"!$# %'&)($#+*,.-0/
13242 ,65879&;: *=<>&?5@( AB&C<D!
EF: *HGI# JK#8($5@&L&)(MG *NLB*
O
*NLP# Q<DR9SUT
Q<V#8&)( WX,65@(UGIL<Y*S
ZX[V\]^`_baDced8f`gh^jiHf`^lknmH^j\go\
pFq rtsuv`wVvx qyvyvz
[\['[V\^ d ]
"!$#&%(')+*,%-,./1032
45 "6(7,03% 8903)/: 53;,;,<
! #"$&%('$") +*,"$-/.01')"$2')35476698:;9')
<=>?A@B") DC53"EGF+.2')-HI") %J')-K')6MLN=,,"$')-H89'),
'$8G>;')68&M'$8MLPOQM'$8G:/.0..";"$3@B"$-H+R2'$65S7"M38G:?T')R"$03GU
M')+."$:;1')-/-/:EV6"$I>?XWY')2')3@7MEZ3M')[')3:?R1'GEVM')3D')2')3@G/\]"$.Z"$3"$:;@^5')8
-_03>;')`')6M')36030MLa56;E2"$-H_R2'$6T0333bRZ_1')8(')8c."M>?8J')8
"$-HdXW')-/.333,RZK:;>?')3"$:(K'@?L(eQ')-/.T2'$')3"fRZg-K'$8
"&-K')S?/-K')`')3h.I8i'$j-_06g3k lUA0GmK6I'$+.";R3;En"&2')[
M'$8=6M')fM'$8c_"$3jQ"$0=-K')S7:d1>?1')3n>7"Kj3"76M')3V3RGU
1')@?LKa5"$.X ]033@?En[j33,')3"9R0X ]03D o"$_"$-Hd'$8G>$')68YM'$8_"
-/:;I=2'>?+ o"$:?"$p[R2'$6ML
qr)sVtnu7vKw]xIybz|{ix}tZ~ LH,"$0383S?Y"2')S-_@'$8G>}1"$p") #1"$f+pF[')3
o"$.2')6_')8&.:K8G160"$ML ='$8G>7"$')[2')8&"/6"$-H[R}@?L
e=3"EGNh"$038p3S?+"T2')Sp4}0.."$Q')3"$:d*h.3XWK o"$3.99+I'>;'?;*h.3XW
I '$6;EGQ6"$3"G5"$:?')PQ<=>?@H") n4}2'j o"$N.P3`'):"jQ0
')8iXWG"$i") T%(')3`')R|;*h.3XWi} o'$6;LpC=K.Z"$ii.2')603`')MEN4}>?
}p')/cF5.2')-H}B") [G #"$-K')6K')K9<Q>?@") jC53"Eh2'$/R'
>;')302')R3c'$H6"$6:g@G-"$d')8."M>78G:i.K:?1')3
3`'):H"/_%(')3`')R|;*,Nn')8pI'M>$'?;*,NnI '$6ML
Qk, )N¡}¢$£5¤)N¥7¦?¦;§
xr?x
tZ~ uyr;~]u|tuZwn~]u|t _u"!$#Zx yxI~Mx {%#tnx}y&(')M~Mx}{*u+-,.]t)/
x0 21"3 G~]uZt
4 5
uZt(#|x ~#tnz ~6nx7-8 u+9Dwlx7{ ~Mu%%, : u+9Dwlx7{ ;
<
L>= 47"$-H_ '$6_*,"$6.Q") -K'):?jeQ2')3@G L[LjLjL[LjL[L_L[LjLjL[LjL[L ?
< L< e 4}-/.3T%f"783 #"$F+"$:dA-K'):? LjL[LjLjL[LjL[L_L[LjLjL[LjL[L @
< LBA T4}-H"}"$:Bb')1')-H(LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[L C
< LD a=" F+"FE _47j "$08G')8IHKJ LjL[LjLjL[LjL[L_L[LjLjL[LjL[L L
<
LB? *,"$I>?"$J") \
< L<
^h"d'V "$R3- L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LM=ON
<
LB@ *,"$-/.2'): /47"$30"$ L[LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LM=
<
< LQP
SR
"$R3-pEUT5 "$R3-H E|*,NV')8(*,"$I>?XWGA@ LjL[LjL[LM=O?
< LBC e O=-/8Q"$(*,"$I>?XWGA@ LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LM=O@
V
)9bz
yWlx7tZ~X!FY~]{Z[\G~]u|t
4]
AGL>= %f"78*=F^Nn'):;1'):?TOQ3`' W')"$ L[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[L < =
AGL>=;L>= F58G06:Kjn'):;1'):?_F502')3n") N'V LjL[LjL[L_L[LjLjL[LjL[L < =
AGL>=;L< 4}0R:;1'$8GI L[LjL[LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[L < ?
AGL>=;LBA V"}6M'):B'%(' WG-_0-_^P51'$8GI`N0=4}0R:;1'$8G} L[L
< L
AGL>=;LD jeQ3:?"$- LjL[LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LaAb=
AGL>=;LB? e8')."$c") DN"$R3- \ < LB@?^')8f*,"$-/.3XWGA@ L_L[LjLjL[LjL[LaAcA
AGL>=;LB@ eQ0:;-H}:de=3:?"$-d= L[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LaAc?
AGL< %f"78 < ^_4}0R:;1'$8G}5"fe6"$f%("78 LjL[L_L[LjLjL[LjL[LaAc@
AGL
<
L>= g8G:B'H4}0R:;1'$8GI+") b9g\
< L< ^ LjLjL[LjL[L_L[LjLjL[LjL[LaAc@
AGL
< L<
%(')}1'):gM'$R3@ "$0:; "fe6"$h^!g4}0RGU
:;1'$8GI=N"fe6"$(eQ3:?"$- L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LaAcC
AGLBA *,"$I>?:?6OQ03 o"$T4}.(4}>iM_O03") P476"$jAGL>=;LDLjL[LkDN
AGLBAGL>= T4}.f4}>iMjO0354l=XU 4AgL[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LkDN
AGLBAGL
<
T4}.f4}>iMjO0354"Dmj4? LjL[LjLjL[LjL[L_L[LjLjL[LjL[LkDcD
n o
xp ~]rpqdw]z|u `~6b{*
n)q
DL>= "$}A%("}8Gsr26M')"$ LjL[LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LkD0P
DL
<
T51'$8GIU 4}0R:;1'$8G}j"fe6"$f%("}8L[LjL[L_L[LjLjL[LjL[La?
<
DLBA 4}-H"}"$:&'="$-H"7"$tg06"$cUPaQ0R%cUAN-K')"$ L[LjL[La?cC
?GL>= *,"$-/-HI5"$cA8G>78G02')3n%("}8L[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[La@
<
?GL>=;L>= *h2').
< U *,"$I>?"$("H'/V ."$R3- L[LjL[L_L[LjLjL[LjL[La@
<
?GL>=;L< *h2').AI^P4}0R:;1'$8GIjC=.-/>i ')"$ L[LjL[L_L[LjLjL[LjL[La@\P
?GL>=;LBA *h2').DE[a506j%("}8L[LjLjL[LjL[L_L[LjLjL[LjL[L P N
?GL
< e *,"$-/.2')"$(") De=33V%("}8&LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[L Pp=
?GLBA 4}0-/-K')@;*,"$630"$ LjL[LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[L P <
q uu+ltny 6xIu '
eL>= "}") N") N')8p"$@&OQ3`'):H"HN"$.Z";"$jAGL< L[L_L[LjLjL[LjL[L PcP
eL< "$@&O=3`'):H"H"$.";"$7AGLBA L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[LaC <
G~ w 9 5
uybx (;
,R3"$:;1').I@ LjLjL[LjL[LjL_L[LjL[LjL[LjLjL[L_L[LjL[LjLjL[LjL[L_L[LjLjL[LjL[L"=ONc@
$
D
D
! #"%$
e=I@08Ip2'M>}: 08G8 3M')c')3:?R1'')( o')-/3`')p(."$R3- ")
"$3>7:H"M>?8-/8J@G-H") D3M')Q'&I02')"$
(
8*)8*+)8-, .'.'./,
(
8*)01+32 4 58
LLL LLL LLL 4 LLL
(
0)8*+)8-, .'.'./,
(
0)26+32 4 570
\ =;L>= ^
8:9;NLh0-K')R3@?E|_08}5')3"/S7"M=2')=06c@G-HQ89"$
2'>?='=1"$30"$VLa=6;E;,-_0,'$8fe 0"$0P')-HMLDV:=<?>A@CB 4ED=FHG @98"$
[8G02')3Ehj6M')pM'$8 r8p'>?6"$@JI561c"$3>?
