Rapport de recherche n° 3412 — April 1998 — 27 pages. Abstract: We address
the problem of asymptotic stabilization of certain configurations for the general ...
Exponential Stabilization of Certain Configurations of the General N-Trailer System David A. Liz´arraga, Pascal Morin, Claude Samson
To cite this version: David A. Liz´arraga, Pascal Morin, Claude Samson. Exponential Stabilization of Certain Configurations of the General N-Trailer System. RR-3412, INRIA. 1998.
HAL Id: inria-00073278 https://hal.inria.fr/inria-00073278 Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destin´ee au d´epˆot et `a la diffusion de documents scientifiques de niveau recherche, publi´es ou non, ´emanant des ´etablissements d’enseignement et de recherche fran¸cais ou ´etrangers, des laboratoires publics ou priv´es.
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Exponential Stabilization of Certain Configurations of the General -Trailer System David A. Lizárraga — Pascal Morin — Claude Samson
N˚ 3412 April 1998 THÈME 4
ISSN 0249-6399
apport de recherche
!" $#% &"')(* #+ , - . 0/1 $#243657# $#198:,; < =)>@?%ACB!DFEHG$AJI@KMLLN>MOP>MQSRUTV>MWX@>MY[Z!\]LAC^"RH_9YC>M`UBUaFb>Mc-W\]^ dfehgikjl9mon@pqirhsutwvxpzy|{)jv$y~}vxpzikputvpqy~{ j@
vgikj$y|ik}hszjj y~jv$t~j t~}h}My~v j+jehjehj{MU~lNm}hxpzs~|m}t|j
¡¢£w¤h¥~¢~¦¨§ j$t h xjx%vehjf}hxy~©hsqjiy~ª6t~@ik}vy~vpu«
vxt~©hpzsqpq¬twvxpzy|{y~ª6j
vtpq{y|{|rhxtvpqy~{;ª®y~ vxehj¯°±M°²³w´µ¶Cvxxt~pzsqj%vxji¸·®pº¹ j|¹%ª®y|%»$ehpuevejehpzvxehpq{h}My~pq{vy~ªhjt~eVvxxt~pzsqjpq%{hyv{hjjxt~pqsz sqytvj y~{vehj:xjt~+twszj9yª«vehj:}jj pz{h¼~jehpusqj½¾¹9¿{7~j{hjtsºÀ]vehpu+@
vji4pu{hyvÁ6tv+t~{ À vxehjxjª®y|j|Àt{{hyvf©6jVvxxt~{ª®y|ikj pq{|vxy9vehj+sut~xpqts]etpq{hj ª®y~xiÂ@
vji)¹UÃÄyw»«j¼~jÀ»«j+ehyw» vxetwvpzvÅt~{©MjƳÇ|Ç6²ÈÉ|ÊÌËk³ÍΰÏwÀtv
y|i9jy~{|rhtwvpqy~{6À«©-vehjSet~pz{j ª®y~xiÐ
vji¹Ñdfepq t~szsqyw»rvy j rj$pzik}hsqjvpqi9j¶º¼wt~@pq{h[y~{vpq{@rhy~rª®jj ©t|Ò»$epqej{rhxj«sqytsj}6y|{hj{vputs
vxt~©hpqszpzvyªvejjV}6tvpurhsut$y|{|rhxtvpqy~{¹ ÓÔÕ]Öx×Ø £wÙ¡~¦ Ú }My~{hj{|vxpqt~s[
vxt~©hpzsqpq¬twvxpzy|{;Àvpqikj¶Î¼Nt~@pq{h7ª®jj ©t|ÒMÀfehy|iky~~j{hjy|r9ª®jj ©t|ÒMÀ |j{hjxt~sPÛ$¶ºvtpqszjfvxji)¹
ÜÝ%ÞßáàâãäºÞNå¾æßáà;àºãNçNçå¾æ®äºèéêëVì;íUîïìMðUÝPñ®òó¿ôßáõåNö
Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France) Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65
, o : U « $#% Å $,Å'(* # Å, * ,;8:,P < 2 # < # :*Å $,
¡ ¦ Ûy~r6y~{p xy~{+sqjÅ}y|©hszgikj jÅsut
vxt~©hpqszputvpqy~{ jjvxt~pz{j}My|
vrj}My~rh sqj@
vgikjky~ik}My| k rh{j:¼~y~pzvrj9vt~vxt~{|v+µ jiky~|rj t{6szjt~ { ts$·JpC¹ j~¹sqj:}My~pq{|v tv
vxt|ehj jet |rjVxjiky| rhj{ j
v}t~f{ jxtpqxjikj{vfszyt~szpu rhs jx
pqjr)txpqgxj j+sqtkxj¶ iky| rhj}h j{vj½¹ «jvxgikj{ j
v%j{+ { xt~sw}t~P}sqtv%jvÀ}6t%y~{ rhj{|vÀpqs~jv%pqik}6ypq©hszj js pqxj
y|rfª®y~xikjet u{ j~¹fÛy|riky~{vxy|{vy|rvjª®y~pu rhj~À t{6Äj
vtpq{hjÄy~{h~rhtwvxpzy|{À sqj
vgi9j}Mjrv vxj)t~}h}hxyNpzi }6tkrh{
vgikj)j{ª®y~xikje6t Ì{ j| }6 tvrhpupqxrhj sqpzgjjÀxjvxvy~y|rrhvj {) t| vxtrhvtpq{{v«
vxrtw{hvxpzjy|{h{y|{t~¼|pzxjjx~j{y~{j[vpqj{@r}6! y|{hrhjpf{vx
pzvxjtszsq©j~pz¹sqpqj{vsq¹ y«t~szjji9p$j{h{y~vr6kj}6j}Miky|
jvvrhx jj ""Ø ¢¡ Ö $¥ # ¡)¦ n@vxt©pzsqpqxtwvxpzy|{)j}6y|{hj{vxpzjszsqj~À6jvy~r vxtvÄpq{vtwvxpzy|{h{tpqxj~Àhxjvxy~rh vxtwv[ehy~iky¶ |g{hj|À¼~y|p vxrhjtN¼~jÛ!xjiky| rhj¹
HÉÇhÈw±]°±6ÍCÊJ³´¾Íγ¾ÊÌ´ ʳÍCÊJȱ
# * dfejµ)¶ºvtpqszj[vxji ·®pº¹ j|¹+tÅt~
v¶ºsqpqÒ~jy|[t~
¶ÎsqpzÒ|jiky~©hpqszjy|©6y~vĪ®y|szsqyw»«j ©@Sµ {hy~{h¶Ît|¾vr6twvj vxxt~pzsqj½:et|Å©Mjj{!ire!
