HAL Id: inria-00071818
https://hal.inria.fr/inria-00071818
Submitted on 23 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,
Stability and Unstability Matrices for Linear Evolution Variational Inequalities
Daniel Goeleven, Bernard Brogliato
To cite this version:
Daniel Goeleven, Bernard Brogliato. Stability and Unstability Matrices for Linear Evolution Varia- tional Inequalities. [Research Report] RR-4768, INRIA. 2003. �inria-00071818�
ISRN INRIA/RR--4768--FR+ENG
a p p o r t
d e r e c h e r c h e
THÈME 4
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Stability and Unstability Matrices for Linear Evolution Variational Inequalities
Daniel Goeleven — Bernard Brogliato
N° 4768
March 2003
1
2% 4356 "78/ "
9:;2<>=@?BADC=E?F=HG5=@;JI@KML=ENO;P:NOQJLNOC5R?F<S:UTVC)W
XZY\[]8^_`badce].f\gih&jkcmlEn^j"lHopjkcm]8ciqrhsjrcelHn
t ^qrudqvjr[w]8^wq"xlE]8o\gm^yp^wq
zM{rlH|}^jB~!cmolHo
BhsoUolE{vj t ^{k^wxY\^w{kxYU^n_dsH `hH{kxYDsEH`bEoUhHH^wq
w&\HH XZY\ceqMoUhso^{ t ^Ohsgiq2"cjkYjrY\^BxYUhH{khExjk^{kceqkh&jkcmlEnlsjrY\^BqvjkhH\cegmcmj}uhHn t fUnUq}jhs\cegecj}u]8hsjr{kc
x^wqMlH{ZhxgihHqkqMlHf\n\cegehsjr^{hsgegeuxlEnUqvjr{hscen\^ tt udnUhH]8cexwhsgqrupq}jk^]qw E{k^o\{k^wqr^n@jk^ t hHq¡gmcen\^Ohs{¡^w¢HlEgmfpjkcmlEn
¢&hH{rcih&jkcmlEnUhsg2cen\^w£@fUhHgmcmjrce^wq0¤>¥¦M§©¨vª«2adfUxY¬qvupqvjr^w]8q.xhsn¬hHgeqrl^0qr^^wn)hEqhDqvlE{vjlH t cm5^{k^n@jrcihsgMcenp
xgmfqvcelHn dlE{®¤¯cmnqvo^wxcehHgxwhHqr^wqª¡hEq¡gecen\^whH{ZxlH]8o\ge^]8^n@jhs{kcj}u8qvupqvjr^w]8qw d"Y\cixYcenjkf\{rnhs{k^©hxgihHqkq¡lH
Ydud\{kc t t
udnUhs]8cixhHg2qrupq}jk^]qw«.¦Py\hs]8o\ge^wqqrY\l&jkYUh&jjkY\^q}jhs\cegmcmj}uDls°jrY\^8f\nxlHnq}jk{khHcmn\^
t
qrupq}jk^]
hHn
t
jrYUhsjBlsjrY\^xlHnUqvjr{hscen\^
t
qrudqvjr^w] p]8hVu
t
{hHqvjrcixhsgegeu
t
c5^{O«P§Mhs{kcelHfUq"x{rcmjr^w{rcih8hs{k^©o\{klHolEqr^
t
jrl
xYhs{hHxjk^{kcm±w^BjkY\^q}jhs\cegecj}u0lE{ZjrY\^cenUqvjkhH\cmgecmj}u0lsP¥¦M§©¨«
²D³@´5µk¶.· &¸H ¥u@hso\fUn\l&¢¬q}jhs\cegmcmj}uH ¡f\n\cegehsjr^{hsgZxlEnUqvjr{hscenEjq ¡¢VhH{rcih&jkcmlEnUhsg°cmnU^w£@fUhsgecmjrce^wqw ¡xlEn@¢E^y
hHnUhsgeupqvciqw @Ydud\{kctt udnUhH]cixqw \xlEol@qvcmjrce¢H^]h&jk{rcix^Oq pqvjkhH\cmgecmj}u]h&jk{rcix^Oq df\nUqvjkhH\cegmcmj}u]h&jk{rcix^Oq«
¹Mº»¼½º¿¾°ÀsÁÃÂVÄÅÆ}Ç>È>ÄɿʩËÌ\ÍdÎZ»ÃÏ}ÐVÂOÄÑËÂ@ÀHÒOÎÄÑÂÉ>Ó¿ÔÆ}ÂVÄÑÈrÀVÕÖkרØOÀsÙ&ÇFÎÂVÚ}ÆÀHÔ2ÎÂVÄÑÆ}ÛiÜÝËÆ}ÛÑÆ}ÅÆ}ÂsÞÐOÂVÄÅwÓiÇ>Æ}ÐVÂVÄÑËÂEÜÌeÇ
ß