KMLON
P6QSRUT1V
<?>A@CB
V
o"$="$-H_"$-XWL-g2"$W%Y[Z]\[^`_baIEZ'H>?6"$=61J'$66"$-/.35=1'$S&33
R+-H8c' "$30"$f") \ =;L>= ^XEZ')8&hj8 r_ "$- '$
V
<U>A@CB
V 4dc
0
efhg
8ji
< f
>A@CB
i
lk 8nm
pj.Z6`')33-/:K6M'$1
V
<U>A@CB
V7o 4qp
LOK
sr
o V
<?>A@CB
V 4 KHt`u
f i< f
>A@CB
i
V[0j6"$8j"M "98-/K &"$30"$[ o"$vWwYw^sxzyS{|y7_}aILXE $r
"$T2')['):;-/
V
<?>A@CB
V
R=4 '):;-/
V
<?>A@CB
V RR
LQT6"$}>?XW H."$R3-H[')
\#[6"$ < LBC #"$_6"$6.Q") ')8c"$-H+03Q"$p6"$}>?XW7@^
.R ."$R3-d^ -/-/>iM
0
efhg
8~
5 f F 2 e g 8 ( f) +
'
R \ =;L< ^
8 ."$R3-d^ -/-/>iM
0
efOg
8ji 5 f F 2
e
g 8 ( f) + i \ =;LBA?^
o
."$R3-d^ -/-/>iM
KHt`u
f i5 f F 2
e g 8 ( f) + i \ =;LD}^
4
13 G~]u|t
"$R3- \ =;L< ^P,."$R2')R3@d5-H";h ')-/3`')"$;LPA,,002')33@K-H8B53M')
3M'$Q &I02')."$R3-pL4}6[j"$Rbe6>?[ #06"$p_\#6"$}I0"$03@^Q8G }kU
')R3j')896"$I>?XWE2'6')@&')890GmK6}Q6"$8G"$9 o"$ @ 4 >+)8 ysy +32 Bh"R
':;3"$R2')3n-/-T0- _\#1[6"$DL< ^
+
0
efOg
8 ~ 5 f F 2
e g 8 ( f) + R 4 > 4 {|y y*;CB
2
e g 8 c 0 efhg
8 ( f) ( f) k + 4 0 efOg
8 5 f ( f)
>
4
{|y y*;CB
d3`')1") ='&}02')"$/') e 0TK"$-K')3'&}02')"$!6"$-/."$I o"$-
')8-K'M@RZ&-K')kW #"$- '$ GCG @ 4:GJD LK@G- ')3'@G
2'$p'!"$30"$ '$9"$..";8 "!Y"$JY"$:;2')3[."$R3- \ =;L>= ^(E=R09
-/:;IQ"$2'>?j'0O&}0["$30"$VLNA E7"M,>?ME1')S>B 4 ;\l ]0331')S^XE
"$:;03`')MEZ')89+"$-K')3'&}02')"$33V2'M>?T'0O&}0j"$30"$
@ 4 >
B 8 D
g"$- 3-HI1')@dI0-H6M')3Z3M')')3:?R1'GE7h=S7"M 2')6M')3603`'):Q}>?
o"$/3`'):?p@G-HH6";3@?La56;Eh-H"}8/2'M>?pRI>?}8 o"$H6M')3603`')U
:ic0O&I0f"$30"$" p"$-K')35'&I02')"$d6 8"7K"$d3@"$
6M')3603`')"$i") I>?;LH47"$-H/8G6j-H"78j')K[')0`') 3-/2')"$g')8
>;')"$0Q '$6"$>i ')"$Y-H"785") 06 '$ \#6 ="$:;03`')^XE
\#6 D@7-/-H6 ^D')8/*h"$3S}@[ '$6"$>i ')"$f\. E$6
@7-/-H6[')8K.";>?58 r\47PF[^XLG53`')."$.Z@H8G0Q"T #03321')S^XL
a5"Mh>?ME -K'@_,33GRZh33kUA6"$8G"$8c\]h'),8M')3:[h&}02')")
6"$8G"$p}0-_R") [^XLa=6;E"$[6M')9660-_>?}Q+."78G06 RI@B0:
"$+4}:;03`')`P')30d\"!$#
^86"$-/.Z";"$VE|RI@c6M'$:K}0-H6M')3
"$R0 LN[3`')Q-H"78p6M')f')31"RZj')..38ck % 8"7"$2'>?[ ]033V1')S
\],-H"}8337$r8"$") 2hbr"$30"$^XLg"$N'QR2'$6,I"78G06"$
"&8G6[-H"}8 EX #+"p')}@cI"78G06"$@JRZ"7"$SpJI0-H6M')3h3M')_')3:?R1'GE
;L:LNV"$'&<c<)( L
C=-K'M@K')3"_')..3@/1')>?=-H"}8h"$KQ"$-K')3|'&}02')"$MLA1')>?Q-HGU
"78K@}.6M')33@'&}0p31d"$1'):?(')8 @738 '$B6"$I>?:?6;E5.Z6`')33@ o"$
3`'):?p."$R3-H L 47"$-Hc63`'$6M')3Q1')>?c-H"78K6308ccI'$6"$REQj')0U
47839\j4^XE54}066>?!C=>?U3`' W')"$\4C5O+^9')8 !*,"$ e0:I')!51'$8G}
\*j^-H"78L1')>?9-H"}8d6"$I>?:?c08K61') 6"$8G"$MLg"$HGU
1')6;Eh2') K47NF K0GmK6I/ o"$H6"$I>?:?6f") 5c_4')8* ')3kU
:?"$-HML g2"$4C5OTEIk 1"$-H+'$6631')"$9.2')1')-H*!&'$88G"$9Y > y x BXEG,
2'>?&6"$}>?:?6;LKg"$TBI'$6"$R-H"78EDk x F '$88G"$_.";U
>?8 r;E| Q8G`'):?"$2')3D,+
ff
R:dT8G`'):?"$2')3D3-H}[") $ E
6"$I>?:?6_"}660ML[68G`'):?"$2')38"$-/2')6j") - ')3":;02')1')}
6"$I>?:?6;E|X o"P"$0: &BAcC ( ')8I`P'):I' &BAc@ ( L
e=-/."$1')I&:!2')B2'$B"iRZf-H-_R8 ')RZ"$0B1')>?(-H"}8 E
2')[1')") 6"$}>?:?6H8.8[:;M')3@("$J/6"$8G"$ }0-_Rd\#"$+
.61')3N."$.^[") H6"7XmK6IT-K')kWLBe=_-HI"$8')RZ" >?;E- -K'@
>?@Jh33hRZ/R2'$8G3@ 6"$8G"$8LcC=K,'M@Y"96M'$K6"$}>?:?6&.Z8 jRI@
.6"$8G"$:EDL;LH-T03.3@}:(H@G- g'9-K')kWY06i2')_/
@G- 2'$B1')-HB"$30"$')8!061g2')d 6"7XmK6I-K')kWi2'$/'
-K')33j6"$8G"$ }0-_RML%c061 "$[2'$+RY.0+I" r8G:pXmK6}T')8
I0-H6M')33@J1')R3T-H"}8= o"$="$3>7:B_3M')+3M'$+&}02')Q."$R3-pL g"$j'
6"$-/.>?_M')-HIME|X #"H e$6S,&B@ ( L
"$R3-Hi\ =;LBA?^B')8\ =;LD}^d6M')"$9Rf"$3>?8 2')9M'$3@8G0J"g("$8G
U
I`')R3@c") Q"$Rbe6>?[ #06"$\]61c-HM')2')=hT6M')"$:?"H>7`'
"$-K')3n'&}02')"$^XLNa56;Ehj-_0Q1S&')32')>?T"$30"$c1'):;ML
b3373`')R"$1')"$T8G I1'):; #"$D"$3>7:Q 8 ."$R3- T
6"$IXWG=") D-K'):?_')2')3@GMLN%("$j.6sr26M')33@?E33b"Mc2')='/61')p-H"783
o"$=-K'):?/8"$:&:;>?+"&')Y"M>?8-/8i@7- ") P3M')['&}02')"$
pR"$08')@96"$1')IQ -8 ."$R3- ") DA@7.
-/-/>iM
V
D[F G @ V 8 \ =;LB??^
0Rbe6" @%Y@ 8
y*@
R
5
6 Yn~Mx 4
3386RQ o')-/3`')1'):;@K") V6M'$: 8 ."$R3- \ =;LB??^
I"d' X
KHLON
MLML
D
\ =;LB@?^
Y 8 y
R
Y "!
)#
Le=3"$0:;c-H"78 o"$Q"$3>7:K o
')8 SR ."$R3-H=33
"$NR, #"760N") ME?h33"$31N:;>?Q'5RX V6"$-/.2')"$VE}0:
XW')-/.3MEn") "$30"$j-H"$>;'):p/01H") , 8
"$-pLKe=3"E
6/"$.-/>i ')"$ "7"$3P*,NV &< = ( 33RZ08f o"$["$3>}:9V ."$R3-HME
hT33"M 2')5 .R ."$R3- ='H&}02'$8G1')6T."$:;1')- \ T5h^XE|6(-K'@9R
"$3>?8&R}@&*,NVN '$,33L SR
"$30"$2'>?+R9.Z"$.03`')ME')8&I:
"p6"$-/.2');E H6"$}XW7") "$0_-K'):?/."$R3-pEbH&I02')3@Y") ,H1"$30"$
')89["$30"$c-HQ") D -8 ')8 .R ."$R3-H=0:d*,NnL
5 6 Yn~Mx V 33Q86R&A,"i0R:;1'$8G}(\]3`')82^-H"78MLp6"$IXWG
") =2r-/.3-H}1')"$VE+\ =;LB@?^T33R&6"$I>?8}"J'(")UA6M')338'):;1'):?
8G02')3V."$R3- ") DA@7.
KMt`u
$SQSR&%
KHLON
'
Q)(
'+*
)
',.-&/
10
,2 >
D F43
0
B65 \ =;LQP;^
3 6M')cRjJ'$798 ')8:8j8"$=j8}A@f-K')kWLVEZ"$
>?"$B") VQ0R:;1'$8G}')3:?"$- 332R-/.3" @?8dB"$8P"T"$3>?=n'):$U
n
13 G~]u|t
96"$8-H"78E,8G0RRZ8 & ¢ X£ o $£ Eh33090RGU
:;1'$8GId"$.-/>i ')"$8G63@"$."$R3- \ =;LB??^XENL;L!"$0/9XWG1'J.
'$"76`')8&p r-H"}8L
5
6 Yn~Mx n
33h}>?:I')&A,"(XWG.-HI1')3l 06p')3:?"$-HT o"$"$3>7:
\ =;LB??^8G63@?Lhj')3:?"$-HQ61c33R+8c')
u#tZ~vX x {iuyDr\G~]u|t
4}1'): ')`')35"$30"$w@NE,1'@!