vr pzj yw¼~jÅvxehjF}t~
v ª®j»4~jt¹¨dfehpuÒ@pz{ yª9
vji pu)vt{¶ t pq{Fiky|©hpzsqj9y|©6y~vpuÀ;»$ehpqszjkpzvxehpq~ehsqS{hy|{hsqpz{hjt+et~xt|¾vjpu
vpu[szjt vy¼~jxSet~szsqj{h|pz{ y~{vxy~s«}hxy~©hsqji:¹F¿{iky|
v9y~ªvehj)
vr pqj9y|{-vepqk@
vji)Àp v:et|©Mjj{t~xrhikj vxetwvkjt|e vxxt~pzsqjpq9ehpzvxej tvvxehj ikp h sqj y~ªvej xjt~twsqjÅy~ªvehj}hxjj pq{h¼|jehpusqj~¹7 y~{6
j|rj{j y~ª[vxehpuÅt~xrhik}vpqy~{ pqvetv:vehjÒpq{hjiktvpu)j rtvpqy~{:y~ª[vxehjvxji0t{©MjSj}hxjx
j m pq{ ³wÊ̱]°Ï Èw²¾Ë9¹ dfehpuk»t|}yw¼|j pq y~ikj)t j rtwvxjyy| pz{tvj¿m pq{ÆvxehjS
y~¶Îtsqszj { z $ª®y~ t t~
v9»$p vxeÆy~{jvtpqsqjÀHt{ pq { á ª®y|9t~{t~©hpzvtx{@rhi©6jy~ªvtpqsqj¹7dfehjż|jx
pqik}hszj
vxrvrhxj)yªÄvxehjSet~pz{hj ª®y|i)Àft{ y~ikj
}Mjp 6)}y|}6j
vxpzj9t|yputwvxj »$pzvepzvkm re t~ ÁMtwv{jx ;t{ ehy~iky|~j{jpzvy~ªPvehjy|{|vxy|s¼|j¾vxy~«js «»$p vxeÅxj}6j¾vvy9t+ªJtikpqsz:y~ª pqsqtvpqy~{ zm À6etN¼~j©Mjj{r6
j vxy jxpq¼~j¼wtxpzy|r$
y|szrhvpqy~{vxy:©6y~vevehjvt©hpqszpq¬tvpqy~{}hxy~©hsqji ·C
jj+j~¹ ¹ q hÀ|ÀU@ÀUlhÀUÀUhÀP| Uª®y~+t:vxpzikj¶º¼wtx@pz{ª®jj ©t|Ò)t~}h}hxy|t|e; À q~ÀP Uª®y|t puy~{vpq{@rhy~r t~}h}hxy|t|e;À%t{ @ÀU «ª®y~tSe@©hxp t~}h}hxy|t|e6½¾Àt{ vejvtwj¾vxy~xS~j{hjtwvxpzy|{ }hxy~©szji0·Jjj j|¹ 6¹ %t{ vej+{ri9jy|rfy|{|vxpq©hrvxpzy|{fy~{ vej
rh©hj¾vpq{ ̽¹ § ehpqsqjStFtk»$pzvetFpq{h~sqjÅvxxt~pzsqjkpu:vxpzsqs$Á6tv:»$ehj{vehj)ehpzvxepz{h7}My~pq{vyªÄvxehjvtpqszjkpq sqytvj tv
y|i9j pq
vxt~{j:y~ª«vxehjÅt~ xjttsz!j qN ÎÀvehpupu+{hysqy~{h|jvxehjÅt|
j:»$ej{Fvehjj t~jv»y:m y~iky~xj¾m
r6jpq¼~jvtpqszjx[»$p vx#e "
y $M¶¿twszj %ehpzvxeF}6y|pz{vx¹dfej{;À;pzv©Mjy|ikjVpzi9¶ }My|xpz©hsqj9vyvt{6ª®y|i1vxehj:Ò@pz{hji:twvpu9j rtvpqy~{y~ªvej
vji pz{vyt)et~pz{hj ª®y|i)À%t~{ vehj xjrhszvx$y|©vxt~pz{j ª®y~vehpusutwvvj[sut~x$yªH@
vji:t~{h{hyv[©6jt~}h}hsqpzj ¹fdfehj+ªJt~vve6twvÄ{hy
pqik}hszj t{hy|{hputsUj@}jpzy|{Sª®y|vehj:Ò@pq{hji:twvxpqkiky jsqy~ª«vxehjj:
vji:+puÒ@{hyw»${FiktN t~y~rh{vVª®y~ vxehj:sqpzikpzvj xjjt~xe j $]y~v+vetvveje6tN¼~jkxt~pqj rh} rh{vxpzsH{yw»+'¹ &hy|y|{~rxtvpqy~{txy~r{ »$epqe:vxehj
vji¸pufy~{vxy|szsut©hsqjm pC¹ j~¹Hxtwvxpq
jHveh)j (;pqj[Äsz|j©htÄt{hÒ «y~{ p vxpzy|{@mÀy|{hjÄi:tN t~}h}hsqÅikjvxehy [jj{vxsz j¼|jsqy~}Mj ª®y~[~j{jts;y|{vxy~sqsqt~©hszj xpzªÌvsqjxÄ@
vji:À6j~¹ *¹ %ª®y~Ävehj vxxtjvy~xk~j{hjtwvxpzy|{Å}hxy~©hsqji)Àht~{ q~ Pª®y~fvejt|
@ik}vxyvpuvt©hpqsqpz¬twvpqy~{ yªt jpzxj y|{¶ rxtvpqy~{y~ªHvejkvxji)¹ÃÄyw»«j¼~jÀMvejky~ik}hsqjpzvyªHvxehjjki9jvehy i:t~Ò~jÄvejpqt}h}hsqputwvxpzy|{ vxy9vehj
jvxji:fj@vxjikjszpq{@¼~y|sz¼|j ¹UdfehjxjpqÄt{jj ª®y~[
pqik}hszjt}h}yt~ehj¹ ¿{ vxehpu}t~}6jÀU»jÅy|{
p j+vehj vt©hpqszpq¬tvpqy~{ }hxy~©szji yªÄty~{6~rhtwvxpzy|{Fy~ªfveh+j "|j{hjxt~s µ¶Cvxxt~pzsqj+@
