HAL Id: inria-00000877
https://hal.inria.fr/inria-00000877v2
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Polar IFS + Individual Genetic Programming = Efficient IFS Inverse Problem Solving
Pierre Collet, Evelyne Lutton, Frédéric Raynal, Marc Schoenauer
To cite this version:
Pierre Collet, Evelyne Lutton, Frédéric Raynal, Marc Schoenauer. Polar IFS + Individual Genetic Programming = Efficient IFS Inverse Problem Solving. [Research Report] RR-3849, INRIA. 2000.
�inria-00000877v2�
ISRN INRIA/RR--3849--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Polar IFS + Individual Genetic Programming
=
Efficient IFS Inverse Problem Solving
Pierre COLLET, Evelyne LUTTON, Fr´ed´eric RAYNAL, Marc SCHOENAUER
N ˚ 3849
December 21, 1999
TH ` EME 4
,
-./" 0 1 23(4&567%&8#9) ('
:;=<?>@>A<CBDFE9E9GHJIKGL2<NMPO!QR<SE9THHUDJVCIXWX>AYNZ&Y?>@;\[^]`_baFVU_cEI
dfe2>A[SgRBihcDJG(V_`TG(]kj
l4mon#piqsr3t1uwvxpyoz|{~}v?cq} }vpiv|{}vx
q(w}nApiqA?piozq# qA
Xq}&9 lR6u
9{o2} qq@moq#moq!?rN`t q@q#p0¡¢qA£ ¤?¥¦¤A?st £3§{¨?qA
©UªR«A¬#~®o¯¬° l4moqvw±?q#qo?¡ozxq#p³²´3µ¶}qA{}q oy§§}v?§`uw }q#pc·¹¸§ v§¨S{ºµ»u½¼m§?q
{}}{?}?`v|{¾}{¨q#}£¿m¢{2q@À¼v}mÁoo¶{Ãi§qFµ»uÄvx{ű?q#Æ#piozxqÄ}{?ÇÈÉuwy¢#q@²´yoz
{oo?{?moqA0m§{ʱq¡2q#q#Äp{ qJy§vxo¨½Ëbq#§q}v|cX¨?{p3pivxo¨§¥K¡oy }}m§q#qv|`}vxzzwp7²´?vp3Â
§~±?q#piq#N}4vc¡2}m}moqµ»uU{ }moqËbħ{}#È
l4moqcp{vx vÌÃ`#yozÌ}º¼vÌ}mƧ ¶zvxoq@{3µ&uºv|3}moqcqÃ`#vqA?}m§{ zxv§¨S²b#N}{}{¢q# Â
}{vxN}AÈl4mov|(¢{2q#(vxN} y§q@(&z|{µ»u¥R{F2qA#v̸2qAoqAq#N}{}vxS²4µ&u¾²´yo§}v?§}m§{~}
mov§ÇwR}moq9qA{m0§{?q }spi?}zx0#N}{}vx±q²´yo§}v?§AÈRÍJ?qA~±qAA¥@}m§qR?zx{»qAoqAq#N}{}vx
¨?v±?qA vxqA}({?#q@b}c}moqi¸§wq ¢?vN}(² }moq²´y§§}v?§#¥!¼moq#qA{?b}moqi¸§wq ¢?vN}(²4¨qAoq#{z
§ ¶zvxoq@{4µ»uA{ozx`¡2qwyopiq#vxA{zxz`q@}vp{}q È
Î }moqsqA±zxy }v?§{v q¥w}moq9Ïvx vx±wv y§{zÌÐb{§oN{m`v|vpivxzx{}3}moqÍJv|movx¨?{{o§N{m
²z|{v¸§qAu w}qAp#ÑsqA{?m^vx vx±wv y§{z»²K}m§q¢?oyoz|{~}vxSq#p0¡¢ vxqA{cv§¨zxq0²´y§§}v?S{~}moq#
}m§{3}moq9¼mo?zqµ»uÈN?zyo}vx3}s}moq9vxN±?q#q4o¡§zqApÒv|&}moqA¡oyovxzÌ}K²´?pÉ{q}K²2vx vx±wv y¢{z|#È
Ó }mÅvpio~±qApiq#N}mo~¼Ô{ {?}vx#y } ~¼¾ºKÕ9Â\}vpiq?Ñ0¨?N qAyozÌ}{qi¡o}{vxoq
¼v}mJp{zxz¦¢?oyoz|{~}vx¢4v²´q#¼f¨qAoq#{~}v?§AÈ
ÖJ×NØÙÚÛ ~ÜR«° Ëbq#oq#}v|(9zx¨?v}m§piA¥o? }vxpivÝ@{~}vx6¥oµ¶}qA{}q ²´yo¢}vxF }q#pA¥ovw±?q#qso¡ Â
zxq#pcÈ
Þ|ߦàá¶âAã4àäRåxá¶æ=çè
é^êë¢ìîíïPï\íðñòóîóîíõôö(÷oøíóù@úÊíðûwüAô\ô\òúNöý~ïPíþÊíï\ìîÿðùAúóRìîúÊïPì@ð xïö "!#%$&(''$)$*+-,Aö
. ï\ÿð/Aÿ10@òAíúüÊíï 32òóùAô\íÿ10ÊúÊì54#üÊíð xïö67++$$89:*);+%!<+&('
Unit´e de recherche INRIA Rocquencourt
' Ri%³) ¿4./""³ 56(#`!#(
&8c9)+¿3(4R5!^( 5 2
« ° ?Nyoq`z?½vN}#qAqU{y ¾µ&u·P }n#piqA q`²´?§}v?§v} A AqAÀo?½{~Ãoq@#¥
z|{3 @?zyo}vx yco?¡ozxn#piqsvw±qAqi·P!qA}Â#"~ vxq }y§±q#4zµ»u ??}9z{~}}{?}q#yo{§oÊ vxpiqb{y
pivxq#y 0yooq4²´piq4¡ov vpiq#¢vxo§q#zxzq ?o$#qÊÀ q#±wvxq#N}Xyo3o?¡ozxn#piq }nA»?piozq# qÈ&q§?¡oznApiq
{ %"&} cAzxy {ʱ?qAUy§AnA'"Sz{v q qF}{~}#¨?vq@ qco¨?{pipi{}vx½¨(#$#}v)Nyoq¥K²´ AqA
yoyo§qqAo @qAN}{~}v? qAb²´¢}vx¢(?y§b²´piq {¡oq@#È!{covx§#v§{zq vÃ`yoz} q`q#}}q
{oo moq*#}{N}izx{S¨?qA}vx½q#ÃA{#q q@iN}{vN}q@ qc#N}{}{§qyoizxqA0²´¢}vx¢#¥X§y§
§?¢N?§ vx#v6zqAp3§z?v yooq(q#oAq#N}{~}vx¢?zx{vq qA9µ&u§J{~Ãoq@#¥§#q#N}#q(yozxq(2vx?}
¸§wq q(m¢{+Nyoqb²´§}vx ÈKq#}}qq#§ @qA?}{~}v?{ q#yoov¢vx§{y {ʱÊ{N}{¨?qA Ñ
¤È4yooqN}{vN}q`vxp3§zqyo0zx{ ¸§§vÌ}v? qUz|{F#pi¢N{N}q{ v|{zxq qUm¢{+Nyoq²´?§}v?