"$1-K'):?,E N.Z"$}AhM')61'):;@+1')V"$0:;T>?@[3-H}
+ f
/"$-H,"$8ME?6"$8:[k 2"$Rbe6>?, ]06"$>;')306M')R,3"M,8
R}@&6M'$:K"$Q86M'$:
+ f L
6nx z y]x}tZ~ / 9bz y]x7tZ~jY ux}r;~]u|t w]z|u `~6b{ eQ')-/.33
R=-K'$8Q"6"$-_R+=:;1'$8GI."fe6"$B-H"78dB50R:;1'$8G}
."fe6"$c-H"78L
4}6Q"$0P."$R3- \ =;LB??^bh6"$I>?XWE7')}@3"}6M')3|-/-_0- 33RZ='+:;3"$R2')32-/-T0-
\#/6"$ < LBC& #"$j'B."7") X^XL_03@f-K')S?jjM'$MEVY"$@?L/a5"M,>?ME
')33')3:?"$-H5") P612'). Dd6M')J"$3@9:;02')1')I/'/ oM'$R3T"$30"$VL5*,"$}1')@c"
+"$-H"}8816RZ8B&,ME7j')5"T03h"0.."$
6"$I>?:?6T"H')c"$.-K')3n1"$30"$VL
5 6 Yn~Mx ; 6"$}1')[6"$-/.01')"$2')3V03=')8BXWG.69+-HGU
"788L
D
B
612').Q"$:I')>iM8cp5 #"$33" :K-K')
=;L_6"$ < L>=XU < LB?GE$hP:;>?h')TI"78G06"$T"Q-K'):?h')2')3@G')8_I"78G06
'=-/.3,-H"783I o"$-K'):?8"$:+61@738')" >?8-/8H@G-
") N3M')+'&}02')"$MLE Tf" " -8 ."$R3- 6"$.Z"$8G:&"
=@G- -K'@&RZ[1"$3>?89RI@96"$I>?"$p"K'V ."$R3-pL
< L6"$ < LB@GEPhp6"$-/.2')9 J"$30"$ o"$ W Y^ {|y xzy7_}a(0:i')
XW')-/.3;L33:;3:;}K"$-H98G
6HRAh &&"$-H
')8f')3"-H"$>$')_+0[") D -8 "$-pL
AGLn ."$R3-H33hRZH1"$3>?8 0:Y*,NVLDAi16"$
<
LQP7EbhB"M 2')
3M')3M'$P&}02')D."$R3- \
SR
^."$R3-2')N6M')338K'&}02'$8G1')6
."$:;1')- \T5,^XED66M')')3"(RZB"$3>?8R}@*,NVNL .R "$30"$2'M>?
R ."$.03`')MLKa56;EV[_I:f"96"$-/.2')HH"$30"$i-HK')8
1"$30"$&I02')3@!") 5 -8 ')8 SR ."$R3-96"$}XW7K") +"$0/-K'):?
8"$:K."$R3-pL
DL K3`'$_6"$ < LBCGEn,H:;>?d'c' &I061SYI"78G06"$g"pK6"$6.T")
6"$}>?XW7@i')3"$:ci1"$-H03j2')j33PRZ08LB*,"$I>?XWGA@Y_'&S?@
3-H}QpML
j8G601"$9RZ3" .8pRI@Ig2'):? &>=
< (
')8f*hI> )1')3"&>=ON
( L
"!#$&%#'()+*-,./10"324!#65879.:
T-
H $£|
/¢
E"$Q:;@c16M')3_-K'):?;EZX oQ"&'Hh")UA8G-H"$2')3
3:;IIA@Y #06"$; >A@CB Y Ev@#Y4
R
EHd>;')30K") <;')')}@Y.Z"$}
=
Q."$."$"$2')3"KTR:;I1["$5:;1'M@p3>?3") N-K'):?')
=
L[4}6T3:;}
j'K #"$- ") :;@?E ; >+ B?>_ LjeA@ ¢$ H $£| ) H¢) \]6X o"$
/¢
^8"$5'H-H"$"}61"$-H-K'):?j6(58G6>iM8cR"$cf.6Q"
.2')`')3D6"}"$8G2')j')8fR:;I1ML+eQ(-K'):?-K'@?EZ6;ERZ_.I8JR}@f'
-K')kW q E > G B f)
QjR:;}5')=6"}"$8G2')>CByD6BQ") [-K'):?;L
3-HIh") Z-K')kWK')6M')3387
E
H¢:F7X X£
"$
HG
o"$"$ML
OQ3`')"$.nRA,P.kWG3b") |')_-K'):?h-K'@[RP816RZ8_0:Q,6"$6.
") b')&-K'):?5:;1').VLNe=d08G68&:;1').fJI \`Eh^h6"$,") 'r+ # ")
"78H\#"$[>?6^XEn')8 'XrH[") h0"$88 .2') 4 ^l^OHJy3a
i
HJy]Y # aIE
6M')338p8G:?MLPeQ98G:? ^OHCyUaT") #c-/.3@Bf'$-H|Lnh"H"78-HCy Y #
')1')8("BRZ:;IR"$0[k SH YKL_A ')J-K'):?:;1').VE"}8j').kW3ML
J:;IR"$0p") 'g.kW3 W 4 >CB yD6Bd-K'@R(8 r8 >;')"$0&,'M@7ML C=
>?@2')01')3_,'M@ 9"8 rYY:;}RZ"$0c1p") /'!.kW3W 4 >CB yD6B&"R
"U>6B 4 ^6>CB F {|yD6B7y >CB , {|yD6B7y >CByD F { B7y >CByD , { B aILNj8 r"$p,[33
0[fQMLa=" h>?MEZT')T"$Q,'M@7="K8 rT_6"$6.+'$Q,33L
C=/ >W B 4 ^6>CB , {|yD , { B7y >CB , {|yD F { B7y >CB F {|yD , { B7y >CB F {|yD F { B aB')8
')"$, >W B 4 >W B \ >W BXLD+')3301')8dXr:;0
<
L>=U
<
LBAGLe=
-K'):?H:;1').i l>WB= #"$-K')Tj" Kr:;0 < LDL2g"$T'&-H"$Hi8.
')2')3@GME5 o"$1')6["$ i ')3 &>=P ( L
*
*
* !
*
"$#%'&)(+*-,/.0'1325476 8:9;<*>=
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?:?
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@:@
*
$
* A
!
*
$
* B
*
C
*
"$#%'&)(+*,/.,/12-DE6 8:93;<*>=
F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F:F
G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G:G
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
AC
*
'
*
B
*
$
* A
$
* 7
*
!
*
$
* B
*
*
"$#%'&)(+*-,/.J)1325K76 8:9;<*>=
LLMM
NNOO PPQQ RSR RSRT
T
UUVV
W XZY\[7]
WXZY<^]
W_^<Y<^] W`^<YA[7]
"$#%'&)(+*a,/.bc1dZe#fhg%'*i%B(Sgjck
l
# =+knmpoqrets/u)*v;wjt# x)*vy;Sz#e
=+kt*E2
4
6 8{9|_s(+fhg}=
2 /% 5~ # 5 * 4 !9":.:!90/, /60+
j #'&I0}3@Y2')..Z2')T8G:;1')3,.60/')d0Rbe68i"f"$-HKS}8g") Q8GU
"$"$p"$"$;L5M'$"$')+>;'$')8B"$.2')603`')3@&8GkmK603"I>71'):?;L
V,"p@}.j") 8G"$"$T')/6"$-/-H"$&^+.Z"$}AB')8Y.2')`')3LH o"$-HjGU
>?"$3>?'p62'):;:J") H:;@ 6M')3K>$')30T") .kWG3T3HK3`')_2'$T"c8"
62'):;:g96"}"$8G2')d") 5XWG:Y.kW3/39"$38G: /:;@7"$
J6M'$1="$1T5"7"B:;M')MEV"$8+"B@c"B6M')/"$:;2')3
.60'$b-_06B'$.";R3;Lbe5n-H}"$8/T,3`')D.2')1'):;1').VE}')-K'):?6M')
RT.1I8JRI@Y'd-K')kWL47"E3 Y
0 )2
.}[/8G"$8J.60;E
8 ')8 ;p')I0-_RP") Z.kWG3D>?6M')33@H')8"$>iM"$I1')33@?E}.6>?3@?L
g"$6"$I>?6+1')S?;E}h=-K'@H>?6"$>iMYE71'$6S7:"M,XWGP"M'$6&"$
1'):c ]"$- H"$.i"M \] jMEV,H33P01/H6"$I>?}"$2')T')I@
>?6"$ Y 2
I.8f'$Q6"$30-/c>?6"$^
4 >+ 8 8 y y + 8 2 y + R 8 y y + R 2 ysy + 08 ysy + 0j2 B
e 8G"$8 .60Kj6"$-/-H"$3@ 62')1'$6>iM8gRI@J:;03`')T.Z"$[g"$
"$-H"$:?"$0p')M'$ML c."76B") j6"$06"$"$B8"$:!-K'@?EQ6;E
')- ')j-/-/>i:(H8G 6_RA,i:;}RZ"$0:(.kWG3 LKjT6M')338
H M l£ LMEN" h>?ME,39R:i'(61')@g6"$8G"$06 '(61GU
O&}0;E"$Q0GmK6}ML E _')31"/89"3[>;')30+
f
2'M>?T'1'M@2"$;E
'&d"$jR3`'$6SJ-K'):?H,"$038i8"9K6SL&47"E
i+ f F + f i
6M')"$_R"7"9:;M')ME
+ f
h="$30"$B>;')30;LbB'$88G"$VE7,Q'&}0Q2') + f
YG y H E7"G y H
')j"$-H+.";>?+M')3n6"$1')IMLh4}6j.kWG3V>;')30Q')+"$:I')>?;E
GE')8
6_.kWG3V>;')30+')jR"$088f')R"M>?;E|hj-T0Q2'M>?_2')H4>E_ L,%("$j33nR
1')8p')R"$0[.";R3[61"$6 o"$GD')8Hcc6"$ < LDL
p0-phj2'>?j_6`'
5 l~Mx ]u|t + f
6M')"$RZ+"7" ') ]"$- + f
5 l~Mx ]u|t 4 + f
6M')"$RZ+"7" ') ]"$-j>$')30") N')33V:;}RZ"$0 L
5 l~Mx ]u|t
V G + f
HL
5"MjE}.1'$ ¢;££| ¢ 8,'+.6=8 r"$KK"$8h"[:?