vj,i %m ª®y|szsqyw»$pq{h zw ºÀ»«jkrj9vehpu+j@}jpzy|{Svxyxjª®jvy)vxehj:µ)¶Cvxxt~pzsqj+vxji »$pzve }My|x
pq©hsq y $M¶Ît@sqjÅep veÆ}My~pq{|v¹ § j)jehpq©hpzvt jvkyªy~{h~rhtwvxpzy|{t~y|rh{ »$epqevehj vxji $j rtvpqy~{[t{)©Mjt~}h}hxyN@pqi:twvxj Àhpq{Sy~ikj
j{j~À©@ vehj9etpq{hj ª®y|i1@
vji)¹fdfepq Ò@pq{ y~ªt}h}yNpqiktvpqy~{kpu«.r -pqj{vvyt|jvHvxehj[sqyt~sMy~{vxy~sqsqt~©hpqszpzvy~ª;vehj@
vji ª®y|i vxetwv y~ª$vehj)t}}hyNpqi:twvj
vji¹7Îv:tsu
ypzik}hsqpzjÀ«t~»«j
et~szsfjj~ÀUvxetwv9vpqikj¶Î¼wtxpq{hª®jj ©t~Ò sutN»U}hxj¼@pqy~rsz j¼|jsqy~}Mj ª®y~e6tpq{hj ¶ºª®y~xi vxji:Ht{k©6jÄr
j vyt~epzj¼~j$sqy@tshj}6y|{hj{vputs
vxt~©hpqszpzvyª«vehj
jk}t~
vxpqrhsqt~Vy~{6~rhtwvxpzy|{¹ }xt|¾vput~sUpz{vjjvyª«vehpu+t}}hyt~eSpu[vetvp v @pqjs $pzik}hsqjt{ jt|
pqsq:vrh{6t©hsqjy|{|vxy|s]sqtN»¹ dfehj9}t~}6jVpu[y~x|t{pz¬j t~[ª®y|szsqyw»¹ § j9pq{vxy rjpz{7n@jvpqy~{7kvejky~{j}vVyª«+t "y~{vxy|s vxji »$p vxe)t:e6tpq{hj ª®y~xi t~}h}hxyN@pqi:twvxpzy|/{ %Vt{ }My~pq{vy~rvÄy~ikj+}hxy~}Mjvpqj$t|yputwvxj »$pzve ret:@
vji)¹ § j
ehyw»!pz{nj¾vxpzy|{9vetvvehj+|j{hjxt~s;µ)¶ºvtpqszj
vji et~Ät:etpq{hj ª®y~xi t~}h}hxyNpzi:twvxpzy|{Ftvj
vtpq{ y~{h~rhtwvxpzy|{À%t{ }yw¼@p jkvpqikj¶Î¼Nt~@pq{h)ª®jj ©t|Ò@+ª®y~+vxehjÅsqyts j}6y|{hj{vputs6vt©hpqszpq¬tvpqy~{:y~ªMvxehjj[y~{6~rhtwvxpzy|{¹ &pq{t~szsq~À@
pqirsqtvpqy~{:xjrhs vt~j$}hxjj{vxj pq{ nj¾vxpzy|{ l6¹
0021354768:9
l
UÊ ²¾²³¯³
Èw²¾Ê̱ ³w±MÏ
]³Ë Èw±
$,* ¾ , dfej9xjrhszvxVxj}My~vj pz{Fvxehjk}hj
j{vV}t~}6j+jszy|{vxehjk}hxy~}MjvpqjVyªehy~iky~|j{hjy~rV@
vji:À y~ikjy~ª;»$ehpuetxjjt~szsqj ehjjtwªÌvxj¹ Vpq¼~j{ t{ ]¶ºvrh}hsqjÄy~ª;}6y
pzvpq¼~jÄjtsu Àvehj ªJt~ikpzsqyªUi:t}h}pz{h pq{ j@j ©@t}My|pzvpq¼~jjts St~{ j{j t~ ·½ putsqsqj t9ÏwÊÌ´z³ÍCÊJȱ È °Ê ¯ Í @¹ Vpq¼~j{t pzsutwvxpzy|{ Àt$ª®rh{6¾vpqy~{ pq ÈËkÈx¯°±]°xÈ / :È Ï~°Î¯~²°° ÊÌÍ ²x° ÎÇh° ÍÍÎÈ ·®pq{
ey~v ÈwË:Èx¯|°±M°È /:È Ï~°Î¯²x°x° ½pzª ·C~½ ¼~j¾vxy~;6js pq ÈwË:ȯ°±]°È /È $Ï~°Î¯~²°° ÊÌÍ ²x° ÎÇh° Í;Í¿È pzª pq ¶Îehy~iky|~j{jy~r6;yª j|jj Àwª®y| ¹U ÈwË:ȯ°±]°È /f±MÈw²¾Ë ³ È ÊJ³ÍÎ°Ï ÊÌÍ ³9ÏwÊÌ´q³wͺÊJÈw± puHty|{vpq{ry~rÀ}My|p vxpz¼|j j{p vxj$ikt~}h}hpq{h »$ehpue9pu ¶Îehy~iky|~j{jy~r6 y~ª j~xjjk~¹ &pq{tsqsz|Àj¼~jxt~sP
rh©6
j |rj{vvtwvjikj{vxfi:tÒ|jr
jy~ªvxehjª®y~sqszyw»$pq{h j6{hp vxpzy|{ Ô ¢ ®Ø :· á ̽ fÊ N°±-³ ÏÊÌ´z³wͺÊJÈw± ³w±MÏ)³ ÈËkÈx¯°±]°xÈ /±MȲ¾Ë «Í °kȲ¾Ê ¯Ê̱ F:È Ê +³wÊJÏÍÎÈ x°szytsqsz |¶Îj}6y|{hj{vxpqt~szsq
vxt©szjSÊ kÍ °²°°É|Ê ¾ÍV³±ÈÇh°±Æ±M°Ê ¯ xÈw² ÈÈÏ È kÍ Ê +ÇhÈwÊ̱Í+³w±]ÏSÍ ÈkÇhÈ ¾ÊÌÍºÊ N° ²°³´ ³w±]Ï Í ³wÍ Èw²³w± [Í ° È´ ÍCÊJȱ [Ê 7 °Ï ²ÈË ³Í«ÍºÊÌË:° ³ÍCÊ «° &y~ hÀt Ê̱@¯´q° ³Ê̱ Í¿°Ë ·®ehj{jª®y~vetsqszj ÀV³ ³Ê̱M°Ï Ȳ¾Ë ¾Í¿°Ë+½pq j{hj ©
*) + ,.-0/
'21
>=
?
