#" 35. ) .835" & "10 2 ' 8K35. &(' 0,92 ' 4 ' 35. =8 254 -" 3 2 35. <
'4
: ' 35. * .82 0 " * , 2 &(') ' ' 0 ') . 35. 8 ) 2 .43 :
29. * 8 4 , 2 3 ' : 2 ' 2 5" 4 * * ,9" &8' < 92 . &8' 4 2 35.3 2 3 ' * 5
3 . 8 ) 2032 29" 0 . 4;254 . 2 ,G>26" 2 " 35.
29. .829.4= * . 2 8 ) * 8 &8' 0-7@850=, ' 35. ) .(35)" 5 . * Z Z " . * &8' 4 /"13 2** ' 526.18
M L 35. 8 ) 2 2 )
3 . L L <
& 2 ) 2 3 ' 5
" ' 8 7Q )
2&052
29" .
2 2
0
4
254
-, .0/12
M N
)
2
8
. '
) ' * ,G2
2
2
"
2
,9>29"
N2
(
.
(
2
2
=
CL
* .(053 '7' /,9"13 2 *
(* ) (
+
"!$# %#'&
3/4
J
= M
FM * ' 3
26,9"12 3 2* . =8 2
:;2
2
(
2
3
)
' * ,G2
3 ' 8505" 0
& 3 23 '
2
2
* ) .(35"-3 2 *
35.35" *9: .(2 *! '
. *
2
,G.82 )C'
8
)
T
= -F
S
4
JI
% 0 ' 2 ) 6 "' 0/35.
254
35. *@0 " ' :62
T
<
3 ' * . 4 . ) .80=, ' * 35.
/ 15# & 6798;:=<?@ > 7A@ >CBD
/ #E / 1
2
") : ' 2 , 2 =
0 ,9. 2*6: . & , ' * ' 526. 2*: 2 ' : 26"1.(3 2 35. * 35. 8 ) 2 032 29" )0 . 4254 . 2 ,G>26" 2 & 2
* 8 2 " =85.C"10535" & 2 2 29. 8 0 & " 2 /
3 . 03254 ' 92 . *!:62 2 2 5
3 " .(26.(0=,G. * "-0,9.(2 05234 ' * 3
: 2 2 ,G" & 8 4+2 2B,G. ) = * . 2 35" * ,929" 85" 5 ' N ' 8 P
N " & 8-7 2
. ) . * ,7853 ' < ) 6
' 2 ) 2 35. 8 ) * "-0 '#" 35. : .80535. 35. 3 ' " *`6: 2 2 ) .S,G2 ' * 2 )+& 35" 2 . ' 3/. *@0 " ' :;2 352 ' "
. " T < 2 2 , 2 = * .%35. 8 ) 2 35" * ,929" 85" 5 ' : 26. * .(0=,G.F. ) "10 ) .(2 ' * .805> ) .(0 ' * 29.
)
=$
.82 * ''"
: ' 2
-4 F5 M 8
.(26" 0 & " 2 &8') 8 )
* " <0 2 3 2 35. -4
K;L;M
& .(2 & 2 35.
: 2 26,9"12I3
3 2 ' 2F6
5
2
)+&
B2
B2
2 * .(2 F5 M. *
3 2* '
35" 2 <
T
032
QP
G
=.= H
2 *
. * , ' &(' 0,9"13 0=8 )
"10=,G.82
'
2 )
29" 2032
& 852
<5852
2
"*
03254
3
2
2
.
0
"
032
2
0
<
3
2
T
*4'
ON
' 35.
2
4
T
' W
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-3
" <8/2
J
2
-2
H" * ,929"B2 5" 5
T
<
-1
' 0 ' 2 )
8
N 0
. * ,G" :
4+2
8
&(')
254
4 5. 4
=8
35.
2
+
8
B2
M ON
N
)
N(
N 35. * (& ' 0 5. & 1" 3 ' :62 2 292`: ' : 8 4 2 5
* ' 529. * . ' "-0=G, .(2 03254 ' 35. &8' 0
0 ' 2 ) 234 "/' 0 .(293 2 35(. "-2 ' 03254 ' 2<3
2
0 3/. ' 5
"!+"-, & 5. 4
03254
' 2
(
35.80 ' ,
'
/
35.(0 ' ,
T\VV P
2
"
35. && '#
4
)
8
K
<
)
2
<
2
2
<
0#5
2
)&
2
8
)
8
053 '
35.K.
=8
2
) 2`: ' : 8 4+2 5 '!&(') 8 ) 2 )+& 35" 2
0 ) (. 2 ' . 4 . 032 3 ' 35.7. 4 . ) (. 0=, ' * " .80, '
: 2 2 2 8 ) 2 35" * ,G26" ;85)" 5 ' 0 ' 2 ) 254 ,G.80535.82 6
&(')
29.S,G"-2 2 3
1
"
2
)+& 35"
2
2
.E3/. *@0 " ' :62 352 ' T
2
2
<
)& 35"
2
02
2
/ E + "
2
.!35. *@0 " ' :62 352 '
2
)
2
<
"
) ' * ,G2 2 35. . 0 (. 0=, ' * "1053/. : .(0535.80=,G. *
: 2 352 '
8 )
3/. *@0 " ' 6
05" , ' "&(' 0, &() 8 )
3 " * ,G29" ;85)" 5 ' 3 22 ) ' * G, 2 2 " &(') )+& 35" 2
5
)
8
Z )
3
3/.
05234
'
^
7
* .
8
2
S
<
4 5.
' 26. *
=8
*
8
* ,G.80=, 2 )
*6* ' & " 2 3 ' 2 . * ,9. -" 0,9.(2 05234 ' .;3#" * ,G. 8 ) 2 * 8 * ,9.(0=, 2 ' 8 0 ' , 254 :62 2 ) .S,G2 ' < 2 2 2
35" 2 . * , &(' 0,9"13 ' 358. 0=,G2 ' 3 ' 1" 0=,G.82 03254 '
N E +
35" * ,G26"B2 5")5
:62 2 ) S. ,G2 '
ON N )
8
2
8
)
2
'
;8
<
/ I 2
0 3/.(0=,G. 2 ' 0 * 0 . 4 5
3 . * " <0/" & 0 & " 2
8& ' 0 * , 2 0=,G. &8' 2926. *9: ' 5
<.82 254 " 8/,9" 4 " ( 2 = * .8 ) 0 * 0 . 4 35. * ")<05" & 0 & " 2 /3 .$#% " 6: 2 2
/ ;M
"
2
2
Y.
'
4+2
4
<
=8
234
T
'
T
I 2
2
Y.
4 2
<
T
254
' 29. * 3/.
*
0
.
4
:;2 2
2
35" .(29.80=,G. * 0
M /
35. * " < 05" & 0 & "
%
K;L LQMM
M# %;M
#;LQM
##QM
*
2
0
<
T <
#
S
S
<
T
<
T
<
SW
T
0
1V 0
<
W
< / .8" * 35. * ")<05" & 0 & "
0
P
2
<
V
T
' ' /. * . * .<8/. * .82H35. * & 29"-, 3 . 4 ' * 3/. : 29. 0 " * ' 1" 0 *6: 1" 2 2 3 ' *
' &(') ' * . : 2 '#& . 6* *722 & 29" 2 5 ' 3 ' * C
) ' /
0 ' * : 2 '#& . *9* ' * 35. . 0 ' 4 8#5 ' : 92 > : 26" ' * 3 ' *D* .(29. * 0 " 0 ' * "&(' 0 * "1/
3 .(2 2 5
0 3 ' 2E* & 26"1. ; (;
' . & =
5 ' < < * , 2%* & 26"1. &8' 0=, &() 8 ) , ' , 234 53 .FT ' * .(2 032 5#. * 2 . 4+2< T " 85. * .(2 ' 35" 0 1" 3/"13 2*
. ) 3 ' " * &8' 0 7@850=, ' * I
/,G" 4 )" (
"!$#&%!(' N*) "
"!-#.!0/(#1! "
03254
4
I
<
2
2
8
' 29. *
. 4+2;< T
29. * <
X,YZ[Y
X,YL_La
X,YL_X
X,YL_L\
X,YL_L^
X,YL_Z
X,YL_L_
X,YL_L`
X,YL_Pc
X,YL_L]
X,YL_LY
X,YL`La
"
8
:62 2
3 ' *<:62 2
"2 2
2)03254
'3#54768':9 )
. )
2
2
0
2
2
2
,
2
&8' 0 * ,92-8#5
2
.
8
254
4 2
"-3
2
35.
'
A"BC
XLX,]
X,\L`
X,_La
X,]La
X,YL`
X,]L]
\L^L^
\PcLc
^LaX
^X,]
^Z[\
e[o?l
D->E
X,^L\
XZbX
X(cd]
X,YL^
\L^L`
\L^L_
\L`Pc
^X(c
^L_L`
^L`L\
Z[aL`
hjldo
FHGIE
X,\LY
X,^L_
X,`L^
X,]X
\L^L_
\L\Pc
\L`LY
^X,^
^Z[]
^Z[]
^LYL`
hjfPl
.(2 &
8
& "
2
3 '
T 03254
' 29. *
,+
.
) ' 35. 4 ' 3/. : 29.
0
"* '
;4
,9" )C' * T
<
< .("-2 ' * 35.
) .82 'K) .80 *7234 :;2*9*-2 =?>@
XLX,\
XLX,_
XZ[_
X(c7X
X,YL`
\LaZ
\Z[\
\L]Z
^X,_
^Z[a
^L`La
hmln
' 3 ' ) ' 35. 4 '
D->J
X,\X
X,\L_
X(cd\
X,]L^
\L\LY
\L^Z
\Pcda
^X,]
^L_L_
^L`L^
Z[\La
hpn0g
8
=LKI@
X,^L_
XZ[Y
X(cd]
\X,]
\Z[^
\L`Z
^X,_
^PcZ
Z[\L\
Z[^L_
Z?cd\
kLe?k
T 5
T
)
2
&8') :;2 0<5"
=LKIM
XZ[]
X(cda
X,YLY
\L^La
\L`Z
^LaL\
^L`Z
ZbX,^
Z[`L_
Z[YX
_Z[]
fg[g
FHNPO
XZ[]
X(cda
X,YLY
\Z[\
\Pcd\
\LYL^
^Z?c
Z[aL_
Z[`Pc
_LaL_
_L_LY
f[iPf
2
2
&
Q7BR
X,^L`
X,_L]
X,]Z
\LaLY
\L^Pc
\L_LY
^X,\
^L_L_
Z[aZ
Z[aZ
Z[`L^
k[idq
29.
2
"-0,9.(260
SHKIR
XLX,Y
X,^L^
X,`L\
X,YX
\XLX
\L\LY
\PcZ
^LaL`
^Z?c
^L_LY
Z[aPc
hjfPl
2
& "' 0
TUO,C
X,aZ
XLXZ
XZ[`
X(cd\
X,]La
\LaL^
\L^Pc
\Pc7X
^LaL_
^X,a
e?fg
ePo?i
254
VUBW
XLX,]
XZ[a
X,`L`
X,YZ
\LaX
\L\LY
\Pcd]
^LaL`
^L^L`
^L^Pc
hjiLk
hbeLg
. )) " =
T 2
2 8 ) 2 8/. * , ' 35. * " ) :;4 " 2 & 2 5 '#"' : , 2 2 = * ;. =. : . 4+2 . * &(' 4 < 2 35. )C' /
3 . 4' * 5
3 . : 62 . 0 " *! ' 35. ) .(0 ' 2
' /
& 2 2935"-0 254 -" 3 2 35. " 8/9, " 4 ")( 2 0/3 ' = * . 2 N !(6 . !
L ) % 6 !0/(68' ( N #.! & Z & Z & < )" <852 2
< T!;. 3#. ) ;: 4 " 2 & 2 8& ') ' *! ' <.(2 2 3 ' * ' * & 2* ' * 53 .`,G26.("-0 ' 2 ;: 2 26,9"12 35. * , 2 7 2 05. 4+2 <
#
L L &&& K% % # K && Z & &
&& /Z & ")<852
#%$'&
2
Z
< T "!
/Z
/Z
* ' * 5
3 .`,G26.("-0 ' :62 2
2
&
Z
K
& &
F* & 92 "-. :;2*9*-2 < .("-2 ' *
2:2
<
(*),+-),.0/1),24365879;:<.>=?7-:<+:@3A),BCBD:5E79F:'.
IKJ <8MLON 2 " PI J'Q RN J'GSUTMIWVXQ 2 N SRY'SUGSRIPJ[ZQPS\Y'J'IKI 2 2 2 ZMQKJ'T NML)( 2 < J'G Y<SUG S]I^G_S N J 4 SUI N J
22 Q 2 2 Y L 4 L V 2 Q 2 J 3 ZSUI L)5 S " 2 ZJ'T 2 IcIKJ'Q 8 V L 4 L ( 2 N S_S-ZMQ L G_J L QPS_Y 2 IKS N JEVXQKJ L TMS ed /'b
&& Z && /Z && % Zgf h & " J'IPY<S 4 < J'T N S = IPJ 8 G 2 VPSUZS 4 S <UL 2 Y<SUG 2 ZJ<T 2 I 8 GiTMS N S L T VPJ'QPG & =
NML SJcIPJ L IjY'S]TMJ 3j J'I " Y<SUT SUQKG_J N J'IKY'Q L VXShT 2hk L <8 Q 2 < <"l I 03254 SUQKJ'I L T L Y L 2 L I N SUIjZJ'IPS]I N 2 QPJ N J
I S < J<Q 2 N S]I N J SUQPG 2 254 J 2 VXmUQ L 2 " IKJ <8 T N S 2: m]QPG 8 4 2 ZMQPSUZSUIWV 2 ZSUQ%n 254 4 2 T Vo TVV qp : J'Y 5 S
< T < <
2 GJ'IPG 2 2 <8 Q 2 V 2 G & GrIKJ 2 ZMQPJ<IPJ<TV 2 G?SUI 03254 SUQPJ<I N J L T VPJ < Q 2 5 S es " 2 '3#:4768':9 ) J
2
" 2tvu 'xwzye{| YV L 032 5 S N JFY 2 N 2 TS N S
HG
`,a
#
L
#
K / (
(
# d ^ }X€ d 1 ^ }X€ 1 dx ^ }X€ 
s~} # && & && L q & & % & # …„
'/ } # & &
@‚<ƒ # & @
sx† # && # && % & /'} # % K / † # s† #
% K s~}
X
[
[
;
X
X
X
A]
[
X
^
AX
[
X
[
[
O‡ <
[
N L ( 2 < J'G N 2 QPJ N J < 8L PI J'Q 8 V L4L( 2 N S
ˆZ 2 QWV L Q N 'J IWVXJGSUG_J<T VXS " ZS N J L T L Y L 2 Q = IPJ 22 M
Z QKJ'T ‰ `;‹Œ‰ " 8 J N J<ZJ<T N J N 2 Y<SU_
N L <J T VXJ " N J 2 'Y SUQ N SS]I
S 234 < SUQ L VPG_S `,Š
G Z 8 V2 5 S N 
S QPJ<IPZJ'YV L 0 S < Q 2 M
k L)<8 Q 2 < Y 4 Y 8 4 SUI 8 J 2 PI J <8ML Q,IKJ 2 ZMQPJ<IPJ'T V 2 G
1 −0.31
112
Nodo 2
0.24
118
−0.31
Nodo 3
Nodo 4
Nodo 5
−0.27
−56.2 −56.2
−42.2 4.7e−19
k L <8 Q
< 2
fa=linear
fa=logística
−0.01
115
I SUZS
4
S U< L 2 L T L Y L 254 Z
2
Q
2
`,a
2
<
/ † #
f /† # & K % KH # & L /†  †P€ # es† / # & & & # &&
 †P€ # /† /†  †P€ # & L && # & }
/} # /† esx† ^ % # & L & # # / }  }X€ #
…s~} / #
& &
/'}  }X€ # 0/ & / && # %H † & @  }X€ # '/ } /}  }X€ # #H %H & @ # 9K & @
!#"
w5,1=−0.49
Nodo 1
‡
$%!#"
<
$&
$&
−2.0E4
2.6E−15
112
−8.6E−17
2.7E−15
118
2.7E−15
−2.1E4
115
k L)<8 Q
< 8
< 254
SUQKJ'I N S
< Q MN L 'J T VXJFZ Q
2
2
2
2
`,a
<
ZmUI6SY 4 Y 8 4 S N S < Q 2 NML J'T XV J " ZS N J"J 3 <J Y 8 V 2 Q = IPJ 2 ZMQ L G_J L Q 2 L VXJ'Q 2 5 S N S 254 < US Q L VXGS `,‰"`F‹Œ‰
J < J'Q 2 8 G 2 M
T S 032 G 2 XV Q L (ŠN C
J ZJ'IKSUI " J'G 8 C
J IPJDTMS]V 2 8 G 2 PQ J N;8#5 S N S J<PQ QKS N D
J VPQPJ L TMS k L)<8 Q
S 2
"
2
<
J<QPQKS N E
J VXQKJ L TMS 2 T 234 " Y<SUTMI L N J<Q 2 T N S4VXS N SUI ]S I Y 2 KI SUI N JEVPQPJ L TMS " & S V L N S
<21 < HIWV 2 PQ J N L VPJ'Q 2 5 J'I " Y'S]G 8 G 03254 SUQ N J)(+*, .-0/
k L <58 Q 2 J ZMQKS N
l
# S 2 G N J ‡''
'
2
8#(
I IPJ <58ML T VXJ<I
2
‡
w5,1=−0.39
−0.41
112
δξ/δs5=−159.5
−0.17
0.14
−76.7 0.00
118
−33.5 −33.5
−0.41
0.09
115
k L)<8 Q
ZMQKJ 0 L I J<I 1< 2
K
&
8 ;
J Y'SUQKQPJ'IKZS]T N J'G
2
I SUZS
# S ]< L 2 N
4
#
`,a
2
K
U
G0J'QPQKS N JFZMQPJ 0 L I S N J
8
2
ZmUI
L VPJ'Q
2
5 S `,‰Š`;‹Œ‰
2
<
K q % L K & L L
# & #H?L
% & %% % #
(+*,
G
8
/
<
450
400
350
300
250
200
150
100
50
0
0
k L <8 Q
2
<21j
20
0
S
40
#5 S N SJ'QKQPS N JcVXQKJ L TS
4 8
60
(+*,
80
2
S
4
SUT
100
< S N J ‡'' L VPJ'Q 5 'J I
2
<
' #%$
;5;3A:
5E.
"
"
Y'S]TMIKV L V
(+*-+
G
"&%
$#
IPJ<T N SS_GS N J*#OS,+
ZJ "
*#
(
*.+
I
J'T
%
* N ShZJ I 7
%
+
"
"
#
#
ZSUZ
TMJ# " I "
%
#
5 S " Y'SUG IPSUGJ'T VXJ "
"
J
"
*#
!
10
I
<"
2
‡
='
N J
"
P
@0 11
'A0
D
(
+
='
=
@0
'@0
"
2 SUZ
10
J

-K
#
5 S LT LY L
J
}
*-+
F=,?
"
#
"
"
"
4(
ZV LON S (+*,
N L" N JFG & M
J ;
K ? L & 1  %
9K;L 1 "# & & U 1 U  1 9L #  #
0
‡
'
10
$;
, " IKJ'T N S < J'Q N SUIAVPQ <I6TMS S]I L T NL * N SUI "
"
(
HG
)(
%
I
J
0
I
J'G % J NM N J'TMS]V " S < J'TJCT " ZSUI L)5 S N S L T NL)( * N % SO " P" ZSUZ % # " 5 S Y'SUTIKV L V % * N " ZJ*#OSUI TMS ( SUI
LT M
N L)( * N % SUI <" J# " 0 " " % G " NML IWVXQ L % L)5 SRQ CS /0/(' CT S %UT ) %@
6 Y<SUG G & NML " J
N J<I (\L SZ " N Q S " " J K & % G ( " # S]Q < J'Q " N S " # J " VXm]Q L SEJcZJ<QKVXJ<TMY'J<T N S " S L T VXJ<Q ( " # S & V0
l ZMQ L G_J L QPS L T NML)( * N % S & Y<SUTMIKVPQ % * N S " VPQ " ( & I N J % G " G % V " 5 S IPS QPJSVXJ<QPY'J L QKS < J<TMJ


N S L T NM4L ( * N % S_ N " ZSUZ % # " 5 S L T L Y L " #  0 l IQPJ<IKV " TVPJ'I L T NML)( * N % SUI J I S^Y'Q L " N S]I
"
VPQ " ( & I N SY<Q % ( " GJ'T VXS " Q L VXG & V L Y<SJ'T VXQKJFSUIjZMQPS < J'T L VXSUQKJ'I J N " ZSUZ % # " 5 SESUQ L)<UL T " # " IPJ<T N S
L N G'T V L Y'SUI N J (\L N S " S W" Y<VPS N J K
'% 0
2" Q " Y'S]G_8Z #OJ<V " Q " L VXJ'Q " 5 S " QPJ'IWV "X" IPJ# J'Y 5 S N SUIIPS QKJ (\L)( J'T VXJ<I 0 / " Z8# L Y " 5 S N S]I ( " # S]QPJ'I
I
# 0
1CB1
I
LK
I
0
-0/
+6587
# L# 1# # # 1 # ?L 
%
60
ZMQPJ<IPJ'T V " G "
J
"
'% & %
& % '% & %
% & % & 
"
SUI
%
,
N S>=,?