'T-K')-K')6M')3n-H"783" +:;"$08L E +-/:;}6"7";+"/8 r+5.1'$j'$
¢$
+ f 4 + f
>CB 4 {|ysy*8 ;CB \ < L>=M'?^
+ f 4 +
>CBD Y B \ <
L>=R|^
+ f Y Gny H >CB 4 {|ysy*8 ;CB \< L>=6 ^
` ')Y"M>?8-/8 @G- ") [email protected]'). =;L[<502')33@?E
/'&}0-HI&\< L>=M'?^j')8 \ < L>=R|^[33P6"$6MED')8 6"$'&}0I3@?EbH@G-
33V"$2'M>?T'"$30"$VLN_1'):;@B") r8G:d' 8
"$30"$p,'$:;>?p9
.68G:d612').MLP 8 ."$R3- '$"76`')8&g\< L>= ^,
-/-/>iM f
Q
i+ f F + f i , f Q
i+ f F%+
i
0Rbe6Q"
+ f
YG y H
9/'#:!90 (/ '
V
8
>A@CB
4 fQ i+ f F + f i
')8
R
>A@CB
4 f
Q
i+ f F + i
fT.68G:p0RGU
6"$VL 8 6"$6[8')1'>;')30Q')8 R [-H"7"$:LNe602')33@?E5-H"783
&+3`'$0R6"$&:I'>?['&}02')3h:;}"+8')1'>;')30=')8&-H"7"$:LN
-/:;I+"$+')3,'@G5RZT06Y'd-K')=1'):;@?L=e==-HI"$8Y')R"M>?;EZ"$_-K'):?
')[") #&612')1'$6>iM8pR}@d:;03`')."$&"$-H"$:?"$0=')M'$MLF+.8G:K"$
1&}02')3A@d") V"$Q-K'):?;E7"$5"$038KRZ5')R3Q"_>$')@58:;=") n-H"7"$GU
:L/[-/:;}_R/8"$RI@JI"78G06:('B.2')1')-H 9 Y ]"$}j") R >A@CBXE
6f@}38+."$R3-
-/-/>iM J>A@CB 4 8 >A@CB , R >A@CB
\< L< ^
0Rbe6" + f
YG y H >CB 4 {|ysy
i# iB
- R >A@CB5-H5 #"$- -T03.36M')"$g") hR"$Y8+") h'&}02')"$
:;>?RI@c16"$8 '&}0-HI \ < L>=R|^HRI@hEL;L + f 4 +
>CBCD Y BXL A
>> {;ED-H"$d,:;I/33RH:;>?"c&8')1'c>$')30/')8!k 9 {d-H"$
h:;}=33nRZ[:;>?c"H-H"7"$:LSE [" 2'M>?_'.6_-H"}83V61f6M')pR
')..389"K')}@&-K'):?j") ')}@B #"$-K')ML
"$R3- \ < L<
^_33RZdd #"760") Q Pd.0.";B"$T"J6"$-/.
(jR=") N8"$:B-H"}8 LE _6M')f"$_2')50:B"$3@p"$T-H"7"$GU
:.2')1')-Hp0 K #"$- |' 2')&BM')p')33[')M'$9") _(-K'):?Y"$
.2')MLF5 }=')M'$") D')&-K'):?+-K'M@?E"M,>?ME28G ,9.Z6"81')3n')8
6"$I1'$ ^Q/')M'&63";+"B- 8+"dR-H"$"$-H"$:?"$0j3
6I1')3Q')M'f2'$-H"$&81')3H')86"$I1'$MLZg"$H'c-_08G:?8-pEB>;')30B")
K-H"}"$:(.2')1')-H-K'@YRK6";1g:;VLg2"$Td-H"$K81')38!.2')T")
/-K'):?;En[["$_'&/61"$6H6K'B:;i>$')30/") /-H"7"$:p.2')1' U
-HP33|6M')0"$-H"$:?A@?Lhe:;3-H"7"$:_.2')1')-HP332"$PR')R3"
"$3>?5,."$R3-pL,C=5332'>?+"7"T33+-H"7"$:p\]-d^,"$"}"T-_061
-H"7"$:f\#6I=.2')^XL
e.";R3'@/"$0N") |N.8G6M')-HIPN"+I"78G06-H"$2')H"$-H"7"$:
.2')1')-H ^b"$, #"$8G:?NRZ:_'5."$.N0RN") -pE?"$ o"$D8G:?
R:c'K."$.j0Rj") ,/6I1')3N.2')_')8Y"$ o"$[/8G:?+1'>?:p
A,"d')M'$ML%J')-K')6M')33@?E|XW7"$c") \< L< ^33V1')S?[5 o"$-
-/-/>iM ef
Q
i+ f F + f i , ef
Q
i+ f F + i
,
e
f Q
i+ f F + i
,
e
f Q
i+ f F + i
0Rbe6" + f
YG y H
E +')8 !b8"$5+0R") Z B+6I1')3.2')ME7- ')8dR"$VE
-pL4}6j-K'):?Q8G MEQ33n2'M>?j"/Rj389R}@9[.2')603`')5-K'):?j
&}0"$VL g"$='-H"$jGUA8.(')2')3@GME5 o"$1')6g2'):?&>=
< (L
a+'>7:g86882')(\< L< ^K" R99 o"760K") [KME')"$d}U
:%&}0"$8/"(RZ9'$88G8L!VMK'$10-H;E o"$91')S?&") 5-/.36@?E
2')8 4 ;NLT4}"$038 4 v>A;CBJH')h[ k hI0-TRZT") P-H[
8
>A@CBN')8 R
>A@CBD')") 8G
}h"$8MLDA/2')N6M'$1;EI"$8"j1 (061/2')
5-H"}"$:/ 6h,51')-H/\#"$,-/3`')^ o"$h8G I;NLDa5"M,>?MEG=}0-U
RD") Z-H 8 >A@CBD')8 R >A@CBD'),") Z1')-H"$8ML 8 >A@CB2'$
i# i 4 8 ; 4 ; R
-H[')8 R >A@CB2'$
i i 4 >A8 F { Bn; , >A; F { Bn8 4 x`8 ; F 8 F ; 4 x?>A;
R F ;CB
-H,d l>WBD o"$-K')+\]Q o"$-K')h61B,08Kd,X^XLb "$9')=")
"$8;
R
LDa=6;E?h33"$,')-/.N" r8H')KXWG."$ o"$j>A;CB>?H"$0:;
r8G:d06f')cXWG."$c-/:;IQ& '$6R[") N"$-HK\]:;3:;R3 ^-/."$1')6[ o"$
-K')33V>;')30") ;NL
4 ''##!- !-
V+ 4
KMLON f + f
')8 + 4
KHt`u f + f
LBe66"$8G:("p o"$33"M:(."$.Z";"$VEn o"$
"$0,."$R3- \ < L<
^XE7k ')33 + f
')Q ];E}B&')B"$.-K')31"$30"$ @ I h52'>?=2')
')33 + f
Y+ y + L
u+YNul~]u|t
4
BxIyWr;~]u|tpu
4 4
E < L< F + 4
KHLON f + f
¢$£ + 4
KHt`u f + f
+1 ) +¢$] + f ¢ X£ l£p¢$£c H¢$2 $ o $£ @ I
$)
> 1BjY #B + I
f
Y+ y + \ <
LBA?^
M M V /4 > F _by GBXE"! 4 + y + ')8 4 >HJy7_BXLg"$d'(:;>? >?6"$M@NE
I"78G06j5 o"$33"M:d1') o"$-K')"$
# >+ fB 4 $%
&%' + k + f Y
+Kk + f Y
+ f
"$
4}-/3`')3@?E73(#M>A@CBN8"$Q>?6"$>)#M>
+ 8
B7y y*#M>
+,+
+B
LN*,"$8
8
>A@CBXLE
2'>?
i+ f F + f i 9 i
#M>
+ f B F + f i 4.-
i+ F + f i
k + f Y
i+ F + f i
k + f Y
6f-HM')2') 8 >A@CB 9 8 >)# >A@CB*BXL
5"$f2')9&1') #"$-K')"$ B2')9,Y6M')33[' o $£ L Y6"$6.9
8 r83`')DT6"$}XW7N") 20R:;1'$8G}."fe6"$/-H"789\#6"$ AGL
< L<
^XL
g"$5"M -/.3@f'$66.52')[6/!
)
')8
$£ 0 G
E"d."fe6+')}@p.Z"$}
+ f
"$081! "$}"2! -HM')j2')[h/.61Sf/63";[.Z"$}j3! \]6i-HM')
2')5hT.6Sp + "$ +7^XL=eQ8ck Nh_."fe6['/."$I + f
')3M'$8G@p!"$I"4!/E
f f
5"MjE6"$8 R >A@CBXL E j"$R1>?[2')
+ f y + Y + f y + Y i
#M>+ fB F #M>+ B i 4 i+ f F + i
+ f
Y2! >+ Y + Y =B
i
#M>+ fB F #M>+ B i > i+ f F + i
+ f Y + Y i
#M>+ fB F #M>+ B i > i+ f F + i
6i-HM')[2') R >A@CB R >)#M>A@CB*BXL/a56;EV6 9 E"$38J>A@CB 9
J>)# >A@CB*BXL
Y'):;0-HIc')R"M>?J" &2')Bk T')}@"$30"$E@ 2'$p')I@ 6"$-/."$I + f Y
+ f Y EZh6M')jr8 'HR["$30"[email protected]:963";1+.Z"$}5" + f
[}>$')3 + y + LP:?"c\
<
LBA?^XL
A =9R"$08 + ')8 +')&:?"7"}8"$0:;VEhhp6M')"$3>? \< L<
^T"$0KR"$08ML
N,"$038d03@-K')S?QWe"$RKM'$MLWE -K'M@/H-H"M>?=Q.NI>?"$3>7:
R"$08Pd')&')3:?"$-pLNa5"Mh>?ME7P.0..Z";1N2'),Q')3:?"$- 33Z6"$GU
>?:?+"H')9"$.-K')3n"$30"$VLhC=1;E"$+338&"/6"$I"$3V= oM'$R3A@
") D[1')=')8&1')S?[j61')@&.ML
_T"$8GkmK603"cSg") Q6M'$_B"$dh"$038!"$TRK') r28 !