VU
Z
U
54W! P (YX
!#"$"#"%!:3
6
+4W(9! P (9( C= ^ xt 4W5y (W¢
'
N
/
(
:/
?
4
>4
y
4W7y(W¢
.4 ! P (
I !
4W P (¢
K
GF
F
K
ut
£
x
5
F
(7
x a
z
4
P
4R=
F
5
y
Z
j
r
ut
) + ,
Z
) + , K f¡Rg
F
U
U
! P (
Y$
U
! P (
( 0
! P (
U
) + ,
0
`
`
U
! P (
! P (
X
`
GF
K
Z
[
U
! P (
ut
! P ( G
(
`
! P (
(
! P (
z
U
s) + ,
¢g
e) + ,
¢I£
W) + ,
y
B) + ,
e!
0021354768:9
Bi
|i
5y (
! P (
x
z
z
U
P (
5y (
(7
x a !
P (
y
! P (
i
U
K
UÊ ²¾²³¯³
Èw²¾Ê̱ ³w±MÏ
]³Ë Èw±
ª®y|9t~szs h¹-dfepq9ikjt~{vetvvxehjy~sqrvxpzy|{Æ»$pqszsf©Mj)y~{6{hj vxy sqpqjpq{-vxehj)
jv C C BlZ C C À«»$ey|j)y~ik}t|¾v{jxkª®y~sqszyw»9ª®xy~iÐvehj y~{vxpz{@rhpzvÆt{ }y|}6j{hj y~ª B Z ¹ &hxy~i W[j6{hp vxpzy|{ S»«jetN¼~j
+t{ +t{ Àpz{j put p $]jy|i9y|}ehpqi t~{ ¨puy|i9}6t~¾vÀhpzvª®y~sqszyw»vxetwvÄvehjj+j@pu
vxt:y~{
vxt~{|v Z :
r6e vxetwv ª®y|tsqs P
y
'
/
-
5
7y(
N
(
s4W P (.
P (&(
4
5y(
W
y
P
y j
C
I C
4 P (W¢
4
C
ZC
dfejy~i©hpz{6twvpqy~{yª$·º~½t{ · ½«pqjs
D C Z B Z C
C
4 P (W¢
4
C
P (
5y (
P (&( ¢
5y (
C
·º½
"
C
·J|½
x a "
(7
npzikpqsqt~sq~Àw©@+¼@pzvrjy~ªhvejikjt{¼wt~szrhjvxehjy|jiÀNvxehjxjjpq
vxtVy|{
vxt{v revxetwv C C C C t~{ ve@rÀt}}hsz@pq{h$vxehj{hy|{¶ jjt~pz{hfª®r{¾vxpzy|{ B Z vxy©6y~vevjxi:;y~ªvehpuj rtsqpzv 5y (
4W7y( ¢
4
oj
BZ C
7y(
»$epqe;Àhy~i©hpz{j »$p vxe ·J|½«pqik}hszpqj C
C B Z C (
4
4 5y(¢
4
(
J· |½ ¹ [{hjk¼~jxpzj[pzikikj pqtvjsqvxetwvVBFpu+t sqt|A¨ª®rh{6¾vpqy~{ À]ehj{jt{@)
y|szrhvpqy~{ vetvVxtwvpu
j C C G?
D C HB C
4W P (W¢
D C
I C
4W7y(W¢
4
x a !
(7
»$pzve B Z B]Z Ät{ C @ t~{ ve6twv$?
C
»$pqsqs%tsu
ykxtwvpu
ª®·J½«ª®y~ tsqs @ ¹ dfehj[
jvHyª pzªÌvsqjxHvxji:»$pzvekv»y+pz{h}rvxpuHy~ª]}Mjputspz{vjjvvxy+r©Mjtrj$p v«pz{szr j tk{@rhi©6jyªÒ@pq{hji:twvxpqi9y jsqyªiky~©hpqszj+xy~©Myv¹fdfehj+ª®y|szsqyw»$pq{hk}hy|}6y
pzvpqy~{
vxtvjÄ
.r -pzj{|v y~{ p vxpzy|{À@ª®y|tk
vji »$ehpqe)©Mjsqy~{hvy9vepqjvÀvyketN¼|jVt:e6tpq{hj ª®y~xi t}}hyNpqi:twvpqy~{%¹ ( £ *Ø )HØ ¡ ¢ ®Ø Hȱ ¾ÊJÏ~°²³ ȱͺ²Èw´ ¾Í¿°Ë + ·
|½ ÊÌÍ ³w±]³w´ wÍºÊ ³w±MÏ Í ³wÍ ºÊ !³w±]Ï ºÊÌÊ F³w±]Ï ºÊÌÊÌÊ "! # \ $ &%(' )' ' * Ê ³ Èw±6ÍC²È´Ì´z³ ´z°ÄÇh³wÊ̲:È Ëk³ÍC²¾Ê ° WHQ(
YHQ(
n
HJN
[
n Qm
¥
¡
P
/
(
A
A
AC54(:!
vA0 4W(
+
!
+
54
+
y
(
+
(
G4(eN
4
4] z RA4W(5
54(5Q
`
F
A04W(
@A54(6
4W7y(¢
-
=
4 P (
y
y
+
4
+
(
4]4QG!$"#"$"!94x'o(
/
@A
54(
4W(
+
4
+
\#^
+
h54
!$"$"#"!&4o'o(7¡
(
y
^ : !
\
V4
+
4
+
(
¨
î0 ï ¨
HÉÇhÈw±]°±6ÍCÊJ³´¾Íγ¾ÊÌ´ ʳÍCÊJȱ
9°±MÈwÍ¿° [Í ° È ° ÊJ°±6Í È:Í ° ³²³ Íΰ²¾Ê ¾ÍCÊ ÇhÈw´ w±MÈwË9ÊJ³w´³7È ÊJ³ÍÎ°Ï ÊÌÍ Í °Ë:³wͺ²¾Ê É ! Î Ê Ì° Ï|°Í ! : °± Í ° ÈÈw²ÏÊ̱M³wÍ¿° ͺ²³± Èw²¾Ë:³wͺÊJÈw± , ÊÌÍ Z
f6
y !#"$"#"%!&
¢
(
+
7
1
c4W!9W(
O¢
'
(]
'
¤'
+ ` >54(9! 54W!& (&(=
! ?(
7
>4W(6
¢*
54
4
AC 4 (
!
Z P '
! +
+
4
+
( +
·
~½
`
(7
5f
y ( Z
P '
G ¢ +
P
!