{y§q9{(?w±q#¨qA§q4±?q#»yo2vx?}¸o q·´zxq92vxN} qAN}{z qb{sq#§q@qA?}{~}v?32z|{vxq@À¥
£ È4z,{An@{y¢?vN}4¸o q
qm§{+Nyoqb²´?§}v?q@}
vxq@}(·´vxz -qA}9ozxy§4$@qA{vxq
qsz,qA}vxpiq#
?p3piq
{§4z{oowm§q qAc#w
o.#qA4A{} Avxq#ooq@ÀÈ
/y§ oAq#N}?§q#§yov}qsyooqs}{} A¨vxqvx¨vx§{zxq qbo¨?{p3p{}vx¨+A$}v0Nyoq?¥N²´ Aqbyo
y§oqq ozxv}{}vx3ozy¢6Ï1@?opiv)?y§qÐ qA»}{~} A¨vxqAA±zxy }v?o§{vxqA Ñ6z{oo moqXÏvx vx±wv y§q#zxzqÐ¥
(2m§{(?y§qKvx vx±Nv y qKz|{2§yozx{}vx(q#§ @qA?}qXyooq4q#yozxqX²´?§}v?U·P{yzxvqAy yoµ»upiozxq}ÀÈ
!{?zyo}vxF{yco¡§znAp3q3}{N}9²´yoovxq§{yoFq#¢qAp¡ozxq v v±wv y§ q(z|{i¢?oyoz|{~}vxc¸¢§{zxq¥
qA @y§zÌ}{~}4N}4¡ }q#wy§ q ²P{+4?Uozxy§4{ov qbq}4ozxy§4qÃ`#{?q5Nyoq {§ z|{±?q#vxU#zx{?v)?y§q
(2U}y§4zxqA9v v±wv y§ qsz|{3¢?oyoz|{~}vx¸§¢{zxqs{yo²!yoÅ·´zxqpiq#vxzzxq#y§À4N}6AA{} AAÈ
7ÒÛ ¬@« Ù ¯+8 ° 9zx¨?v}mopiq@(Ë9#$#}v)?y§qAA¥6o}vxp3v|{~}vx6¥!w}nApiqA q@s²´§}vx§sv} A AqAA¥6oÂ
¡§znAp3qvxw±qAqÈ
,
206&"K!(
µ¶}q#{~}q §yo§}v?§Fuw }q#p ·Pµ»uoÀU}moqAÆv|c{Ávpi2}{N}}?ovx^vx²´{}{z|#¥b{ o~±wv qA
2~¼ q#²´yoz }wz|3²´i}moqJvw±?qA}vx¨?{~}v?½²b²´{}{zq}AÈl4moqF{}vx ² }q#p3²?N}{}v±?q
p{oovxo¨?}So y§q²´{?}{z4q#}0m§{3¡2q#q#Æ?§v qAq ¡wÅpi{w¾{y }m§·\qAqU²´?0q# {piozq
-
¤. ¥?£ ¥o¥? ¥o¤Ê£/´À¥w{ pi?}»²´{?}{z vxpi{¨q?pioq@vx0}qAm§ov0Nyoq@X{q4¡§{q iµ»u
-
.w¥o¤10w¥§¤32/=È
p{~Rm§{zxzxq#o¨?qX²o¡2}m}moqAq}vxA{zw{ §{?}v|#{zvxN}q#qA}6v| }moq q@?zy }v?² }moqKvxw±q#q
§?¡ozqAp54^¸§ vxo¨C{ŵ&użmo?qU{~}}{}v|3{c}{¨?q}0£ m§{2q
-
¤A ¥&£ ¥»£ ¥Rr/¶ÈC9Åq#o{}
zxy }v?A{¡¢qs²´?yo vJpiqs§{}v|y§zx{4A{qAA¥w¡oy }9vx¨?q#oqA{z\¥woq#o{}9zxy }vxv|4ÇN§~¼ È
6786 9+:<;>=@?BA=@?DC+?DEGFIHJF@K8LEMC
l4m§q µ»u0vxN±?q#q o¡ozxq#pÒo?¡ozxq#pÒA{3¡¢q4²´?p0yozx{}q {?»{3 }vpiv|{}vx3o?¡ozxq#pcÑ!piq?p0Â
§y }{}vx§{zX?zy }v?§q#wv|}A¥6¡¢{q q}q#pivov|}v|(} m§{?}vx3o}vxp3v|{~}vxSpiq}mo #È
}moqb²´yo§}vx}i¡2q }vpiv|q v|4qw}q#piqAzU#piozxq¦¥opiqNOP2qA}v|}vx±qbmww¢}moq@q@{q
§qAq@{ÈÕ y§{zzx¥¢}m§q0qA{mJ¢{qvx9}m§{} ²K{Ãoq(µ»u¥2¼vÌ}mC{i¸o q Ny§p¡2q#²»²´yo§}vx§
-
.w¥¤3Q ¥&£R03/¶Ècu zxy }vx§(¡§{q ¾X±?zxy }vx¢{^9zx¨?v}m§pism¢{ʱqqAqAN}zxC¡2q#q#ŧq@qA?}q ²´
{Ãoqsµ&u
-
£ ¥6¤¤¥¢£SQ ¥§£ ¤ /=È
uw?piqoq#±wvxy§ ¼?Ç
-
¤@/ qA{zÌ}b¼vÌ}mC¨?q#oqA{z6o? ¶{Ãoqµ»ucy§vxo¨ËbqAoq}vx0X¨{pipivxo¨
·=ËbÀ¥§}qApiq (*UT+V) ¢Ñ
W
y¢mµ»u{q#{¢{¡ozxqb}qA{}q{3¼v q±~{vxq}²&m§{2qAA¥
W
ËbXq#4{cqA{?q#oqAq#N}{~}vxU²´qA±zx±wv§¨0¨?q#oqA{z¢²´y§§}v?§#È
Y~¼qA±q#@¥@¼vÌ}moy }&}moq#R¨y§v
qAzvxoqK}m§{(}{¨?q}!m§{¢q@#¥@²´yo§}vx§
q#¸§oq
¡w(ËbC§{qÂ=}q#q@
{qb{q#zx`N}{?}vx±q?ÈRÍFq#~±qAA¥?}m§q#vx¸o q ¢?vN}9oqAq }¡¢qwyopiqAv|#{zzxqA}vxp{~}q È
l4mov|3§{2q#3?§v qA0{º{zÌ}q#§{~}v±?q`qAoqAq#N}{}vxŲ9§ Âõ{~Ãoq`µ»uÈ&K{?mŲ´yo§}vx vx
q#§q@qA?}q vJ2z|{9#N? v§{}q@¼v}mJqA2qA}}{q#N}{z¦¢?vN}AÈl4moqs}qApÔÏ&z|{µ»u?мvxzz
¡2q3y§q } q@vx¨¢{~}q3{Fµ»uC¡oyovxzÌ}sSy¢mJ²´yo§}vx§AÈl4moqAq3{qp{wJ{ ±~{?}{¨?qA}2z|{
q#§q@qA?}{~}v? Ñ
W
{0vxp3§zq?§}{vx?} U}moqs{ v|{zw vx§{~}qqA§y§q@K}moqsw±?q#¨q#¢q}~¼ { K}m§qb#q# Â
}{z¦2vxN}A¥o¼mov|mcm§{§¢qA§ }¡2qs}moqs¸§wq 2vxN}9²!}moqs²´yo¢}vxÅ·\qAq(q@}vxc?À Z
W
¢?zx{µ»uU#{¡¢qbq#oqAq#N}q {4Ëb ¢{q#Â\}qAqA»¼v}mc{vpiozxqb¼{o¢qA3Z?}m§qb{? v|{~}q
vw±?q#qbo¡ozxq#pA{cmoqA§qs¡2q(?z±?q y§vxo¨`ËbZ
W
m§{
zvxo¨²i#N}{}{¢qÅ?§}{vN}cvxFvxp3§zqAJ}m§{%¼vÌ}mp3v q
µ»u¥9}moy§¨mf}moq
??}{?}{§#qK}vzxzNm§{6} ¡¢q moqAÇ?q
wyopiq#vxA{zxzZ~mo~¼ q#±?q#@¥}moq§?¢?}v?²§?N}{}v±?q
µ»uivi}moqq} ²¦&z|{»µ»uiv|»²P{K¨qA{~}q#&}m§{`vxi}m§qq#}K² ÍJv q µ»uc·\qAqq@}v?i§È£?ÀÈ
Y9qA§q?¥2z|{»µ»u3o~±Nv q4{spiq q#Ã`vxq#N}·´zxqA»¢{qÊÀ!qA{m3¢{q }s}moq9? }vxpivx{~}v?
{zx¨?v}mop }m§{ÍJv q µ»uÈ
67$# 9+:<;>? %L&(' F@K LGE
zz²}moqF{¡2~±q#Â=piqA?}v?oq ¼?Ç q@{zxvo¨¾¼v}mÆ}m§qJvw±qAqo?¡ozxq#pkm§{ʱ?qy¢q ¼m¢{~}`#{
¡2qi#{zxzxq {}{ { {§oN{mc}qA±zx±q0µ»uѦ{Cvx vx±wv y§{z&v|b{U²´yozxz*)§q ¨?q µ&u¦¥2p{ q0²
q#±?q#{z¢²´yo§}vx§ tvx q#2q# q#N}zxU²6}moqqAoqAq#N}{}vxC·P¢?zx{pivÌ q ÀÈ»µõ}mov|9{oo?{m6¥
}moq¾?zy }v?v|U}moqS¡¢q@}cv v±wv y§{zb²(}m§qC¸§¢{zb¢?oyoz|{~}vx6ÈÔzzvx vx±wv y§{z|U¡§y }JoqS{q
vx#{ q ¥N¼movxmqAq#p4{¨?q@{~} ¼ {?}q¥w{}moqbq#z|{¡2{~}v?`²!qA{mU²6}moq#p m¢{ y§q }moq{piq
{piyoN}²XKÕÂ=}vxpiq{ }moq¼v§oq#@È
Ä{zÌ}q#§{~}v±?q{oo?{?m½m§{3¡2q#qAƧ?¢Nq vxº}moqCzx{?v̸¢q#3²´{piq#¼ Ç2Ñvz|{v¸§q#
u w}qAp ·¶4uoÀ¥}moqXÏXvÌ}}¡oyo¨mwÐ4{oo?{?m
-
0N¥£S./ovx vx±wv y§{z|»{q#piozxq}q4yozxq¡§{?q@#¥~¼m§q#qA{
vx`}moqÏÍJv|movx¨?{wÐ {o§N{m
-
¤#ro¥¤Ao¥wR21/¦v v±wv y§{zx4{q vxo¨zxq yozxqAA¥ { }moq?zyo}vx`v| ¡oyovxzÌ}
y¢vxo¨qA±qA{z2vx
vx±wv
y§{z|·´yozxqAÀ ²6}moq2oyoz|{~}v? È
µõ3}m§vx»¢{2q#@¥~}moqKÏÍJv|movx¨?{ Ð {o§N{m(v|R}{§2?q
v3}m§q²´{piqA¼?Dz¢µ»uÈ,+Sq§{piq
v} VOSOP'3R#.- ·PqA}vxÅrwÀÑ0vxo¨zxqU?N}{}v±?q3²´yo§}v?§3{qq#±?z±?q y§vo¨SËbR¥&{
µ»u{qs¡oyovxzÌ} y§vxo¨vx vx±wv y¢{z|(·¹²´yo¢}vx¢À ²´p}moq2§yozx{}vx È l4moqp{vx vÌÃ`#yozÌ}²R}m§vx
{oo?{?m v| }moq q¸§ov}vx²w}moq§{}v|{z¸o}§qA¦²´R{9vo¨?zqX²´yo§}v?st³}moq vqA} }{¢2?vÌ}v?