5 S N S
I
(
"
1#
#
J IKJ < % LON " " & " Z8# L Y " N "E" M
C
Z Q L GJ L Q " L VXJ<Q "
Y<SUQ N S Y<SUG*SUI,Y # Y % # US I % J " IPJ < % L ,
Q IKJ
%
"
# 1
*#
P
J
VPQPS L T NL)( * N
%'"
SUQ G OJ PV SUQ L GJ'T XV J
S * T NML Y'J N S L T NML * N S
9L % # 1 %  
& 9K & 1 " ## 1 '%  9L & 1 K  1
& & & & & & J 3 L J " Y'SUT 2 < % Q " 5 S N " ZSUZ % # " 5 S L T L Y L " # " SUT N J"SUI < 'J TJ'I
J,VXSUG " Q " G ( " # S]QPJ'IŠTMS L T VXJ<Q ( " #OS & & " V " J*# " " " Y<S$# % T "32 N J<TM]S V "
T " ZS]Z % # " 5 S " J'T %'" T VPS % J " Y'S$# % T " +6587 N J'TS]V " SFQPJ'IKZJ<Y<V L)( S ( " # SUQ N
9
IKV " ZSUZ % # " 5 S " ZMQPJ<IPJ<TV " = IKJ8Y<SUG % G ":" ZV L N ShG * T L G " N JE$; 2
/
‡
),7 :'BD58.0)E5<2BD:5E7!c36:5E.
2 Q J'IKV J 3 ZSUI L 5 S S L J'IKY'S <ML N
"
1
!
0
‡
I
J
<"
='
2
‡
P
‡
*#
2 SUZ
"
10
‡
'A0 1
%
(
G #
I
J
"
2
‡
=' P
(
+
'A0
A0
‡
2 SUZ
"
0
P
'A0 1
%
#
"
5 S
0
P
+6587
%
"
Zm]I
(
ZQ L GJ L Q
"
*-+
"
<"
0
;
0
;
*#
"
0
0
1
?K;L 1
% 1
% 1
%
Q
"
D
%
"
"
*#
#
< J'Q 5 S
"
% & & "
$;
1
W"
9L & 1 K  & 9K & 1 U  " ## % 1 ' %  U 1 & #  A0
='
*#
& 1 ]  & % 1 "#  & % 1 " #  %
4(
# K M } ( Y<SUG JIKJ 7 G IKJ OJ'Y'Y L SUT N SUI
" 1 " J 1 I J - JhTMS]V
* T L GS " S OSUQHG & NML S NML G L T L P N Q S % V L # L)( " N S]IhTMJ'IWV " PV J'IKJ &1" L T NML)( * N % SUI N JhY " N "% G " N " IcZSUZ % # " 5 <J I J
% J J<G US Q " IPJG " T VPJ'T < " S ( " #OSUQ N J " ZV OL N ;
S G
"
*-+
5 SY<SUG*SUI,TMS SUI L T NML * N SUI
"
#
"## % 1 '%  U 1 & #  U 1 & #  (
+
1
A0
'A0 1
Z
0
0
9L#  " # &  " #  " #  +6587
$;
P
1CB1
0
;
GS N J # SSUZV L G L ( " N S " Y<SUTMI L N J<Q " T N S % G " ZSUZ % # " 5 SZ " N Q S 1
' L T NL)( * N % SUI " & S V L N S
"
& " 'J G
S 2 G N " < <J Q " 5 S ‡''
' k L)< % Q "-0 0 " Y'US QKQPJ'IKZS]T N J'T N S "X% G%J<QPQPS N J (+*, -0/
%
0
!


J
& " + (
] U J *-+
& & US G J'KI VPJ
G S N J # S " JFJ'G0VPJ'QPGSUI N JFZMQKJ (\L I J<I " VPJ'G = PI J % J l
# K
# 1 K
% U &
K
U # 1 L K
# % ]S QPJ'IJ'IWVXJ<I % J^Y'S]QPZSUQ L)( " G % G J # J ( " N S 'J QKQPS N JZMQKJ (\L I S
J'TmUG_J<TMS N J / ) % ! $ S /(# -! T # ) "j % J " % L S <Y SUQPQKJ 0
"
(
#
F
# K K # & " N J \L N S
%%%% %% (+*
,
/
(
"
S
' ‡
36
34
32
30
28
26
24
22
20
18
16
0
k L<
%
Q
"
0 0
9
200
(
S$# %
400
5 S N S_J<QPQPS N JcVPQPJ L TMS
600
(+*,
800
"
S:# S]T
1000
< S N J ‡''
' < J'Q 5 'J I
"
0
P
‡
;
! " Z OV % # S
S SUQ " G " ZMQKJ'IKJ'T V " N SUI N J % G G_S N S I %
%
V L # L " N US IDTMJ<IKV " VPJ'IPJ 0Cl ZVPS % IPJcZSUQjJ'IWV " SUQPG " N J (\L N
VXQ " " # < SFJ'IWV " QŠTMS % IPS N SUIŠGS N J# SUI N JZQPJ (\L I S " IKJ " N
N SUI,IKJ'QPJ<I (\4L ( SUI ~J;T S " N J J'I " N J % G ":" Q % L VXJ<Y<V % Q " N
I % IKVXJ<T V " G 0 S N " ( L " xTMJ'IWVXJ " Z G<T NML Y'JEZQPS\Y % Q " Q IPJ N "
N J (\L IWV " N S % V L # L " N SUQŒS % ZMQPS UQ " G " N S]Q N SI L IKVXJ<G "@0
'
$'&
(*),+),.
,+
65
#
=
/1),2-3A587 9F:<.
-/.
"
%
"
"
#
"!
Y L TVPS "SUI " G L J'T VXJ<I N J ZQPS UQ " G " S
S " S " YVXS N " G'T " IPJ % JFIPJFZ ]ITJ'IKVPJ
S]IŒTMS]IŒZMQKS Y<J'IKIPSUI N JJ ( SC# % S8ZQPmUZMQ L SUI
SUI " G L J'T VXJ<I N JFZMQPS UQ " G " S % J8S]I
Q % G " ( L I S NML J<QPJ<TVPJ IPS % G ZS]TVPS
)(
*D:<9F:'.
3 :
0 21
43
‰Š`,a ^ZSUIKI L PV S N S G
"! ` ! "!0/ a ! % ) ' / %,#&' (9 ' ' /
Q LON Q Y<SUG `,a / TMSUGJ N G J'T VXJ,Y'S]G QPJ N J'I"I ZJ'Q \L I L SUT
QPJ<Y'SUQKQPJ'T VPJ
G IKJ L N I S N J'IKY'Q L V I IY IPIKJ'I N JES KJ<Y<VPSUI
N J `,a / "
S
#
=
0
"
"
T
"
728:9<; ;>=@?
ACBEDFB
G u>HI wzyKJML |NM ! IPIKJ J L N Y<SUG*SY'S]T65
OQP {|SR | HUT wqy tVI yXWVY~y H
Z Y 'H u>H\[^] y I6v_ u yewz|a`
G u>HI wzyKJML |NM ! Q L SUI,Y IPSUI N JcVXQKJ L TMS Z
egf u>h Wjei |VMgk>lmnmpoqsrutwv>oqsryx{z l|~}FV€
#
':! T #1!"! ‰ % ) Q % )
Y'S]T % T VXS N J % TMY L SUT " # L N " N J'IHZ "
N " I N S_V L ZS % T LONML QKJ'Y<Y L S]T " # S %
%
T N " G_J<T V " L IjZ " Q ":":" Z8# L Y " S
l
# %$ &
9
=
%
"
"
"
QKV L Q N J

‡
PB
%
G
%
=
"
T VXS N JFY " KI SUI N JcVXQPJ L TMS
%
=
"
"
*#
%
5
(
"
0
4b ] y I6_vu yew|dc
2 Y < J L QPSY'SUG0STSUG_J
6
%
0
"
‡1
'
H Y h | W u w/Y{|xw [ T Z `
G u>HI wzyKJLM|NM! GZMQ L GJ SY'SUT VXJ#" N S N SUI,Y IKSUI N JcVXQKJ L TS Z Z Q SZJ'Q L %$ Q L Y'S N J;I N T&
egf u>h Wjei |VM '\)q (>+| ** v k>lm~q>m zn-,>rn/.10 q24350>}6** oqr<€
7 |yKR H Y 7 u"[^] y Is_ u y…w|a`
G u>HI wzyKJML |NFM ncQ SUI,Y IKSUI N JcVXQKJ L TSZ Q G 2 Y < J L QPSY'SUG S_TMS]G_J4b ] y I6_vu yewz|c
egf u>h Wjei |VM%oqryx^m9l 8n t:v>oq;r :<x z l|~}FN€
y t {h{ u>H { [ `
G u>HI wzyKJML |NM <,J<VPSUQPT ST="MGJ'QPS N JFY IPSUI N JcVPJ'IKVPJ
egf u>h Wjei |V>M .10 | |nm/;| ?\odqsryx |nm/|<t)N€
y t {h{w/~
Y y t y tA@j[ `
G u>HI wzyKJML |NM <,J<VPSUQPT ST="MGJ'QPS N JFY IPSUI N JcVPQPJ L TMS
egf u>h Wjei |V>M .10 | | r /l .10B.C0;D?\oqryx |>r El .10B.10;D<t)N€
egf u>h Wjei | R |GF |xw h Y {| R |IH I6_ u yew|GJLK u I | t { P h | HUI Y H | H R u {w u y t |NM
MON ,>r El .10B.10;DP'lmnm
| {w u
"
" (
"
"
"
"
"
"
"
"
"
"
"
"
%
0
0
0
QIR=R : R=RCSTR=R5UWVQXR :Y V
QIR=RCSTR N : R :=Y VQXR1Z[R\V
QIR N : R :=] R1ZBR^VQXR N U_V
M :`, 6'
QIR :=] R : RaR N UWVQXR : U_V
QIR : RaR N UPR : UWVQXR1Z ] V
nm6| lmnm
728:9<; ;>=+bcb
G u>HI wzyKJML |NM $ Q V 6 IPJ
"
"
N
"
Y*# " IPIKJ;Y<J'T VXQ
"
#
Z
"
Q
"
"
s ShJFG
Y<Q L "
"
T LZ
%
#
S
"
N J `,a
/
0
0
‡1 ‡
OQP {|SR | HUT wqy tVI yXWVY~y H
] ] [ e ) u] `
G u>HI wzyKJML |NM ! Q L G `,a Y'S]G G Y G N L T VPJ'QPG $'NL zY'SUG VPSUZS S L Y<SUGZ JV GJ'T VXJ
L TVPJ'Q L N e SUT N J e J N J<TMS]V G S]QPJ'I N S,V L ZS L T VXJ L QKS y t { IWVXJ"Y'SUTIKVXQ VXS]Q
N SUZV
T S N J Y<V L SZ Q VPS N SUI,SUITS N S]I N J 2 T L N ZJ S S]Q N
G
GJ'IKG
Q L J ] eJ OS IWV L Y IŠJ'T VXQ N I J Y'S]TMIKV L V J'G
Q L J L I N SFV L ZS S S J TMS
N J 2 T L T N S J L IKV 'TMY L N I L J<I N J +' / J N J V < S]IY IKS,SIKJ
SUQ IKJ:5
J<Q N N J L QKS
"%
"
#
"
(
(
"
"
"
"
"
"
"
"
0
#
0
"
{w)K u %
"
":%
"
"
%
"
"
#
"
HG
"
"
4(
/
0
(
"
"
"
C#
"
"
8#
%
9
#
"
"
"
%
"
#
"
"
"
(
"
(
"
#
(
*#
%
"
C#
(
"
"
#
"
#
"
"
(
0
egf u>h Wjie|VM r nzn t4: : R "!#{|>r (n$l&% mndN€
] ] [(' )c O `
G u>HI wzyKJLM|NM ! S]TMIKVPQ VPSUQ UJ'T $ Q L Y'S "! Q L G `,a Z QKV L Q N N J 2 T L S N J 'X S 5KJ'YVXS J
QKJ'ZMQKJ'IPJ<T V SY<SUT65 T VPS N SUI8TMS N SUI* L J T J'I N J YV L S + ) J<Y<VPSUQ N J L T VXJ L QKSUI
Y<SUT VXJ'T N ScS T="MGJ'QPS N JDTMS N SUIAZS]Q6Y G N + J O z G VXQ LŠN JCZJ'IPS]I N S V L ZS T L NML QPJ'Y<Y L SUT
eY IPIPJ ] ,] + O egf u>h Wjei |VM
- .10>| Q N V €| Q. V ?:C€| Q RCV ?:C€| Q : V ? R 0
€ //`,d2q 1 3q %~q D .sl
R
(=0 '6| .5q 0,&4516
n $ ?&7"! 8€ (=0B'/| .5q 0;,34519n $ : ?;:<2=>3?;@ €
- n '/| qs;r *5 (0 '/| .)q 0A9$u4t :dNB
€ $ Q. V ?$ R B€ $ Q R1V ?;$;:C0€ //C (=0EDFnm
: 5l 4 n\rd6
m %Vt:|FNG€ // k>l Hdl\z lm
=qsz n^
m 0 t %I$ N0€ //C=qszdq>m
5JKHyLt %
{|>r (n $ &l %>mn9
 //Ml|>r .2N z Mn 1nm\q>m
r nz n t 0#{O| PHaN€
] ] [^] y Is_ u y…w|a`
G u>HI wzyKJML |NM ! Q L G `a Z QKV L Q N J G 2 Y < J L QPSY'S]G*STMSUGJ4b ] y I6_ u yew|c
egf u>h Wjei |VM r nzn t:vnon H31<%~qux:l 0=0>}"N€
7 |yKR | K { W K { [ Q e RQ `
G u>HI wzyKJML |NM ! Y S J'YVXSUQ N JFI N Q N QPJ N J Z QKV L Q N S J<Y<VXS]Q N JFJ<TVPQ N Q e %
0
"
",%
%
"
0
"
*#
"
"
"
0
"
%
"
"
"
)(
%
"
"
(
%
"
0
#
"
"
#
%
%
#
"
"
(
"
"
"
%
"
"
0
"
"
(
"
"
0
‡1
egf u>h jW ie|VM
- @n~l % n t : mNt R V€
n Q. V ? R x . € n Q R1V ? . x . € // - l&%~qsrnmpz n n 0 |>r lz l
r nz n x 5q (>|;1(>|<t^n m>N€
OQP {|SR | H u w6RNYdvR | H RVY Z iXY HH'u
u Ydi u MY w6i H {| WV6W y t @ [w&T Z T Z CT Z ) VT ) e `
G u>HI wzyKJML |NM J'Y V SVPQPJ L TMS N QPJ N JM Y<SUG Y<Q L V $ Q L SUI N J Z Q UJ<G
\Z Q ShY'S]T65 T VXS N J Y IKSUI
N J4VPQPJ L TMS Z
IhQKJ'IWV T VXJ<I
Q L J L IQKJ J<QPJ'G IKJ m T ZJ'Q L %$ Q L Y'S N JI N Z Q S]I
QKJ'I OV N SUI N JhJ<QPQPS +uZ T J<Y<VXS]Q N JhQPJ L I JY'S]TV $ G?S]IcZ QqG_JVXQPS]I N SUIcY<Q L V $ Q L SUI N J
Z Q U J<G + T Z J'YVXSUQ N J L T VXJ L QPS]I"IKS QKJ NML J'QKIPSUIŒZ Q]G_JVXQKSUI N SUI"Y IKSUI N JVXQKJ L TS*eJ T="MGJ'QKS N JY IPSUI N JjVPJ'IKVPJ" + ) &] SUQ L VXGS N JjVXQKJ L TMS + T J<Y<VPSUQ N JQKJ L I J N J'TMS]V
SUIEZ QqG_JVXQPS]I N S U SUQ L VXGS N J4VXQKJ L TMS + J ) e SV L ZS N J4J'QKQPS
T VXQKJ-S VXQKSUIHJ<IKV S
NML IPZSUT J L IŒS]I U SUQ L VXGSUI N JVXQPJ L TMS `,‰A`,‰ Y'SUG #1!(%
) "! ) -! # ':9 ‰ % ) J
%
9
"
0
%
"
"
/
"
"
#
"
(
"
"
(
"
"
"
"
(
`,‰Š`;‹Œ‰
#
#
"
%
#
"
"
%
4(
"
"
"
(
(
"
"
"
"
"
"
"
"
0
"
(
0
%
%
9
T
S
0
egf u>h jW ie|VM
// k\r . |\r .q>mpz nlr l D nH
'\q50Fm6|P.10 | =<)? . €0//C=;H nrqMH10B. HFq z n./|nr l DFnm
'\5q 0Fm6P
| .10 | &?<)? R2.3.. € //C=;Hdn\rMq H!o . H"qpzn . |n\r l D;Fnm
.10>9
| ,;? U € //C /l .6o l z n |>r/n .10 q
@n~&l %M3>;? . x R 0
€ //Mnz .6z l z n nr>rq nm/|l ';.5q 0"r .q
- @n~l %a'"1yt N NI
€ '"1 Q . V ? =<NG€ '"1 Q R1V ?&?<NG€ '"1 Q : V ?; ,y€
// k>lm\q>m z n |>r /n .C0 q
k>lmnm 'Ntwv>oqsryx{z l|~}FV€
//#l%r $H n|>rq>mpzq m 'lm\q>mpz n |>r /n .10Fq
.10>| |nm/| ? . 0
€ //C=;Hdnrdq z n 'lm~q>mpz n |nm/|n
.10>6
| > m/;| ??%%6|>r € //'&"mlr |dqszq>am 'lm~q>Mm 1lr l |>r /n .C0 q
- .10>K
| 1 'Nt :N€ 1 ' Q. V ?5> m/|y€ 1 ' Q R1V ?|nm/|y€
//`, . 1 qpz n >>r~rq
>>r~rqr |nCt @;>"N€ // @;>)( @ 39,63>3?= +*,& ?@>!9>@@ 5@@t4?C@;"*5>F
S
0
"
‡1
//C?% Dqsr . |5HFq z n_,>r n/.C0 q
.10>| l|;?5@1 rq21y€0//C?% Ddqsr . |5H"q z n |>rn/.10 qC@+@ - @ n~l % 1 lCt4:N€ 1l Q . V ? . x R € 1 l Q RCV ? U . x . € //#lr%$H
//`,>r /n .10Fq z l r nzn
r nz n x:n~lr%4dm/|dq2131B.10;Dut '\q5(>|O '"1# 'I 1 'I^l|O 1dl:|ndN€
n|>rq>mC@@
dY i u ww|xw [) e Z `
G u>HI wzyKJLM| ! Y SJ'QPQKS N SV L ZS ) e N QKJ N JsIKS QKJ;SY<SUT65 T VXS N JFY IPSUI N JcVXQKJ L TMS Z
egf u>h Wjei |
k>lmnm 'Ntwv>oqsryx{z l|~}FV€
>>r~rqr |nCt@;>"N€ // @;>)( @ 39,63>3?= +*,& ?@>!9>@@ 5@@t4?C@;"*5>F
@n~&l % n ?\rnz n<x:n\r~rqsrutw|n '>V€
7 |yKR @ YdiXi Y t { u y @"_ { H\[ `
G u>HI wzyKJML | ! T L Y L L SUI ZJ'IKSUI N QKJ N Js ] J'Q N SUI N JG_S N S OJ VPmUQ L SD IKJ T N S mUQKG
I U J'Q L N ZSUQn
T Vco ‡
p
egf u>h Wjei | %r n\z n<x D l %%l 0>| /n .5D >| mNt)V€
h | W u w/Y {|xw [ T w u R u `
| H {w u Y G u>HI wzyKJML | ! GZMQ L GJ SY'SUT VXJ#" N S N w u R u Z Q SZJ'Q L% $ Q L Y<S N JFI N &T egf u>h Wjei | '\)q (>+| ** v @nzn 2 350>+} ** rnz nC€
7 |yKR H Y 7 u"[^] y Is_ u y…w|a`
G u>HI wzyKJML | FncQ SY'SUT VXJ#" N S N J G `,a Z Q G 2 Y < J L QPSY'SUG0STSUG_J4b ] y I6v_ u yew|dc
egf u>h Wjei | %r n\z n<x^ml 8n t:vn\o n H31<%>qCx:l 0=0 }FV€
u y @"_ { H\[ `
yt {
G u>HI wzyKJML | <,J<VPSUQPT ST="MGJ'QPS N JFZJ'IKSUI N QKJ N J
egf u>h Wjei | >.10 K| 1/?\r nz n x /n .5D >| mNt)V€
u
"
%
#
#
"
"
%
"
0
%
"
"
#
"
"
"
# #
"
B$B
"
"
#
"
%
"
0
%
"
"
"
"
"
0
" (
"
%
"
"
":%
"
"
0
0
#
"
s
egf u>h jW ie| Rv|_F |xw h Y{| R |WH I6_vu yewz| I K'| I | t { u R | P K h Y
J/n .)D >;| l|>r ./o2
‡1
I | h Y {| HW |Fi…| @ y Y
QIRWRaR V
QIRWRaR V
QIR a
R R V
= 2
Q .5DH . R .5D5H ;. R %;.10
: 54 2
Q .+R^V
Q : N V
Q ZWV
x
qsznm
m Fq /z m Fq /z
l nrdm
n~l\r R
V
x
728:9<; ;>=+bcb
G u>HI wzyKJML | IPIKJ J8G T L Z G G VPQ L& N JFZJ<IPSUI T LONML QKJ'Y'Y L SUT L I
OQP {|SR | HUT wqy tVI yXWV~Y y H
] ,] + O ([ ) `
G u>HI wzyKJML | DS]TMIKVPQ VPSUQ J_Y'Q L G G VXQ L&hN J_ZJ<IPSUI8Z Q G N N VPSUZS S L N QPJ N J
) Y<SUG_Z J<V GJ'T VXJ L T VXJ'Q L N IFJ'T VPQ N I J Y<SUTMIKV L V J'G Q L J L I N S-V L ZS
S S J TMS N J~T L T N S
J L IKV <TMY L N I L s J'I N J + J N J V MSUI#vY IPS S IPJ
SUQ
IKJ:5
J'Q N N J L QKSB {w)K u egf u>h Wjie|
- .10>| Q N V €| Q. V ?:C€| Q RCV ?:C€| Q : V ? R €0// k>lHdl\z lm
: 5l 4 n\rd6
m %Vt:|FNG€ //`,d2q 1 3q %~q D .sl z l r nzn
5JKHdl| r .2NuLt %
{|>r (n $ &l %>mnN€
] `
7 |yKR @ w/YdvR y u\t { [ Q e Q ) G u>HI wzyKJML | Y SUU Q NML J<T VXJ Z QWV L Q N SUI J'Y<VPSUQPJ<I N JcJ'T VXQ N JcI N Q e J Q )
N VPSUZS S L N QPJ N J ) DJ N S_Y<SUT65 T VPS N J T J'I N J Y<V L S ] egf u>h Wjei |
- @n~l % n t : mNt R V€
"
#
%
%
"
%
"
"
(
"%
#
"
"
#
"
"!%
"
A#
C#
%
G
"
"
%
"
"
/
"
"
"
"
"
"
#
"!%
"
0
"
"
"
%
"
"
"
(
"
"
#
"
"
%
0
C#
%
#
"
#
"
"
"
"
"
"
%
(
%
"
)(
"
"
"
(
"
$#
"
0
"
(
"
#
‡11
n Q. V ? R x . € n Q R1V ? . x . € // > 0>|>r l\z lmpz l r nz n
m Q. V ? . x U €0// - l&%>qsr z nmn>lzq`0l ml"/z l
- .10>| Q N V €| Q. V ?:C€| Q RCV ?:C€| Q : V ? R €0// k>lHdl\z lm
: 5l 4 n\rd6
m %Vt:|FNG€ //`,dq21 q3%~q D .sl z l r nzn
(=0 '6| .5q 0,&4516
n $ R ?&7"! €8 (=0B'/| .q50;,3451n9$ : ?;:<2=>3?;@ €
- n '/| qs;r *5 (0 '/| .)q 0A9$u4t :dNB
€ $ Q. V ?$ R B€ $ Q R1V ?;$;:C€
=qsz n^
m 0 t %I$ N0€ //C (=0 D;Fnmpz n l '/| .58l D q
.