+
`
(
+
[7
y
7
y
`
4
4
§h ¤C!#"$"$"%! ¤'
7
s=
¤
(
¢
+
+
"$"#"
I I ¢
j7
54W!9W(6
54 V +
·
~½
!$"#"$"%! P 'o(
Z
P 'Q! ` &g{fe{O¢ ¤(
¤'
ͺ²³± Èw²¾Ë,&8 Op+Ê̱ͿÈ' ÊÌÍ ³±MÏ, 9³ÎÇ° Ê «°ÏÊ̱ ° H±6ÊÌÍCÊJȱ/ ° ± È È¾Ê̱¯ @ : °²° Èw²x° + %"$# Ȳ @ 5 ( £ Ø;*Ø J!K (;jv 3 ÀyvxetwvHvxji¨·|½%iktN+t~sqyÄ©Mjf»$pzv
vxj{t| SÅtkdtN@szy|j}t{pqy~{Åy~ª t{ tv Ày~{hjy|©vxt~pz{
=
'
N
4e¢
4 (
I£
]¢
B
5
v=
E£
4
z
A
y
o
y
+
4(5
4 ( y
`
A
`
( +
`
¢B
`
+
¹
4W(5Q `
·
|½
?
`
+
4 (
`
A
#j
! p?
z
{
(
»$pzve ! À xÀ À ÀÄt~{ ? À ? y~rh{vt©hsqjrhi:Äy~ª}My~sq{y~ikpqt~s%vxjxi:Äpq{ yª j~xjj t~{ ~À]j
}Mjvpq¼~jsz|¹VÎv pu»«jszsfÒ@{hyw»${7ª®xy~i sqpz{hjt9
vji vxehjy|·Jjjj~¹ ¹ l®½¾Àvxetwv9vehj i:twvxpzT7 ~pq¼~j{Æ© ·
~½ vxxt~{
ª®y~xik«vxehjsqpz{hjty~{vxy~sqsqt~©hsqjVvxji t|yputwvxj »$p vxe vxehj}t~pz "! # Hpq{|vxykvehjy~{vxy~s t{hy|{hputsMª®y|i "! ! @ »+¹ ¹ v¹thj ª®tikj~¹ ¿{ª®y|ikj[vxr pqjÀ6jjª®y~Äpz{
vxt~{j á t{ q ºHÀ > @ »ft~$ehy
j{t~fvxehjikp ¶º}My~pq{6v > Vy|{)vehj xjt~twsqjÄy~ªPvehj[sqt|v«vtpqszj©Mjt~rjp v t~
vxjpqt~{y@y~ pq{twvxj«y~{6vxp vxrvjVt+Á6tv«y~rhv}hrv«ª®y~«vehj vxji)ÀMve@r[ªJt~pzsqpzvxtwvxpz{vejvxxt~{ª®y|i:tvpqy~{yªvehj9iky jsUpz{vxyvej9et~pz{j ª®y|i)¹+Ãyw»j¼|jÀ »$ej{vxehjVehp ve y $]jv«t~jVtsqs]{hy~{h¬jxyt~{ µ hÀvehj+@
vji¨jt|
jHvxy©MjVÁ6twvÀ j}hxpq¼pq{hI > y~ªvxehpuÄ}6jputs;ikjt~{hpq{h¹fÄ[
ehyw»${ ª®rhvehjÀMtk}ht~¾vxpqts%t ¼wt{vxt~~jyªvej}hxy~}My|j t}h}yt~e pu«vyktsqszyw»vxehj+
jszj¾vxpzy|{yªUt{Åt~©hpzvtxk}6y|pz{Gv > @ twvvxt~ej vxy)³± [yª;vxehj¼~jepqszjpq{@¼~y~sq¼~j pq{ vxehjy~ik}My|p vxpzy|{:yª;vxehj[vtpqszj«@
vji)¹ § jV»$pzsqsMve@r
rh©6
j |rj{vsq:t~x
rhikjÄvetJv > @ pu@j vy ¼|jehpusqj ª®y|
y|i9j xµ |¹ dfehj
vxtvj¼~j¾vxy~ pu j{j ©@ E 0! Q! (
C(
y
6
6
?
¦N
TgC!#"$"$"%!
g
`
*4
KK
K 4
4
KK
ML 4
0021354768:9
4%
=
NL
O QP
ѵ
{
·
|½ O
( `
UÊ ²¾²³¯³
Èw²¾Ê̱ ³w±MÏ
]³Ë Èw±
PM+ 1
β
dy PM
PG y jC iC
dx
PC
C s
C0
pq~rhxj &
: -?-*+ &$ M7 N9# 3)
j
fd ejy|{vxy~s;pq{h}hrv À]»$pzve j{hyvxpz{vejt pqry~ªvehjkt~ fª®xy~{v[»$ejjsºÀPt{ Ät~jÄvehj9²È´Ì´ Ê̱¯Vt{ ¾Íΰ° ²¾Ê̱¯Ä¼~jszypzvpqj«yªPvxehjt ª®xy~{v«»$ehjjsº¹ § p vxeÅvxehpq«{hy~vxtwvxpzy|{;Àvehj iky js]ª®y~$vxehj+t$»$pzveµ vtqp sqjÀ@y~©hvxtpq{hj pq{vehjÄ}h}6j{ pzPÀhpq
h
QV
z
#j
4] z RA4W(5
»$pzve
`
·
N½
"$$ @ = ! $$ @ @ $$ ¹ $$ $$ @#"$ ¹ @" "$ " %$ ^
^
^ 8
¢
^
A4W(
¢
w4 !
%'&)( & +*,
$
4W(
(
4(
-(# & /.
¢
=
++ ++
^
++ +
^
y
-
5y !#"$"#"%!9y !#gG(
(
^
^ 8 ^ 8 ^
¢
8
++
(
8
8 ^
)&
* ++
^
^ 8 u^ w4 ! 54(6¢
4
Q
(
^
%'&0( & /.)1 32 , 45,
`
$
(
4W(
T(
!