8X ')03QR"$087+ y + LQC=T>?@9"$RI>7"$0+XW')-/.3TTj"$_Q>?@p8Gk ]U
oI #"$- 5") n+-K'):?H\"$03 ^XE;L:LN'_3:;}-K'):?+p8')Sd."$
"$Q'/8')SB-K'):?[p3:;}=."$ML
dK335"$K1')3"$Bf')3:?"$-H&"!'Y.2')603`')B-K'):?;L a56;E
')3:?"$-H=33VRZ+-K'$8_:?1')3"$0:;p6"$."$1'):&06c6M'$1Q'$-H}"$8
')R"M>?;LDN") Z6"$01-HM')D2')h8"+0,R"$08ME?"5h'$10-H,"$0:;GU
"$02') G y H + y + L
E [" :;>?_'1'):;@B o"$"$3>}:c\
< L<
^RI@96"$I>?"$f"H'3M')Q."$:;1')-pL
"!" 8"! +* ' 5
VM6"$8"$0n"$:;2')3}."$R3-H,\ =;LBA?^n')8K\ =;LD}^(rME j:?1')3>iM;LN47"$3>7:
\ =;LBA?^,Q'$602')33@9'&}0>$')3}"H"$3>7:/+ o"$33"M:BV."$R3-
-/-/>iM
0
efOg
8
f
0Rbe6"
f , 2
e g 8 ( f) + 5 f
>CB 4 {|y y*8 B \< LD}^
f F 2
e g 8 ( f) +
F15
f
>CB 4 {|y y*8 B
EI@ J& 6M')0Ph6"$1')}b&\< LD}^V-/.3@[2')
f 5 f F 2 g 8 ( f) + ')8
f
F > 5 f F 2
g 8 ( f) +
B BvY ^ {|ysy*8!aILha56;E
f i5 f F 2 g 8 ( f) + i
Lh%f"$" >?ME
c')c"$.-K')3n1"$30"$ I8 y y I0 y + I8 y y + I2 EGh[33V2'M>?
> 1BjY[^ {|y`y*8!a`B If 4 i5 f F 2
e g 8 ( f) + I
i
e50-H;E"$p[6"$}1')@?E2')f')p"$.-K')3b"$30"$c") \
< LD}^
>$BjY[^ {|y`y*8!a`B If 9 i5 f F 2
e g 8 ( f) + I
i
VE o"$5 #"$
f
0GmK6I3@J-K')33EV,-K'@J6"7";
f 4 I
f F f
E6 @738_'
oM'$R3&"$30"$'cRp\#-K')33^"$Rbe6>?B ]06"$>;')30;EP6"$I1')@!"
"$0'$0-/."$VLNa56 ^ I
f 4 i5 f F 2
g 8 ( f) + I i B Y ^ {|ysy*8!aj')8 + I8 y y + I2
Q' 8 "$30"$c") \ =;L>= ^XL
c'-/3`')-K')ME\ =;LD}^:?6M'$89}"/+ o"$33"M:dnDU."$R3-
-/-/>iM
0Rbe6" , 2
e g 8 ( f) + 5 f
>CB 4 {|y y*8 B \ <
LB??^
F 2
e g 8 ( f) +
F15
f
>CB 4 {|y y*8 B
,@=')-H3N") '):;0-HIb'$V[D #"$:?"$:E T')j"$.-K')37"$30"$ > I`y + I8 ysy
+ I
2
BN") \ < LB??^XE I 1')S?"$B53`'):?") nx`8 3" hR"$08ME')8 > + I8
ySy + I2 BN
' o
1"$30"$c") \ =;L>= ^XL
&0-pE}VEh+2'>?+1') #"$-H8&h"/"$-H"7"$&-/-/>i ')"$c."$R3-H}"
A,"K3M')5."$R3-H/\]A,"Bn."$R3-H E2"KRZ_-H"$TXW'$6^XLT')R"M>?')2')3@G
M'$3@&XW788&"p\< L< ^XLP["$3@B8G
6+RZh\ < L< ^')8&+."$R3-H
\ =;LBA?^H')8 \ =;LD}^/Kp6"$B"$ f86"$ >;')`')R3ML<5:if1')-H
1'):;@p'$Q')R"M>?;En\< L< ^6"$I>?8c"
-/-/>iM
ef
Q
f , e
f
Q f
0Rbe6" + f F f + f
>CB 4 {|ysy
i# iB
F+
f F f F + f
>CB 4 {|ysy
i# iB \ < LB@?^
+ f F + F f >CBD Y B
+ F + f F f >CBD Y B
+ f Y Gny H >CB 4 {|ysy
i# iB
iHXWGT16"$VEDhd33h6"$-/.2')d p"$30"$T #"$1WbY ^ {|y xzy7_}ap0:
')JXW')-/.3") ,'d"M>?8-/8Y@G- ") N3M')+'&}02')"$ML5+XW')-/.3T33
:;3:;Ij1"$-H_8G 6+RZhJ_"$30"$[')8f-H"$>$')T0_")
"/% 3 !90
"5 '(8"!
E " :;>?Q')KXW')-/.361K33:;3:;},"$-HQ8G 6PRZhB"$30GU
"$") "$0 _."$R3-H_\=;L< ^XE\ =;LBA?^')8(\ =;LD}^XLNO=X #,"%(')3`')RB #06"$
G?¢ ce=..Z8GkWp o"$_6"78;LhTXW7.-HI+6"$c3"76M'):B'
88J0609\]_:;1').J") h'/ #06"$|^=')-H"$:d"$;L=eQ3"$0:;J=33R
'/:;3@f6"$I>?8JXW')-/.3;E|Q33b3301')'K612')1'$66") D -8
"$30"$
6f["$A,"H3`'$61SZL
j@G-,[330+ o"$j1')S?[") D3301')"$p
8 ,
R
R
LON
> { + B ,
+ R
p > O{ , + B ,
> O{ , + B 4 ; f
>CB 4 {|ysy*8 B
8 99 LNA9-K')kWB o"$-
,! #"
6 %$'&)(
*9 ( ,
*+*-,/.
6$0-213&)(
* 9 *
465
*
)7
,%8 ! #"
6 %$'&)(
*9 ( ,,
*-,/.
6$0-213&)(
, 9 *
465
*
)7
%8
LLL LLL LLL LLL
9
,%: ! #"
6%$&;(< 9 ( ,<
*-,/.
6$0-213&)(< 9 *
465
*
)7 : =>>>>>>
? @ *
@ ,
@A
@ 4 =>>>>
? B C *
C ,
LLL
C < =>>>>>
?
w\,/.D'z
l
') " >?8-/8i3M')j@7- 016.>?"&/1')-HS}8Y") ,M')U
-HIj") ,6"$I>?:p"&')YV."$R3- '$[8-H"$1')8 ')R"M>?;LT47"$-HXW')-/.3
") [p i').."MW7-K')"$p')f"M r:;0 < LB? U < LBCGL IrXr:;0
" 2')
o
"$30"$9M'M>}3@&8.8IQ"$9+.3`'$6-H}Q") bH\l o=^
"$03MLd SR 1"$30"$ [R_3/ 8 "$30"$ij"$T' 68!')T')33
\]88!RZ8 ')h ^XLfAi o'$6ME_"$K") d62')1'$66/") -8
').."WG-K')"$)^h:;>?h31Nh:;}"j:;";h2'$6601'$6"$P38K.Z"$}h2')d
"$A," /').."MW7-K')"$MLh6M')pM'$3@KR+08"7"}8d #"$-5 #"$-T03`' U
"$c") b[[."$R3-HT\ =;LD}^XEV\=;L
<
^')8i\ =;LBA?^')RZ" >?;LP"r-/-/>iMQ
-K' WG-_0- "$MLa=6;EZ:;3T38p."$I=33b6M')@9:;M')5h:;}MLQT6"$8
-/-/>iM+&I02')") N"$ME|3TT8J"$3@c6"$85')R"$30
>;')30c") [p"$ML *,"$'&}0I3@?E"$03d33=6M')@-H"$ch:;IB SR
"$30"$p2')f9 -8 1"$30"$VLP r:;0
<
LB@GE-H"$["$1[Q'$888ER0Q -8
"$30"$pQ33[ML
=');E7") V6"$0;E76M'$N= R \o')8 o
^P').."WG-K')"$&33|8"[R
2')9 -8 ').."MW7-K')"$VL4}1')6M')33@?E SR ').."MW7-K')"$+') e 0sr28dk b
"$FE 4 ^ f a 4 ^ 5 f
FHG f @ ad')8.Z8}')8("$-K')33@Y8GR08J
6"$1')}b>;')`')6JI
R
')8XW7.68>$')30 >KE B 4 Lgb:;0
<
LQPQD'Q6M'$1P.Z"$}ML
e="$5'$8G>;')I1'):?") SR \o')8 o
"$30"$|^Q2')==8p"$=I."$3`')
"K')}@&") Dj8')1'H'$Q"$..Z";8p"/ 8 "$30"$VLh 8 1"$30"$f')3,'M@7 r8
"$-Hd8')1'p."$IT"p3`')61"$g"L9A%r:;0
<
LB?c')8
<
LB@f"$-Hd8')1'p."$IT3
"$c ')h T:;1').VLAIr:;0 < LBCK')33b8')1'/."$I+')_"$ME|R0Q"$31
o"$-HQ'/6"$6R2')889.2')VLhA9=6M'$+j6"$6Q1"$30"$ppRA,VE
R0+ 8 "$30"$J2'$5"B8')1'K."$I+"d:;1')RJ"$38f") hf2')j')M'GL g"$+-H"$
81')3Q"$9 E5 o"$1')6Ei')"$ &BA\P ( L
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5
10 15 20 25
x
f(x)
data points L 2
L 1
L ∞ answer
"$#%&c(+*-,!.!1
* ,
gBe un;<s'y&c=+#set; =+s jc(+s ty*vf
l
# =+kg|`*
l l
#yu j{s#e/=+;
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2 4 6 8 10 12 14 16
x
f(x)
data points L 2 L 1 L ∞ answer
"$#%'&)(+*5,/.)1 sB(+*ets'#;<*gutu)*u ./s'y&c=+#s'ec;u)(Sg%%'*u &cj
l
gB(Su);
t&c=3=+kt*
*
;<s'y&)=+#se #;Z;=+#yy{*v;=
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2
4 6 8 10 12
x
f(x)
L 2 L 1
L ∞ answer
"$#%'&)(+*-,/.D/1xtgBfijty*
l