.
D? x 0
€ //610[. '.s&l % .2N l Dq z-q D~r lz .n 0>|n
5J D?H l|>r .2N x D~r lz .sn 0>|<t n Rm %
0# DFN€
] ],+ O |FW u w/Y {|xw [ `
G u>HI wzyKJML | IWV J OJ'Y'JcVPS N S]IS]IZJ'IKSUI N G VXQ L Y'S]G*S SUQ N J egf u>h Wjei | Hdl|>r .2N? . x . €
7 |yKR | K { W K { [ Q e ) C]IQ `
G u>HI wzyKJML | Y S J'Y<VPSUQ N J_I N Q Z QKV L Q N J G J<Y<VXS]Q N JJ'T VXQ N Q e N
VPSUZS S L N QPJ N J ) DJ N SY'SUT65 TVPS N J T J'I N J YV L S ] egf u>h Wjei |
- @n~l % n t : mNt R V€
n Q. V ? R x . € n Q R1V ? . x . € // - &l %~qsrnmpz n n 0 |>r lz l
- .10>| Q N V €| Q. V ?:C€| Q RCV ?:C€| Q : V ? R 0
€ // k>l Hdl\z lm
: 5l 4 n\rd6
m %Vt:|FNG€ //`,d2q 1 3q %~q D .sl z l r nzn
(=0 '6| .5q 0,&4516
n $ R ?&7"! 8€ (=0B'/| .5q 0;,34519n $ : ?;:<2=>3?;@ €
- n '/| qs;r *5 (0 '/| .)q 0A9$u4t :dNB
€ $ Q. V ?$ R B€ $ Q R1V ?;$;:C€
=qsz n^
m 0 t %I$ N0€ //C (=0 D;Fnmpz n l '/| .58l D q
Hdl|>r .2Nyx 5q ( ;| 1=(>|<t n %I 0, m>N€
OQP {|SR | H u w6RNYdvR | H RVY Z iXY H'H u
7 |yKR @ YdiXi Y t { u y @"_ { H\[ `
G u>HI wzyKJML | !!" ! $#%'&)(*%+#%', .- /10 " ("0 ,2#%',2(3-$#4,2# ( /150 # %+( ,# 50% ("0 , 3&6#087
/:9<; =
eg?f > h WjAi @ Hdl|>r .2Nyx D &l %%9l 0>| En .5D >| mVt)V€
"
9
"
*#
"
(
"
0
#
"
"
C#
%
#
#
"
"
(
"
"
"
%
%
"
%
"
(
"
)(
"
"
"
0
%
"
'"
"
#
F"
'"
# #
"
B$B
"
0
H"
!"
#
*"
%
"
,%
#
"
;1
H Y h @ W > Y @ [ T O `
G.> HI JL2@ ! -$&20 -$( # # /1( " ,2# , 3- /+0 ,2('&)(*%+#% O & 0 3#
eg?f > h WjAi @ '\q)(>|+** v;l| r .2N z nM1dnm\q>m24350>}6**MHdl|>r .2N<€
> %@"_ /H\[ `
G > HI J2L @ < (*/+#0 # =" -$("0+# ,2('&6("%#% , - /+0 .
eg?f > h WjAi @ >.10 K| 1/?Hdl|>r .2Nyx En .5D >| mVt)N€
728:9<; ;>=+b
G > HI J2L @ %+%( ( , #- 4("%8,2( / #
.
OQP @SR @ HUT VI WVY XH
] K VI @ ([ ) ] `
G > HI J2L @ 0 - #.,2( / # ,2# / &)#*) ] ( .
2 ! #
eg?f > h WjAi @
//C (=0ED;F\nmpz n l '6| .C8l D q z .\"m 1F5q 0 C8En .\m 2
//C:<2=;>3?@ Lt % .10n~lrF
//#;J >@t 1 qr |>rd3q D\q>m>
// 7"! Lt %~q D ~m/| . 'ld
//`,3?= @t:|l 0 D n 0>|n B."1nr 3%;. 'l
// 2= t mn 0 q
// 3k t '\q>m9n 0 q 
// ;? &772?=@t D l ("m~m .sl 0dl
// +*,& ?;@3> t (lz~r l\z l
(=0 '6| .5q 0,&451n ,3?&7"! €
@n~&l % ;? R x . €
(=0 '6| .5q 0 $ut ,& FN€
@ >
'"
>"
'"
"
T
&)(*0 %$ 0 # ,2('%" ,'"
0
"
8"
"
0
#
"
%
#
'"
%
3"
(
"
80
">%
)
"
*#
>"
%
,"
0
*
/.
10
20
+-,
(
"
N0
0
! #$% #"HQ$ &%(' T (
#"
;
Ydi4R > 7 > [ `
G.> HI JL2@ ! ,2("0 , , # ,2( / # & 0 3( /+0 , eg?f > h WjAi @ @n>l&% z?;$yx znr .C8nCt . x] UU N€
> Ydi @ W > Y @ [ ` [ `
G > HI J2L @ ! # #0 , #$,2( / #3& 0 ( /10 , $
.
eg?f > h WjAi @ @n>&l %-8;?;$ut . x ]=] U V€
h @ W > Y @ [ T C] `
@ H > Y G > HI J2L @ ! -$&20 -$( # # /1( " ,2# , # ,2( / s#U] & 0 3# &6("0 %$ 0 ! #3,( % , UT
.
eg?f > h WjAi @ '\)q (>+| ** 3v (=0 D q z Cn ? '/| .C8l D q 2 3)0>}P** <€
7 @ R > YdR [ Z `
G > HI J2L @ 2- #$,( / # 3& 0/ 0 , %+( *2" $,( 0 /1(*0+(*% Z
.
eg?f > h WjAi @ $yx{r n~lzutwv m .5DH";q ./z R x . }FN€
728:9<; ;>= A yD B
G > HI J2L @ %+%( ( (*%/ ( ( ( 3/+#&6# # ,2( 2.
OQP @SR @ HUT VI WVY XH
+Y > 6H\([ ) `
G > HI J2L @ # %/+0 /+#0 ( / 2- ( /+#0 ,2( ! /1( 0+#% ) .
eg?f > h WjAi @
- .10>| Q N V €| Q. V ?:C€| Q RCV ?:C€| Q : V ? R 0
€ //`,d2q 1 3q %~q D .sl
: 5l 4 n\rd6
m %Vt:|FN€
W K /H[ `
G > HI J2L @ ( # ( # =" - (*0+#$,2( #4,2#% ,2('( /10 , 3, 0+(*,2(
.
eg?f > h WjAi @ >.10 T| .C01=(>| 9m ? %Cx .1031=(>| mNt#N€
>
"
%
#
"
"
#
"
(
'"
'"
%
3"
(
"
'"
":"
"
'"
0
"
%
#
#
"
(
"
8"
#
%
3"
(
"
'"
H":"
"
'"
0
'"
%
3"
(
"
'"
"
H"
%
G
"
%
"
(
"
"
'"
'"
%
"
G
"
#
"
%
"
3"
#
#
"
F%
"
0
=
H%
%
%
#
"%
0
(
D
(
#
(
H"
'"
'"
C0
"
0
8"
0
;
;
Xi Y > [(' `
G.> HI JL2@ ( # ( # =" - (*0+#$, - , 2( # / $ - # #4,2# '
eg?f > h WjAi @ >.10 | 0Fqsz n&%l;4 nr? %ux%l54 n\rut N N€
@aR > H\[ `
G > HI J2L @ ( # ( # =" - (*0+# /1#/ ,2( #4,2#% , 30(",2(
.
eg?f > h WjAi @ >.10 | 0/? %Cx 0 qz nmNt)V€
> Ydi @ K W K /H[ `
G > HI J2L @ ( # ( # =" - (*0+#$,2( #4,2#% ,2('% , , 0+(*,2(
.
eg?f > h WjAi @ >.10 |)q (>;| 1=(>|Fm ? %Cx )q (>;| 1=(>|FmNt)N€
h @ W > Y @ [ T ) `
@ H > Y G > HI J2L @ ! -$&20 -$( # # /1( " ,2# , /1#&6# # , $0(",2() & 0 3#$&)(*0 %$ 0 #3,2('% , T
.
eg?f > h WjAi @ '\)q (>+| ** =v ,d2q 1Fq %~q D .l 2 350>6} **9%j€
7 @ R > h @ 7 > ([ ' `
G > HI J2L @ < ("-$# ('# #4,2# ' , 3/+#&6# # .
eg?f > h WjAi @ %Cx{r n HF)q 8n t N N€
,H > [ `
G > HI J2L @ ( # ( # =" - (*0+#$,2( - , % , /1#&6# # .
eg?f > h WjAi @ >.10 |9m ? %Cx^m .N n t)N€
,H > [ Z `
G > HI J2L @ ( # ( # =" - (*0+#$,2( #4,2#% , - , Z
.
eg?f > h WjAi @ >.10 T| .C01=(>| 9m ? %Cx^m .N n t . V€
D
(
D
(
D
(
'"
(
#
"
"
'"
%
0
"
(
#
'"
#
N0
(
#
"
'"
"
'"
'"
C0
'"
#
8"
(
8"
"A0
#
D
(
D
(
"
(
#
"
'"
'"
"A0
#
#
(
'"
"
"
'"
0
"
"
'"
0
;CB
728:9<; ;>= DFB
G.> HI J2L @ %+%( ( ,
#4,2("% c # (*% # 2 ,2# ,2(
# ( ,2# #4,2#',2( 2
#
"
%
#
"
(
#
&6#,("0 " !2# % 0 -
"
65
#- %2# % /+# ,2( % 4("% ,2( " / ( " #80
# / " .# /1(*0+-$#
(
,2# "# " /+# ,2( (*%/ " # "%%+( - " 2 &8% # "0" ! #0+- " # &20("%+( /1(
%
"
0+(*,2(C0 / +% % - &'"0":#$%/10"% "0 % /1( /%20H"% ,2( = ("% / " *# "%+%(
% ( # *( - ( /+#% &'"0H":" # $ - ,'" % # ,2(3" / ( " #80
#
'"
OQP @SR @ HUT VI WVY XH
' @aR > H\[() IQ ] `
G.> HI JL2@ # %/+0 /+#0 2( / ! /1#&)# # ,( 0+(*,2( ) ( # ( /1#0 Q ] 2(
&6( % 2 # ,2( / # &)#0 , / &)# ,2( - , / A! /1(*0+- $ , % , , 30+(",(
eg?f > h WjAi @
- .10>| Q N V €| Q. V ?:C€| Q RCV ?:C€| Q : V ? R €0//`,dq21 q3%~q D .sl
: 5l 4 n\rd6
m %Vt:|FN€
(=0 '6| .5q 0,&4516
n $ R ?&7"! 8€ (=0B'/| .q50;,3451n9$ : ?;:<2=>3?;@ €
- n '/| qs;r *5 (0 '/| .)q 0A9$u4t :dNB
€ $ Q. V ?$ R €B$ Q R1V ?;$;:C€
=qsz n^
m 0 qzq>mNLt %
$ N€
7 @ R YRjR [ T ] `
G > HI J2L @ 0+(*% ( / #$,2( / #U] &)#% # T
.
eg?f > h WjAi @
(=0 '6| .5q 0 $u(t 72!O :<x . N€
0 qszq m x:lz~z<t N $ V€
,H > [ `
G > HI J2L @ ( # ( # =" - (*0+# /1#/ ,2( #4,2#% , 30(",2(
.
eg?f > h WjAi @ >.10 | 0/?90 qszq m x 0 qsznmNt)N€
h @ W > Y @ [ T ' `
@ H > Y G > HI J2L @ ! -$&20 -$( # # /1( " ,2# ,2#% #4,2#% ' & 0 #$&6("0 % $ 0 ! #3,( % , T&
.
eg?f > h WjAi @ '\)q (>+| ** 3v =qszdq>m 2 350 } **`0 qszq>mj€
"
H"
"
'"
H%
&%
"
%
%
%
'"
,"
"
#
(
"
"
#
"
"
%
(
'"
"
>"
8"X"
(
"
C0
/
"X"
%
3"
(
"
"
0
D
(
"
(
#
#
'"
N0
'"
H"
H"
8"
0
"
# /$ #$% ,2(
;
R > h @ 7 > [(' `
G.> HI J2L @ < ("-$# ('# #4,2# '
eg?f > h WjiA@ 0 q zq>m x rnHFq)8nCt N N€
' !
7
@ 0
(
#"%$'&()
+*-,./0%+*
21435&760%8#:9;<#*
#CEDFC5GIHJ=%+%( /K= (*- ML =/10# ON # #% L2 R ) L N =# N =%%+( T @ W Kji ) #SC5GIH N =%+%( /+("-$& N =8-W= % ,2( Q4! /1( N =%+%("% , XQ4 , ,P=% &6( N #%
5
( ("%% ,O=,2("% ,2# L / N =,2#0 ( 2 # /+0=6%+( #0]=
=,P= ,2( /+#,O=% (*%/K=%'9 < # =5^ ( Q ("% @_= A
& # &20 !2* &P= N ,2#:C5GIH ML ( #&/ - = -$#,2( N #%
# #0+-$( ,2(*% 0 /+#= /1(*0 #0+-$( /1( ?> ( #:@BA ;
,P=-$( /= % #% , RQ , L #% N =%%+( 7 = &6#&
(=S= Q = N = # A N =%+%+( 7 A
T # /1#4,2# ("%/+(U=- ( /+( ,2( &20+# 0=-V= # # ON # #% 0+( ("0 ,2#% YL ( &6#,("- %("0Z= [L %/K=,O=%Z\%
,2# - /+# ,2(*%/1( /10= = N # L -V= ,2("% 0 # ,2(*/= N T %% - #&/K=0 %( &)#0 L -V= ( &6#% # ,2# 54, C a`C
5 w )
e Ydi
// !n5$ .C0B.;D q zq#>rq
+<%nHdl
, mnr .n t:v;1lm~mn 0;Dnrdm x |Fm/}FN€ // +r .sn |nH&1 qsr l&%
- @ n>l&% ?;@<t4:V€ - @n~l&% &?ut4:dN€ @n~l&% & €G// kq\n5$ . '.n 0>|nmK?;@;&?
.1>0 |a,E)??;@ x^m.N n t)cb5&?yx^m.N n t)cb R € // ,lHdl 0 q zq .10 z .C8 /z (Fq
.1>0 |9= ;? R1Z €0//C=;Hdnrdq z nC1 r n 8 .\m;Fnm
// 1nrlzqsr nm_D n 0"|B. '\q>m
.10>|9=& ?;:C€0//M=Hdnrq z nQq21nrlzqsr nm
1n\r l| .q)0lrq21 R t ? - . xYed : : . R x . N€ // k\r (&N lHdn90>|dq lr ./|5H!| .='\q
1n\r l| . q)0 lrq21E: t 5 & ,O . x NN R R . R x . N€ //M=(>|l D q_D l F( m~m;.sl 0l
1n\r l| . q)0 lrq21 Q =& V € q21 Q. V ?q1 R € q21 Q R1V ?q21E:C€
// ~n&%n/'D q
.10>|a,+;? U. €0// k>lr~z .C0l&%;./zlz n z lC1 q21=(E%l D q
@n~l % , =? . xYgf),+ € //`,lo l z n mC( +Fm6| . | B( .D q t4Y .eh z lC1 q21(<%l Dq 
~ n&\% n /' | . q)0 lr m"1yt 2= , , @ ,& : J *>>&: @&?3=0E=& !3>\k 5@&? =0# R , R
V€
- ; ;
//#dq21=(E%l D q '\q2HO8l %~qsr nm |dq2Hdlzq>mpzqpzq"H 10B.q
dq21(<% *@ 3@E10 z 5. 8 AK1 q21yt , q21# =& m"1EN€
1 q21 x .10B. |3@ l 0 zq2yH t)N€ //610[. '.sl&% .2N l Dq l&%n~l| ,sr .sl
zq>m
0+;H
nrq>mpr n~lE.\m
q z n l98l&%;.sl D q
fn 8l&%W?`0n K>=8l&%?;@; ?ut mnr .sn &, ?;@O &?O= "V€
//#lr%$Hdn|>rq m zM
q ?3;>
.10>| &?? R2..3. € //C=;Hdnrdq H!\o . HFq z W
n D nr l D;Fnm
;? lr;* dq 1=(<% *@ @E10 z .C8O @n>&l %5A A-Dl 1lrut 2q 1#8=& "m 1# 9n 8l %I
,E . . 89,3? , 5?:: V€
/ /C (=0ED
>=8l %?;@;&?
5&?+ ,+O
/ /C?35>
;?aD l t Dl1lr 1 q1"N€
D l<x{r (=0 t)V€ // >>on 'C(>|l\rqpl&% Ddqsr . |5H"q
'
</3V7*$
./8* !7*
,2("% & =,P= /H F &6#%% N /K= # L %+# ,2#%:, (*0+( /+("% / &)#% ,2(3&20( Q4 %^#
-$( 2* # =,2#% =/1("%( 8 #-$( =,O=- ( /1( C H C a`C H ( `
C5GIH C5GIH A
=0=3/K= N 0+( #00+(=#%a=- ( /+("% ,2('&20# 0]=-W=s# C D UC (#CEDFC5GIH (\ N =%+%( )!A
728:9<; ;>=
G > HI J2L @ N =%+%( ML ( &6("0- /1( 0 =0 (:-W= & L N =0 % $ 0 ("%A
.