²&}moqÓ y§Ç?q}Ó v¨N{ q{zx¨?v}m§pvx^4uvxvpi2?vx¡ozxqÈ9uwqA}vx .3oqAq#N}9{o¡ozxq#p3Âõ2qA#v̸2
{oo?{?m È
Rvx§{zxz?¥oq@}v?<Q qAv¡2qA mo~¼ M `{ }moq P3JVOSO3R#.-{qvxp3§zqAp3qAN}q
}Å?z±?qpiqcv¢}{§#qAi²bµ»uºvxw±qAq§?¡ozqApcÈÄ9qAyozÌ} }m§qAqvxp{¨?qAA¥X}?¨q#}moqA3¼v}m
#pi§{v|?§&¼v}moq#±wvxy§»qAyoz}X²´?p
-
¤A1/{qoqAq#N}q { {Çwo~¼zxq ¨q }moq ¢~¼ q#K²}moq
§?¢Nq {§oN{m È
/
§R4RsR U"X!#( 105¦!9)+5
l4m§vxXqA}vxi¡ovq2)§(qAA{zxzxR}moq9¡§{?v|&²µ»u(}moq#?3{ }moqwyopiq#vxA{zo{zx¨?v}m§pi&piN}X¼v q#zx
y¢q }`pioyo}qb}moq({}}{?}? ²R{cµ»uÈ
# 786 3 L FIH F@KLEC H E454?6 EMKF@K LEC
7×98:;¬ ;PÛ<:>=2Ñ6q}*[email protected]¡2qJ{^#piozxq}qpiq}v|§{?q¥{ ?FEGHDIGKJLNMPOPOPMQ ¡2qc{^?zzxqA}vxº²
²´y§§}v?§ q#¸§oq ²´pR@ÒvN}!@iÈ
SUTWVX@BY?AE GD GZJ L[MPOPOPMQ\ v|9#{zzxq { ^] ! ! V BIP# ! `_Xa! (b~È
#q#N}{zo}vxcvxµ»uU}moqA`v|4}m§{}²»N}{?}vx±qbp{o§vo¨N#Ñ
7×98:;¬ ;PÛ<:Rc ÑFp{oovxo¨dEfe@hgi@i¥ ²´p {Spiq}v|J§{#qj?A@B(CkDivxN}Åv}q#z²¥ v|`A{zxzq
#V!"S# !4v²!}moq#qsq v|}{i¢Nv}vx±qsqA{zwyop0¡¢qAlmonsy§m}m¢{~}AÑ
p ?FqB(rsDtu@vwBxCyAEz?Fq<D{BIE|?ArsDI}z~UlC`?AqB(rD
l4m§qsp{zxzq@}²&y§mNy§p¡2q#lv|#{zxzxq }moq #V !'S# ! !b²E(È
#y¢v|{zq@y§zÌ}{¡¢?y }9N}{?}vx±qbp{o§vo¨N4vx }moqs²´zxzx~¼vo¨¢Ñ
×wÛ
× !"S# !"1 'OSO+&NUT V) !<-V (
µ¶²[email protected]{piozxq}qpiq}v|§{?q?¥o{
e@ g @Év|9{??}{?}v±?q p{§ov§¨§¥ }moq#
m§{
{3yo§v0Nyoqs¸o q
2vxN}AÈ
zz6pi{oovxo¨?A{c{z|3¡2q({oozxvxq }yo¡§q}9²@i¥¢{ ¨vx±qb}m§qs²´zxz~¼vxo¨§Ñ
7×98:;¬ ;PÛ<:6ÑX9µ»u SUTWVX@BY?AEG DGZJ L[MPOPOPMQ \ vx y§#qA{2q#{~} q#¸§oq U}moq§{#q ²
yo¡§q}4²@ ¡wÑ
p @B ? D T
G2MQ E G ? D
7×98:;¬ ;PÛ<:6Ñ49Jµ»u*S T VX@BY?AEG DIGKJ L[MPOPOPMQ \ vx #{zxzxq -k_'O '#3·´?*#V !R# !"À4v²K{zxz ²´y§§Â
}v?§ EGR{q#N}{}vx±qÈ&l4moq #'!"S# !" !² SÆv|X}moqbp3vxovxpyop ²¦}moqb??}{?}v?{}vx
²6}moqEGÈ
ÛKÛ « ;¬ ;PÛ<:cµ¶²6{µ»u SUTWVX@BY?AE G DGZJ L[MPOPOPMQ\ vxN}{?}vx±q?¥~}m§q#q9q v|}K{syoov)Nyoq q} @i¥
A{zxzq }moq !"!"S# !K²!}moqµ»uuSb¥¢y§m}m¢{~}AÑ
? DT
l4moqy§ov0NyoqAoqA&²¦{i{~}}{}R²´?XN}{?}vx±qµ»uv|X{bqAyozÌ}»²¢}moq N}{}vx±q ÍF{o§vo¨
Rv q R?vN}Xl4moqAq#p%²´R}moq4pi{oovxo¨ {?}vxo¨b "?A@D{B(C"!(¥¼m§vxm3vx»#N}{}vx±q {## vxo¨
}3}moq Y {y§ X v|}{§#qC#!Ñ
7×98:;¬ ;PÛ<:%$¦Ñ»l4moq|)ka S'& a! P#V4¡2q}¼ q#qA}¼iy§¡§q#}({ *) ²@Év| q¸§§q ¡w2Ñ
C#!z?|B) DT+-,/.10+-,/.
2
43 y5+687
9
;:
C<?Fq BIrsDID{B<+-,=.
9
;:
y5+687
2
43
C<?Fq BIrsDI}?>
# 7$# @ LA A' F@KE(B FDCM? H F FI=@HFEPF L=
l4m§q#qs{q }¼ 3p{v}q@moov)NyoqA }i#pioy }qs}moq({}}{?}?4²R{#N}{}vx±q µ&u¦È
W
7× ¬ × ;$: ;«#¬ ;¯ × ¬ Û ÜK°
op{w`ÇqAoqAzHG¥§¡oyovxz }m§q(q ?y§q#§#qzV=GJI \ ²&yo¡¢q#}4²@iÑ
G
I/K L
T
?5G I D T Q
GZJ L E G
?5G I D
o?zx{¨?q ±~{zxyoq@²ML»¥GJI`v|9{{ooÊwvxp{~}v?U²!}moq({?}y§{z {}}{}? ²SbÈ
WON
¬ Û ¯
®§«#¬ ;¯ × ¬ Û ÜQPõ¬ Û «@« Ù ¯ Û<;A:FR °
q#}qS(¡2q}moq¸o q 2vxN}9²»§q²R}moqEGX²´yo§}v?§AÈ +Sq(¡oyovxz }moqqNyoqA§q²R2vxN}
qIc{ ²´?zzx~¼9AÑ qTI/K LT EG(?AqI D¥DUX¡2q#vxo¨{ ?p3zx`moNqAvx VnwZV \ È
l4moq#XW
I
qISv|{Å{o§Ê vxpi{}vxF²}moqqA{zX{}}{?}?s²SbÈ`l4m§qzx{¨?q#YL»¥ }moqpiq
oqAv|q }moq({§oÊ vxp{~}vx6È
# 7 9+E %?B=C+? AM=@L &?HA
l4m§qbvxw±qAq §?¡ozqAp ²´b£%µ»u#{¡2q(}{~}q { ²´zxzx~¼9#Ñ
P <#V!"S# !$ !F-@ !!"S# ! - #N- a)T S# !"_<*& a(-@VO@ ] * [_
( 3&R bw
Y~¼qA±qAA¥?}mov|o¡§zqAp vx9¨q#§q#{zxzq#z|{~ q vN}§Ñ
P #'!"S# !"1* !F-@ !!"R# ! N -I#.- a XaN# a < aMOXaNa &S1
a(-@'O )$OP8SV a! #'VIP# !"<
}wz¦}m§{~} vxy§y¢{zxzy§q
²´9}moqvxp3§zv¸¢#{}vxJ²R}moq(oq#±wvxy§9o?¡ozxq#pv|}moq &+
!F-@V (3¥2¼movxm^}{~}q@}m§{~}9¸¢
vxo¨{Jµ&uSf¼mo?q({~}}{}9v|bzx?qs}{`¨vx±q#Fm§{¢q¢¥2vx
q Nyov±~{zqA?}4}3pivxovxp3v|vo¨i}moq v|}{§#qC#! y`BW Q
GZJ L
EGN?kDI}s¼v}m}moq¢}{vN}4}m§{}9{zxz EGK{q
#N}{}vx±q ²´yo§}vx§AÈ
Û 88\® × ¬ ×wÛ × - rS/
6q} ¡¢qi}moq{~}}{}b²}moqmww¢qA¡2zxv|µ»u S T>V @B ?FEGHDIGKJLNMPOPOPMQ \ ¥6{ }moq`#N}{}vx
{~}v3² SbÈXl4moqA Ñ
p @BWC !"y B ? D } m C ! ? B Dm
n B
Y~¼qA±q#@¥ ?piq
vÌÃ`y§zÌ}vq@9{vxqb¼moq# C ! y B W Q
GKJ L E G
?9D(}svx}i¡¢qpivxovxp3v|q
Ñ
W
l4moqi¸o}oqA qA¢qA (?C}moqU#N}{}{¢q3² }moqp{§ov§¨?3Z!v²oqi² }m§q`p{oovxo¨Nsvx
¢w?zx#N}{}vx±qi·´v=Èq?È zx?qs} n@À¥ }m§q#c}m§q}qAp
L
L
p{ÊU¡2qA#piq±qAUzx{¨?q¥o{
}moq¡2y§ }mwy§¡2qA#piqA4piqA{ovxo¨zxqA#È
µõs}moq#{q&² {~Ãoq»µ»u¥AvÌ}6v|¦2?vx¡ozxq&}q@}vp{~}q { }mwy§}pivovxpivxq
L
L !