¨
î0 ï ¨
HÉÇhÈw±]°±6ÍCÊJ³´¾Íγ¾ÊÌ´ ʳÍCÊJȱ
|
t~{ vehj+xjrhxpq¼~jVj}hxjx
pqy~{
*
*
%'&0(
Z
/* +*
Z
2
Z
% )& ( #(
4W(6
C $ #(
$
$4
G4W(6
%4 Z
Z
(
(
·
|½
µ xµ dfej}My|
vrhxj
vxt©pzsqpz¬twvxpzy|{}hxy~©hsqji t h jj ehjj«y~{6
puv;pq{+{ pz{htfª®jj ©t|ÒVy~{vxy~s|»$ehpue sqyt~szsqÅ
vxt©pzsqpz¬j$y~ikj jpqj }My|
vrhxj.% ¹ ÃÄj{jª®y~ve%À~»jt~x
rhikjve6twv4;kpuHy|{
vxt{v¹dfehpuikjt~{Uve6twv#Åpujpzvejt
vtpq~evszpq{hj$y~Ht pzsqj~¹{ jvehpuUt~x
rhik}vxpzy|{;ÀNp vUpupqi9}szj«vy[¼~jxpzª®[vxetwv$·w½;et~%vehj«ª®y~xi¨· |½Py~ª6xy~}My|p vxpzy|{ hÀP»$p vxe -t{ t~{tsqvputN»ftNª®y|i4y|{~rxtvpqy~{[
revetv1; ~¹ Uy~xjyw¼~jÀ t~{ t~jÄ©6y~vepq{ j}6j { j{vfyª wÀ@
yvetvy~{ pzvpqy~{ ÎÊ pq{:vej[}hxy~}My|pzvpqy~{kpq«ikjv¹HĪ®y~«y~{ p vxpzy|{ ÎÊÌÊ wÀ~pzvi:tNy|i:tN{yvH©Mjtvpuj k j}Mj{ pz{h+y|{vxehjjsqj¾vxpzy|{kyª ¹ &hy~pq{
vxt~{j|À~y~{jxjt pqsz ¼|jxp 6jve6twv[t~{ }6yvxrhxjyªUvej+ª®y~xi HÀ»$ejB{ ; À6y~xj
}My~{ pz{h9vxy:vehj t~j»$ehjj9tsqsU¼~jepqszj[t~j9tsqpz|{hj ÀPxtwvxpq
jÄvepqy|{ pzvpqy~{;¹+ {twvxrhts |rj
vpqy~{»$epqevxehj{ t~pujpq»$ehjvxehj$vxehjxj+jpuvy~vehj$}6yvxrhxjf»$ehpuetsu
y:xtwvpu
ª®vepqy~{ p vxpzy|{;¹dfehjª®y|szsqyw»$pz{ xjrhszv$~pq¼~jftk}My|p vxpz¼|j+t{»«jvy9vehpu rhjvxpzy|{;¹ «Ô 7¤ %Ȳ³w± ȱ ¾Íγ±Í ² w³wÍ ² ° ; x°´zÈw±@¯Ê̱@¯Í¿È ÈwË:°+Ê̱6Íΰ² N³´ E; 7; ȱͿ³wÊ̱6Ê̱¯ O HÍ °²x°°xÉ|Ê Í ±F
$F
F
t
F
4
t
C!:y !#"$"$"%!:y(
O
y
t
7F
(9!#"$"#"%! 4x' (
29¢
G !
G(
!
¤(
F
`
N E; ; ÊÌÍ ³w²ÊÌÍC²³² Èw±]ÏwÊÌͺÊJÈw±^º ÊÌÊ ÅÈ: ²È¾ÇÈÊÌͺÊJÈw±/ÅÊ )³wÍºÊ «°Ï Èw²) ¾ÍÎ°Ë 8 ²xÈÈ:+Ê̱SÍ ° Ç~Çh°±MÏwÊ É w ¹ dfehj
jvy~ª@}6tvpurhsut}6yvxrhj }6y|pz{vj y~rhv%pz{vehpu%sqjiki:te6t~;pq{+ªJt|¾vtÄ
pqik}hszj«~jy~ikjvxput~s pq{vj}hxjvtwvxpzy|{;¹¿{ jj ÀvehjÄvtpqszjvxji¨t~{ikyw¼~jÄt~szy|{h+vejVpzsqj # y~{hsqk»$ehj{tsqs6¼|jehpusqj jxxpz©Mjpzrsqt~}6twve6y~{6j{vxpuHvxyU# ¹Udfehj$y|xj}My~{ pq{hVy~{6vt{v¼|jehpusqj¶ºvy~¶º¼|jehpusqj«t~{h~sqj :txjvxehjxjª®y|j ~jy~ikjvxput~szsqy~©vtpq{hj © xtN»$pq{h-vxehjjF}twvxe)t{ vehj vt{h|j{vpq{h9szpq{hjtwvfvej+}6y|pz{vx6> xµ x¹ ¿{y~ j«vy9}hxyjj À@»«jVir6vf¼~jpzª®9vetv$y~{ p vxpzy|{ Î ÊÌÊÌÊ Ä yªUxy~}My|p vxpzy|{ puftsu
y9tvpu6j À pº¹ j~¹Vvetv[vxehj9}tpq "! # fpqy|{vxy~sqsqt~©hszj|¹*&y~ ; hÀMvehjª®y~sqsqyw»$pz{h }hxy~}My|p vxpzy|{~rt~xt~{|vxjj 4
=
h
!9y?! 4
(9!#"$"$"W! 4
%(9(
'
L
!
E
4
Z
4
fc
?!$"$"#"%!&6(
Z
5f6gC!$"#"$"%!
gG(
`
vxehpu$}hxy~}Mjv~¹ $ &% ' ' ) * ( £ *Ø )HØ ¡ ¢ ®Ø fÊ w°±D ÊÌÍ :Í °Ç³Ê̲ ! È ¾Í¿³wÊ̱]° Ï ²ÈË 8 ÊÌÍ ; HÊ Èw±Íº²È´Ì´z³ ´z° ²xÈ:È +Ê̱SÍ ° Ç~Çh°±MÏwÊ É w¹ Sft~j y|{)vehpuÄxjrhszvÀ6y~{hjt{pq{¼|y~Ò|jy~{vpq{@rhpzvt~|rhikj{vxvxy j rj+vxetwvVp ª ;hpq[
i:t~szs j{hy~r~et~{ p $]jxj{vVª®y|i ¬jxyÀMvxehj{7y|{ pzvpqy~G { ÎÊÌÊÌÊ 9yªHy|}6y
pzvpqy~{ ÅpuV
vpqsqsHtvpuj ¹dfehj v
n
n Qm
r
+
ut
=
0021354768:9
E
!
+
(
4
s
2
C!:y !#"$"$"%!:y( y
=
#2N
y
/
s
+
!
+
(
^ !