OQP @SR @ HUT VI WVY XH
)&u[^] XIs_ > @a`
G > HI J2L @ 0 = L -V=3% $ 0 ( /+("-$&)#0]= N =3&P=0/ 0 ,2( L - ( 0# #- # #-$( b ] XIs_ > @c A
.
eg?f > h WjAi @ , mnr .sn t:;v 1dlm~mn 0 D nrdm x | m/}FN€
h @ W > Y @ [ T ) `
@ H > Y G > HI J2L @ ! -$&20 -$( # # /1( " ,2# ,P=3% $ 0 ( ) &P=0= # &)(*0 % $ 0 #3,2('%]= ,P= T !A
.
=& N ! = # &P=0]== D
T
%
;e@
egf?> h WjiA@ '\q)(>|+** v +r .sn-,nH31 qsrl&%2 350 }P** mnr .snC€
> Ydi Y sh Y [( O ) e e ) e ]RQ T `
G > HI JL2@ ( / L =:= &0+( Q4 % # ,2( L 0/+# &20= # Q4 = -$#4,2( N #C a`C ,2("%,2( #.( N (*- ( /1# e .
=/ $ =# ( N ("-$( /+# e ] &P=0= #% #( " ( /1(*% O ( A Q ( /1#0 Q T
# / $ - #%
Q = N #0+(*% ,P=% &20+( Q4 % 4("% %+( ,2# ,( Q # N Q4 ,2# # ("00+# ,# / &6# ) e ,2(= 5[L %/+( ,#% ,P=,2#%A
eg?f > h WjAi @
- @n~l % lr<4t :N€ lr Q . V ? R € lr Q R1V ?!( . x U € // k"q H&1 5q 0n 0 |6
n ?;@
R
Q
.
V
.
.
- @n~l % HdlCt N€ Hdl ? x ]C€ // k"q H31F5q 0n 0>|n &?
- @n~l % 8;1yt R :N0
€ // - n '6|dqsPr '\"q Hlm 1 r 9n 8 .~;m Fnm
@n~&l % nr~rdqsr ?mn\r .sn<x:l\r Hdl t^l\r PHdl R x :@;5># R N : RCZ=Z 81"V€
> Ydi Y 7 @j[ `
G > HI J2L @ < (*/+#0 = = - $ , = ,2#% ( N ("-$( /1#% ,O=$% $ 0 ( A
.
eg?f > h WjAi @ @n>&l % 9l 8D?mnr .sn<xw9l 8Dut)V€
) e e ) e ] RQ T `
> Ydi _ @Fi
> 6H\([ i W _ Y > Y Y h h Y
G > HI J2L @ ( / L = L -V= &20( Q4 %^ # ,2( 7L 0/1# &20]= # Q4 = CEH ,2(*%+,2( # ( N ("-$( /1# e W=/ $ =#
.
( N ("-$( /+# e ] &P=0]='#% &P=0 - ( /10+#% iXW _ YE > Ya Y h h Y (
A Q ( /1#0Q T # / $ #% Q = N #0+(*% ,P=% &20( Q4 % (*% %+( ,2#$,2( Q # N Q4 ,#$#$("00+# ,2#$/ &6# ) e ,2(= [5 L %/+(',2#% ,P=,2#%7A
eg?f > h WjiA@
- @n~l % 8;1yt R :N€
@n~&l % nr~rdqsr ?mn\r .sn<x Fq %6| .C0>|nrdmVt . x : . x : . x Y R :@;7># R N : RCZ=Z 81"V€
7 @ R H Y 7 > [^] XIs_ > @a`
G > HI J2L @ 7:0= Q =S=3% $ 0 ('&P=0]= L - ( 0# #- # #-$( b ] XIs_ > @c A
.
eg?f > h WjAi @ mn\r .sn<x^m9l 8n t:v 1lm~m9n 0;D nrdm :<x{z l|~}"N€
,H > [ `
G > HI J2L @ < (*/+#0 = # =" -$("0+# ,2('( N ("-$( /+#% ,P=3% $ 0 (_A
.
eg?f > h WjAi @ >.10 |;m .2N n ?mnr .sn<x m .2N n t#N€
- ; Z Y H > H @ Z Y H > H\[ e ) e ] e A `
G.> HI J2L @ 0 = L - # 65[L2 /1# ,2( =%+#% ,2('/10( #W= &P=0/ 0 ,2( L -W= % $ 0 ( #-$(7= ,2#$,2("%,2(
# ( N (*- ( /+# e :=/ $ # ( N ("-$( /+# e ] ZL / N = ,2# =% 5 = ( N =%$/+("-$&)#0= % ,2(*% N = /+("% ,2(
( /+0=,O= e ( %]= ,P= A~$ 0]=/K=6%+(8,2( L - - $ /1#4,2# YL ( &)(*0+- /+( = (*0/= ! /1(*0= # ,P=
)
% $ 0 (
#-
=%
A
egf?> h WjiA@
- .10>| ~n t N N€ ~n Q. V ? R € ~n Q R1V ? R :u€ ~n Q : V ? R N €
- .10>| mNt R N€ m Q. V ? R €
k>lmnm ' ?dmnr .sn x |dqk>lmnmNt . {| m x^m;.2N nCt# >nm>V€
eg?f > h WjAi @ R @GF@ 6h Y @ R @IH I6_ > @ I K"@ I @ > R @ P K h Y H P
R=R :
=R RCS
RN:
R :=]
R:R
RNU
R1ZS
RNY
=
> >
h W @ Yi
8 <; g9 :8 E9 g9 9g8"9
; i KH Y h > @ egf W @ > VI Ydi
Z @ h Y R @ | m $ 61lm~mn90;D nrdm RCZPR :
> H KVi YdR @
, .HK
n ~n\r .snm 2P1lm~m9n 0;D nrdm
qsrn 'lm/|Fm 2 R1Z
dq%s| ( JB.10 |nrdKm A A >5l N5q 0l %;. 3| 42 R :
\r .6z . x . R mn~lEr ' 2 @;> ? R2. x U :=Y=Y6?%21 l ? . x :=] n|l=? . x . N > lHHdl ? . x] U
, k R N Y=: N ZS x S Y N
: Z&.=U N S d x N dY
*

x~x~x
;
x
1R ZaZ N : Z =N N S=S=S
@;7>;? R Y U
<x
x~x~x
,dq6|l&%p| . Hdn 2 N : Z m x
> R > H ' > K @ Y XH R > I\I @ Y KH
Z @ h Y R @ | m$W061lm~mn90;D nrdm RCZPRM.+R N R R : R N
> H KVi YdR @
, .HK
n ~n\r .snm 2P1lm~m9n 0;D nrdm
qsrn 'lm/|Fm 2 R1Z
= n (r &l % = n| qsr m A,AC@9l 0 zdmn~n\z 2 ]=Y S : N S Y S Y
@ (=0"m 2 R >5H n| qsz 2 . ;? QIRWR : R N V
./z>z n 0 =qsz nm 2 :
J/n .)D >;| l|>r ./o 2
: R R .
*
QIRWRaRWR V
QIRWRaRWR V
QIRWRaRWRaRWR V
= 2
Q .5DH . R .5D5H ;. R %;.10 R V
: 54 2
Q .+R : V
Q N ZaV
Q U-V
>;12 . 2 . @;7> ?;: . : U :=]6@;5>
x
qsznm
m Fq /z m Fq /z
l nrdm
x
n~l\r
|
~|>r <x
~| m ? N : Z x Z Y S
x~x~x
|dq11B.10;DQk\r . |nr .C(;H 2 ,>rl/.10B.10 D >rq D~rnm~m2 1 ? . x . RCS R5U d:
nm6| ,>r/l .10B.10 D2 >;1 ;q ' R2... , . Hdn R1Z @;>a,>r ]<x]=] . ] Z , m RCS x d]Y=]
x~x~x
*( %/+(S=& ,
0( =%$0+( N ( Q =
H "
' "
# A("0 2* =%
8& , "-:9
# % )
B $ C
0+( = N =,P= L -W= #-$& N = # %# (
/+("%$,P= /+("%+( D ! " ! A T % 0( A("0 2* =%$( # /10]=- %+(
0+( Q4 %/K=% N RQ 0+#% (*, /=,2#% ( L2 = ,(
)
'& ( ") +*
$# %
) ?=
0( L
! " ("%/10
& ', "-
<;
-
"!
$# %
/ "021 , 435(
>=
# [L /+#.,2( 0( A("0 2
* =% 0+( N =/ RQ =% \%
C ! % ' (
%
%(' "
" G
L / L 0]=,P=% ("- YL =/+0+# 0 L &6#%$, %/ ! /+#%
% ! %A
! =%
.
= A@ - -
-76
</3W*$
DFE } E } G IH KJMLONH QPR
S @ - % ! - % ""- UT 021 " , 0 ""-WV " ! ' &% -YX[Z @ VM\^]
S V " ! ' &% -YX_V - - ' ` %a` " * ZbVcV ` \^]
S V +* ! :V " ! ' &% ! / ""-ed ! - ' ZbVfV / \g] (
S " &% ! * 0 , @ - % ! - % ""- / ""-ed ! - ' h
DFE } Eji k mlnL R
9po #e
q ^sr( Ot! % ) ;eu =9vo 0+# Ktgw ( NXN ^xE= Q % ) ;yu4u=9 =/ ( N , ) ;yu4z4u =9p{ = |t ( ^ }8( /1% M) ;yu4z4u =9v~ "= ;
t 0 ,P= t %^€ ("( N w 0 = / ) ;yuz4u=9 ( =( ,^ 7'(*0+% ( #A( N , ) ;yuu‚=
DFE } „E ƒ … JMl QR |PR
S @ - % ! - % ""- † " , ! - Q" d‡V
" ! ' &% -YX) ;
N %+( Q4 ("0 >* ( 2 (
N % ("0+%
L O
]
;
S † " , ! - "Qd V " ! ' % -YX) r#  N (W^ > # % ) /1, ] (
S † " , ! - "Qd , - 2V " ! ' % -YX) %/ / L /1(:# #fo L % ! ("%+%! #0+(
DFE } (E ' … J ALOR R ) J L *H R
=#" o$!&%$h
=%/ +,.-0/21/434,5/4687:9;<90=>,@?A3B9C3ED
GF IH<HKJ M LL
w w w ;NJPOQ5R<STP= N AVU L R5OBWSOAYXZSTO=4R5 AYOB[ L A = L L]\^A_T`[`XV=4TCLEa > x L
o%=4R5O[ O[P=4[`S4R ) R<SU = = N =4[O=Z[`O}hSU {h_T`[`XV=4T ) WBSXiXW=EjkRh[`O
Gcb HIde Jf`g F
JSQ=EjkR7A
+Q5jkORHKOX ;
lR
m 34,.no,qpsrt/46vuBwxu`3y/zo{9C6E;@,.n}|
GF IH<HKJ M LLE SJ`R7A w P=4Q@HKST A L J OBT T VA O[ L L"#(S4Q5OBW7=4R<HL
Gcb HIde Jf`g F
SQ<H= N ) WBQ5j =4[`S8JSQ?rgA T 5Q XlR<H5Q5ST|= ) ST`[ O~R5O~OBT WBSTAHKQ]=4XQ<OBR L XZj€[`SRSRJ Q5jkT WB‚kJ jkSR
U^ƒER5jkWSR>[P=„J`Q5O Q jkR ESOA
… n;K/434n&9C;†,5u`n9Cr … n6E;@,†;†‡};K/ˆuBw#x‰u 3y/o{9^64;K/4346‹Š …y…zŒ^
IH<HKJ M LL"#(S4Q5OBW7=4R<H5jkTO=gAVW w Q L YA OB[ L L T`R<H5j€H L HKO{L
cb de f`g F ƒ =j€PT =SE^WBj = N P[ = @%@ †Y)L XW=jkT R<HKj‘H L j e4ST E S
OR<HKj€X L N =4Q$S„W =4XlJSlO[ =„J Q5O Q j€R 4OS A
cŽGF
G H I J
N L WBQ=HKj Q =c’ L
OZH5OBTAHK=#[`OBR<OBT Q S N Q O Q~O
xu`3y/zoy9^6E; m 3zu”“•u -0/ m 9`|/
cŽGF
IH<HKJ M LL
Gcb HIde Jf`g F
#ƒ4Wj N L R5SOA
w w w A(# SQ<OBW =ER<HKJ Q5SOAYWBSX–L
ƒ=j€TP=ZR<SU`Q5O—S Vs˜™Kš›5œ D ™K˜")FL XžJ`Q5S4=4Q=4XV=l[ OJ`Q5O Q jkR ES8UP=4R@HK=4TAHKO—JPSJ L N =4Q ) [`O
+,.-0/21/434,5/46cŸZn9CrkD^6E,.6:9Cn 0xu`3y/zoy9^6E;@,.n}|¡+¢/zoE£¤ns,@¥I‡/46
cŽGF
IH<HKJ§¦MLL L `U XW=Ej N A L UP= N H AYOB[ L ]L \^P=4Q<R5P=EX8LER@HK=EH ;.[P=HK=ALES4J`Q5OB¨¨©!^SQ<OBW =ER<H AYAHKX
Gcb HIde Jf`g F
X–ƒEQ5jkS:R5SU`Q<OX HKS_[`SR[`O:=4T`ƒ N €j R5O8Oc[`OJ`Q<O Q jkR+4Sv[`OcR+Q5j€OBR~HKOXZJSQ=EjkR ) R<SU
[`j€Q5OW eESl[ O {hSR5R<OBj€T T Q5R5O=4X A
>ML
=
# ¢ B
*
$
O
6 <+7*) 0%*
DFE inE } G IH KJMLONH QPR
S @ -^œ†š™ -4œ ˜"- †^˜ -^œ / ˜"-ed{š™Kš'-¤›š˜"S H8, ™˜K^1 š5- UT 02^1 ˜y , 0 ˜"- C ™ œ . › S @ ^- œ†š™ - 4œ ˜"- l˜™ / ˜"-e{d š™Kš'¤- ›š>˜"'&
C
"!
š , ™<
Z @ † / I\g]
š , ™< šœ ˜™ y Z H BC 8g\ ]
™œ . › ]- * 4œ , ™< š , ™5
šœ ˜™ y
"!
*
,+
$
-/. *
0. * =EH5H5OBQ<R5ST
"!
S @ -^œ†š™ -4œ ˜"- / "˜ -ed{š™Kš'-¤›š˜"- H Y- X -¤šš™ -YX C ^1 1
DFE inEji k mlnL R
o SR5O^ j =4TO= ) yu4u { ={ t jkT ) yuu4u
#
%
(
›54œ ˜"- ˜Qd
#
1
4
<;
DFE inE(' … J ALOR R
/‡ 3B9Cr
?
)
"!
šœ ˜™ y
"!
&
ZH
8\^]
C
C
%
8\ h
%
-0. *
-/.
2!
?
š , ™<
šœ ˜™ y‡Z @
) yuu G} S ! =4R ) yu4u
DFE inE„ƒ … JMl QR |PR
S @HZH H ™<- B_›œ ˜"- ˜"- š , ™5 šœ ˜™ y')^ ]
S š , ™< / ˜"021 , œN4œ ˜"- ) ~ a Q5OBR<R ]
S @ ^- œ†š™ -4œ ˜"- †^˜ , ™ - ˜Qd š , ™K˜y›˜"021 , œ -YX) N R5O N Q jkOQ > WBj€OBT`WO
S ^† ˜ , ™'- ˜Qd C ™œ . › š , ™< šœ ˜™ y Zj† C I\ T o ] O
S š , ™< D ™K˜y›š -YX }šœtœ.š™K') N L^w OQ T W =4[`OXZj€W L U N j€R5`OQ5RA
3
5
)
"!
#
76
8+
U N kj R<`OBQ<R ]
L
:9
>=
* H R
) J L /; —u 3 ]6x3z/{¥A‡/n;@rkD”Ÿc6 C/{ ‡/6E;@,5u n6
A@
CB
0B
ED
cŽGF # HKJ§¦MLL"# H5J AVR]=4R7AYWBS4X8LEJ L UCLET`O L Q= N L4! T AYAHKX N
Gcb HIde Jf`g F G} OBJSR<j€H 4Q5jkS [P=4R8JOBQ%= L TAHK=ERcXW=4j€R #(Q<OB’ L OBTAH5OBRR5SU Q5O
 =4Q5Q<OBT > =4Q N O A
%F
"G
IH
C
= [`j€Q5OBW$e4Sˆ[`O
') R5SU ”
4z
7
4/ noE£¤-ˆ9^3 ],.n¢|‹u{w2r/y9^34ns,.n¢| 9Cr‘|Pu 34,†;.£¤-•6
cŽGF IH<HKJ§¦MLL w w w WBR R@HKj€Q W LOt L]\ N R<RL TAHKQ<SIL
CB
Gcb HIde Jf`g F ƒ =j€T R5SU Q5O Q N j e4SZ[`O N =SQ5j‘HKXlSRh[`O J`Q<OBT`[`j 4= OBX ) WBS4X
H ’ L O J Q R L
3H
X (# SQ<H5O[`OBRQ;
/ ‡ 3B9Cr /; —u 3 ]6 9C; m
=
cŽGF IH<HKJ§¦MLL w w w OBXlR J T =S¦4©z©ALEJ`Q<S ! LET`O`Q5S4TCLET`O`Q qL
cb de f`g F SQ<H [ $_› . › ˜™ œ ` šœ 4œ ˜"- §˜™<4œ.˜™ T Z U\") WSTAHKOBT [`S Q<j [ j€|T #(SQ5X 4SR5S4U`Q5O ¦WBS4T|#(OBQ%BT`Wj R ) USQ H Q<jkSR ) W`Q5R<SR ˜"- -¤š')Py˜Qd œ 4™Kš') OHKW ?
?
A@
G H I J
??
CB
H
;
%#;
"G
)
… n;K/434n&9C;†,5u`n9Cr /4‡ 3B9Cr /A; —u 3 1&uIo,5/;@D
cŽGF IH<HKJ§¦MLL w w w jkT T`R SQ+=AL
cb de f`g F ƒ =j€T S4^Wj [ @ -^œ.š™ -4œ ˜"- š , ™< šœ ˜™ ˜y› šœ T Z @
\") `X R5R<S]Wj ;
4SZj€TAHKOBQ<T WjkST ’ O j€T`W`j§WBj€OBTAHKj€R<H R ) OBT|=OBT` OBjkQ<SRhO OR<H [ TAHKOR ) WSX ZS SU ! BO WHKj!Sl[`O
[`j! = Q$O XZOk`SQ Q Sl[`SXl‚kT jkS[ :›"˜ 021 , œN 35( ˜<-¤š , ™K˜"- "
?
G H I J
?
@
CB
4
)
"!
%
# 43 ‡`p u ¤/$l/y ¤/46 /‡ 3yu n&9^,.6
% cŽGF IH<HKJ§¦MLLEj&`R<jkST j€T`OBR<W J H L
Gcb HIde Jf`g F' OBQ(_j€[`SQ‡   [`S =Q`JSc[`O„Q5O[`OBR T`O`Q5S4T jkR[ S[@ - œ œ , œ†˜ * š )8-YX_š'- ` 4 ™ * š
* œ.'š 0lš / "˜ 021 , œN * ˜™Kš Z @ +) * / % ) jkR5US ,
?
B
.
+
/1032 457698;:=<;0 >@?AB=6DCE=8 ?GFIH30KJ5LEMC0KALNOPC8
DFEbƒ .E Q GSR +H TKJMLONH+UWVQPR
S X š'-¤šœ ›—- * ) & ˜ , œ ˜"-4™ TW/ ˜"021 , œ 4œ ˜"- / ˜"-ed{š™Kš'-¤›š<Z X ) / /
Z ^\ ]
Y
S / ˜"-YX4™Kš—˜"-) & ˜ , œ ˜"-4™ T/ ˜"021 , œ 4œ ˜"- Z / ) / \g]
S @ -^œ†š™ -4œ ˜"- *UT 021^˜y , 0 ˜"-[ * '1œ & š *UT œ.š'0—\
) & ˜ , œ ˜"-4™ T / ˜"021 , œN4œ ˜"-#- *
œ › X ™<'1 `_ ›5 `_•˜ * š M Z @a* * \b O
S ) , ™˜K^1 š5- / ˜"-e{d š™š'¤- ›š ˜"- X š'¤- šœ ›c‰™K˜+X4™<0<0 -YXZ)3d ;Z X \^
0
0
0
H
‰™K˜^]
_
DFEbƒ Eji k VmlnL R R
o T #OH ) yuu4z
*
0. *
¢
S €[`UPOQ+=
4u
h
%
) yu4z4u ~#j€W kO w jkW ) yu4u
/. *
0. *
' W w O$#(O )
DFEbƒ „E ƒ … JM
l VQR |PR
S @ ) ) ) `™<- B_›œ ˜"- ˜"-) & ˜ , œ ˜"-4™ T/ ˜"021 , œ 4œ ˜"- )` ]
S ) & ˜ , œ ˜"-4™ T/ ˜"021 , œ 4œ ˜"-†C˜ , ™ - ~ a &Q5OBR<R ]
S ™ œ . › d{š') ~ a &Q5OR5R ]
S ˜ k˜+X ›5 /fT š™ -¤šœ ›') ' J`Q<jkTO=4OBQ ; OBQ( = ] O
S ˜ *UT œ.š'—0 C† ˜ , ™ - }˜Q>d ˜ k˜+X ›5 ^- * @ -ed{˜™ 0l4œ ˜"-[‰™K˜y›š -YX
yu4z
.