C !"y`B W Q
GKJL E G ?9D}
}0~±q#?piq}mov| vÃ`yoz}È Y~¼qA±q#@¥²´?Ko? ¶zvxoqA{Xµ»u¥?}moqbN}{?}vxi{~}v(p{Ê3o}
¡¢qy§ov̲´?p ~±qA}moq p{v @ ¼m§vxmcp{Ç?qA vÌ}{zpiN}vxp32?v¡ozxqb}q@}vp{~}qÈ
W
pioy }v§¨s}moqY {y§ X v|}{§#qvÌ}qAz̲v|KÕÂ=}vxpiq?§yopivo¨¢È!ÍJ?qA~±qAA¥@}m§qMY{y§Â
X v|}{¢q4²¹}q#ivxKy§?}q#Â=vxN}yov}vx±q?Ñ6Rv¨?yoqb¤4oqAq#N}R}¼s§{vR²¦m§{¢q@
-
·\{?À¥¢·´¡2À/
{ -
·\{$îÀ¥»·´¡-îÀ /»¼v}mC ! -
·\{?À¥»·P¡¢À /" C ! -
·P{$îÀ¥»·P¡-À /=È +movxzq·P{NÀ9{ ·´¡¢À {q2q#q#vx±q {
vxpivz|{@¥ ·P{.À4{ ·´¡-îÀ4zxN?Ç*Nyov}q vX2qAqA?}@È
l4moq@q {ʼ¡§{Ç »zxq ?piq {yo}mo?K² }movx §{¢qA
-
¤A/2}0#§v q#4{¸o}oqAX²´y§§}v?¡§{?q
?F}moq3}?¶#vxC{zx¨?v}mop{ ?CpiqvxN}yov}vx±q v|}{§#qAb¡2q}¼ q#q#Sm¢{2qAi·´§{piq#zxJovÌ qAzx
vUXq#q#§#qA4?Xy§zxv vx{ vx}{§qÊÀ¥ vx§}qA{ ²6}moq Y{y§ X v|}{§#qÈ
uwq@}v?<.s¼vxzz q#pi?§}{}q9m§~¼ }moq Ïvx vx±Nv y§{zÐ{oo?{m{zzx~¼9»§q9}y§q vo²´pi{}vx§
}qApip3vxo¨²´?p¡¢}m¾?zz|{¨?q(}m§q#q#p { }?Âõ?v^{zx¨v}mop vx^? qA}zx±q0}m§q0vxw±q#q
§?¡ozqApcÈ
(a) (b) (a’) (b’)
Rvx¨yoq¤ÑY {y§ ?8X v|}{§#qipi{ÊJ¡2q?yoN}q#¶vN}y§vÌ}v±?qÈ Yq#q¥C ! -
·P{NÀ¥K·P¡¢À / " C ! -
·\{$îÀ¥K·P¡-îÀ/
}moy§¨m}moq(m§{2qA{o2qA{±?q# vX2qAqA?}@È
((
l4m§vx&qA}v?0vxN}
y§q@!}moq4&z|{RqAoqAq#N}{}vx(²¢o? ¶{ÃoqKµ»u¥{
vxy§qA!}moq#N}{Â
}{§#q(v|yoqÈ » ¢qAvxpiq#N}b{q(oqAq#N}q
}m§~¼Á}moq0{
±~{N}{¨q(²X&z|{9µ»u NaVka4¨qAoq#{z
§ Âõ{~Ãoqsµ»uÈ
786 L&8H = =@?BA=@?DC+?DEGFIH FIK8LE
l4m§qpi{v vÃ`yoz}C¼mov|mÅ{vxqAb¼moqA¾pi{ovxoyoz|{~}vxo¨co? Â=zxvxoqA{µ&u^v|b}moqUm§{ zvxo¨c² }moq
#N}{}{§qK#§}{vxN}AÈ6l4m§q#qKv|!§¨qAoq#{zw{¢{zx?}vxK¼ {Ê }smoq@Ç}moqN}{?}{§q»²¢{9§ Â
{Ãoq²´y§§}v? ¥§{ q#w2q#vxp3qAN}{z2}qA}4qNyovxqbmoqA{ʱw?pioy }{}vx§4¼m§vzxqsozx¨vx±wvo¨i{3movx?}
?^#N}{}{¢qȧsv¢}{§#q¥¦zxqA}m§{~}¤1.² { p ²´yo¢}vx¢{}y§{zxzxc{qi?N}{}v±?q
·\qAq
-
¤A/¶¥~{ {z|q#w2q#vxp3qAN}!²oq@}v?oÈî£ÀÈ!l4mov| qAp3§vvxA{z²P{}Rpi}vx±~{~}q }moqKvxN} y§}v?
²R{c{zÌ}q#§{~}v±?q q#§q@qA?}{~}v? È
A=A= KÛ ¯?®$84¯ Û<: ¬#~®o¯¬@® : ¯ ×
l4m§q ¸¢}9v qA{3vx } q¸¢oq({3¼q@{ÇqA #N}{}{§qs? v}vx}m§{}9¼vzxz ¡2qqA{vxq# }`moq@ÇÑ
7×98:;¬ ;PÛ<: 6Ñ&Áp{o§vo¨zE ew@ g @i¥N²´?p {(piq}v|§{#qz?$@B(CkDKvxN}3vÌ}qAz̲¥wv|4#{zxzxq #V_
#V!"S# ! !- [a"OV# !%! O@!Òv²!}moq#qsq v|}{i¢Nv}vx±qsqA{zwyop0¡¢qAlmonsy§m}m¢{~}AÑ
p tu@ v B
g
]H1bsm^l 2g
l4m§qsp{zxzq@}²&y§mNy§p¡2q#lv|#{zxzxq }moq #V #'!"S# !" '!"b²E(È
µ¶}v|s¡w±wv?y§9}m§{~}v² E vxszx #{zzxJN}{?}vx±q0¼È@È}AÈi¥ }moqA v|b}m§q0yo§v0Nyoq3¸o q 2vx?}
²E(È /q#±qA}moq#zxqAA¥Nzx #{z#N}{}{§q Nq@4o}4vxp3§z`¨?z?¡§{z?N}{}{§#q¥w{ qAp3?§}{~}q
¡w}moqs²´zxzx~¼vo¨i?yoN}qA¶qo{piozxqÈ
A=c
©¿¯
Û : ¬ × Ù×
®$
8×
µ¶² q mT n E
?Fq BIrsDT 0
q ^n
r >
µ¶² nmTUq*mT n E ?Fq BIrsDT 0
?Fq v wq n D
?jq<D r >
µ¶² qTWn E ?Fq BIrsDT 0 qr >
µ¶² q*mT n E L ?AqB(rD T 0
q
r >
µ¶² nmT q*mT n E L ?AqB(rD T 0
s? q
v
,q n D
s? q<Dr >
µ¶² qT n E L
?AqB(rD T 0 n
,q
r >
§yo§}v?§E1q}ELb{qb#N}vxwyoy¢#È&l4moq#vx4¸o q ¢?vN}{q qA¢q@}v±?q#zx HT ?sB
D{
L T ?B
D¥o{
}m§q#U{~}vx²´Ñ
p t B `B!HB C y I B(E I ? D } ~Ul C<? I B D¼v}m lmon
l4moqA{qbmo~¼ q#±qA4o}9?N}{}v±?qb{ o} q#¸§oq({3yoov)Nyoq({~}}{} ²´?4}moq1V EBIEL \
µ»uѧ}moqAqq# vx}9q#±?q#{z¦q}A¥¢y§m}m¢{~} T ?5D T E1k?D#" ELw? D·Pq#qs¸¢¨yoq£À4{ }moq
I ? D q Nyoq#§#qA{qso}{z¼4{Ê 4w±?q#¨q#N} ¼moq# L*g%$ ·Pq#qb¸§¨?yoqsNÀÈ
l4mo?yo¨m}movx ?yoN}q#¶qo{piozxqqAq#p4}UyovxJ{zxz6q X2?}4}`q@{vzx q@vx¨F#N}{}vx±qbp{ Â
§vo¨N }y§q0}¡oyovxz µ»u¥}moq0§qw}(q@}vx¢¼vxzzXmo~¼%}m§{~}vx q#q ¥¦¡2q#oq#¸o}A{^{v|q(²´p
y¢vxo¨iz A{zxzU#N}{}vx±q ²´yo§}vx§4vxcµ&u¦È
A= &* ×# × « ×9: ¬@® ¬ ;\Û`: ® : Ü Ú ~® ×
+m§q#Cy¢vxo¨JËb}q#q@ }Uq#§q@qA?}bµ»u¥2}¼c{o§N{moq@9{q2?vx¡ozxq}`}{Çwzq0}m§q3#N}{Â
}{§#q qNyovxq#piq#N}AÑR}{§²´?pËb }q#q@4vN}3#N}{}vx±qp{oovxo¨?A¥ 4q#zxvxp3vx§{}qNOXa!
§J??}{?}v±?qbp{oovxo¨?AÈl4moqz|{~}}qA{o§N{mc{zx¼ {Ê ¼?Ç A¥o¡oy }b#{c¡2q(±qA`}vxp3q0¢y Â
pivxo¨§¥X{?p{N^}q#q@(}m§{~}i{qU¨?q#oqA{}q
{z?o¨FqA±zxy }v?Åm§{ʱq}C¡2qqAzvxpiv¢{~}q
·Pq#q
-
¤@1/´ÀÈ
l4m§vxq#yo¨?q#ov|}vx{oo?{?m¼4{§?¢Nq
¡2qAA{y§q(o`#zq@{oqA9¼4{Ê?yoz
¡¢q²´?yo
}`¨qAoq#{~}q
#N}{}vx±qbp{oovxo¨N4v}¼ vxpiq#§vx§AÈ
Ó y }@¥w}¨?q}moq#¼vÌ}mUzxwA{z??}{?}{§#q¨wqAK}moqbv qA{² 2z|{ qAoq@qAN}{~}v? Ñ6v²6?oq #§vÌÂ
q#{Jzx #{zxzxS#N}{}vx±qp{o§vo¨ E ¼v}mŸo q ¢?vN} i¥&}moqA½¢?vN}0A{Å¡2qUq#oqAq#N}q
y¢vxo¨ ?'`B(D3w vx§{~}qA0q#N}q#q ? *)~¥K{ Ev}q#z² #{½}moq#§#q¡2q q¸§§q q@{vzx¾y§vo¨
+
ì|ðíð-,.0/214365798;:<3>=@?BA5:CDE3>=@??