\
\#^
+
N
UÊ ²¾²³¯³
Èw²¾Ê̱ ³w±MÏ
]³Ë Èw±
}y|©hszjiÐy~ª jvjikpq{hpq{h!³w´Ì´¼Nt~szrjy~ª1;ª®y~Å»$ehpqevxehpu y~{ pzvpqy~{ pu:ikjvpqÅehyw»j¼~j:iky~xj pq{@¼~y|sz¼|j ¹ Ã[tN¼pq{hjvt©hsqpu
ehj ve6twv%vxehj|j{hjxt~s|µ)¶ºvtpqsqj%vxjit~{©6jt}h}yNpqiktvj Àpq{+vxehjj{6
jHy~ª W[j6{hp vxpzy|{)hÀ©@tet~pz{j ¶ºª®y~xiÂ
vjiÂtwvfvehj+}6jpz6y|{~rxtvpqy~{«}6y|pz{vxj y~rvfpz# { (;jikikt |À;»jkt~j9{hyw» pq{Fvehjk}My|p vxpzy|{ y~ªt~}h}hsqpq{hxy~}My|p vxpzy|{Ækpq{Fy| j[vy)j@vj{ vyvepq+vxji }j¼pqy~r6+ª®jj ©t|ÒF
vxt~©hpzsqpq¬twvxpzy|{ j
rs vy|©vxt~pz{hj pq{ vehj)t|
jÅyªÄet~pz{hj ¶ºª®y~xi vxji:¹ § j »$pqsqs;pzsqsqrvxxtvjVvepq$}My|xpz©hpqsqp v©@:6x
v$jtsqsqpz{h:t9xjrhs v$pq{ zN º¹ ( £ *Ø )HØ ¡ ¢ ®Ø [ ( £ ]Ø )\K ]°´z° Í +²°³w´ Èw5± ¾Íγ±Í Í ³wÍUÍ °HÇÈ´ w±MÈ Ë9ÊJ³w*´ > &)&(& Ê ² ÊÌÍ È± ¾ÊJÏ~°²Ä*³ °Í%È °Ê ¯ Í N° ÍÎÈ7² $³±MÏk³ 7È ÊJ³ÍÎ°Ï ÈËkÈx¯|°±M°È /ıMȲ¾Ë ' : °± Èw² )´z³²C¯°°±MÈ ~¯ ³w±MÏ.@ Í ° Èw±ÍºÊ̱ È /VͺÊÌË:° Çh°²¾ÊJÈÏwÊ È±Íº²Èw´ n
n Qm
p ¥
'
B C(
9gC!:£
`
I£
`
=
!$"$"#"%! ¤'
¢
! P (
F
>=
t
`
0
F
GF
GF
oE¢Og
` ` ¢?!$"#"$"?!:£T(
¢s!9£
` ?
E
'
T'
£T
`
?F
+(
¢
¤
¢
0'
i
( 0(
P
GF
(h X
Z
'Z
[
K
¤7£T(6 (
_
8
K
)(#
P (
Q (
·
|½ $ ! * #" [¯~´zȳ´Ì´ °ÉÇhÈw±]°±6ÍCÊJ³´Ì´ Í¿³ ÊÌ´ Ê°Í ° wÈ ²¾Ê ¯~Ê̱!È Í ° ³ Ê̱M°Ï Ȳ¾Ë
! P (
¢
i
0
(
`
Z
'Z
! P (¤X
Q P (
[
Z
Z
'
8
ÊÌÍ @ @ ¾Í¿°Ë Q «y|{
p j{hyw»vehj[~j{hjtsµ¶Cvxxt~pzsqjHvxji »$p vxe µ O¹ (;jvVÅ ©MjÄt~{9yª]vxehjÄ}My|
vrhxj }My~pq{vj y~rhvpq{ (%jiki:tÅV
r6eve6twvfvehjV}t~pz ! &% ' ' ) pqfy~{vxy~sqsqt~©hsqj~¹5S«:t~}h}hsqp ¶ twvxpzy|{yª%xy~}My|pzvpqy~{S|À|vxehj[y~{vxy~s À@y~©hvxtpq{hj ª®y|i ·½H©@9vejVet~{h~jÄyª%y@y| pq{tvj }Mjpzj pq{)y|}6y
pzvpqy~{Àsqyt~szsqj}My~{hj{vputsqszÅ
vxt~©hpqszpq¬j6 ¹ $ : D@!pq+hj vyvej:sqt|v+vxxt~pzsqj " »$pzvey@y~ pq{twvxj -. . 1 x¹Udfej j
pqxj }My|
vrhx9j ) t{ vej[pq{hpzvputs]vtwvjV¼wtsqrhj txj jvt|ª®y~sqszyw» MÊÌË ´q³wͺÊJÈw± 8) * hÀ +' -, -, ., ., -, x¹ * MÊÌË ´q³wͺÊJÈw± /-) ., (/., 0., 1, 2% 0.', À * =
y
'
y
i
K
K
+
!
+
(
4
`
h \
^# !
+
\^
o4W! P (
(
4
*
4]
4w7y !:y ! 4
y
%(:!$"$"#"! 4
s
y
'
(&(
wg g
Z
Z
f g0!$"#"$"%!
fL|!#"$"#"%!
B
^
#j
!
(6q5y !#¢gG(
4
4
gG(
vF
4]
y
4oLh7y ! !9y
!9y
!:y
!9y
G!9y
(
vF
4]5y?!9y !:y
!$g " g
!#g " y
!#g" y g ! "
(
¨
î0 ï ¨
HÉÇhÈw±]°±6ÍCÊJ³´¾Íγ¾ÊÌ´ ʳÍCÊJȱ
+' -, -, ., ., -, x¹ dfehj|t~pz{ pz{vxehjª®jj ©6t~ÒsqtN»¨·|½$t~j~pq¼~j{)©@ .% O O O % 0 À »$ejxjt~ 'kt{ h¹&pq{t~szsq~Àvehj¼wt~szrhj pq{@¼~y|sz¼|j pz{)vxehj»jpq~ev¼~j¾vxy~ fet~ ©Mjj{Åehy
j{j rt~shvy h¹ &pz|rhjt{ l
ehyw»vxehjÄpq{hpzvputs]t{ Å jpzxj }6yvxrhjHy~ª;vehj pqirhsutwvxj
vji)Àht|f»«jszs%t|vehj}tve jpq©6j ©@ >A@f¹ *
4oLh7y ! !9y
!9y
!9y
G!9y
!#"$"#"%!
@
!:y
h"
(
(
'
5y?"