0
0
6
4;
0
OT`WBO `Ukj€R5`OQ5R 0
* › š'-¤›š') €R5O_jkOQ ' WBj ;
!
DFEbƒ E(' … J U ALOR R R
#"
'
$
?)(+*
%$
)J U
&
L *H
VU R
R
'
W t L ~#jkQ<Q5SQ<RL"# H5J [ O T`OHL LEW€j #(OyL
cb de f`g F ¢SQ<H R5S4U`Q5O / X ) ) j€T`W`jkT [`S ) OTAHKQ5O S H5Q5SR¦JPOQ+= `TAH RGX j€R #(Q5O’ `OBTAHKOR ) [`OBRQ;
WQ5j 4S–[ SRX H5S][`S4R[ / X 8) ) = j [ O—Q5OW`Q<R5SROkOWH5Q T`j€WBSR ) =4Q`JSRh[`O—j€T 4OBR@HKj= e4S–O
JOBQ<R5ST kjk[ [`OBR
€j= [ R SZQ XZS -
% c
ŽGF IH<HKJ§¦MLL
32
/.10
w w w WBR U X
,
G
# Ÿ Ÿl3{¥A‡ , C/46
54
% c
ŽGF IH<HKJ§¦MLL
w w w j€W T`Q T I Xlj& L"= kj€R<HL
cb d e `f g F G} OBJSR<j€H 4Q5jkS—R5SU`Q<O X -
32
/.10
"G
… r.rq,.nu`,.6 # /4n/;†,5o#Ÿlr€|u 34,†;.£¤-•6=&9P?Eu 3{9C;Ku`3ED
-
% c
ŽGF IH<HKJ§¦MLL = ‚ =O `j`W OB[,CLEj&kj = `SX„O A HKX cb de f`g F ¢SQ<H [`S UPSQ H 4Q5jkSc[ O X `[ O &€jkT`Sj€R )
S k[ UPO+Q = 32
/.10
"G
678
)
R5S4U [`j€Q5OW eES2[`O
x
_j€[ 4©
/
'
^u rq‡};@,5u n&9^34D
(
4
u -ps‡};59C;†,5u`n 9C; m
?
?
=
w w w OBXlR J T =S¦4©z©ALEJ`Q<S ! LET`O`Q5S4TCLEO4S 4OyL
de f`g F ¢SQ<H >[ ) WSTAHKOT`[`S Q<j [ j€T|#(SQ<X 4S2R<SU`Q5O /
UPS4Q H Q5j€SR ) W`Q<R5SR ˜"- ] ¤- š'P) y˜Qd œ 4™Kš') OH5W % c
ŽGF IH<HKJ§¦MLL
cb
-
/.10
32
#%;
G
+£¢/#“2,†;Ko4£<“:, /43 6 # ‡ ,@ §/ ;u
B
% c
ŽGF IH<HKJ§¦MLL
w w w WBR U X
X R@HKS = `j cb d e `f g F
O x _jk[o O RkO -
/.10
32
7
X ) &¦ WBS4T|#(OBQ%BT`Wj R )
^u`rq‡};†,5u n&9^34D
'
4
(
u`-p‡};<9C;@,5u n
W t L ~#jkQ<Q5SQ<R"L # H5J [ O T`OHL EL W€j #(OyL w w w L
OkOWH5Q T`j€WBSZR5SU`Q<O / X )8) R5SU`Q<O `[ j€Q5OW eES8[`O<r4Q+= h{ OBj€H t 4 H<HKOQ
,
G
R5S # H =w Q<O[`OJ`Q5O]j€R 4S Vs˜™Kš›5œD ™K˜ +`X X Q5W Q5O$=jkR@H [ [ oM`R5j€T`OBR<R$!^SQ<OBW R<H ' ]R@HKOXZR )
T`W )
Z ` œœ 1W\ h d{˜™Kš›5œ 1™K˜ h ›˜"0^\ h
@ -^œ.š O Gš'-^œ , 0 R+4SZX Q<W R>Q<O =j€R<H [ R>[ „ TAHKO" ` œtœ 1W\ h -^œ.š h ›˜"0 % R<H H5OBR<O (# SjOBR<WBQ5j‘H WBSX " ` œtœ 1W\
h Tgh ˜™jX % ) OBQ<R 4S E q ) S:J`Q<jkXlOBj€Q5SJ`Q5S ;
WBOR5R [`SQ [`OZH5O'_q HKS2[ S#HKj€JPS * @ _ ! # WBjkj€H =OQ 4S[`O–[`S_W XZOTIH5SR #" ) "AH<HKJ§¦MLL w w w H5O'qg.; J Q5S ! OWH SQ%I= L% ) X R<jkR@HKOBX [ O:J`Q<S][|e4S [`O:[`S_W XZOTIH eES”WBj€OBTAHK‚‘^W O
H WBT`j€W |) [ O OkO [ ’ kj€[ [`O X j€SQ—J Q<H5Oc[ R~ = `Q R_(# SQ X [`OR5OT` [ R _j . X " ` œœ W1 \
h$ . X h ˜™jX % ) `X J`Q5S ;
= Q X [`Oˆ[ OBR5OT``S OWH5SQ5j J Q S XU`j€OBTAHKO = QKƒE`WBS - * ˜ TAHKS S4RW= Q5ƒE^WBS4R
U`j€[`jkXlOBT`R<jkST jkR ) OBR@HKO (# SQ X S4U HKj€[`SR3_j X- , 1 k˜œ " ` œtœ 1W\
h X- , 1 k˜œ h -ed{˜ % ) `X J`Q<S4= Q X jkTAH5OBQ WHKj!S„J Q Sl[ OBR5OT``SZ[`O W`Q. R J Q@HKj€Q$[`O JPS4TIH5SR ) €jkT` R$O R`JOBQ (# ‚kWjkOBR &78
$
$
&
;
$
&
I
;
;
8
$
&
$
$
%'&(')+*-,.0/21435!12.0,6-708:9<;>=?A@CBEDGFHJIKIMLKN<;O=4?G@PBQDGFRSIK?GTEU
/
F
0
$
/
8
W t € O }j‘H5H5X T ) yu4u ‚ W t kO ) x { T`[ j€H<HKX T ) ~ i›5yšId{˜™ §0l4™K› -”š & ˜^]
, œ ˜"- ) J =OR¨
y© [ [`jkR<ST ;  OBR(kO ) }GO [`j€TO= ) ~ 3
W O ) yuu
W O ) 3 * Nœ 4œ œ ›;] / ˜"-¤›šm1œ( - * n1^1 ›54œ ˜"- & }M ) ' 3
= J jkO = J`j€O ) eu4u = J`j€O ) 3 T`[ = J`j€O ) 3 !^SQ<OBW R<HKj€TO= H5`O WST`SXljkW _WkOR o ;
R<OB[”S4T T q_H5OBT`R<jkST”S #$HK`O {S ‘%H ;j jkTAHKOQ5R ~#S_[`O OBT`OHKjkW =SQ<j€HK XZR J`J`Q5S W  T
‰™K˜y›šš * -YXQ˜ d œ ` š @ ) ) ) / "˜ 021 , œ 4œ "˜ - @ -^œ†š X_'š -¤›šcd{˜™?V --¤› UVs˜™Kš›5œ -YX)8-YX -¤šš]
™ -YX) J =OBAR u u4u 2t^ j t O ) yu 4¨ 2t^ j t O ) { A |T #(SQ5X H5jkSTa>`OSQ< T`[ T q_HKOBT R5jkS4T S #]HK`O ~ q]j€X`X j t OB`S_S_[
&Q<jkT`WjkJ€O T sOHKQ5S ) o T [ R t j ) ! ) O[`j€H5SQ5R )^- * @ -^œ.š™ -4œ "˜ - U* T 021^˜y , 0 "˜ @ -ed{˜™ 0l4œ "˜ - ` š˜™ T ) J =OBR+ , z ) oM`[ JPOR<H 4OBR ) 4©©
4OBR ) šy˜ , 35( ˜ * š3‰™K˜ kš'0l–š'0 20 š'-^œ†š œ™ ,„* ˜y]7d 0l / ˜"- ]
Ϫ , a 35( <
˜ - ™Kš5 * @ -^œ†š X'-¤› ;™ œ . › }š * * * š & x¡HK OBR5j€R ) xOBJ Q@H XlOBTAH5S~[`O
T #(SQ5XZƒEHKj€W | ) R5WBS [`O OT =OBT Q5j | ) T`j4OBQ5R<jk[ [`O [`S ~#jkT` S OT =Okj€T`OOH ) yu4u‚ OT =OkjkT O ) ) ' `[`OQ5R ) ) T`[ sS W tU) r T OS HKj€ST Q@ =SQ<j€H5`X
H5 HWBST`R@HKQ(`WH5RQ5OW`Q<Q5OBTAHT`O`Q ]T`OH w S4Q t R @ ) ) ) ™< - h "˜ - š , ™< šœ ˜™ y' ) " z%¦ ‚ Q5T S w  OBjkR<R ) yuu4z Q<T`S w?) x T`_
[ ˆOjkR<R ) @ -^œ™K˜ *, ›œ ˜"-–œ.˜ ‰™K˜+X4™<0<0 -YX , -YX † & \
2 - Z {š›œ ] Z ™ 'š -^œ†š * n 1^1™K˜B_› ` [`[ jkR5S4T ;  OBR(kO 2 S ) yuu‚ 2 S ) š , ™5 šœ ˜™ 0–š * š™ šV¢˜™Kš›5œ -YX ˜QdV --¤› _ 4™ Ašœ(
r4S4`[T  jkO ' ST`R o t OQ ) yu4z ?o t OBQ ) r }GOB[`WjkOT =>o j R T`[ T`"O !lWBjkOT`W‹j€T‹H5`O ' OkOWH5jkST =SQ5j‘HK`X 0 T
Q5O|T #(OBT R<HKOH5H5O ) r ) OB[`j‘HKSQ ) * š›"˜ - * @ -^œ†š™ -4œ "˜ - / "˜ -ed{š™'š -¤›šc"˜ - X 'š -¤šœ › pX_˜™ œ ` 0—8 - *
œ ` š ™+n 1^1 ›54œ "˜ - e w Q5OT`WBO QkU `X R5R<S]Wj H5OBR *
+
8
$
*
8
*
.
-C.
8
+
8
+
8
8
&7
$
2!
8
8
8
;
0.
8
/8
8
/8
68
8
,
8
8
-
*
8
-
C.
8
,
)
*
.
8
8
H
0
*
.
8
7
8
*
8
E+
C.
8
<
(
)
"!
(
8
*
8
*
8
.
8
"!
-0.
8
$
+
8
4¨
/
"!
/
*
‚
$ h o T #OH ) yuu4z o T # )  ) S4Q5[`j€T ) ) O&€OBQ ) } ) T [ !^Q T WBST`O ) ! X š'-¤šœ ›
‰™K˜+4X ™<0<0 -YX 92- @ -^œt™K˜ *, ›œ ˜"- ~#S4Q+= T |#(X T`T `U,kjkR<`OBQ<R )^ T`W ) ' K
o Q5T OH5H ) 4©© o Q5T OH5H ) ~ [ J HKj!O O`Q OH w SQ t R #(S4Q TIH5Okj=4OBTAH JPO ;
Q HKj€ST S # HK`O WHKj! HKO[ ' & [O=O &Q<S]WOBR5R  `j‘HKO J JOBQ ) j& U€O #(Q5SX
AH<HKJ§¦MLL w w w = OBT R<_X WBS4X8LEO q]JPOQ<H SJOBQ HKj€ST`RKLEJ JOBQ<RLEJ JPOQ IH5X o O R(kOcOH ) yu4u ¨ ‰o O R(kO ) x ) Mo ) x )9 T`[>~ Q@HKj€T ) } T•S 4OBQ.]j€O w S # =OT`OH5jkW =S ;
Q<j€H5`XZR¦ Q<H ) Q<OBR5O Q5W#HKSJ`j€WBR d - & š™K œ TW/ ˜"021 , œ -YX) "a‚I%¦ 4© yz o ST UO #OH ) yu4uu o ST UPO ) ) x SQ5j = S ) ~ ,) T`[–a>O Q , ) * 4™ 0 @ -^œ.š X_š'-¤›š\
d ™K˜"0 - 4œ , ™5 œ.˜–4™ œ . › T œ.š'—0 q (# S4Q5[ T`j!OBQ<R5j‘H. &Q5OBR<R o SR5O j TO= ) yu4u ‰o SR5O ) T`[ j TO= ) š , ™< šœ ˜™ V , - * –0 š'^- œN M œ ` X ™<'1 ` p_X ˜™ œ ` —
0 - * 1^1 ›54œ ˜"- ~ W Q ew ;Qh{ j&& ) ' 3
o SR5OQGOH ) eu4u o S4R5OBQ ) o ) ST $) M) T`[ J`T`j t:) H5Q j€T`jkTO= = SQ<j€H5X (# SQ„SJ H5j ;
X X Q+4= jkTW R5R<j€^OQ5R G T ™K˜y›šš * -YX ~˜Qd œ ` š V d œ ` 2- - , l˜™ y ` ˜K1 ˜"- / ˜"021 , œN4œ ˜"- ~ S4Q+= T |(# X T`T }š54™ - -YX ` š˜™ T ) J = OR e‚4‚ ' T ~ HKOS ) ¦#
o Seq 4r OBT t j€T`R ) eu o Seq ) T [s4r OT t jkT`R ) –0 š * š™ š 2- T \ ¢V ˜™Kš›5œ -YX - *
/ ˜"^- œ™K˜ " { S €[`OBT[x ) ' T#!CQ T`WjkR5WS ) ' 3
o Q X kOH5H5O o S W Q5[ ) yu4u ‰o Q X kOH5HKO ) ~ M T`[ ‰o S `W Q<[ ) OBT`OHKj€W = SQ<j€H5`XZR„j€T
Q XZOHKQ5j€W2x OBR5j = T8S# T jkQ5WQ # H T x _jkR ) ) OB[ j€HKS4Q ) - * ˜y˜ „˜Qd X š'¤- šœ ›
p_X ˜™ œ ` —
0 T SR<H5Q T [ o Q T t O ) yuu o Q T t O ) r OT`OH5jkW 4= SQ5j‘HK`XlR (# SQcT O`Q T`OH w SQ t [ OBR5j = T T`[ HKQ jkT`j€TO= T ‰™K˜y›šš * -YX ˜Q#
d œ ` š V ™Kœ ˜™ * › l˜™ y ` ˜K1 ˜"- X š'¤- šœ › p_X ˜™ œ ` —0 ') J = OBR e‚ ¨ )
T`j4OBQ<R5j€H.8S# R |) !sjkT T`[ o Q5OOB[ X ) yu4u o Q5OOB[ X ) 3 T T €_R5j€R$S}# HK OO POBWHGS P# €S]W jkXlJ`Q5SOXZOTAH>SJOBQ HKSQ<R
j€T = OT`OH5jkW = SQ<j€HK XZR T`[ R<jkX, H5OB[ T T`O €jkTO= (# SQH5`O34OB`j€WkO—Q5S H5jkTO–
= J`Q5SU,kOBX }
 SQ t j€TO= JOBQAu L e‚ ) T`j!OBQ<R5j‘H.cS# TAH w OQ5J o Q5S_W t^w O& x _jkR ) yu4u o Q5S_W t^w O& ) T`[x ]j€R ) } @ ^- œ™K˜ *, ›œ ˜"- œ.˜ –0 š * š™ š ¢V ˜™Kš]
›5œ -YX ' J`Q<jkTO4= OBQ ; OBQ( = ) O w SQ t:) ' K
o Q5S_SXl`O [ }S w O ) yu4zz o Q5S_SXl`O [ ) x T`[ S w O ) x ~ €H5j Q5j U€O?# T`WH5jkST jkTAH5OBQ ;
JS HKj€ST T`[ [ J H H5j4OT`OH w SQ t R / ˜"021 kš *UT œ.š'—
0 ') ]¦V¨ "]¨ C.
06
*
=
=
.
&7
C.
8
*
C.
*
#
5
$
+
7
0.
*
&,
7
*
&
"!
=
8
.
26
8
8
0
8
)
$
C.
"!
;
7
-C.
>
,+
/
*
8
8
8
*
+
8
7!
8
*
.
"!
1
$
7
*
&
C.
8
8
7
*
-
7
8
-0.
*
+
7
8
C.
+
$
,
8
$ G 7
oM`Q+=4OBR5R ) yu4u o `Q+=OR5R ) OBT OHKj€W =SQ<j€H5`X #(SQGHK`O J]HKjkXlj HKj€STS# ~€H5jkJ`Q<S]WOBR ;
R<SQ S4XZJ]HKOBQ Q<W`j€H5OBWH`Q5O a¢OBW`T`j€W }hOJPS4Q<H ' a } ;mu ;.© ‚ ) xOBJ SXlJ HKOQ ' WjkOT`WBO )
T`j4OBQ<R5j€H.8S#f‰o Q5jkR@HKS j OH ) yu4u
j ) ) O tU) ) x ) ~ ) T [ {+ H ) a a>jkXlO ' OBQ5j€OBR ~#S][ O&€jkTO=
T`[ !^SQ5OW R@HKj€TO= R5jkT|= OBT`OHKjkW =SQ5j‘HK`XlR T ‰™˜y›šš * -YX:˜Qd#œ ` š V ™Kœ @ -^œ†š™ -4œ ˜"-
/ ˜"-ed{š™Kš'-¤›š˜"- -¤˜ kš * X_š] hyš * @ -^œ.š X_š'-^œ+) kš›œt™K˜"- › *UT œ.š'0—') S `XlO ) J =4OBR ©
4z ) [`O j€[`O ) `R@HKQ kj Q<IH5ST`j& t `OT ) 4©©© Q<IH5ST`j& t:)  T`[ `OBT ) ~ OBQ< ' `SQ@H%;NasOQ5X S [v!^S ;
Q<OBW R<H5jkTO= R5j€TO= Q@HKj‘^WBj O`Q OH w SQ t R @ ) ) ) `™<- B_›œ ˜"- ”˜"- h˜ š™ *UT œ†š'0—')
" z% ¦ ¨ , z H5`Ok[ ) yu4z4u H5^Ok[ ) ` š+2- T ˜Qd –
0 š * š™ š;] 2- @ ^- œt™K˜ *, ›œ ˜"- J`X T
T`[W{ & ) `OBT ) yu4uu `OBT ) ' T [ D ) ˆ
 S k[ 4S & H5jkST Q< SXlJ H HKj€ST<{ OkJj€T<x OR5j4= T`R
S # Rj€T2!^SQ<OBW R<HKj€TOZ
= !CS4Q5OBj = T ]q W TO= O<} HKOR T ™K˜y›šš * -YX „˜Qd œ ` š / ˜"-Y4X ™Kš
˜"-) & ˜ , œ ˜"-4™ T/ ˜"021 , œN4œ ˜"- ) S &`XlO ) J = OBR+ , ‚ `jkQ J` [ T t OH ) yuu
`j€Q J` [` T t ) ' ) x TO= J`Q R5OQ<H ) ) T`[ H5W T ;
t SQ5T ) OBT`OHKj€W !^SQ<OBW R<H5jkTO= = SQ<j€HK X w j‘HK#!jkT T`WBj J Jkj€W H5jkST`R T ‰™K˜y›šš * -YX ˜Qd
@ -^œ†š X_š'-^œ @ -ed{˜™'0l4œ ˜"- *UT œ.š'0—;] @+@ * e) J 4= OBR ‚ z SQ<H5O OH ) eu4u
SQ@HKO ) ) ~ W [ S ) r =) T`[ OOR ) r T S & H5jkST Q< Q<H5j€^Wj O`Q OH w SQ t a>j€XZO ' OBQ<jkOR„!CS4Q5OBW R<H5jkTO= ' _R<HKOX T{ X ) ~ { ) OB[`j‘HKSQ ) @ * ) @ -^œ†š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›š$˜"-K™œ . › @ -^œ.š X_š'-¤›š ) 1^š™œ *UT œ.š'0—$- * š , ™< šœ ˜™ y')
J = OBR+ z ,z ) { S4T`S &,& ) { j ` ' a x
a &Q<OBR5R SQ<H5O OH ) eu4u SQ@HKO ) ) h} S_W |) ~ ) ~ W [`S ) r ) T`[ OOBR ) r O`Q OH w SQ t
o R5O[ !CS4Q5OBW R<H5jkTO= ' _R<HKOX T @ / ] @ ) ) ) @ ^- œ†š™ - 4œ ˜"- / ˜"-e{d š™š'¤- ›š ˜"- š , ™<
 OR<H5OBQ5T `R@HKQ kj ,{
SX ;
šœ ˜™ y ‰™K˜y›šš * -YX') S `XZO Y) J = OBR 4z4
u , 4u ¨ ) sOBQ@HK ) ˆ
*
.