A0 B0
A1 B1
A2 B2
A3 B3
x0 x1
Rvx¨yoq£oÑ
?
" )
D1T " ) ¥
?5n " )
nXD T n " ) n¥
?5 " )
wD T " ) ¥
?5"
)
9D T% "
)
o¥o{
?FqS " qL{D TUqS ""q L~È
? D v ? D ? D
? D
? D v ? D ? D ? D
? D v ? D ? D
? D
Rvx¨yoqb§ÑXl4moq#qsqo{piozxqA ²´?¼mov|mU}moq(q Nyoq#§#q I ? D vx±qA¨?qAAÈ
y§m½#N?
v§{}q@#ÈJl4moq`vxpi¢?}{N}(²P{?}v|(}m§{~}}moqz #{z#N}{}{¢q?
v}vxš2qA?piqA{
#N}{}{§q#
vÌ}v?`}moqboq#Â
vxpiq#§vx§{zo²´yo§}vx¨vx±wvo¨ 't{
vÌ}v|}{vx¨mN}²´¼ {
}3}{§²´p{3{
?p oq#Â
vxpiq#§vx§{z¢²´y§§}v?JvN}{i?N}{}v±?q²´y§§}v? È
7×98:;¬ ;PÛ<: Ñ6Å&?zx{ µ»ubvx!{9q#}6²wzxwA{zxzs?N}{}v±?qR²´yo§}v?§EG§¼vÌ}m(q@2qA}vx±q&¸o q
2vxN} GRy§m}m¢{~}q@{m!EG!vx q#¸§oq vU¢?zx{w? vx§{}qAK¼È@È}AÈ G!¡w3}¼(?oq vxpiq#§v?§{z
²´y§§}v?§@G»{ G&¡wÑ
E G '
( T
'
? G @ G ?'<B!(D(D n
GI?'<B!(9D
·¤@À
²´?9?piqbqA{zNy§p¡2q# G È
l4moqK§{}v|yoz|{²´?pÁ²N}moq '²´yo§}vxq#¢yoqA2}moqXzx #{z?N}{?}{§q6t{
"!$#
&%
M'$()('K L
v m
ns¼m§{}qA±q# }moq±~{zxyoq²@ GÈ
z #{zzx0#N}{}vx±q ²´yo§}vxUA{imoqA§q9¡2q9q#oqAq#N}q ¡w0?oq¢?vN} fvx
B2n v { }¼
²´y§§}v?§@Ô{
*
¥2¼mov|mF#{¡2q(qA±zx±q
{Ëb}qAqAAÈ ?y¢{~}vx¢(·¤ÊÀ{qy§q
{9¼{o¢qAA¥
¼m§vxmq#§yoqA }moqz A{z ?N}{}{§#q ²6}moqp{oovxo¨¢ÈXÍJq#~±?q#@¥¸§¨?yoqsrmo~¼9 }m§{}{3¼v
q
±~{vxq}²&m§{2qAA{¡¢q?¡ }{v§q
y§vxo¨i}m§{~}q#oqAq#N}{}vx È
Rv¨?yoqbr¢Ñ»»o{piozxqA4²R&z|{4µ»u{~}}{}
7$# @ LEGF =H EPFIH E E? FI?DCRF@C
l4m§q(oq#±wv?y§yo¡§qA}v?cmov¨?mozxv¨?m?}q }moq²P{}9}m¢{~} #N}{}{¢qb±q#v¸¢#{}vxJ#{oo}9¡2q{ʱ?vÂ
q ²´i&z|{iµ»uÈY9~¼ q#±?q#0}mov|q@}v?º¼vxzzq#w2q#vxp3qAN}{zxzx½mo~¼ }m§{}3}moqJo2}vx½²
0 0.2 0.4 0.6 0.8 1
-4e+07 -2e+07 0 2e+07 4e+07
x
Rvx¨yoq . Ñr1T
2
('K L
v
y§±?qb¼v}m T n
#N}{}vxo¨`p{§ov§¨? vC}moqiq#} ²Kz A{zxzJ?N}{}v±?q(p{o§vo¨N q¸§oq ¡wcqNy§{}vxº·¤@Àvx
z|{¨qA }m§{U²´?9¨qAoq#{zpivÌ q µ»uÈ Y9q#¢qs}m§q(?}²»??}{?}{§#q ±?q#v̸¢A{~}v?U¼vxzz ¡2qpy¢m
zx~¼ q# ²´&z|{4µ»uU}m§{²´9ÍJv q µ&u¦È
l4mov|&q@}v?oqAq#N}Rpiq}{}v|}vxA{zN}q@}6}m§{~}&m§{ʱ?qK¡2q#q#0¢qA²´?piq }¼ vUXq#q#N}»q#}
²w²´yo§}v?§ vx qA¦}9q# ¢qAvxpiq#N}{zzx {ooÊwvxp{~}q!}moq#vx6qA2qA}v±?q»o2}vxs²o?N}{}v±?q
²´y§§}v?§#È»l4moq¸§}4q#}²6²´yo§}v?§vxK}moqsq}² pivÌ q µ&u¦¥Nv=ÈqÈ&¨qAoq#{z¢o ¶zxvoq@{µ&u¡oyovxzÌ}
²´p$¨qAoq#{zX{
p³Ëb%}q#qAAÈJl4moq`qA?
q}v|s}m§qq}² zx #{zxzxS#N}{}vx±q3²´yo§}vx§
q¸§oq
¡w
q#¸§ov}vx 0s¼mo?q9?p32§q#N} @f{
{q9{
?p ËbÅ}qAqAAÈ!µõ¡2}mU#{?q@#¥}moq
{
pÔ}qAqA{qs¡oyovxzÌ}²´p }moq¡§{?v|bo
qA{
}qApivx§{z|
qAvx¡¢q
vxJq@}vx . Èx¤È
9{{§{zN}v|#{z¦pioyo}{~}v?²6}moq(??}{?}v?`{}vxivx4¨?q#oqA{zzxiy }²Rq@{m ¥ {3wyopiqÂ
v|#{z6qA}vxpi{}vxc²&}movx{}vxm§{}¡2q ?oqq 2q#vpiq#N}{zxzÑX²´?9qA{?mcpi{oovxo¨ E(¥{{piozq
²§{vs² v|}v§}(¢?vN}!? GB GDbvx
B2n v
v| q¸§§q ¥&{ }m§qp3vxovxpyop$² y
( M (}
M (
¨?v±?qA}m§q({ooÊ vp{}qsN}{?}vx{}vx²´?E(È
l4moq3N}b²»}m§q0{§oÊ vxp{~}vxcv|²K?yoq(o2}vx¢{z¦}`}m§q0wyop0¡¢qA²X2vxN} vC}moq
{piozxqÑ ²´yo&}qA}&¼v}m vX2qAqA?}X{piozxqARm§{ʱ?q¡2q#qA}vxq L LUvxpi{¨q@#¥{ }moqqAyozÌ}&{q
§q@qA?}q
vil!{¡ozxqA ¤¥£ {
oÈRl4moq#q}qA}»{q ¡§{?q
3{§q#Â
q#¸§oq
q}»²2§{vx ·
q#2q#
vxo¨
?U}moqqAzxy }vx²R}moqvxp{¨qÊÀ¥ ¼movxzxqs}moqs²´?yo}m?oqqAzq@}¢?vN}4yoov²´p3zxÈ
¤È ©*8,8Ù ; × 8\«¬ × «A¬ Ñ
X±qAiov q#z²¦}moqbvp{¨?qv|4moqAÇ?q ¼v}mUqA±qA3}moq# ovwqAz²¦}m§q vxp{¨q?È&µ¶} v|X}moqbp3N}
{Ayo{~}q }qA}A¥ ¡oyo} {z|0}m§qp3N} KÕ9¶#§yopivxo¨§È
£ È Ú ;«#¬i¬ × «A¬ Ñ
l4mov|}q@}3}{}b²´p$}moqi}¼ JovwqAzx0{~}}¼ Jo2?v}q`?§q#s² }moq`vxp{¨?q¥!{ qA{?m
¢?vN}X#{¢Rwpip3q#}vxA{zxzq@{m(m¢{z²¢vxpi{¨q?¥~zvxoq4¡w(zvxoq?¥yoN}vxzw}moq#q#N}qAR§vÌ q#z v|Rq@{moq
·Pq#qs¸§¨?yoq$QNÀÈ
oÈ
N
R® × ¬ × «#¬ Ñ
9zxz ov q#z|²!}moqvxp{¨q{qb}q@}q {¨N{vx§}4}moq#vxvpipiq vx{}qoqAv¨?mN¡2y§(·Pq#qb¸§¨y§q 0ÀÈ