# =+k utgB=Sg wets= ;<kts
l
e{z etsB(+fhgyyauc#;=<(+#t&)=+*u
l
kc*>(+*
=+kt*
,
;<s'y&)=+#se #; fhgB(+%'#etgyy{*>=<=+* (=+ktgea=+kt* *
;<s'y&c=+#s'e
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 2 4 6 8 10 12
x
f(x)
data points L 2 L 1 L ∞ answer
"$#%'&)(+* ,!.)1xcgfijcy*i#yy&t;=<(Sg}=+#ec% =+k g}=-=+kc* *
;<s'y&)=+#seucs!*v;-etsB= kcs!s';<*
#e{*>=
l
*v*ve E;<sy&)=+#s'et;gB;Zsjtj{s';<*vu =+s=+kc* ,
gBe u ;<s'y&c=+#set;
612').2?fh&336"$-/.2')9 -8 ')8 SR "$30"$/") +"$0/-K'):?&."$R3-
0:p*,NVLa=6;E|h33b"M "M 2')+"$0 .R ."$R3- 52')=56M')338
=
9 R ( 58 5 !- "!" 8' 7
4}6/\
<
LB@?^33R=1"$3>?8K0:H*,NVNEG,Q33"$=2') .R ."$R3- -K'@&')3"
RH"$3>?8 0:(*,NV RI@Y:c'$T'p1")UA6M')338 &}02'$8G1')6H."$:;1')- \T5h^XL
4}6+ SR "$30"$92'$RZ&."$.03`')MEI:K"/6"$-/.2')[ SR ')8
8 "$30"$cp.6"/"$30"$ &}02')3A@p')890:H-H;L
e &I02'$8G1')6[."$:;1')- \T5h^,8 r8pp_*,NV -K')}02')3b'$
-/| -K' W {
x @
@ , @
LML G @ D
@ Y y
#"$_M'$61i" G @ D -K'@YRH')I@Y")
y 4 y jEb')8*G f y H f
8"$_
3"M,')8i0..Z_RZ"$08"$ H>;')`')R3 + f
En.6>?3@?L&K6"7XmK6I{|x
J #"$Ij") h &}02'$8G1')6/- -H5 #"$- '$652')j #"$j')I@ ')8!@NE
&}02'$8G1')6+ #"$- @ #@ 6M')9R+c'$
8
R @
@NEG
4 , E'@7-U
-H65-K')kWLP*,PV 33:;>?=@?"$0p')B"$,-H1'):?=k n@?"$0B@H0:/'j-K')kW
6f"$@7-/-H6;L
A +,f')f8M')3:g 'Y-/-/>i ')"$ ."$R3-pEQ*,NV '&I0dp-K')kW
"RZ+.";>?j1-/kUA8 r
> @ Y 2 B @ @
\].";>?H8 r^H> @Y 2
F"! B @
@b9 ^XL g"$'&-K' W7-/>i ')"$i."$R3-pE
-K')kW
P'&I08d"[R:I')>?5-/kUA8 r\]>?Q'&I02')3,
j8 r"$c #"$.";>?H\#-/kU ^ 8 rX^XL
b";>?T1-/kUA8 rH\].Z";>?_8 r^=')8p:I')>?-/kUA8 r1
\]:I')>?j8 rX^,'&}0>$')3}"/6"$I>?XWGA@ \#6Q6"$}>?XW7@^')8p6"$6M'>}U
A@\#66"$6M'M>}@^T") d"$Rbe6>?d #06"$VED.Z6>?3@?Lf_."$R2')R3@
"$K"Y"$R}>}"$0 L a56;Eh,96308f'Y."}") L4799XWGH6"$ #"$K'JRX
I"78G06"$c"K6"$I>?XWGA@?L
u+YNul~]u|t
4 4 5
7
X£
; >A@CB 4 @ @ ` $£ 0 G4Eo $£ 0 G F
l
) 0 [ $#&%N£ E
$ 0 %N£ :F
M M h@&6"$I>?XWGA@i\#66"$I>?XWGA@^
; >&' @ , > { F 'B)( B > > B*' ; >A@CB , > { F 'B ; >&( B
"$
4}6 ( @ 4 @
(PE+3X #2')8p8[") \< LBC?^6M')cRZ+f'$
>&' @ , > { F '*B)( B
>&'n@ , > { F '*B)( B F ' @
@ F > { F 'B)(
(
4 ' R @
@ , > { F '*B
R ( ( , x ' > { F '*Bn@
( F 'n@
@ F > { F '*B)(
(
4 >&' R F 'Bn@
@ , > { F 'B h> { F '*B)(
( F (
( , x ''> { F 'Bn@
(
4 ' >&' F { Bn@
@ , ''>&' F { B)(
( F x ''>&' F { Bn@
(
4 ' >&' F { Bn@
@ , ( ( F x`@
(
4 ' >&' F { B h>A@ F ( B
>A@ F ( B \<
LBL?^
5"MjE''>&' F { B o"$'56"$}>?XWT #06"$VLWg"$P'563@6"$}>?XWT #06"$VE''>&' F { B >
')8 @ 4 (hL,a56;Ej3`'$3_") Q\< LBL?^,33b1') #@J\< LBC?^ #"$QRZ"$pT6"$I>?XW
')8p63@&6"$I>?XWp6M'$;E|'$'&I08L
R ."$R3- '$1"}6`')8YiK@G- \< L>= ^+'$602')33@ ' &I02'$8G1')6K.")U
:;1')-pE69\] G ')8f>?6"$ D 8"$+6"7XmK6I_-K')kWJ')8(
:;IQ2')8p8j") D['&I02')"$ E.6>?3@^
-/
V
D!F G @ V RR 4
-/ >
D!F G
@CB
>D FG
@CB
4
-/ @ G G @ F x D G @ , D D
G G @7-/-H6;LN%f"$" >?ME G G .";>?j-/kUA8 r
@ G G @ 4 >G
@CB >G
@CB
4 V G @ V RR
')8f_"$Rbe6>?j #06"$(") N R ."$R3- =6"$I>?XWLQA G 2'$ #033n1')SE2,
2'>?d6j6"$I>?XWGA@ \o')8i.Z";>?/8 r^XLKO=X #["p/XW7T6"$i"$
6"$I>?XWGA@ ')8."$.";"$ < LBAf o"$/."7") #ML g2"$K')I"78G06"$ "Jc')M'J")
&}02'$8G1')6[."$:;1')-/-/:E2X o"H;L:Lh+33E%c01'M@9')8EY:;I &>=OA ( L
2 :!-9 "! ! 9 ' 7
o"$33"M:+n."$R2')R3@[ o')-/3`')"-K')}@?E$R0n"$')33E M'$8 La56;E)hN:;>?'
&}06S_}"}8G06"$/"=0Rbe6')3"$:+/"$-Hh03b2')D2'>?')3M'$8G@_R
\o')8B33RZ ^N08LWE 5RZ:;&&+6"$6.") b'6"$I>?XWB1MLP47Q o"$,1')6
S;'$ &BA
(
\#"$Q')I@&}"}8G06"$@9R"}"$Sdc"$.-/>i ')"$|^, o"$-H"$j81')3ML
x t`~]uZt
4 ! 2 ! l ¢$] $£ 0 G
> @ y (Y !=B > ' Y
yS{
B ' @ , > { F
'*B)( Y2!
G #"$-K')33@?E;8 r"$H1'M@7D2')N')}@_3,RZhd')}@_h"+."$I @ y ( Y2!3
!HLFg:;0
<
LBL&3301')jK8G 6/RA,g6"$}>?XW ')8 "$6"$I>?XW
=
x t`~]uZt 4 4 7£ o $£ ; ! 2 l ¢$] ;£ 0 G( $£ 1 $£ 0 G
!
> @ y (]Y!=B > ' Y yS{ B ; >&' @ , > { F '*B)( B ' ; >A@CB , > { F 'B ; >&( B
7£ o $£
;
` ¢$] g
$£ 0 G
f¢ 0 l£ ¢$
;)
]£ ¢$ ¢ @ 4 (Y ! ¢;£ ' Yw> yS{ B }£ # $£ ; l ¢$] ;£ ¢ 0
F ; l $£ 0 G) ¢$£ 0 l£ T¢) 0 ]£ ¢$
e=XW')-/.3f") T'i6"$I>?XWE63@ 6"$I>?XW')8"$6"$}>?XW #06"$B"M
r:;0
<
L>=ONGL
1 6
9
"$#%&c(+*,/.)1xcgfijty*v; sB| vs'e 7* xage u ets'e vs'e 7* xh;<*>=+;
47"$-H-/.3T."$.Z+") h6"$}>?XWc #06"$=2')533bRZT08ff5+')
+ o"$33"M:
u+YNul~]u|t
4 V ! 2
!
!
$£ 0 G)¢;£
;" !
E¢ F$#
;
`[l£ ¢
X£
;
l 1 $£ 0 G E ¢$£ $£ 1¢ 0 :F?
E F ; >A@CB 4 V @ V
l $£ 0 G) ¢$£ £| V . V
E F%#
; f
1 $£ 0 Gc¢$£ f B 4
{|y y*;
X£
; >A@CB
4 2
fhg
8 f ; f
>A@CB
` ;£ 0 GI
E F <; >A@CB 4 2 fOg
8 ; f
>A@CB & p¢ ¢) $£ ; f
lK 1 $£ 0 G¢$£ ; l
$£ 0 G ED 4 B F? X£ ; >A@CB l+ ;£ 0 GI
E F"#
;
l 1 $£ 0 G$
X£¢i ¢; l£ `c¢$ ¢ $ ¢$ ]£ )K'#
;
l
$£ 0 G) £ G` _¢ H ) $£ $ ¢; l£ H
( %) ]k¢ 7 $) Eo F ;£ ¢ 0 7£ o $£M
M M \o'?^ g"$33"M=8G63@K #"$-+3M')A@9") ;DE7L;L#; >&' 8 @ , ' R ( B 4 ' 8 ; >A@CB ,
' R ; >&( BXL
C
Convex, but not strictly convex function
C
Strictly convex function
Nonconvex function
C
"$#%'&)(+* ,!.0)1 xcgfijcy* sB| g vse 7*>x
;=<(+#>=+y vse '*>xgBe uEetse vse 7*>x|_&te >=+#s'e ."tsB(=+kt* ;=<(+#>=+y vse
7*>x |_&te >=+#s'e
ge y#et*3;<*v%'fi*ve!= {* =l
*>*ve-=
l
sZj{s'#e!=+;s'e5=+kt*3%B(Sgjck
l
#yycy#* g {s 7* =+kt* %B(Sgjckw*>x v*vj)=
|_sB( =+kt**vetucj{s'#e!=+;Sz .! kt#; #; ets=;<s |`s(Zg vse 7*>xh|_&ce >=+#s'e .