,
,
8
8
8
,
,
*
7
,
/.
,
,
,
0
*
C
8
0.
,
7
*
8
8
,
,
A
C
,
8
+
0
,
,
C.
,
,
+
,
*
7#=
+
,
C.
<+
,
8
,
0
*
,
,
0.
,
8
>/
-C.
,
,
8
8
/
*
-
8
8
*
-
58
8
26
,
,
,
2!
J, HKOQ ' S]WjkOH. *
2!
&8
%
8
.
,
8
,
SQ<H5O OH ) eu4u4u SQ@HKO ) ) }GS_W |) ~ ), T [ O OR ) r T 4S & H5jkST Q< T`[ 4S T`T`OBWHKj ;
S4T`jkR@H J`J Q5S W #(S4Q$a>jkXlO ' OQ5j€OBRG!^SQ5OW R@HKj€TO= ¢ T ‰ ™K˜y›šš * -YX ˜Qd @ -^œ.š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›š
"˜ - U* T œ.š'0—c)8-YX -¤šš™ -YX] @ / * ) ) J =OBR yu
, ‚ ) R O$= R ) ' K^ ' C.
,
8
,
8
+
&7
8
,
$ h /
SQ<H5O OH ) E ©© S Q@HKO ) ) }GS]W ) ~ ) T`[ OOR ) r X Q5W t j T
O`Q OH w 4S Q t a¢Q €j T`jkTO= š , ™< W‰™˜y›š -YX }šœtœ.š™K') " 4%¦ y© *
0.
,
,
,
;
J`J 5Q S W (# SQ
+
8
*
8
$7
Q XlOBQ ) yu4z Q XlOBQ ) Q5OJ`Q5OR5OBTAH HKj€STs#(SQZH5`O [ J HKj!O =OT`OBQ HKj€ST S# R<jkXlJkO#R5O ;
’ `OTAHKj &J`Q5S4=4Q XlR T Q5O'#(OBT`R@HKOH<HKO ) r r ) OB[ j€HKS4Q ) @ -^œ.š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›šZ˜"- X š'-¤šœ ›
pX_˜™ œ ` 0— - * 1^1 ›54œ ˜"- ') J =OR ez¨ yz .
,
8
$
$
-
x Q w j€T ) yz u ?x Q w jkT ) ` š Z ™ X - ˜Qd * 1^š› š T 0–š5- :˜Qd -4œ , ™5 yš kš›œ ˜"- ~˜™8œ ` š
1 ™Kšyš™ & 4œ ˜"- ˜Qdfd & ˜ , ™š * ™5_›š -:œ ` šœ™ , XyX kšd{˜™ d{š r ~ Q5Q ) }S4T`[`ST ) xOBT`S_OYq }Gj T`[ ) yuu xOT`S]O q ) a T`[ }Gj T`[ ) T €_R5j€R$S#}Q [ Q$j€X =4OBR#(SQ$Q jkT ;
# &(# S4Q5OBW R<H5jkTO= `R<jkTO=„T`O`Q T`OH w SQ t R š , ™< / ˜"021 , œ -YX8- * n1^1 ›54œ ˜"- ') ¨ xjkTO„= OH ) yu4u x jkT|= ) ) = T ) ' ) T`[[xOT`S_O q ) a O Q §T OH w SQ t U R5OB[XlS][`OkRn#(SQ
(# S4Q5OBW R<H5jkTO= & T ‰™K˜y›šš * -YX —˜Q+d (# Q<ST a>jkU R5`j€Q T`j ) yuu ¨ (# Q5ST ) o T [8a>jkU`R<`jkQ T`j ) } 92- @ -^œ™K˜ *, ›œ ˜"-œ†˜—œ ` šG˜y˜œ œ™5'1 J`X T { ) ' K
! kX T ) yu4z4z ! kX T ) ' ! R<H5OBQ O Q<T`jkTO= Q<j H5jkST`RST>o W t ; &Q5SJ = H5jkST§¦ T X ;
J jkQ5j€W ' H [ Z T x a¢S `Q5OH $t ) { D T`[ ' O ! T`S w R t j ) a ) OB[`j‘HKSQ<R ) ‰™˜y›šš * -YX –˜Qd / ˜"- ]
-¤š›œ ˜"- œ _ ˜ * š M *U, 0<0–š™ * › ` ˜y˜ ) J = OBR‰¨4z ) SR €H5SR ) ' K #~ SQ+= T (# X T T
*
C.
,
*
%
*
.
+
.
6
&7#=
8
$
,
9
*
*
,
C.
7
8
0.
+
8
`U,kjkR<`OBQ<R 0
+
8
,
8
/7
8
=
! k WBS~OH ) yuu4z ! kWS )^ ) j€SJ`J ) 3 ) O H5H | ) 3 ) H kO ) ) T [#a Q ) J H5jkXlj jkTO=
T O`Q ^T`OH w SQ t R#(SQH5jkXlO$R5OQ5jkOR&J`Q5O[`jkWHKj€ST C T ‰K™ ˜y›šš * -YX˜QdGœ ` š `_ ™ * l˜™ * / "˜ -ed{š™Kš'-¤›š
"˜ - * Q˜ d œ / "˜ 021 , œ -YXZ * / \^
*
C.
#,
8
&8
&
/&
! t O T `OQ ) yuu‚ ! t OBT ` OBQ ) ' OH5H5jkTO= O w j€XZj‘HKR—j€To jkT W t jkTO= w j€H5 Q5S `J`jkT|=
R<jkTO=}hO[`WHKjkS4T a¢BO W T`jkW }GOBJSQ@HW}2 {©4z ) } ! ;Q}GOBR<O Q<W O TIH5OBQ[#(SQ[o O =j T
~OH w SQ t jk|T = T [`R<H5Q< *
8
.
7
)
+
,
,
! Q [ H<^O€[ ) yu4uz ! Q [ ) r W T`[ H<^O€[ ) a>j€XZOR ' OQ5jkOR !^SQ5OW R@HKjkT|=
O`Q OH w S4Q t RB¦ = R5O ' H `[ = 1^1 š * * œ 4œ œ ›') ‚ ]¦ 4 ¨ , © *
,
*
8
C.
,
,
,
$
w
j€H5
! kO q OQ ) yuu ! €O'q]OBQ ) 3 ' H HKj€R<HKj€W O H5jkSTZS#¢T`O`Q ¤T OH w SQ t RGO'q]JOBQ5j€XZOTAHKRB¦I~jkT`j€X`X
Q<OB’ `j€Q5OBXlOBTAH5R T`[ W Q5Q5OTAHJ`Q WHKj€WBO T ‰™K˜y›šš * -YX•˜Qd#œ ` š œ ` ) , ™K˜K1^š5-I_•ššœ -YX ˜"/fT š™ -¤šœ › - * *UT œ.š'0— šyš54™K› ` ) S `XlO; ) J =4OBR y©© y©©4z ) jkOBT T |) R<HKQ<j ,
-C.
8
H
$
8
$ G *
7-
!CS=O§OH ) yu !^S4=O ) ) w OBT`R ) 3 ) T`[  kR5 ) ~ ™ œ . › @ -^œ.š X_š'-¤›š ` ™K˜ , X `
* 0 , ‘4œ.š * ) & ˜ , œ ˜"- r4S`T  j&€O ) O w SQ t !CQ<OBj€RkOUPO
T }hj€J`JOBQ ) yu4u !CQ<OBj€RkOUPOT ) o T`[ }GjkJ`JOBQ ) WBS4T`SXljkW!^SQ5OW R@HKjkT|=
R5j€OT = O`Q OH w SQ t R T @"/ ] @ ) ) ) @ -^œ.š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›š ˜"- š , ™<
SXlJ H5OBQ ' S_WBj€OH. šœ ˜™ yc‰™K˜y›šš * -YX') ¢OBQ@HK )  OBR<H5OBQ<T `R<H5Q €j ,]
TAH ) yuu¨ & TAH ) ' š , ™5 šœ ˜™ }š54™'- -YX - * ) 1^š™ œ *UT œ.š'0— ~ a &Q<OBR5R )
= XU`Q5j€O[ =O ) ' K
S €[`UOB+Q = ) yu4zu S k[`UOB%Q = ) x X š'-¤šœ ›c pX_˜™ œ ` 0— - * š54™K› ` Z 1œ 0 4œ ˜"-ˆ- * _ _› `_ -¤š
}š54™ - -YX [`[ jkR5S4T ;  OBR(kO Ukj€R5`j€OT = SXZJ TA )` T`W ) <) ' 3
S|T = xOBT WBOY q ) yu4u
S4OT = ) T`[ xOT`WBO q ) a Q5U T8R<H5SQ5X wM HKOQ JS & HKj€ST<#(SQ5OW RQ;
H5jkOT = R5jk|T =ZQ<OBW Q5Q5OTAHT`O`Q T`OH w SQ t R A †^˜ , '™ - Q˜ d U* T œ.'š 0—c8) -YX -¤šš™ -YX) ¦ y¨ ‚ Q<OB|T #(OT`R<H5OH5H5O ) yu4z
Q<OB|T #(OT`R<H5OH<HKO ) r J H5jkXlj HKj€ST S # WBS4TIH5Q5S hJ Q XlOHKOQ5R #(S4Q OBT`OHKj€W
=S4Q5j€H5`XlR @ ) ) ) ™5 - B_›œ "˜ -•"˜ - U* T œ.'š 0— _ - - *W/fT š™ -¤šœ ›' ) ^" z%¦ z Q(  `j‘H kO ) yu4u¨ Q ) ! , T`[  `j‘H kO ) x [`[`jk|T =kO Q5T`j€OT = HKS—H5`OWO& Q[ OO ;
€SJ`XlOBTAHS #&T`O`Q ¢T`OH w SQ t RB¦ S HKj€ST T [#HK O—U €[ w jkT#O POBWH c) & ˜ , œ "˜ -4™ T / "˜ 021 , œ ]
œ "˜ - ) ¨^" z%¦ y
¨ ,4¨¨ ~ a &Q5OR5R { R xSQ ¤T`OQ ) yuu4z { & R ) ~ T`[ xSQ ¤T`OQ ) WBS4XZJ Q H5jOR<H`[ ST #(OOB|[ #(SQ w= Q5[
T`[ Q<OBW Q5Q5OTAH:T`O`Q T OH w SQ t R2j€T H5jkXlO R5OBQ<jkOR#J`Q<OB[`j€WH5jkST `R5j€OT ==Q [ jkOBTAH[`OR5WBOTAH kO Q ;
T jkOT = • T ™K˜y›šš * -YXQ˜ d8œ ` š[) , ™K˜ 1^š5 - _ ššœ -YX:"˜ - /fT š™ -¤šœ › - * U* T œ.'š 0— šyš54™K› `
Z) _ / * $\") j€OBT`T ) `R@HKQ<j , e w Q5OT`WBO Q€U `X R5R<S]Wj H5OBR { T t O }hOj€H5R5W ) yuz4u { T t O ) r T`[[ }GOBj€H5R5W ) K‰ , -¤š2V¢˜™Kš›5œ -YX &‘_T T`[ o YT ;
WST Ukj€R5`j€OT = SXlJ TA T`W ) ~ R5R W R5R5OH5H5R ) ' 3
{ t j€T ) yu4uu { t jkT ) ' š , ™< šœ ˜™ y;] / ˜"021™Kšš'- & š‡V¢˜ , - * 4œ ˜"- &Q5OTAHKjkW'O ;m{ )
O w r4OBQ5R<O ) T`[#O[`j€H5jkST {S T`[ ) yu {S T [ ) r * '1œ 4œ ˜"- - 4œ , ™< - * ™ œ . › U* T œ.š'0— & xiH5`OBR<jkR )
T`j4OBQ<R5j€H.8S # ~jkW`j = T ) T`T Q5USQ {SJ `Ok[ ) yu4z {SJ `Ok[ ) r O`Q OH w S4Q t R T`[ &A]R<jkW ' _R@HKOBXlR w j€H5 XZO+Q =OTAH S ;
€OBWHKj4O SXZJ, H H5jkST U j&kj‘HKj€OBR & T œ ` š 4œ "˜ - W›5 * 'š 0 T Q˜ d * › 'š -¤›'š ) S `XZO u ) J =OR
‚ z -C.
*
+
8
0
=
.
=
7
* 2!
,
E
7
* 8
C.
)
"!
,
C.
,
;
* ,
&7
C.
6
8
67
* C.
8
* $
26
7
6
C.
$
68
*
8
8
;
=
#
0
C.
/8
H
*
H
*
8
C.
8
8
"!
8
,
5
.
7
8
7
C.
*
,
*
+
8
8
0.
8
,
z
$ h /
{h_T`[`X T ) 4©4© {h_T`[ X T ) }
0–š * š ™ š 4 œ B™54™ T j U€O (# Q<SXAH5H5J§¦ L4L
JOBQ<R5ST U`R<OBWBS XlST <R OB[ CL{A]T [`X CT LEa ' x ¢L *
.
%
www;
8
;
3+
r4SQ5[ T ) yu4u r4SQ5[ T ) ~  A„HK`O kS4=4jkR<H5jkW # T`WH5jkST H HKS4Q5j ^[`jkR<W`R<R5jkS4TZSTZJ`Q5S4U U`jkj€H5OBR
T`[#T O`Q T`OH w SQ t R u ©¨ ) ~ R5R W `R5OH5HKR T`R<H5j€H HKO S#sasOW`T`S €S4=4 ) ' K
; UPS [ T ) eu4u4u US `[ T ) ~ K OT`OH5jkW S HKj€ST S # }GO =Q<OBR5R<jkSTs~#S_[`O€R #(S4Q oM R5j ;
T OBR5R T`[ WST`SXljkW„!^SQ<OBW R<H5jkTO= Z T ‰™K˜y›šš * -YX8˜Qd„œ ` š / ˜"-YX4™š–˜"- ) & ˜ , œ ˜"-4™ T
/ ˜"021 , œ 4œ ˜"- ] / ) / ) S `XZO; ) J =OR 4¨ OXZR(kO ~ Q<HKj€T`O ) yu4u OBXlRkO ) x ` T`[ ~ Q<HKj€T`O ) a ' `Q(4O 2# O`Q OH w SQ t
G} OBR<O Q<W T`[!jkOk[`O[ J Jkj€W H5jkST`R @ ^- œ.š™'- 4œ ˜"- ^^† ˜ , ™ - ˜Qd š , ™< šœ ˜™ y\ šyš54™K› `
- * n1^1 ›54œ ˜"- ') ]¦ 4¨ y¨¨ OT`T`O[ UOBQ5 Q<H ) yu4u OT`T`OB[] ) r T`[ UOBQ< Q<H ) } Q@HKj€WkO ' Mw Q5X J H5jkXlj HKjkS4T T@"/ S
] @ ) ) ) @ ^- œ.š™'- 4œ ˜"- / ˜"-e{d š™š'¤- ›š˜"- š , ™5 šœ ˜™ y7‰™K˜y›šš * -YX ') J = OR
eu‚ eu‚^z ) sOQ<HK )  OBR@HKOQ5T `R<H5Q €j ,]
S4XZJ]HKOBQ ' S]WjkOH. OQ5T`j = X G} j€H5W`jkO ) yu4z4z OQ5T`j = X ) o T`[h} j‘HKW`j€O ) x ` š / ‰™K˜+4X ™<0<0 -YX §- ]
X , y_X š &Q5OTIH5jkWO { & ) R<OBWBS4T`[:O[`j€H5jkST S4H T [OH ) yu4u `SEH T [ ) 3 ) U O ) K P) T`[ ~ Q H t X ) x T [ J]HKj4O
~ S][, Q G} OBW`Q5Q<OBTAH O Q OH w SQ t o R5OB[ sS w OBQ ' _R<H5OBX S [#!^SQ5OW R@HKOBQ & T ‰™K˜^]
T`[ ›šš * -YX~˜Qd @ / @ ) ) ) @ -^œ.š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›š~˜"- š , ™< šœ ˜™ y') sOQ<HK )
 OBR@HKOQ5T `R<H5Q €j ,
S_OB`T ) eu4u‚ S]O`T ) SXU`j€T`jkT|= OBT`OHKj€W = SQ<j€HK XZR T [ O`Q OH w S4Q t R a>`OBR<jkR (# SQ
~ R<H5OBQ ' WBj€OBT`WOx O = Q<OBO ) T`j4OBQ<R5j€H.S # a¢OBT`T OBR5R<OBO ) T`Seq _j&&€O ) ' K
S _j ) yu4u S _j ) } ' H`[ vS# Q5SR<R ; kj€[ HKj€ST T`[ o S_S4HKR@HKQ J (# SQ WBW Q W RQ;
H5jkX HKj€ST T`[ #
~ S_[`O ' OkOBWHKj€ST $ T ™K˜y›šš * -YX ~˜Qd œ ` š @ ^- œ†š™ - 4œ ˜"- M^† ˜ ^- œ / ˜"-e{d š™Kš'¤- ›š˜"~ STAHKQ<O ) `OBUOBW ) = T [ ™ œ . › @ -^œ.š X_š'-¤›š Z @ † / @ \") #
S`S4T`OBT ) eu4z S`ST`OT ) a ' O # N; SQ+= T`j OB[s(# SQ<X HKjkS4T S# HKSJS €S4= jkW &‘ WBS4Q5Q5OWH (# O H `Q<O
X J`R ˜ k˜+X ›5 /fT š™ ¤- šœ ›') A‚ ¨ ¦ u 4u SQ # ) yu4z SQ # ) } x OJ HK ; ^Q5R@Hj€H5OBQ HKj!O—[ OBOBJOBT jkTO`= ¦ T2SJ H5jkX [`XljkR5R<jkU€OHKQ5OOR5O Q5W ™ œ . › @ ^- œ.š _X š'¤- ›š') ]¦ u y©4u *
.
&7
*
=
C.
8
=
8
0
*
=
0.
8
8
=
.
*
$
(
H
2!
=
#
>
=
$
8
$
*
/
8
=
0.
"!
,
=
;
*
=
.
8
=
68
8
8
%
06
8
+
)
"!
8
*
=
.
=
6,
8
&7
*
=
.
8
=
7
=
8
,
8
*
=
0.
0
*
=
.
F
,
=
8
=
-
$
u
$ G 7
S |) yu4z4u S |) r {j€OBQ Q5W`j€W :=OT`OH5jkW =SQ<j€H5`XZR&S4JPOQ H5jkTO= ST8JSJ HKj€ST`RS#}WBSXlJ ;
H5OBQ J`Q5S=Q XlR l T ' Q5jk[ Q T ) ' ) OB[ j€HKS4Q ) ‰™˜y›šš * -YX–˜Qd) kš & š'-^œ ` @ -^œ.š™ -4œ ˜"- †C˜ -^œ
/ "˜ -ed{š™K'š -¤›š ˜"- ™ œ . › @ -^œ.š X_š'-¤›š @ † / @ ] ) S `XlO ) J =4OBR z ‚ ~#SQ+= T |# ;
X T`T *
=
0.