r§È6
® : Ü Û
*¬
×
«#¬
Ñ
L^¢{vx ²&2vx?}{qqAzq@}q
{
pizx¥ yoov²´pizUv
B2n v È
Rvx¨yoq QoÑXl4moql!¼vx}}q@}@È Rv¨?yoq 0 ÑXl4moq(u Ny§{qb}q@}@È
§Xpiqq#}&y§§zxqA{»q@{§A¥Ê}moq9l!¼v|}»}qA}KqAq#p Nyov}qvxoqÃ`vxq#N}@¥¼movxzq4}moqu Ny§{q }q@}
q#qApKp0y§m`piq{Ayo{~}q·´v=ÈqÈ»¨vx±q@XqAyoz} zx?q#X}(}moqbzz¶ovÌ qAzxK}q@}ÀX?`&z|{Kµ»u}m§{
?`pivÌ q µ»uÈIY9q#¢q9}moqu Ny§{q9¼4{K²´yo }qA{zvxÝ#qb{¨w #piopivxq9¡2q}¼ q#qA`qÃ`vxq#¢
{ ?}A¥o{ ¼ {? y§q ²´9{zxz¦q 2q#vpiqA?}4oqAq#N}q vx}moqs²´?zzx~¼v§¨§È
lR{¡ozxqA9£3{ 3mo~¼}¼3}moq#p{~?q@y§zÌ}sÑ
¤Èl4moqu Ny§{q }q@}9qAyoz}{qbo}9±?q#i²P{4²´p }moq(9zxz̶ov q#z| }qA}9qAyozÌ}²´&z|{µ»uÈ
oyo}m§q#p3?q?¥2}moqi{~}vx`²X²´yo§}vx§ qAq#piq ??}{?}v±?q wqAbo} q@qA{?q {?}vxA{zxz
¼vÌ}mC}moq3q@?zy }v?F²»}moqivp{¨qAAÑzxqA9}m§{¾£ È.S. vXq#q#§#q0¡2q}¼ q#qAjn jn `{
n sn Èfl4mov|`piqA{§}m§{~}`}moq^u Ny§{qc}qA}A{Ä¡¢qS?§v qAq {? Nyov}qC{?#y§{}q¥
qA¨?{ zxqA²R}moqvxp{¨qsqAzxy }vx{¡2~±qn n oÈ
£ È }moqUo?¢?}v?C²4#N}{}vx±qi&z|{sµ»uSpy§m¾z|{¨q#b}m§{S}m¢{~}(²ÍJv q
µ»uÆÑ piq
}m§{ .2 pi§{q
}zq@ }m§{S¤32`È
2( &((" 4((U!0 "0) U!s!#(
l4m§qK}{
{
{oo?{?m ¼moqAy§vo¨qA±?zy }v?§{9piq}mo
6{?6} m§{?}vx&? }vxpivxq#¦v|¦}q#±?z±?q
{02oyoz|{~}v?U²6¢}qA?}vx{z¦?zy }v?§}0}moqso¡§zqAp {~}4m§{
¥Nq@{m² }moq#pA{zxzq
vx
vx±wv
y¢{z|#È
l4m§qFy }oy }U²s}moqS{zx¨v}mopkv|`vx}m§{~}A{qc}moqC¡¢q@}v
v±wv
y§{z q#§#yoN}q#q
Ä
yov§¨Å}moq
qA±?zy }v? È»9zxz }moq#vx vx±wv y§{z|{q vx#{ q ¥w¼m§{}q#±?q#vx ²´p{~}v?`}m§q#Upivx¨mN}9¡2qA{@È
µõUpiq9A{qAA¥mo~¼ q#±?q#@¥~¢}q#N}vx{z¢zxy }vx§K{qzv|}K²¦vÌ}q#p#¥w{ {`{z}qA§{}q2?vx¡ovxzv}
v|K}qA±?z±?q{(2oy§zx{}vx`²!y¢m`vÌ}q#pA¥w{ }0¡oy§vz {0?zy }v?¡w`p0¡ovxov§¨ vX2qAqA?}4v}q#p
²K}moq`yoq#N}¢?oyoz|{~}vx6Èu y§mÅ{¾{oo?{?mFv|±qAJ2oy§zx{vºz|{v¸§q#(uw }qApiA¥6¼m§q#q
v}qAp{q`yozxqAA¥R{ ?zyo}vx§({qUyozxq`¡§{?q@#Ñ3l4moq`¼ q#zxz̶Çwo~¼ÅÍJv|mov¨N{Å{§oN{m¾q#±?zx±q@
yozxqAA¥~{ { ?zy }v?vxR{9yozxqX¡§{?qXp{ qK²§?p3qK² }m§qK¡2qA}Rvx vx±wv y¢{z| ² }moqX¸¢§{zN¢?oyoz|{~}v?
²E
G
?p3§y }q
²»?pi§{vx¢
{zz¦§vÌ q#z| L v
I L(
I
v (
v
}¼v|} L v
I
v
Ny§{q L v L v
{ p =L L
l!{¡ozxq3¤?ÑKpiozxq vÌ}U²R}moq±~{vxy§}q@}
² EGX?pioy }q {zxzÂ=ov q#z| }¼v|} Ny§{q { ?p
¤3Q £R.Q ¤2oÈî£Q £~r¢Èr+Q £o¤ÈQr ¤#r§ÈQ+0
?£ ¤2?£r ¤2oÈrRQ £~r¢È¤Q £o¤ÈS2 ¤AoÈ0~
Qr r+2RQ §Èrw£ £§ÈRQ £o¤ÈQ?£ ¤AoÈî£S.
¤@£ ¤Qr  £~r¢È2? £?£ È2 ¤AoÈ
£S.SQ Q+.S.RQ  £§Èr £o¤Èx¤A ¤AoÈ2r
. ¤Ê£ £QN£ ¤Arr  £§È§¤ £o¤Èx¤A Â
l!{¡ozxq£oÑ»X2}vxU²&#N}{}vx±q ²´yo§}vx§·0À4²´qA{?mU}qA}4²´ (*UT+Vbµ»u
² E G ?pioy }q {zxzÂ=ov q#z| }¼v|} Ny§{q { ?p
¤3Q £R.Q QN£ Èr? S2§È.SQ Qr§Èr 0Êr§Èî£
?£ ¤2?£r .oÈ?£ §È§¤ QR2oÈ0£ QoÈî£
Qr r+2RQ .SQoÈx¤@£ §È2? .+0wÈo¤ Qr§ÈS2
¤@£ ¤Qr  +0 È? .SQoÈrr Q?£ Èx¤#r
£S.SQ Q+.S.RQ  +0 È£r .R. Èî£Q QS2oÈ2S2
. ¤Ê£ £QN£ ¤Arr  +0 È2? .oÈ Â
l!{¡ozxqs§Ñ&X?¢?}v?²R#N}{}vx±q ²´yo§}v?§(·0À²´?qA{?mU}qA}²´%O µ»u
-
¤#r§¥»¤A ¥ R21/=È
Î
^}moqi}moqAm§{
¥¦}moqÂõ#{zzxq
XvÌ}}¡oyo¨m¾{o§N{mFqA±zx±q@2§yozx{}vx§s²
#piozxq}qbyozxqs¡§{qA
-
0w¥§£R./=È
uwvxpivz|{zxs}b}moqÍJv|movx¨?{0{§oN{mvx4u¦¥Ê}moq$P3'OSOS#N-bo2?q
m§q#q #§vx}
vxq#±?z±wvxo¨i{2oy§zx{}vx²!zx #{zzx`??}{?}v±?q²´yo¢}vx¢#¥o{ }i¡oyovxz {µ»uU¡wov|Çwv§¨3y§
²´y§§}v?§vx}moq2§yozx{}vx È
zxqA{zx¥?ozxo¡§zqApiX¼moq#q4}moq ?zy }v?#{i¡2qq}K{¢{}XvN}(q#¢{{~}q#pi¢?oq#N}X#{
¡2qUm¢{ zxq y§vxo¨C{½vx vx±Nv y§{z {oo?{?m È Y9~¼ q#±?q#@¥R{o}moq#(§qAq@{^# vÌ}v?½vx}^¡¢q
{¡ozxqs}U{?#y§{}q#zx`qA±Ê{zy¢{~}qs}moqN#V !"P{aNaK²X{vo¨?zq(#pi2oqA?}@¥§v=Èq?Èv}y§q²´yozxoqA4}}moq
¨?z?¡§{z2¸o}oqA²6}m§q(?zy }v? È
§}yo§{}qAz?¥ }moqµ»uvxN±?q#qbo¡ozxq#pXq#?p3q§vx#qb¼4{Ê }iq#±~{zy§{}qs}moq(??}vx¡oy }v?