\]R|^n
V . V
RT')}@9"$-pL61S '1Y4
yS{
')8 @ y (wY!
2
E|/! 6"$I>?XWL
VER}@B+`'):;3_'&I02')3@
V
'n@ , > { F '*B)(
V V ' @ V , V > { F '*B)(
V 4 ' V @ V , > { F 'B V ( V
\#6 ^55>}:BT."}") o"$=h"d #06"$=33D0GmK6;L+T:?1')3D6M'$1[ o"$33"M+RI@
8G06"$VL,47"3 ; >A@CB 4 8 ; 8 >A@CB , R ; R >A@CBXLN
; >&' @ , > { F 'B)( B 4 8 ; 8
>&'n@ , > { F 'B)( B , R ; R
>&'n@ , > { F '*B)( B
8 ' ; 8
>A@CB , > { F
'B ; 8
>&( B
?,
R ' ; R
>A@CB , > { F
'B ; R
>&( B
4 ' ; >A@CB , > { F '*B ; >&( B
\#82^+."7") -/3`')"/2')Q") \#6 ^XL
\# ^/n ;Rc6"$I>?XWL e=10-H;E"$ c6"$}1')@?E2')B'Y3"}6M')3=-/-_0- @JI&
"$d'J:;3"$R2')3=-/-_0-pLVE,RI@c8 r"$") ['J:;3"$R2')3=-/-_0-pE z@Y
! @ 4
@JI ); >A@CB > ; >A@JI'B LN5"M 6 ;cQ6"$I>?XWEh_2'>?[2') 'jY yS{
I I I I I
=
K6"$}1'$8G6K2')M@ I K'J3"76M')3-/-K'GE6&RI@8 r"$VE @ I K'J3"76M')3
-/-K'/") 9;J"M>? ! k
>9 B > @Y2!=B V @ F @ I V > ; >A@
I B ; >A@CB
T.2')603`')ME;-T0XW7D'Q.Z"$}"$,3hRZh @p')8@ I E) #"$ 'vY>
yS{
061p2') ; >A@JI'B
; >A@CBXL
5"MjEV'$0-H ;i+63@f6"$}>?XWL g"$j'd6"$}1'$8G6"$VEb'$10-H_/XWG5A,"
l ]£ h:;3"$R2')3V-/-K'GEU@JI`y ( IY2!/L ,@&8 r"$f") 66"$I>?XWGA@
; >&'n@
I , > { F '*B)(
I B > ' ; >A@
I B , > { F 'B ; >&(
I
B7y ' Y%> yS{ B
5"MjE-/[email protected]`'$6-; >&( I BhR}@; >A@ I B')8&hj2'>?_'6"$}1'$8G6"$VLha56;EG
6M')pR ¢ H ) "$+:;3"$R2')3n-/-_0-pL
-
E
_612')._33,86RZHAh"f0R:;1'$8GI9\]3`')82^+-H"78MLdK62').T
"$:I')>iM8p}0
=;LFr+-H"}8En:;>? 6"$%AGL>=;EVj'B-T03. ."76[61Kr
1') #"$-HB3M')/."$R3- \<
LB@?^T") =B3`'$/62')./}" 'f.6
3M')p6"$6M'M>?J."$R3- RZX o"$f3`')06:J6"$J3-HIME+0R:;1'$8G}
"$.-/>i ')"$VLKg2"$M'$1"$XWG.3`')8E0R:;1'$8G}H"$.-/>i ')"$8"}T"$
@738p1') o'$6"$@B>}02')303MLNa56;E'/V rW7: [.p33Rj'$888L
< L=476"$ AGL< :;>?')"$-H"}8E8G0RR8 K ¢ .£ # ;£¢$#
I
E76p')..30R:;1'$8GI"$.-/>i ')"$p8G63@H"T."$R3- \ < L< ^
"$0+')I@9."$Q"$=0R'&}0I=.3S?jpj.>}"$0Q-H"}8L4}6
_060}>?"$3>?8p33VR[-K')33ME"$.892')0:K-H[33
R+8G068L
AGL=476"$ AGLBA5:;>?D6"$I>?:?603Q\#"$-H,/."}") X^") Z.H>iM
03=86R89p6"$6"$cp_0R:;1'$8GI=-H"}8L
8G601"$HR3"M N.2')3@R2'$18H"$H-K')I@H1"$06MLDeQ-H"$:j- ')Q XU
S;'$,\ &BA
( E &D (
^XE$ "M@G89\ &QP
(
E&BC
(
^XE$ 'fi ')1';'&
<)(
E$ -K'$')8nS}3&B?
(
')8Ta=`')U
<=0A@i')8in-K')62')3 &>=OL ( L9Fr_-/.3-HI1')"$'$8').8 #"$- 5-U
2')0T')8*E "$3@ &< L (LH%("$H"$06T')H:;>?iR3"MjLKT62').T33N"$
RpM'$@M'$8G:i o"$H-K')}@?L eQ')-/.d2'$ME," h>?MER -K'$8c" .}
+0Rbe6,p')p'$66R3+-K')MEG3301'):/-/.Z"$1')}.Z"$}Q')8&6"$6.
"$0:; XW')-/.3MLTe=3"EZ "$8["B-K')S?-K')`')3N35RZ38:E"$-H
."7") #Q')898 r"$5") 6"$6.=')j8X o89"je=..Z8GkWL
~ '#E <60 (!90+ 5 1'(8"!
+ !90'9 60 6!#0+ #65 +*-
*,"$8j3M')."$:;1')- \]6X o"$p /¢; ."$R3-d^^
W I 4
KHLON
W > B 4
4 \ AGL>= ^
Y y
Y 0 )2
Ljn # 4 y ')8 ! 4 ^ Y # 4 aILje50-HT2')
\AGL>= ^,"$038RZ&M'$K"Y"$3>?&k =96"$1')}H,9-H"M>?8 \]&S}8")
6"$1')}Q')["$-H-HX o8&"'$ 1 ¢ ]£ $£ ¢l£ ^XL"8E
h_8 r[ ¢ ¢;£ o¢$£ '$"76`')8&g\ AGL>= ^'$
> y ( B 4 , ( > F jB
¢ ¢$£ ¢$ 7£ o $£ \#"$P=n'):;1'):?53`' W')"$&") P\AGL>= ^B.6P"
4
^," 8 r89"/R+[."$R3-
+>&( B 4
KHLON
Q > y ( B \AGL< ^
f
')N6M')338j
¢
¢$£ ) }
"$
¢$ 0)¢
o¢X
'$"76`')8[_6"$1')}
B") +\AGL>= ^XL g"$j')I@ (}Y
0
E\AGL< ^=j': k¢ GI¢ # ;£ ") +\ AGL>= ^ E61YRI@(8 r"$
-HM')D2') { B ! #')8 x B > wY !B +>&( B W > B LD"$.A@ x BnbM'$3@j>?sr28L
V wY !')8 ( Y 0
L
+>&( B > y ( B 4 W > B , ( g
> F
I B 4 W > B
6g-HM')_2')B\AGL
<
^+@738T'&3" hRZ"$08 "$gH"$.-K')3P>;')30K") j\ AGL>= ^[
"$8,"_:;}d=:I').dRA, \ AGL< ^P')8J\ AGL>= ^XEI,Q')I" r8KQRZh3"M,
R"$08Y"$\AGL>= ^XL$g"$[+.0.";;E,/8 r ¢ ¢$£ ¢$ X ")
"$0.-K')3V."$R3- \AGL>= ^h"/R
+ I 4
KHt`u
zQSR
<
+>&( B 4
KHt`u
zQSR
<
KHLN
Q)( ) - / , ( > F
vB65 \AGLBA?^
(."$.Z@ ") _3`' W')"$ -HM')&2')d,f2'M>?(f3`')"$") ¢ ¢$
RAhY.-K')3."$R3-\AGL>= ^5')8J8G02')3b."$R3- \AGLBA?^XL_A(.-K')3kUA8G02')3U
-/"$3"$:;@Z^ #"$
(8G02')3b #M'$R3')8 .-K')3 oM'$R3;EZh2'M>?+ >
( B W > BXL #£
¢ }¢
E +zI
W I)LT."$.A@Y") ,hM')SY8G02')3A@(-/.3j2') ^5k JW I 4 F _ E
9+8G02')3."$R3-G #M'$R3H\]k +8G02')32'$8p'_ #M'$R3+"$30"$VEG,"$038
R,'=3"M,RZ"$08"$h.-K')3"$Rbe6>?,RI@T,hM')ST8G02')3@T3`')"$|^XLDe="$
6"$"$33`')@YX^_k +zI 4 _ En/.-K')3h."$R3- jG oM'$R3c\o'&8g6"$"$33`')@Y
2')Pk R"$H.-K')3')8H8G02')3Z') oM'$R3;E7')8HP"$Rbe6>? #06"$K>;')30
')N'&}02')3E TRZ"$')N"$.-K')3l^XLE 6"$:;>iMNP6"$"$33`')V #"$- Vf"$@?L
p"$@86RZ8 I0d ')B')..3d" :?1')3+"$.-/>i ')"$."$R3-H E3GU
M')9."$:;1')-H9R: e 09'!.6`')3[6M'$\#J;L:L ,1S$'$ &BA
(
"$p "M@G8')8
`P')8IR:; &BC ( o"$/'9-H"$d"$"$0:;8G160"$|^XL(a=6;EbhB2'M>?B'c:?1')3
')..2')1')0T"p8G02')3>iMd')!"$.-/>i ')"$g."$R3-pLp47"Ek ,_1"90_"$0T2')j
8G02')3n."$R3- 5M'$Q"H1"$3>?j2')(j.-K')3E|hT')=3M'$Q2'M>?')(M'$Q'@
") :?:c"$38 ") Q'B3"M,TR"$08 "$ W I LKa=" h>?MEbh/-K'M@Yi'$88G"$i'&}0
2')W I 4 + I EP61 K93`')"$ ") $£ ¢$;L4}"$:g8G02')3@6M')"$
s=+*a=+k gB= #|
l * #ec; =+*g'uk gu *'.%). =+kc* #et*!&tgy# = vset;=<(Sg#e!=+; #e wAJ/.0z
getu
l *
|_sB(+fi*u =+kc*gB%(SgBet%'#gBe 6 9
B
!"