=
8
-
=
Aw S t O`TO= ) yuu4u Aw S tU) a = T`[ O`TO= ) x ST R<HKQ(`WH5j4O =S4Q5j€H5`XlR #(S4Q–R<H5Q`WH `Q<O
€O Q<T`jkT|=•j€T#(OOB[|#(SQ w= Q5[ T O`Q T OH w SQ t R #(SQlQ5O$=Q5OR5R<jkST J`Q5SU,kOBXlR„J`Q5S4UkOXZR¦ R`Q.O @ ) ) ) ™5- B_›œ ˜"- —˜"- š , ™< šœ ˜™ y') z^"t¨A% ¦ 4¨© ‚ JPO[`OBR ! Q<UPOQ ) yuz
JOB[`OR ) 3 T [–! Q<UPOQ ) } S4T ; jkT O Q ' j=T &Q5S_WBOBR<R5j€TO= R5j€TO=
O`Q OH w SQ t R¦ &Q5O[`jkWHKj€ST T`[ ' _R<HKOX ~#S_[`Okj€TO= a¢OBW`T`j€W M}hOJPSQ@H ; }n;Qz y;. )
SR XlSR HKj€ST UPSQ HKS4Q< ) ' K
}O o Q<ST ) yu4u Oeo Q<ST ) o ]q JPOQ5jkXlOBTAH5RjkT O4S &]HKjkS4T Q<^T T`WBO  SQ t jkT|=cJ JOBQ ) T`j ;
4OBQ<R5j€H.S #  j€T`R5WST`R5j€T ) ~ [`jkR<ST ) ' 3
D|= OBQ ' H `U`U,kO`Ok[ ) yu4u4z O4= OBQ ) , T`[ ' H`U`U€O^Ok[ )  ™ œ . › @ ^- œ†š _X š'¤- ›š * œ™ , ›]
* * œt™<4œ.šjX š{d ˜™ / ˜"021 kš ™K˜ kš'0 * ˜ & -YX [`[`j€R5ST< OBR€O }S4TO= X T 4) T W ) ' 3
œ , ™šh- ;
~ t Q5j€[ t jkR ) yu4z ~ t Q5j€[ t jkR ) ' a>`O WBW Q W:S# O ]q H5Q JS HKj€ST”" HKj€XZORR5OQ5j€OBR%hXZOHK`S_[`RB¦
G} OBR(€H5RGS# (# SQ<OBW R<H5jkTO„
= WBS4XZJOH5j€HKj€ST IC† ˜ , ™ - ˜Qd2¢V ˜™š›5œ -YX) 4¦ " ¨ ~ t Q5j€[ t jkR  OBO w Q5j = AH ) yuz4u ~ t Q<jk[ t j€R ) ' S T`[  `OBO w Q<j= AH ) ' sV ˜™Kš›5œ -YX
_•šœ ` ˜ * {d ˜™ _v- y_X š'–
0 š'^- œ 4r S`T  j&€O ' ST R ) O w SQ t:) |# HKOB[`j‘HKj€ST ~ HK j R>OH ) yu4uz ~ H5`j R ) ) o S `W Q<[ ) ) T`[‰o jkR5R<ST ) r G} O .; a>j€XZO JPOQ H5j ;
S4T T^S w !^SQ5OW R@HKjkT|= ' _R<H5OBX T @ ^- œ†š™ - 4œ ˜"- ~4œ†š™ šy˜ , ™K›š)8-YX ¤- šš™ -YX
/ ˜"-ed{š™Kš'-¤›š') #~ OBXlJ``j€R ) ' 3
~ OBQ ) 4©© ~ 4OBQ ) K
j€TY^q L^`T`j q TIUPOT`W j U,kO (# Q5SX
AH<HKJ§¦MLL w w w H q SQ+A= LlX 4OBQKL€_T `q LEU`X Q t AHKX ) aP q Q+= ~ W `R t O ) yu44u ¨ #~ W `R t O ) !^OBO[|(# SQ =w Q<[ T`[#Q<OBW`Q5Q<OBTAHT`O`Q T`OH w SQ t R T`[[= OBT`OHKj€W
#
J Q5S4= Q XlRI(# SQR<H5S]W t X Q t OH T`[ZH5jkXlOGR5OBQ<jkOR (# SQ5OW R@HKj€TO= a>`OR5jkRI(# SQX R@HKOQ‰R<WBjkOT`WBO[`O = Q<OBO )
‰o Q5S w T T`j4OBQ<R5j€H. ) h} S][`O R( T`[ ) ' K
~ W kS_W &j€HKR ) yu‚ ¨ #~ W ,&kS_W )  P T`[ j‘HKR )  S44= jkW = kW&`R S># HK O [`O R
#
XlX T`OBTAHGj€T OBQ.S `R WH5j_j€H. , kšœ - ˜Qd _v4œ ` š'l
0 4œ ›5 P ˜K1 ` T ›') ¦ y¨¨ *
=
C.
,
=
8
* +
0.
+
"!
+
/8
+
+
+
8
* +
.
7
+
* +
+
C.
+
7
.
*
C.
8
,
8
,
&
+
7
H
8
7
*
- $
=
7
,
7
C.
*
26
+
8
0
/.
-
8
C.
*
7
*
7
8
$
8
&7
*
7
C.
8
8
,
+
8
,
-
>
8
yz©
~ OBXlXZj ) yuz4u ~#OXZXlj ) x #
@ ^- œ†š™ - 4œ ˜"- l˜™ y ` ˜K1˜"-
$ h *
C.
:&
"!
,
S4T`T`OBWHKj€ST`jkR<X T`[ Q@HKj‘^WBj } jkTAHKO&kj =OBT WBO G T š , ™K˜^] 0–š š , ™< šœ ˜™ yG- * œ ` š ™ n 1^1 ›54œ ˜"- ') J =OBR ]¨‚ ) €j XZOR )
2!
8/
$
!^Q `T WBO ~#jkW kO w j€W ) yu4u ~#jkW kO w j€W ) X š'-¤šœ ›3 pX_˜™ œ ` 0— 4œN * œ™ , ›œ , ™Kš ) & ˜ , œ ˜"‰™K+˜ X4™< 0— ' J`Q<jkTO=OQ ; OBQ = ) ' ) HK`j€Q5[OB[ j€HKj€ST ~#j&kOBQ OH ) eu4z4u ~#j&€OBQ ) ) asS_[`[ ) ) T [ {O[O=O ) ' xOR5j=4T`jkTO= O `Q OH w SQ t R+`R5j€TO=
OBT OHKj€W =S4Q5j€H5`X $ T ' W ¤OQ ) x r ) O[`j€H5SQ ) ™ * @ -^œ.š™'-4œ ˜"- / ˜"-ed{š ™Kš'-¤›š~˜"- X š'-¤šœ ›
pX_˜™ œ ` 0— ~#S%Q = T | #(X T`T ~#j€H5W`O ) eu4u ~#j‘HKW`O& ) a M_v_› `_ -¤š }š54™ - -YX ~#W Q ew {j& *
-0.
*
8
C.
8
*
7
0
=
0.
;
~
` R5R<OBQ ' j€T`j ) yu4u ~ `R5R<OBQ ) x T`[ ' jkT`j ) 3 *
, œ†˜™ C- * šad{š™Kš'-¤›š X , * š\ / ‰™K˜+X4™<0<0 -YX œ ` œ ` š * œ - * 4™ * Pš'021 ‘4œ.š B™<4™ T [`[ jkR5S4T ;  OBR(kO O4OBR SQ@HKO ) yu4u4z O4OBR ) r T [ S4Q<HKO ) SXU`j€T`jkTO= OBT OHKj€W =SQ5j‘HK`XlR ) O`Q OH w SQ t R T`[ x H !sj&€H5OBQ<jkTO=?#(SQ a>j€XZOR ' OQ5j€OBR>!^SQ<OBW R<HKj€TO= ¢ T[~ R@HKSQ t jkR ) ) O[`j€H5SQ )
* @ -^œ.š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›š~˜"- \ / ™K› , œ( *UT œ.š'0—- * / ˜"021 , œ.š™K] @ _ / * ]
^- * @ _L / W
/ * / 4) S `XlO; ) J =OAR u¨¨ u4¨4u ) &j€Q O`R ) Q5OOBWO C ~ ' O4OBROH ) eu4u4u OOR ) r ) }GS]W | ) ~ ) }GS_[`Q5j = `OBR ) { ) o jkR<W j |) ~ ) T`[ OR ) r [ JY;
H5j4O ' H5Q H5O =j€OBR T`[ˆHK O xOR5j =4T S # S HKj€ST Q@ J`J€jkW HKj€ST`R  T> o T # ) r x jk[ |)
[ } ' Xlj€HK ) O[`j€H5SQ5R ) X š'-¤šœ ›8- * ) & ˜ , ]
K j€UPOT ) ~ Q ST ) {hST Q ) ~ r t jkO | )P T`>
œ "˜ -4™ T / "˜ 021 , œ 4œ "˜ - / "˜ -ed{š™K'š -¤›š Z X ) / /
Z '\") J =O‡R ‚ 4
¨ Y‚ u ) Q T`[`S ) ! kS4Q5jk[ | ) ' 3
~S+Q = T #(X T T J [`S `Q t jkRGOH ) yu4u¨ J [ S `Q t j€R ) ) ' J T S `[ t j€R ) ) T`[ S4HKR<j R ) 3 J Jkj€W ;
H5jkSTvS # O`Q OH w SQ t R jkT ' `S4Q<%H ;NasOQ5X ' HKS_W t &Q5jkWOl!CS4Q5OBW R<H5jkOT = T ‰™K˜y›šš * -YX8Q˜ d~œ ` š
V ™œ @ -^œ†š™ -4œ "˜ - l˜™ y ` K˜ 1v"˜ - š , ™5 šœ ˜™ y -œ ` š / ' 1 œN _v4™ Ašœ ' ) ST`[`S4T ) H<HKOBQ<R5ST ) eu4u
H5H5OBQ5R<ST ) x ™ œ . › š , ™< šœ ˜™ y ] ` š˜™ T - * 1^1 ›54œ "˜ - &Q<OBTAHKj€WBO { ) ' jkOT = JPS4Q5O sOBj‘H =OT#OH ) yuu sOj€+H =OBT ) { ) r`%Q =OBT R ) { )D T`[ ' JPO ) x / ` _˜y„ - * V§™<_›œ M] š
V¤™K"˜ -^œ š™KQ˜ d * › 'š -¤›š ' J`Q<jkOT =OQ ; OBQ = ) O w SQ t sOH5Q5S_R t j ~#W = & ) yu4u sOH5Q5S_R t j ) K T`[ ~W = ) r SXlJ Q<jkR5S4T2S # R<H HKj€R<HKj€W J ;
J Q5S WlHKS = J Q XZOHKOBQR<OkOWH5jkST w j€H5lH5`OhXZOH ; = R&XlOHK S][ P T ‰™K˜y›šš * -YXQ˜ dhœ ` š `_ ™ *
†^˜ -^œ / "˜ -ed{š™K'š -¤›š—"˜ - @ -ed{˜'™ 0l4œ "˜ - * › 'š -¤›š
*
-0.
8
*
,
$
0.
5;
3H
8
;
,
+,
8
26
*
8
C.
8
8
,
68
8
0
#7
8
=
* C.
8
8
* &
"!
-C.
$
%
"!
#
2!
"!
+
7#=
$
* 0.
#
* ,
/.
8
,
,
ez
$ G sS€`OBj€X ) yu4u sS€`OBj€X ) { OBT`OHKj€W
a¢OBW T`jkW Q5OJPSQ@H ) a¢OBW`T jkW T`j!OBQ<R5j‘H.
=S4Q5j€H5`XlRB¦ &Q5jkT WBjkJ,kOBR ) XZOHK`S_[`R T [ =SQ<j€H5`XZR kXlOBT Q<OBW`O€H ) yu4u‚ &Q<OBW`O€H ) I}2?o ; ' OHhS # O`Q OH w SQ t o OT`W`X Q t &Q<SUkOXZR
T`[ o OBT W`X Q t jkTO= }€OBR }hOR5O Q5W[}hOJPS4Q<H ) ! t ,€HH8# `Q T #(SQ5X HKj tU) T`j4OBQ5R<j€HEH Q(kR ;
Q(``O OBQ5X TA Q<OBW`O€H ) yu4u4z &Q<OBW`O€H ) +)$4™ T * œ†˜K1^1 -YX , œ ` š'-” T§¦ š , ™5 šœ ˜™ y\ `™ › y~˜Qd
œ ` š œ™5 * 'š ) ' J`Q5j€OT =OQ OBQ = ) {hOBj€[`O€UPO+Q = }hOW`OBTIUOB+Q = ) eu 4¨ }GOBW`OTIUPO+Q = )} ) & ˜ , œ ˜"- œt™<4œ.šjX š\ Z 1œ 0 š™ , -YXcœ†š› ` - y› ` š™ U* T œ.š'0–š
-_› ` ™ - B 1 'š - * š™; ˜ k+˜ X y› ` 'š -L) & ˜ , œ "˜ - {S US]S = OBQ = ) ' H H<H = Q<H }hj€OB[`Xlj&kOBQ ) yu4u‚ }GjkO[`Xlj&&€OBQ ) ~ ' `JOBQ(_j€R5OB[ O Q5T`j€OT =2j€T ~ ‘HKj& OBQ sOQ5WOBJ H5Q5ST`_R ;2#(Q5SX
o W t J`Q5SJ = H5jkSTH5S [ J H5jO O Q5T`j€OT =a¢OBW`T`j€’ `OBR / "˜ 021 , œ†š™ * œ - * 4™ * h - *‡@ -^œ†š™ d_›š' )
}hj€OB[`Xlj&kOBQ o‰Q `T ) yu4u¨ }GjkO[`Xlj&&€OBQ ) ~ T [ o Q `T ) { xj€Q5OWH [ J H HKj4O ~#OHK`S_[
#(S4Q ! R<HKOQ o W t J`Q5S4J = H5jkST O Q5T`j€OT =`¦ a>`O } }O =SQ<j€H5`X T ‰™K˜y›ššš * -YX8Q˜ d~œ ` š
@ ) ) ) @ -^œ†š™ -4œ "˜ - / "˜ -ed{š™K'š -¤›š—"˜ - š , ™< šœ ˜™ y' ) ' T:!^Q T`WBj€R5WS ) ) ' 3
}hS_W |) yuu ?}GS]W |) ~ X L J Q5eS q]jkX e4S cQ<OBR5S &O 4S#[ S#W j q]OBj€Q5S7_j y! TAHKO _j J`Q5S =Q ;
X 4S =4OBOT HKjkW , a>`OR5j€R #(SQ ~ R@HKOQ ' WjkOBT WB_
O xO =Q<OBO ) xOJ Q<H XlOBTAHKSZ[`O |T #(S4Q5XZƒEHKj€W | ) T`j ;
4OBQ<R5jk[ [`O [`S ~#jkT` S ) o Q = | ) ¢SQ<HO = }hS_W OH ) E©© }GS]W |) ~ ) ~#OBT`[ OBR ) } ) S4Q<HKO ) ) T`[ O4OBR ) r ' j€H5H5jkOT = `OBR@H H  OB[ [`jkOT = Q<H.¦ q JOBQ<jkXlOBTAHKR S4T OBT OHKj€W T`[ S & H5jkST Q< ST`R<H5Q j€T`OB[ J H5jkXlj HKjkS4T y T
‰™K˜y›šš * -YX Q˜ d ` š / "˜ -YX4™Kš "˜ -) & ˜ , œ "˜ -4™ T / "˜ 021 , œN4œ "˜ ->Z / ) / '\") S &`XlO )
J =OBR " z ) ' OS ) SQ<O ,^
SXlJ H5OBQ ' S_WBjkOH. }hS_W OOR ) 4©©© }hS_W |) ~ 9 T`[ OOBR ) r S4XZJ]H 4S OOT H5jkW O 4S & WBjkS4T^ƒ4Q5j ,
1^"˜ -^œ 0–'š -^œ†˜y * š8' 1^˜ ˜ * y› 1 - * š * œ†'š 0l @ -^œ†š X_'š -^œ.š' ) T`j€[ [`Ol[`O T`R<jkT`S ) xO ;
J Q<H XZOTAHKS„[`O |T #(SQ<X–ƒEH5jkW | ) R<WBS [`O OT =OT` Q<j | ) o Q = | ) sS4Q<H | = }hS_W OH ) E©©© }GS]W |) ~ ) jkO |) ) SQ<H5O ) ) T`[ OOR ) r jkO w jkOT = ' W`OB[,kj€OT =
&Q<SUkOXZR HK`Q<S O = OBT OHKj€W T [ 4S &]HKjkS4T Q< =SQ<j€H5`XZR : T OH ) r } ) OB[ j€HKS4Q ) $ ]
™< kš ¤ - * œt™ , œ†š * ‰™K˜y›š -YX @ * l˜™ y ` K˜ 1^ ™K˜y›šš * -YX }š›œ , ™Kš ˜œ†š / "˜ 021 , œ.š™ * › 'š -¤›š ") J =4OBR yu ' J`Q5j€OT =OQ * -0.
7
* .
+
8
7
=
* C.
+
8
5
)
"!
2!
*
C.
0
*
0
0
.
!
+
+
8
*
C.
8
+
*
1
0.
)
8
8
&,
"!
8
&7
8
7
7
*
.
*
%(
,
0
=
,
0.
,
$
,
%
6,
8
06
C.
7
*
,
&
(
"!
26
;
yz
h} S ! R ) yu4u h} S ! R ) }
$ h *
C.
š , ™<
šœ ˜™ y7] U* T  œ†š'0l4œ › @ -^œt™K˜ *, ›œ ˜"- ' J`Q5j€TO=OQ ; OQ "!
=)
BO Q<X TI } `XlO€ Q@H>OH ) yu4z }`XlO€ Q<H ) x ) {hjkTAHKS4T ) )D T`[  j&kj XZR ) } O Q<T`jkTO= TAHKOQ5T }GOBJ Q5OBR<OBTAH HKjkS4T`RUA Q5Q<SQ &Q5S4J = H5jkST T }kXlO€ Q@H ) x T [ ~#W €O T`[ ) r ) OB[ j€HKS4Q5R )
$4™< kš œt™ , œ†š * ‰™˜y›š -YX\ ) 1 k˜™<4œ ˜"- - œ ` š[_ ›™K˜yœt™ , ›œ , ™Kš2˜Qd / ˜+X- œ ˜"- ) S";
`XlO ) J =4OBRh¨ yz _¨ ) ~ a &Q5OR5R ) = XU`Q5j€[O=O ~ K
} `R<R5O& SQ(_j = ) yu4u } R5R5O& ) ' T`[ SQ.]j = ) ™ œ . › @ -^œ†š X_š'-¤›š\M _•˜ * š™'- 1 ]
1™K˜B_› ` &Q<OBTAHKj€WB'O ;m{ ) O w r4OBQ5R<O ) ' 3
}G_WBQ<S # H ) eu4u¨ }>_WBQ5S # H ) } ~jkWBQ<S]WSXlJ HKOQ$R5S # H w= Q<OS#¢jkTAHKOQ5OR<H>HKS_#(S4Q5OBW R<H5OBQ<R>jkT8WSXZJ Q ;
H5j4O Q<O_jkO w @ -^œ.š'™ -4œ "˜ - †^˜ , ™ - Q˜ d2Vs˜™Kš›5œ -YX) J =OBR ¨ ' TAHKSR ) yu4u4u ' TAHKSR ) ~ * œ.'š 0l * š / ‘ . ›5 35( ˜ š'0 20 š'-^œ†š œ™ ,„* ˜y & x
H5`OBR<jkR ) T`j!OBQ<R5j€[ [`O [`S ~#j€T``S ' Q€O ) eu4u ' QkO )  ' HKS4J`JPO[2a¢Q j€T`jkOT = T [ HK`O2Q }GOBXlOB[ jkOBR #(SQ OQ<`H<HKjk|T = $ T ‰™K˜y›šš]
* -YX Q˜ dœ ` š {œ ` U* T 021^˜y , 0 "˜ -œ ` š @ -^œ.š™ d_›š Q˜ d / "˜ 021 , œ†š™ * › 'š -¤›š - ** œ 4œ œ ›' ) J =OR
¨ ]¨ 4© ' Q€O ) eu4u4u ' QkO )  O`Q OH w S4Q t !^Q<OB’ `OBTAH€ R t OB[ OBR<H5jkST R j U,kO #(Q5SX
# H5J§¦ML"L # HKJ R R WBSX–LEJ UCLET`O`Q qL4! AHKX ' W POBQhOH ) yu4u ' W POBQ ) r )  `j‘H kO ) x ) T [ R5`OkX T ) SXU`j€T HKj€ST`R&S #M=OBT`OHKj€W
=SQ<j€H5`XZR T`[ T`O`Q T`OH w SQ t R¦ R(`Q(4O S # HK`O R@H H5OvS # HK`O Q@H T  `j‘H kO T`[
' W POBQ ) O[`j€H5SQ5R ) ‰™K˜y›šš * -YXQ˜ d>œ ` š @ -^œ†š™ -4œ "˜ - l˜™ y ` K˜ 1:"˜ - / "˜ 0 -4œ "˜ - hQ˜ d X 'š -¤šœ ›
pX_˜™ œ ` 0— - * š , ™< šœ ˜™ y' ) J =OBR "]¨ ' W w= Q ) yu z ' W w= Q ) R@HKjkX H5jkOT = HK`‡O xjkXlOBT`R<jkST–S # ~#S_[`O ` š2 - - M Q˜ d * œN4œ ]
œ ›' ) p¦ ‚ Y‚ ' W w 'O #(O ) yuz ' W w $O #(O ) { ; , 0–š™ ›5 Z 1œ 0 4œ "˜ - Q˜ d / "˜ 021 , œ†š™ _•˜ * š M  j&kO [ } XlJ ) } O Q OH w SQ t R T`[ ~ T =OXZOTAH
' Q<[ } XZJ ) yu4u ' Q5[ | ) } T`W
' WBjkOT`WBO{JL JPOQ H5jkST R }hOR5O Q5W§¦ o‰jkU€jk4S =Q J``j€W R<R [8) -¤› T › kK˜ 1^š * 2Q˜ d B™54™ T - * @ - ]
d{˜™ 0l4œ "˜ - * › 'š -¤›'š ) ¦" ‚ , u ' `j OH ) yu4u4u ' `j ) ) a X Q | ) ) T`[ t j ) a ST€jkT`O Q–HKj€XZO R<OBQ<jkOBR#XZS_[`O&kj€OT =
w j‘HK—H5`O$Q [`j _U R5j€R # `T`WHKj€ST ;.U R5O[~R<H HK'O ;N[`OBJOBT [`OBTAH H5SQ5$O =Q5OR5R<jO XZS_[`O @ -^œ†š™ -4œ "˜ -
†^˜ , ™ - Q˜ d U* T œ.'š 0— * › 'š -¤›'š ) ¨4©^" % ¦ *
-C.