²§{v§¨zxqX²´yo§}vx0² }m§q }q#pf} vÌ}!¨?z?¡§{z?¢qA²´?p{§q?Ñ ¢v q#!}m§qX}{¨?q}&m§{¢q Zv²¢{
µ»u·FE GÀ6v|»{b?zy }v?²o}moq4vxw±q#qKo¡ozxq#pc¥~}moq# T "E G ? DÈ Y9qA§q{ z A{zN¸o}§qAR²´»{E G
mo?yoz #§v q#X2?vÌ}v±?q#zx}moq9§{}X² E G ? D»zxwvo¨v§v q (¥w{ oq#¨N{~}vx±qAz(}moq §{}X² E G ?5D
zxwv§¨Uyo}v q(È(§yo}moqApiq¥¢}m§q02?vÌ}v?C²»}moq3¸o q ¢?vN}s{zxU¨?v±?qApiq0v vxA{~}vx¢#È
µ¶}bmo?yoz zvxq(vx§v q}moq}{¨q}m§{¢q¥§¡oyo}}m§q(qAzx{}vx±q2?vÌ}v?§²R}moq¸o q ¢?vN}²&}¼
zx #{zzx^#N}{}vx±q3²´yo§}vx§3{z| q¸§oqqAp3v vx}{§q@¡2q}¼ q#q#Åvx vx±wv y§{z|#¥&¼mov|m½#{Å¡¢q
y¢q }bvxpiozxq#piq#N}Kpiqm§{vxo¨bpiqAm§{ovxp}bÇ?q#qA vx±qAv}v3}m§q¢?oyoz|{~}vx¢»{ oq#±qAN}
{zz²´y§§}v?§vx}moq2oyoz|{~}v?§ }i¡2qA#piq(vxpivz|{@È
(( (
786 ELA A LE?JEF@C
qAv¡2q v3q@}vx0oÈx¤¥~{9zx #{zxzxs#N}{}vx±qXp{oovxo¨v| q¸§§q ¡wb}¼ 9²´yo§}vx§4·$@ ?'<B!(D
{ ?'`B(DÀ { {0¢?vN} iÈ+moq#qA{? v|4vxpiozxqAoq@qAN}q ¡Nv}}¼ 0qA{z̶±~{zxyoq #w vÌÂ
¢{~}q@}m§{~} `o} oq#q ²´yo}moq# qAvx }vx ¥<@Ô{ {qpi q#zxq {? Ëb»Â=}q#q@#¥2vxpivz|{zx`}
ÍFvÌ q µ»u
-
¤@1/KÈ
JÛ Ü × «® : Ü ¬ × ;A: ®$8P« Ñ l4m§qi}q#qAs{q3¡oyovxzÌ}²´p${q}²}q#p3vx§{zxA¥ ¼mov|mS#§v|}s² }moq
±~{v|{¡ozxqA '^{ (o¥R¢}{N}svx nB2n =¥6{ {Jq#}(²4o qAA¥6¡§yovz}(²´p}moq²´?zzx~¼v§¨cq}(²
¡¢{vxbqA{z¶±Ê{zy§q ²´y§§}v?§#Ñ
Õ§{`o
q@#Ñ
W
q
W L
2
²´qtnwB2n
W
?FqD
W 67?Aq<D
W
L
?Aq<D
W l
?FqDT l?U"L ?Fq<D q
W
?Aq<D1T lU"L ?FqD
? qD¥
v̲qT
Ó v¢{`o
qAAÑ
W
W
W
W
2: ;¬ ;®.8; ® ¬ ;\Û`:Ñl4m§q(v§vÌ}vx{zvxÝA{}vxJo q yoqs²´?9}moq3Ëb}qAqAv|{Uvxpiozq0q@yov±?qb{ p
m§v|q»vx?}9}moq ?vN}!q}R² o q{ }qApivx§{z| y§?}vzNq#v}m§q# }q#piv§{zx!{q {ʼ({zxz¡§{§moqA
? }moqp{~ vxpyop
q#o}mcvx4qA{?moq
È
»²´X}moq4¸o q
¢?vN}A¥}moq#3{q{
?p3zxmoNqA3{pio¨s}moq9??}yoK¢?vN}X²2}moq}{¨q#}
m§{¢q È l4mov|`v
qA{½#piqA`²´?p }moq^#~q@}yoqJ¡wÄqAÇwÇNvxo¨
-
/ }m§{}U}moq#qC{zx¼4{Êwiq# vx}
zxy }v?§s}F}moqvw±qAqio¡ozxq#p¿¼moq#qi¸o q ¢?vN}0{q¾}moq`q ¨qA(²4}moqU}{¨?q}m§{2qÈ
l4m§vx4qAyoz}9m§{4¡2q#qA§~±?q#Uvx}moq(A{qb²&{Ãoqsµ&uvx
-
1/¶È
Û
«A«
Û!¢×
Ñ }moq}{
{
ËbS#N~±qA6v|&y§q
?0¡2}m}qAqAAÑ v}X¢qA²´?p&¼4{¢6²¢{
?piz
q#zxqA}q yo¡ Â=}q#q@4¡¢q#}¼qAq#}moq§{qAN}AÈ
l4moqs¸§wq ¢?vN}{qso}p3 v¸§q ¡wU#N~±qAAÈ
7 6¬@® ¬ ;\Û`:$ÑÅvX2qAqAN}pyo}{~}v?2q#{~}{qFy§q ¥4}{Çwvxo¨½vx?} {?#?yoN}`¡¢}m}moqC}q#qA
q#§q@qA?}v§¨}moq@É{ ²´yo§}vx§{ i¥w}moqb#q#N}qA4² }moqsz #{zzx`?N}{}v±?q9p{o§vo¨i{~}
m¢{ È
W
/9p0y }{}vxc{}v§¨3?§ qA4m§{?4¡¢qAq#cq#}{voq ¥ yoqb}i}moqs}N {}v| q XqA}²&y¢m
{3¢qA}yo¡¢{~}vx}moqomoqAo}wov|b¡¢qAm§{ʱwv? ²!}moq(?qA2 vxo¨}q#qÈ
W
o? }m§q{piqXqA{i·¹}w {}v|&q XqA}À¥Ê}moqK?ozxpyo}{~}v?§ ² }qApivx§{z|¸§§{zzxsq#}{voq
{qc}moqCpy }{~}vxIJ }moqF±~{zxyoqA`²(?§}{N}i}qApivx§{z|`{ }moqJp0y }{}vx²s±~{vx{¡ozxq
}qApivx§{z|4vN}`¢}{N}}q#piv§{zxAÈ
W
sa! !AaÑÅ}moq^§q@v|qS{ y§}piqA?}c²3¢}{N}U}q#p3vx§{zxvxv}v|#{zb¼moqAm§{ zxvo¨
wyopiq#vxA{zN}q#q@ ·Pv\ÈqÈ!}q#q@!}m§{}&q#§q@qA?}»{ q@{zÂ=±~{zxyoq ²´yo§}vx¢ÀÈ+m§q#qA{#"?mo%$sÝ@{$
qApiv§{z¼?Çi?§v qAq ozx`{¸¢ovÌ}qsNy§p¡2q#4²62?v¡ozxq±~{zyoq@²´4¢}{N}K}q#p3vx§{z\¥
qAzwvxo¨9?{vÌ}mopiq}vxX}92?vx¡ozxs¨q#§q#{~}q{w ±~{zyoq ·´qȨ§ÈRy§v§¨'&0¥)({
vÌ}&vx6¢Nvx¡ozq
*,+.-0/1
332? ï\íõô\üÊï\ú4Rô 0@í54=ì76úbò 2 ö@ì|ðíð78 +9-0/1
332? 1;: ì 2'<>=
+9-0/1
332? 1;?5: òô0Êíï @6ì74=íð
}{ooÊ vp{}qs¼vÌ}movxC{¨vx±qAJoqAv|v?c{wqA{z ±~{zxyoq²´p vN}qA¨qAvx
BYn
´À¥¢piq
q@qA?}&¼ Çw!?§v
qA6}m§{~}»2qA#v̸2Kp0y }{}vx?¢qA{}?!{q{9¡2q}}qAX{oo?{?ms}}moq ¸§oq
}yo§vo¨²K#§}{?}}q#piv¢{zR±Ê{zy§qAAÈ9µõJ}m¢{~} 2q#¢q@}vx±q?¥2#§}{N}9}qApivx§{zR±~{zxyoqA {q
pi v̸§q moq#q¡wUmow?v§¨i{3oqA¼Á±~{zyoqsyo§v̲´?pizx`²´p{ v|Ç`²R¸o q { vxy§·P{o}moq#
y§q# q#¸§oq §{{piq}qAÀÈ
K{zx3q# ¢qAvxpiq#N}{z¢vxw±qA}vx¨?{}vx§Kmovx¨mozxv¨?mN}q }moq²P{} }m¢{~}¢}{N}X}qApivx§{z|K}q# }
v|{o¢q@{ ²´?p }moq3¢?oyoz|{~}v? È Î oq2?vx¡ozxqq#w§zx{§{~}v?Fvx }m§{~}b}moq3wyopiq#vxA{z! }vÌÂ
pivx{~}v?`²¦}moq #§}{?} ±~{zxyoqAKvx {(piq vÃ`yoz} }{Ç0}m§{`}m§q Np0¡¢?zv|9? }vxpivx{~}v?