1 "
6 c9
=+kc* (+*vygBxcg}=+#se(+*!&t# (+*v;!$# $ . ! kt#;
fi*gBet;=+ktgB==+kt* =+*>(+f "
6 c9#; g-j{*vetgy ==+*>(+fp#ei=+kt*;<*vec;<*=+ktgB= >s'et;=<(SgB#e/= )#syg}=+#s'et; gB(+*
=
R/:;02')1')I8g :?1')3L&[email protected]')33@ "$H2'$_>$')"$0T6"$8G"$T"$ K.-K')3
."$R3- 08h61B"$:8G02')3@K"$38MLDe=BXW')-/.3=") n"$=06&6"$8G"$&
4}3`')MQ6"$1')I &}02')3sr26M')"$p o"$6"$I>?XW9."$R3-HML
g"$d3M')d."$:;1')-HME"Mh>?MEQ"$:!8G02')3@"$38(\o'$10-/:!") j6"$0c2')
+8G02')3"$.-K')3."$R3-2'$' r5"$.-K')3>;')30 ^XL%("$"M>?MEG2')
>?@pM'$@&"K"MjL E -e0Q" 2')=_n'):;1'):?8G02')3n."$R3- 8G06="d'
3M')[."$:;1')- 61 +/8G02')3P") h.-K')3P."$R3- \AGL>= ^XL"pME,
[[.-K')3n."$R3- '$
-/
MLML
4 F F 8 8 ')8 4 F F L'):;1'):?
8G02')3V."$R3- c
+ I 4
KMt`u
+>&( B 4
KHt`u
KHLN
QSR
T
h>
, ( > F B
4
KHt`u
- F ( k
, ( 4 !
F _ "$
,@JhM')S8G02')3A@3`')"$VE5(6M'$1 +zI 4-F _ -HM')92')&(.-K')3[
G oM'$R3;E6Y5"$+>?@pI:L_a56TT3`'):;1'):;`')i8G02')3D8G06+"
jV ."$R3-
+ I 4 -K' W F (
LML ( 4 F
( !
6&2'$'$,8G02')3|=.-K')3."$R3-pL E 5')31"j-H-_R, ]"$- V8G02')3@H2')
k "$[."$R3- "$.-K')3E|"["$ME2')8 + I 4 W I L
5"MjE/\AGLBA?^B-H&>?@6"$-/.3XW6"$-/.2')8" \AGL>= ^XL a=" h>?ME["$091'$S:?
6"$81')R3@9M'$k DhjK\AGLBA?^'$
+ I 4
KHt`u
zQSR
<
+>&( B 4
KHt`u
zQSR
<
KHLN
Q)( ) - / ( , > F ( B 5 \ AGLD}^
')8f"$T2')5 o"$Q:;>? (}Y 0
EZh6M')(1"$3>?_5-/-/>i ')"$ ."$R3-
RI@936:K+0..ZQ"$Q3"Mh=RZ"$08B o"$M'$6
f
>CB 4 {|y y*;CBXE2')-H3@
f
F f ( 9 f 4 f
f
F f
(3> f 4 f \ AGLB??^
f
\]08"7"78 '$_'&6"$30-/Y>?6"$^+8"$jkUi"M L
2 f
^ f y f a y B 4 {|y y*; aIE 2'$+6M')8G2')3A@ x 2
\]T.";R36"$-_R2')"$
" j6"$-/.Z"$}Q" P^XLNa56;Ehj-K'@&1')K\ AGLBA?^'$
KMt`u
6Q R < ; >&( B7y ; >&( B 4 KHLON
Q
/> F >jB
B)( , 5
4
KHLON
f
Q G f (
,w5
f \AGLB@?^
i i 4 i iL
Bx}{* s V 6nxIYNxIrw M~OG~u+ MuZ{ x G f ( ; l £ l£
¢) ]£ M#£ ) o $£ AGLD X D l]7 ¢ ¢ 0 X£ ( b¢$£ G f
G f ( ,%5
f
¢$ l£ ; ` ¢ ¢$]¢/ ¢ X£ #£ ` l1
]] } T $£ + G f
]£ % £ ¢ o $£f [ ¢ X£ ¢$I
]] X .+ X hJ X£ ¢$] H¢$] 1 $£ 0 G l£|¢ # $£/
¢$] G f oM $£ 0 G 7ll l [ + ¢ .X£ ¢ (
e -/.3XW')-/.3"
;
"$1;
4
{_5"M(tr:;0lAGL>=;LQ
033n358G6M')
[>;')30"
;DEG')8p.Z"$} j"$30"$c"
."$R3- \AGLB@?^XL
A
B
"$#%'&)(+*-J).0'1
C
|_sB( q B
"$33"M:&."$.";"$(33Q0 e 0=2') r:;0$AGL>=_3301') 1;Y=6"$6M'M>?;L
e=89
;(Q6"$6M'>?;EZ>?@B3"76M')3V-K' WG-_0- Q':;3"$R2')3n-K' WG-_0- RI@&."$.";"$
< LBA\# ^XL47"h')3:?"$- hP33}86RN"$3@[8n" A3"76M') N'3"}6M')3I-K' W7-T0-pL
u+YNul~]u|t
V
#; >&( B 4
KHLON
^ ; 8
>&( B7y`y ; 0
>&( B a ; f 2 ¢
$£ ¢ 0 B 4 {|ysy*8 X£ ; l 1 $£ ¢ 0 M
M M
=
RI@&8G06"$VLNn ; >&( B 4
KMLON
^ ; 8 >&( B7y ; R >&( B aIE 'vY yS{ ')8 @ y (Y 0
L
; >&' @ , > { F '*B)( B 4
KHLON
^ ; 8 >&' @ , > { F 'B)( B7y ; R >&' @ , > { F '*B)( B a
KHLON
^ ' ; 8 >A@CB , > { F 'B ; 8 >&( B7y ' ; R >A@CB , > { F '*B ; R >&( B a
'
KMLON
^ ; 8 >A@CB7y ; R >A@CB a , > { F '*B
KHLN ^ ; 8 >&( B7y ; R >&( B a
4 ' ; >A@CB , > { F 'B ; >&( B
Bx}{* s V 4 ! Y u+9Dwlx7{ V
p +
¢ ¢$p¢ ;£ X£ + #
) o $£ AGL>= ; >&( B ]£ E AGLB@ F ` ;£ ¢ 0 E ) o $£ < LBA ¢ G f ( ,5
f
l
$£ ¢ 0 :F?
47"h5S7"M 2') ;9Y\ AGLB@?^N6"$6M'M>?j')8d.61=3M')MLP=3`')."$.A@
-/.3[2')+h/6M')"$[01T:;1'$8G}j "$-K')"$ Y"$8["d3"76M')/') "$.-K')3
"$30"$VLa=" h>?MEnh6M')Y0 ¢ X£ E'd:?1')3>i ')"$g" /6"$6.j"
:;1'$8GI LPa56;E[6"$6.="
0R:;1'$8GI=33R+I"78G068pXWGML
+ 0 ( # !'
"$33" :."$.";"$98 r,=6"$6." 'T0R:;1'$8G},B56"$IXWG"
'6"$6M'>? 06"$VL
u+YNul~]u|t
V 4 ;" 0 l $£ ¢ 0
> (CIY 0 B > Y 0 B > ( Y 0 B ; >&( B ; >&(CI'B ,
>&( F ( ISB
M M +."}" \o'$:;>?9 ^,1')3"$:$U88(')8&'&I0Q"$-H+-H"$
"$@?L."7" :;>?KK16"$KeTL>=;E7')3"$:_K8 r"$," 61')@
6"$6.H018RZ3" jL!p03H"
6"$0p')31"J"$38
"$ ;6"$}>?XWEh
')R"M>?['&}02')3A@9>?8L
e >?6"$T61Y1') r2=."$.Z";"$KAGL<
"$+'H:;>? (CI[56M')338J'
¢ .X£
" g') ( I$LHH ^ Y 0
jQ'0R:;1'$8GI5" ') (CIsadj6M')338Y #
X£ o¢$ " ;') (p')8i8"$8!RI@ ; >&( I BXLce :?"$-H6BI.1')"$
" 0R:;1'$8G}TT:;>?i%r:;0 AGL
< "$'p6"$6M'M>? 06"$; 1
L
[email protected]`')^6>
y f >
B*B f > B 4 ; > I B ,
f > F I B a+h'j3M')').."MW7-K')"$&"
\#"M>?-K')/" ^<; 2')50.."[email protected]"$:;1')[email protected]>; B=') >
Isy ; >
I'BXE2'$=
>?6"$ > f y F { B['$T'B"$-K')3h>?6"$')8 f
'$jj3"$.;LK5"$/2')T')_/.Z"$}
I*I$E9;8G
}`')R3;EP2'M>}: 'f0O&}0d0R:;1'$8G}
\][email protected]>; Bj2'$/'p0O&}0
0.."$:[email protected]`') ^6>
y >
B*B a)^XLdT0R:;1'$8GITj/:;1'$8G}T" ;')
I*I
L3`')."$-H"$(."M>?89c "$33" :H."$.";"$VL
u+YNul~]u|t V V 6nx 9NyPx x7tZ~wHu+9yWPx x}tZ~ 9Dw]x r?u|tr\#|x tr /
~]u|t 4 ! 2
¢$£ ; !
! ;£ 0 Gf¢$£ ; $£ 1¢ 0 M%# ;
l X£ o¢X¢ J@
Y9Is> ! B X£
; >A@ B 4
^ ; >A@ B a