¤!$g0" x! x" ! " ?! " ¤!: " (
v£
*¤5£T(
gI vB¢§
8 6 4 2 0
−15
−10
−5
0
pq~rhxj ( .3 ) # . 3 &
5
10
.'07 .39# .07 &B&'( & 3
j
& N N9# "9#,.-8"
10 8 6 4 2 0 −15
pz|rhjVl &
?j
−10
−5
0
5
10
% .3 . '07 :33/ .-7 - !" 3 :
¾ #%$"&('*),+.-/'10 230546-/7$98:';2$=+.-/';?@
4
Z
s54
!
( 65fd
Z
gC!$"#"$"%!
gG(
`
$
`
4 z
z
z
z
oj
%
(
#
(
$
#(
(
!
(
%
(
s
Z
Z
4 z
!
z
Z
z
!
Z
(
Z
6 4 z
!
s5f
Vf
Z
z
!
z
Z
(
gG(
`
Z
z
Z
z
Z
`
¢
Z
z
Z
z
Z
Z
z
Z
Z
¢
Q
Z
Z
4 z
(
Z
$
`
¢
(
"
(
Z
%
!
(
Z
z
(
Z
Z
$
z
(
y "
`
Cj
4 #( 4 %'&0( Z
%"
g
y
y
(#
¢
g
%'&)(
Z
Q
(
*
Z
z
z
Z (
%'&0( ' % 0 & ( )#( %" (
Z
Z
¢
Z
¢
Z
4 z
z
Z
!
! z
z
Z
%
2 `
Z
Z
y
Z
#( %'&0(
Z
Z
$
(
(
z
Z
Z
Z z
%'&0( )(# C (
$ % &))( (#
*
Z
*
(
(
Z
(
2
Z
¢
!
%
(
8
_
(
Z
Z
#
(
Z
*
Z
(
(
_
4 z
- %"
Z
z
z
Z
-
¢gC!#"$"#"%!$gG(:!
f*
g0!$"#"$"%!$g
`
Z
(
Z
Z
(
(
% )& ( (
#
¢
2
(
Z
z
Z
z
_
g0!$"$"#"%! Z Z @ 4 z
2
Z
% Z
(
f
L5f
Z
(
(
Z
%"
Z
·ºwl½ µ xµ ·º ~½ µ x¹Ñd%y|~jvehjÀvehpu:i:twvxpzÆj rtvpqy~{t{ ·C |½kt~szsqyw»Âr fª®y~ µ |¹$ªÌvxj+
y|ikj9pzik}hsqpz6tvpqy~{À]vehj $
Z
4 z
- %" Z
%'&)( )(
(#
%'&0(
Z
%
$» pzve À vxy j¼~jszy|}vej9j}hjpqy~{ xjrhszvpq{hkj}hxjx
pqy~{6«t~j
*
Z
Z
(
(
4 z
z
(
Z
*
Z
z
_
Z
( Z
y
%" Z
Q
Z
$
»$epqepz{vxrh{)@pqjs 4 z
¢
Z
_
_
(5
(7%
z
µ
f
xµ
gC! !$"#"$"%!$gC( `
Q
¨
î0 ï ¨
HÉÇhÈw±]°±6ÍCÊJ³´¾Íγ¾ÊÌ´ ʳÍCÊJȱ »$pzve
À 9
L
h CG!$"#"$"%!
% &)(
Z
Z
(6
$
(
Z
(6
%
Z
(
j
(
(
`
8
8
_
(W¢
8
_
Z
$
8
_
Z
C $ %'&)( $ _
%'&0( (#
C $ #( $
(
(
Z
Z
t{
(7
(
Z
(
(
( Z
(
µ xµ
f6
!
(
¢gC!#"$"#"%!$gG(:"
[ rhikpq{hÅvxehjk}6y|pz{v > @ hj vyvej!¶ºve ¼~jepqszjª®y~+y~ikj µ À]vehjk{hjv
vj}y~{6
puvfpz{j}hjpq{hkp v$¼~jszypzv > @ »$p vxe)j
}Mjv$vy + |¹dfehpupu$jt pqsqÅt~y~ik}hsqpu
ehj ©@)twvvxt~epz{h t tvj
put{ª®tikj6+ , > , V , X , @j y~{vxehj!¶ºve¼~jepqszjt~{ y|pqj{vj y+vxetwv«vehjV}6y
pzvpqy~{:y~ª > @ »$p vxexj}6j¾vvxyP+ , ©6jV~pq¼~j{:©@ > @ , . V , .)1X , ¹Äpz{hvehj sqt|puts]j@}jpzy|{ >D@ >, > @ , , > @ , À»j~jv
N
z
!
!
z
z
`
C(
@@ 4 z
,,
'% &)(
( , , +.+. ¢
z
Q
(
$
`
^
`
`
4 z
z
g
`
z
TgC!$"#"$"Q!
>
¢ ^
(
¢
%'&)( , +.01 (
, +.01 $
(
%
(
, z
"
%jv$rf{hyw» pz{vxy rjÄvxehj+rhx¼~j # t{ pzvx$t~xy@pqtvj &h {jvª®xt~i9j+t~{ vxehj{{ vejVj}hj¶ pqy~{Vª®y| ~À t{ =·C
jj+&pq¹Å|½¾¹ tsqsqpz{h *C vehj:y|pqj{vtwvpqy~{ yª:VC!»$p vxe7j
}MjvVvxy V t{ r6
pq{hkjsqjikj{vtx:Òpq{hjiktvpuÀh»jV|jv ^
(
z
z
z
z
B z ¢
@ %'&0( C @ (
C H@(# *C %@ %'0& ( ,C ; 1
4 z
(
Q
z
(9(
`
4 z
d(
z
d(
`
z V
W C( 0 z "
pq{tsqsq~À©F}My|pz{h = , C t~{ szjv
vxpz{hvehj vtwvj:¼|jvy~ -©6j j6{hj t|+pz{Ñ·
½¾Àvehj t~©6yw¼|j[j}hjpqy~{ft~{ ©Mj+xjtxt{h|j vxy9|pz¼|jVvehjy~ik}hsqjvjiky js«·N~½¾¹ &
F&/0054
054 $I
!#"$"$"%! B¢
Qj
!
y
`
4
¢
g
! L L L
G
[
!
`
y
!$"$"#"%!
¤(
`
*f6
! ,
,
G
&¢gC(
,
4 ,
L `
N , 4 ,
µ
!$"$"#"%! `
#j
Àht{ `
`
! L ,
[
[
,
G*¢
2 ,
4
L
`
! ,
, 45,
,
,
g
¢
g
*f6
`
y
[
! L L
Z