²}moqi}moq#so q@#È3l4moqqAzq@}v?C2q#{~} }mwy§b}q# }{§v zxJq#zxvxp3vx§{}q3²´yo§}vx§
m§{ʱwv§¨ ¼o¨b?§}{N}!±~{zyoq@#È&l4mov| vUXq#q#¢q4y§z ?p3q²´p%}m§qK²P{?}&}m§{}&}moqqA{m
¢{q@s² }moq§ qA({ ±~{v|{¡ozxqAsv|b¸§ov}qU¼movzxqi}m§q`q@{m^§{#q3²}moq`?§}{N}svx
vo¸§ov}qÈ
Î
§qU¼4{ÊC}C}{Çwzq`}mov| vÌÃ`#yozÌ}Åv|0}^vpiozxq#piq#N}{½? }vxpivÝ@{~}v?½zw?Ų´
?§}{N}s±Ê{zy§qA{s{²¹}q#b}moq{oozxv|#{~}v?C² {wJ±~{v|{~}vx^2q#{~}i·´pyo}{~}v?^??Â
~±?q#ÀÈ&l4moy§¨m ?y§vÌ}qsy§AqA²´yoz¦vc}moqA²´{piqA¼?Ç
-
£r/=¥o}mov| }q@moov)?y§q(}vzxz¦oq#q }
¡¢qs}qA}q
vx}moqµ»uU²´{piq#¼ ÇÈ
W
; [aÑipy }{~}v?§²±~{v|{¡ozxqA#§v q#q moq#qv|(q#v}m§q#(}moq#vx}{§²´?p{}vxSvN}
?§}{N}4}qApivx§{z|#¥N}moq±~{zxyoq ²!¼mov|mvx4{ piz {ʼ¼vÌ}mov
BYn@¶¥N? }moqAv4}{§Â
²´p{~}vxvx?}{o}moqA±Ê{v|{¡§zq?È
W
UT+VO!$aÑR}moq9p0y }{}vx?¢qA{}»pi~±?qA&}moq¸o q 2vxN}K² {(#N}{}vx±q ²´yo§}vx¡w
mow?v§¨({o}moqAX¢?vN} yoov²´p3zx3v`{§q#vx¨mw¡¢?m§N ²¦{ vxy§»rovÌ qAzxX²´?pÒ}moq§{qAN}
¸o q 2vx?}@¥o¼movxzq}{Êwvxo¨i}moq¡2yo {`²!}moqs}{¨q#}m§{¢q?È
ov|movxo¨¾}{}q#¨?Åvxip{ {~}S}¾oq#±qAN}i{zzvx vx±wv y¢{z|3}¾{ov zÅ¡2qA#piqJvxpivz|{
}c}moq¡2qA}~±?q#v§¨p{§ov§¨§È Yq#q¥ }moq w§{pivx3ov|moq`m§{v§¨m¢{s¡2q#q#Åy¢q -
£2/=ÈUl4m§vx
}qAmo§v0Nyoqsv|4¡§{q c{izxy§}q#vx{~}v?U²!}moqs¢?oyoz|{~}vx¢4¼vÌ}mqA2qA}4}i{3oq q¸§oq vN}qAÂ
vx vx±wv y§{z| v|}{§#qÈXl4moq(q#zxqA}vx2q#{~}?4vx{zx{ { }q vxc q# }i²P{vzxUqAzq@}{3¨vx±qA
2q#qAN}{¨?q ²R¡2qA}9vx vx±Nv y§{z¦²&qA{?mUov|moqÈ
lR{¡ozxq . Èx¤Jyopip{vxÝ#qA0}moqJ§{{piq#}q#3y§q ²´3}m§qJq#±?zyo}vx Èl4moqJvxpiozqApiq#N}{}vxÆvx
¡¢{q }moqËs vx¡zxvx¡o{ -¤ /¶È
7$# : KF@E?DC C['ME EPF@KLEVL= K8E4MK%K(4'H&C
l4m§q¸o}§qA9²X{Jv v±wv y§{zRvxc}moq0v v±wv y§{zR{o§N{mvx v±wv q vN}`}¼p{vxJ§{}#Ñ}moq
3#Vʸ§}oq@A¥?#pioy }q ²´p }moqm§{{?}q#vx}v|#R²2}m§q9v v±wv y§{zovÌ}qAz̲¥w{ }moq&S4V~¸o}§qA#¥
}m§{~}sv|¡§{?q ^{UpiqA{?y§qAp3qAN}²Km§~¼ {Uq} ²Kvx vx±Nv y§{zxb{}y§{zzxJ?z±?qA9}moq3o¡ozxq#p{~}
m¢{ ÈRµõ3}moqµ&u0vxw±q#q §?¡ozqAp²´{piq#¼ Ç¥Ê}moq9zx #{zw¸o}oq@X}{ÇqA&vxN}({?#?yoN}&}moqq#z|{~}v±?q
2?v}vx§4²6}m§q({~}}{?}4²»{ivxo¨zxq??}{?}v±?q p{§ov§¨i{
}moqs}{¨q}9m§{2qÈ
Óµ1/ / Î u !Ù
Õ / / Î u :!×
=
¯ Û « «
;A:
¬ L
M
«
ʬ
8Û
Î KÕ!»l4µ Î /Òuwµ2 qAqbqAyoz}A¥oq@}v? Q
Î
XK9»l
Î
u 7 6¬@® ¬ ;\Û`:O Û ª&® ª ;8;¬ ;\× «
¢}{N}g*¢}{N} 2oÈx¤.
{## vxo¨}`{Ës{y§v|{
zx{ʼÁ²&±Ê{v|{¢quwµËsÍF
±Ê{v|{¡§zqg+?§}{N} 2oÈ2R.
{ pizxUmoNqAvx nwBYn@
¢}{N}g+±Ê{v|{¡§zq 2oÈ2
±Ê{v|{¡§zqg ±~{vx{¡ozxq 2oÈ2
²´yo§}v?g ²´yo§}v? 2oÈ2
·P{piq{vÌ}oÀ
¸o q ¢?vN}AÑ 2oÈx¤¥ zxvoq@{z qA#q@{vo¨
{zxo¨3}m§q¨q#§q#{~}vx¢#È
( Û «A« Û!¢× Û ª&® ª ;8;¬ Ø
Î uou 2oÈR.²´4}qAqA
o`?~±?q#K²´4¸o q 2vxN}
uwK 4 l4µ Î / ® :;A:
qAzq@}vxoqAy§q ¤ÈR.
XK!KÍJ/ l Û 8P® ¬ ;PÛ<: ×# 8P®o¯ × ×k: ¬3«@¯ × ×
qAozx{?qAp3qAN} 2q#qA?}{¨?q .2
Î
±q#z|{oovxo¨3¢?oyoz|{~}v?§
u l Î XXµ1/bË ®o« × Ü Û`: ® M Û ;½® ¬ ;PÛ<:ÆÛ ¬A®o × ¬
µl4Kµ Î / qAq(q@}vx . È
+99XKK Û 8P® UÜ × «A¯ ;' ¬ ;PÛ<:ÄÛ ¯ Û<: ¬#~®o¯¬ ;!2× ½® M;A: ¢«
qAq(q@}vxc
uwX µ 7UØ: ®$ ;¯ :;¯ × « ® ;A:
!»lÕu 2oÈ2R.
ÍF{~Uw¡²»zxy§}q# 2oÈ.²R Î uwµ2
l!{¡ozqsr¢ÑXl!{¡ozq@{y²´4}moqq#±?zxy }vx²&¢?zx{ µ»u
$ c A= ;
~«#¬ Û
®.8°
E G
? D R«A¬ 8
;\× ;A:
« ;Ü ×
6q} !¡2qs}moqwyop0¡¢qA²RovÌ qAzx²M @i¥§{ zxq}9y§ q¸§§qL,?FEG D4{AÑ
L ?AEG D T EG.? D
E G ?D E G ?D =
L ?FE GD vx4p{~ vxpyop¿·P{ q Ny§{z|s¤@À vXE G ?5D (È
$ c c N × ¯ Û<: Ü Û ®$8° ½® ; ;× ¬ × ® × ® ÛE G ?5D
6q}y§
q¸§oq
v
¥w}m§{}?qA¢?
}3}moqp{~ vpivxÝA{}vx²R}moqvÝAq² EG.? D(Ñ
v
?FE GD T EG.? D
v
?FE GD vx4p{~ vxpyop$·P{ q Ny§{z|s¤@ÀvX E G ? DÈ
$ c {: ¬ × ¢Ê®o¬ ;PÛ<:Û ¬ × ¯ Û<: ¬#~®o¯¬A® : ¯ × ¯ Û<: «#¬AÊ® ;A: ¬A«
qAv¡2q vxºqA}vxº§È£o¥!}moq#N}{}{§q}qA}3A{½¡2qUvx§zxy q vxÅ}m§q?pioy }{}vx½²
}moqcvp{¨q²}moq}{¨?q}1E G ?5DÈƵõÆ}moqJ{piq}vxp3q?¥K}moqcpiqA{Ä?N}{}v?º{~}v l G A{Æ¡¢q
q@}vp{}q ÈUµ¶² }moq²´y§§}v?Sv|(§}?N}{}v±?q¥L3{ v q¸¢oq {¡¢~±?q3{qo}?p3§y }q
{ {q vqA}zxUq#}}iÝ#qA¢È
$ c 8 KÛ ¯?®$8 8 ¬ :!× «@«
l4m§q0zx #{zR¸o}oqAbvx q#¸§oq {? {zvxoq@{?p¡ovx§{~}v?F²LÊ¥
v
{ }moq v|}{§#q}¾¤²}moq
q@}vp{}q ?N}{}v?U{~}v¢Ñ
?AE G DT L ?FE GD
v
?FE GD ? n dl GD
¼m§q#ql G v| }moqsqA}vxp{~}q N}{?}vxU{}vx0² E G ÈX yoqs}}moqs}qAp
v
¥E G ?5D}qA }3¸§zxzH(¥
¼m§vxm`v|o}{}v|²P{?}²´? {`µ»uÈ l4movxq XqA} v| y§?}q#¡§{z|{¢q ¡w3}m§q}q#p n l G ¼mov|m
²´?¡§v }moqs}vx±Nv|{z zxy }v? E G T C¢È
l4mov|U¸o}oq@q#oqAq#N}{vxN}q#oq}{~}vx²}moqS?zz|{¨?qFo2q#} ²{µ»u¥4v\ÈqÈxѾoq
qA{m§qA4²´?}moq3q}s²X¡2qA}E G y§mF}m§{~}Y T W E G ?5DÈ(l4movx v|?q}{o}moqA {¨y§p3qAN}9²´
}moq9y§q9²¦piqov|movxo¨piqAm§{ov|p v? q#»}({ʱv }m§{}{zxzovx vx±wv y¢{z|X¨s}}m§q{piq9¡¢q@}
#~±qA{¨q²6}moqb}{¨?q}4m§{¢q?È»ÍJq#~±?q#@¥?{v qsq XqA}4piv¨?mN} ¡2q{3ÏqA#o?pivxÐ9#~±qA{¨q²&(¥
v=ÈqÈ»¼v}m}moq(p{zxzq@}2?vx¡ozxqEG.? D E?D4²´9{zxzJUNB¢È
7 & L MH&6F@E?DC CH E45K F@C =@?BAH =IF@KF@K LE>LE K8E4MK % K(4'MH&C
Ézxy§}q#v|{}vxc²»}moq0#yoq#N}2§yozx{}vxJ¼v}mFqA2qA} }U{ v|}{§#q q¸¢oq ?c}moqiqA{m
§{?qF·¹}moqp3q@{ v|}{¢q`² }moqUvxp{¨?qA(²9{Fq#}0²{piozxq`2vxN}ÀwvqAz }F}moqq}²}moq