,
$
*
-
#,
7
8
C.
*
8
.
*
+
0.
*
&7
.
*
-
C.
8
F
8
*
F
8
0.
+
6,
8
:&
*
*
)
0.
"!
.
8
-C.
*
-
*
"!
;
0.
(/
ez¨
&Q5S ! OWH2h} O ;
$ G ' `ST`OU`Q%= ) yu4u© ' `ST`OU`Q%= ) Q<jkWO &Q5O[`jkWHKj€STL`R5j€TO= O`Q OH w SQ t RB¦
JSQ@H š , ™K˜y›˜"021 , œ -YX) _¦ , ' HKQ<S `R<H5Q`J ) yu4u ' HKQ5S `R<H5Q`J ) o ` š / ™K˜+X4™<0<0 -YX §-YX , yX_š [`[`j€R5ST< BO R€O ) T`[
O[`j€H5jkST a |T = !jkR< w j€W tU) yu4u¨ a TO= ) T [ !sjkR5 w j€W t:) ! !COOB[ ;j#(SQ wM Q<[ O`Q OH5R ?
R ~#S_[`O€R
#(S4Q>a>jkXlO ' OBQ<jkOBRG!^SQ<OBW R<H5jkTO= Z * †^˜ , ™ - s˜Qd / ˜"021 , œ -YX) "„‚I% ¦M¨ ‚]¨4z *
0.
/
8
*
*
#
-
.
8
8
;
C.
H
-
a>`jkXlX !jkORkOQ ) eu4u a>`j€XZX ) T`[ !jkORkOQ ) &Q`T`j€TO=hS# O`Q OH w SQ t R }hOR5O Q5W
Q<OBJSQ<HGj€[`j J ;.Q<Qnu 5;.©¨ )` x kU Q5jkWAH ) yu4u‚ kU Q5jkWAH ) ~ €H5j ;NQ5OBW`Q5Q<OBTAH OH w SQ t R #(SQhasQ !lW—!^SQ<OBW R<H5jkTO= ‰ T ‰™K˜y›šš]
* -YX—Q˜ d + @ / "˜ -ed{š™Kš'-¤›š') ' O H €O )  R5 jkTO=4H5ST ) ' 3
 o ) 4©©  o OT =j€T`OBOQ5jk|T = R<H HKj€R<HKj€WBR T`[ UPS_S t j U€O #(Q5SX
AH<HKJ§¦MLL w w w j€H T`jkR@H =S`L[`j z4u4zLE T`[ UPS_S tU) ' a ' ~ a { *
0.
*
7
C.
58
7
,
*
7
.
8
8
8
,
ˆOj=OT`[ OQ5R<`OBT|#(Ok[ ) eu4u‚  OBj =OBT`[ ) 3 T [ OBQ<R5`OT|#(O€[ ) 0–š * š™ š ™Kš * ›œ ˜"- \
V¢˜™Kš›5œ -YX„œ ` š V , œ , ™Kš—- * d - * š™Kœ - * -YXZœ ` šc>œ [`[`j€R5STY;  OBR€O ) ' K
 `j€HkO ) yu4zu  `j€HkO ) x a>`O a } =SQ5j‘HK`X T`[ ' OkOWHKj€ST Q<OBR<R`Q<O4¦  I
} T t N; U R5O[ kS_W H5jkST S#:}GOBJ`Q<S][ WHKj!O$a¢Q5j kR¢jkRco OBR@H ^ T ' W #(OBQ ) r x ) OB[`j‘HKSQ ) `_ ™ *2@ - ]
œ.š™ -4œ ˜"- / ˜"-ed{š™Kš'-¤›š˜"- X š'-¤šœ ›M pX_˜™ œ ` 0— OSQ+=4O'; ~ R5ST T`j4OBQ5R<j€H. ) ~#S4Q+= T |# ;
*
.
8
*
8
C.
&7
8
8
8
*
7
=
X T
 `j€HkO ) yu4u  `j€HkO ) x OBT`OHKj€W =S4Q5j€H5`XlR T`[ O Q OH w S4Q t R T sOQ5jkS q ) r )
 j€TAHKOBQ ) ) T ) ~ ) T`[ `OBR@H |) ) O[`j€H5SQ5R ) X š'-¤šœ › pX_˜™ œ ` 0— -)8-YX -¤šš™ -YX8- *
/ "˜ 021 , œ.š™ * › š'-¤›š r4S`T  j&kO ' ST`R §HK[  `j€HkO–OH ) yu4u©  j€H €O ) x ) ' H Q tgw O HK`OQ T`[ ) a )M T`[o S4= Q<H ) OT`OH5jkW =S ;
Q<j€H5`XZR T`[ O`Q OH w SQ t RB¦PJ HKj€XZj j€TO= ST`T`OWHKj€ST`R T [ ST`T`OWHKj!_j€H. $4™5 kš / ˜"0 ]
1 , œ -YX) e‚`¦V¨ ‚ ]¨ =5! ) yu4u©  =y! ) ' } š @ * š5~˜"-vœ ` š * œ™ , ›œ , ™šZ˜Qd œ ` š š™ & ˜ , *UT œ.š'0 - _ - * š™ œ†šB™<4œ.š ~ a &Q5OR5R ) = XU`Q5j€O[ =O ) ~ ) HKQ T`R( H5jkSTZS#}HK`O!^Q<OBT`WOB[ j€HKj€ST–S # ez4u‚ ' T`[`'O q R5j€TO= O`Q S sS4 ) yu4u S ) r T [ ¢S ) { !^SQ5OW R@HKj€OT = HK`O
OH w SQ t R T @ / ] @ ) ) ) @ -^œ.š™ -4œ "˜ - / "˜ -ed{š™K'š -¤›š"˜ - š , ™5 šœ ˜™ y[‰™K˜y›šš]
* -YX' ) sOBQ@HK )  OBR@HKOQ5T `R<H5Q €j ,]
S4XZJ]HKOBQ ' S]WjkOH. .
8
,
*
%+
C.
,
*
,
0.
,
,
,
8
.
=
%
8
*
,
8
,
+
7
"!
yz‚
$ h S]ST §j OH ) yu4u‚ S_ST`j ) o ) {S €XZOR ) x ) TO=`S ) )D T`[ T `[ O ) 3 !lWBjkOTAH =4OBT`O ;
H5jkW =SQ<j€H5`XZRA#(SQH5Q j€T`jkTO=[ OQ5OB[ #(OBO[|#(SQ w= Q<[ T O` Q `T OH w SQ t R @ -ed{˜™ 0l4œ ˜"- * › š'-¤›š')
¦ z *
C
*
.
+
8
=
-
kO ) yu kO ) K T XZOHK`S_[‹S#j€T 4OBR@HKj= HKj€TO= JPOQ5j€S][`j€WBj‘HKjkORjkT0[`j€R<H`Q5UOB[‹R5OQ5jkOR
w j‘HKcR<JPOWBj §Q5O'#(OBQ5OT`WBOH5S w S #(OBQYR$R(`T`R5JS4HhT `XUOBQ<R M `_ k˜y h ™5- h ˜ T4h9* ˜y› h }˜"- * ˜"-L?)
¦ , u4z -/.
7
5H
;
x)
8
5! `R@H XlOBTAHKS [ J H H5j4S ) u4z
kOkS ) ¨4z
=4SQ5j‘HKXlSR‰[ O H5Q5OjkT`S
WQ5j€+H BQ<jkSR$[ O J Q =4OBX ) ¨‚
XlS][ S~[`OHKQ5OjkT`S ) ¨
XlSXlOBTAH `X ) ¨
JOBR<SRj€T`jkWj j€R ) ¨
`j€W t &Q<SJ ) ¨¨
}GOH5Q5S ; Q<SJ = e4S ) u
} }O ) ¨¨
H q [`O J Q5OBT [`j =OBX ) ¨4© ) ¨
=SQ5j‘HKXlSR OB|T HKj€WBSR ) ) ¨4z
=SQ5j‘HKXlSR OOT H5jkWSR2O S `WBj€ST^ƒ";
Q5jkS4R ) ) 4¨ z ) z
XlSR@HKQ =OBX OBR<H5S]WBƒ4R<H5jkW | ) ‚ WSTOBQ<R 4SZJPS4Q>SQ5[`OT 4S ) ‚ XlS][ Ok<
S =4OBOT Q5jkWS ) 4¨ u
Q<OBT`S eESZ[ JSJ eES ) ‚A¨
Q<OBJ`Q<OBR5OTAH ]O2R =OOT H5jkW R ) ‚A©
R<OkOW 4S ) ‚4‚
€jkR XZOTIH5S q JST`OT`WBj ) ¨ ) ¨ ) z
XU`j€OBTAHKOR [`O&J`Q<4S =Q X 4S ) ‚ ) ‚ ) u )
8
8
C
o
o
,
8
8
XlS][ OkS4R ) {©¨
O^W{ƒ4Wj `[ O J`Q<O_jkR+4S ) y©¨
H5OBXlJPSR>[ O WSXlJ H e4S ) y© S XlJ H e4S OBOT HKj€W O S `WBj€ST^ƒ";
Q5j ) e‚
J,kjkW _OBR ) yz
WST`WBOj€H5SRGU`jkS 4=j€WBSR ) e‚
WS|T #(OB%Q BT`Wj R ) 4z
€j_Q5SR ) 4u
Q<OBW Q5R5S4ROkOBWHKQ T`jkWSR ) 4u
Q<O_jkR@H R ) 4u
Q<j TAHKOR )
WBST WBOBj‘HKSRGOR<H HK‚kR@HKj€WBSR ) y¨
G
7
7
G
7
-
,
) ‚4u ) ©
I} ) ‚ ) ‚^u
J`Q<OBT`[ j = OBX ) 8
) z
e‚^u
--
<) ‚ ) ‚^u ) ‚
W R<SZJ QKƒEH5jkWBS ) e‚
WBS_[`j€`W 4 S ) ¨4z
(# SQ@HKO ) z4u
(# Q W |) z4u
WBSXlJ Q eE S~OBTAHKQ<O
/
8
-
7
8
,
8
S_S4HKR@HKQ J`J`jkT|= ) 4¨
Seqg; r4OBT t j€T`R ) ¨ )
o
5
8
-
F
8
8
8
T ESlR(`JOBQ(_j€R5jkS4T [ |) Q<$O #(SQ%BS ) R(`JPOQ(_jkR<jkST [ | ) } ~ )
H5S ;Q}GO =4Q5OBR<R5j!S ) )
H5S]WSQ5Q<O e4S ) ) )
7
7
7
yz yz
† -
WBST O'q ]OR ) ) "‚
WBQ<SXZS4R5R5S4X | ) ) ¨4z
~#OH ; ) u4u
=OBT 4HKj€JPS )
=OBT O ) ) ¨4z
=OBT OBQ kj eES )
Q<j€H Q5j€S [`O T|#(SQ5X 4S
} )u
8
7
x
G
4¨
Q<j€H Q5j€S[`O T|#(SQ<X 4Sh[`O
Q<O = Q5j 4S ) 4¨
R<OkOW 4SZ[ O XlS_[`O€SR ) 4¨ ) y¨4©
R<SU`Q5O ; 5 ! R<H XZOTIH5S )
[ `[ S4Rh[ O H5OBR@HKO )
x Q w jkT ) [`OBR._jkSlJ [`Q+4S ) ¨ Y) y¨
[`jkR@HKQ<jkU`j e4S~T SQ5X ) y¨
,
{
F
-
z4z
!
# WH5SQ>[`O
-
#(OBT EHKjkJS )
G
r
-
7
-
! T`O r T`O [`Oc_jkR5j€U`j&€jk[ [`O )
asOXZJSQ xORkj TAH5O
-7
=
S ST`OBT ) y¨
=
C
)u
!^SQ5OW R@H &Q<S ) ) y© ) 4©
# `OT 4SZ[ O WHKj! e4S ) ‚
`O ]j€R5j€[`O ) €jkXlj Q ) €4S =‚kR@HKj€W | ) R<j =XlSjk[ ) # `OT 4SZ[ O J HKj€[ 4S ) ¨4z ) ¨4u
TAHKO€j=4T`WBj @Q HKj€`WBj ) ¨ ) ‚ ) z
TAHKO€j =4T`WBj ' S_BW j ) {¨ jkTAHKOQ( €SR>[`O WBS]T  TO |) z ) {© ) y¨z
8
/
Q5O[O 4S
y©
-
-
-
7
OBR@HKQ H =4j R>[`O J`Q<S]W`Q ) z
=SQ<j€HKXlSRWBST R<HKQ( HKj!SR )
=SQ<j€HKXlSR[`O WBSQ@HKO ) z
`j& ;.W€jkXU jkOT = ) z ) z4z
J`Q<S]W`Q WO = | ) z ) z4z
J`Q<S]W`Q JSnQ #(OBj q]O ) z4z
R<jkX HKO[ T`T`O kj€OT = ) z
R<HKQ H $=j R 4S &]HKj R )
)‚
{S ‘H%;j jkTAHKOQ5R ) ¨
`SQ<j S4TIH5OHKOXZJSQ )
W`Q<H5SZJ`Q S ) y©
€STO= S~J`Q S ) y©
X B [`j€S~J`Q S ) {©
H5OBXlJPS„Q5O ) y©
F
=Q [`jkOTIH5O ) u ) e‚ OBQ<Q5Sl[`O J`Q5O]j€R 4S ) ~[`j SQ5X €j [ [`S [ Q `[ S>[ SR
Q<Q5SR ) } j ~[`j [`S [`Q [`S[ S R <Q Q5SR )
8
2t^ j t O )
o 4OBR ) ‚
[O
,
+
X Q5W tU) y¨¨
kj€T`O Q<jk[ [`O ) ¨
jkT q ) ‚ ) ‚4u ) 4¨
+
+
) 4u
ez
† o S =SXljkJ`R )
TIUOBT`W ) E¨
4¨
~
4S &Y;
7
8
T`O Q T`j€S
T`S_[`S ) ‚
G
G
-
) )‚
SJOBQ [`SQ5OR =OBTOHKj€WBSR ) ‚
WQ XZOTAHKS ) ‚
WQ XZOTAHKS Q5j‘HKX HKj€WBS ) ‚ ) z )
WQ XZOTAHKSl[`O [`SjkR>JSTAHKS4R ) ‚ WQ XZOTAHKSl[`O`X JSTAHKS ) ‚
WQ XZOTAHKS `T`j #(S4Q5XlO ) ‚
X]H 4S ) ‚A¨
X]H 4S = `R<R5j T | ) z ) e‚ SJ H5jkXlj e4S
XlS][ OkS~OS `WBj€ST^ƒ4Q<jkS ) u4z
XlS][ OkS~T O`Q<ST ) z4z
}
e‚ -7
-
/
Q W jkS_WB‚€T`jkS ) } [`j 7o R<jkR ;.! `T`WH5jkST R ) y¨
}hO[`OBR O`Q5S4T jkR Q<H5j€^Wj j€R )
J Q5OBT [`j =OBX )
Q<’ `j€H5OBWH`Q R ) u
W Q WHKOQ5‚kR@HKj€W R ) z
WST`WBOj€H5SRGU`jkS 4=j€WBSR )
JOBQ<R5JOBWH5j `jkR@H Q<jkW ) H Q5'O # RG[`O J`Q5OT`[`j =OX )
H5SJPS k4S =j R ) u
}hO[`OBR O`Q5S4T jkR 4S &`WjkST`ƒ4Q5j R ) z4u
u
}hO[`OBR O`Q5S4T jkR }GOBWSQ5Q<OBTAHKOR ) y©
}hO[`OBR O`Q5ST jkR T`j€[`jkQ<OBWWBjkS4T jkR ) y©
‚) z
Q<’ `j€H5OBWH`Q ) H k SR ) z
W J Wjk[ [ OBRGOkjkXlj€H _OBR ) ¨
WSXZJ,k'O q XlOBTAH5OjkTAHKOQkj = [ R ) z
8
-
)
7
sOTIH5j&`X ) y© Y) ) 4© ) JPS4J e4S ) ¨4z
J`Q5O_jkR ES ) ) &Q5O_j€R 4Sl[`O ' BQ<jkORha¢OBXlJSQ j€R ) "G
-
/
G
eu
G
-
-
SJ 5H jkXlj e4SWSXU`j€T H Q5j |)
S J 5H jkXlj e4
S T `X BQ<jkW |) yu
-
7
S
7-
8
(
7
-
8
7
8
X [`j ) ¨ ) y¨
~#OH ; =S4Q5j€H5XZS4R OBT|HKj€WBSR—O
WBjkS4T^ƒ4Q5j€SR ) u4z ) u
XZS_[`OkS } ~ )
XZS_[`OkS )
~#S_[`O€S )
XZS_[`OkS } ) 4u
=SQ<j€H5XZSR OTOH5jkWBS4R¢O S `WBj€ST^ƒ";
Q5jkS4R ) 4©
T`ƒ kj€R5O[`O R%BQ5j€OBRGHKOXZJSQ jkR ) ‚
WS|T #(OB%Q BT`Wj R ) [`OWBSXlJSR5j e4S ) €j_Q5SR ) X H5S][`S4R>WBSTOT`WBj€ST j€R ) ¨
Q<OBW Q5R5S4ROkOBWHKQ T`jkWSR )
}GOB[`OR O`Q<ST j€R Q@HKj€`WBj jkR )
Q<O_jkR@H R ) J`Q5O_jkR ESOBX HKOBXlJSQ5O ) y© ) ) u
J`Q5S_W Q OBX =Q<O€ | ) "‚ ) y© ) yu ) ‚
&Q54S =Q X e4S 4S &`WjkST`ƒ4Q5j | )
&Q54S =Q X e4S OB|T HKj€W | )
8
)¨
)
yz4z
† WST|#(OBQ%BT`Wj R )
€j_Q5SR )
J`%Q ';NJ`Q5S_WBOR5R XZOTIH5S ) ¨ Q<OBW Q5R5S4ROkOBWHKQ T`jkWSR )
Q<O_jkR@H R )
Q5O'#(OBQ5OT`WBj ) Q5$O =Q5OR5R ES ) Q5OJ`Q5OR5OBTAH e4SZ[`SlWBST` OBWBj€XZOTAHKS
HKOXZJ HKO ) ‚^z ) ‚^u
HKOT`O[ BT WBj ) asOSQ5j [`S = SR ) ¨
HKQ U €`_
S # H Q5S ) y¨ 7
7-
G
,
7
7
k j€[ 4S Q [ ) E¨
Q5jkƒ4O €O H Q5j |) y¨
7
'
)‚
G
R+Q5jkOR>HKOBXlJSQ j€R ) z
W 4HKj€W R ) ¨
WSX HKOT`O[ T`WBj |) z
OX HKOXZJS„Q5O )
T ES €jkT`O Q5OR ) z
R ST jkR ) z
R ST jkR>WSX HKOT`O[ T`WBj |) z
R5‚€TIH5OBR<O ) R ST €jk[ [`O ) R5OkOB$W e4Sl[`SRGXlS][ OkS4R$[`O J`Q5O_jkR ES ) ‚
kjkR XlOBTAHKS q]JPS4T`OBT`Wj ) ‚
XlOH5S][`S k4S =j [`O o eS qg; r4OT t jkT`R ) XlS][ OkS4RjkT R5J`j€Q [`S4RT H `Q<O ) ’ €jk[ [`O ) u
}GOB[`OR O Q5ST jkR T`jk[`j€Q5OWBWBj€ST j€R )
R5OkOB$W e4SlT H`Q ) ‚
R5j€R<HKOX [`O W R<R5j€`W 4S ) yu
R5j€R<HKOX [`OvJ`Q<O_jk+R 4S‹OBX H5OBXlJPS0Q5O )
G
-
-
8
7
--
Q<’ `j€H5OBWH`Q ) e‚
X ][,kS~[`O J`Q%';NJ`Q5S_WBOR5R XZOTIH5S
X ][,kS~[`O J`Q<O_jk+R 4S ) -
G
'a
G
+
) ‚^z
' `J`JSQ@H OWH5SQA~ W `j€T`OBR ) y¨
a
,
) e‚
-


jkT`[ S w R ) y©
-