ºà»º¿¾á»ÃâVãÂOÆ}Ói¾ÛÑäsÆ}ÈrÀåsº»Òæç½ËÂÉ>èsËÂVÂVËÉvÀéêêëÎ}ÅÆ}ÂwÐVÆìVÆÛií¼ÐVǯËäsÆÀîïîî×4ÒOÎÄÑÂÉ>Óiº¿ÈFð"ÄÑÆ}ÇvÀñÙ&Ç>ÎÂVÚ}ÆÀ
ò ÆvǯÂ&Îǯì@Üò ǯËóÛÑÄôÎkÉFËÞÄÑÂVǯÄôÎÛÑäsÆ}ÈrÜÌmÇ
,®% " "á ". "+ 78/ "
^oUhso\ce^{xlHnUx^{kn\^.gih6xwhs{hHxj{kciqrhsjrcelHn t ^gehqvjkhsUcmgecjhsf qr^nq t ^¥ÃuEhsoUf\n\l&¢5 t ^wq
cenwEhsgecmjwq¢&hs{kcehsjrcelHn\nU^gegm^Oq.gecmnwhsce{k^wq t udnUhs]8ci£EfU^wqw«ñ^6jr^wgeqqrupq}jk[o\]8^Oq.o^f\¢E^n@j0hsfUqkqrcjr{k^6¢dfUq
xlH]8]8^ t ^wq¡xhHq2ohs{rjrcixf\gecm^w{kq t ^Bqvupqvjr[w]^Oq t ^BxlH]8o\g]8^n@jkhH{rcmjE slHf t ^OqPcenUxgefUqrcmlEnUq t cmw{r^wn@jrce^gegm^Oq«
©^wq^yphH]8o\gm^Oq.cegegmfUqvjr{k^n@j8gm^Oq t c{k^nx^wq^wnEjk{r^6gehëqvjkhsUcmgecj t ^wq8qvupqvjr[w]^OqqkhsnqxlHn@jr{hscen@jr^wqw P^j
x^gegm^ t ^OqBqrudqvjr[w]8^wq"hV¢H^Ox©xlHn@jr{hscen@jr^Oq°fUn\cmgih&j{hsge^wqw«
·
O
µ
a@jhs\cegmcmj
t
^Z¥u@hso\f\nUl&¢ VxlEn@jkhs{kcenEjk^wqÃf\n\cegehsj{hsge^wqw VcmnEhHgmcmjOqâ&hH{rcih&jkcmlEn\n\^gege^wqw VhHnUh&
geupqv^xlEnd¢H^yp^E t udnUhH]8ce£@f\^®Ydu@U{rct ^H d]h&jk{rcix^OqZxlHolEqrcmjrce¢H^wqw @]8hsjr{kcex^wqZqvjkhsUgm^Oq d]h&jk{rcix^Oq¡cenUqvjkhsUgm^Oq«
%
3Ã2%/6¡%
XZYU^qvjkhH\cegmcmj}u0ls2q}jh&jkcmlEnUhs{ku0qvlEgmf\jrcelHnUq!ls t udnUhs]8cixqvupqvjr^]q"xlHnUqvjrcmjrfpjk^wq"h¢H^w{ruce]8olE{vjhsn@jZjrlEo\cex
cen&BoUo\gmce^ t h&jrYU^]h&jkcexwqBhsn t ¦¡n\Hcen\^^w{rcen\«¡¨Sjñciq"!^geg'dn\l&"njrYUhsjBcmnjkY\^.xhEqv^lHMh8gehH{rE^xgehEqrq
lH©n\lEn\gecmn\^Ohs{ t cm5^{k^n@jrcihsg"^O£Efh&jrcelHnqjrY\^qro^Oxjk{rf\] ls)(gecmnU^whs{kce±^ t (0lEo^w{khsjrlH{q t ^jk^{k]cen\^Oq8jrY\^
¥ÃuEhHo\f\n\l&¢ qvjkhH\cegmcmj}u lHBhsn)^w£@f\cegmce\{kcmfU]«+*ñl&°^w¢H^{O Ã]hHn@u cm]8olH{rjkhHnEjo\{rlE\ge^]qcen¬^n\Ecmn\^w^{kcmnU
¤>qv^w^,.-0/012,Ñ3-12,E012,H415,H41¿ªBcmnd¢ElHge¢H^cen\^w£@fUhHgmcmjrce^wq©cmnjrY\^wcm{®]h&jrYU^]h&jkcexwhsglH{k].f\gih&jkcmlEnhsn t xlHnp
qr^w£@f\^wn@jrgeuDol@qrqr^wqkqñcen@jr{kcmnqvcix.nUlHnUqr]8l@lHjrY\nU^wqkq«76\lE{®jrY\^Oqv^gehEq}jxhEqv^OqBjkY\^£@f\^wqvjrcelHn ls°qvjkhH\cmgecmj}uDceq
]fUxY)]8lH{k^8xlH]8o\gecexwh&jk^ t jrlD^cmnd¢E^wqvjrceEh&jk^ t hHqcmj.ciqjrY\^6xhHqr^8cmn)E^n\^w{khHg2lH{Ydud\{kctët udnUhs]
cixhHg¡qrudqvjr^w]q qv^w^^H«U«8,-19,@01:,H;19,Ñ419,;1S«<&Bn¬cen@jr^w{r^Oq}jkcmn\DxgehEqrqlH!fUn\cmgih&jk^{hsgegmu xlHnq}jk{khHcmn\^ t
t u@nhs]8cexwhsgMqrupq}jk^]qxhHn ^{r^wo\{k^wqr^n@jr^ t f\n t ^{jkY\^8lH{k]hsgeceqr] lsZ¢&hs{kcehsjrcelHnUhHgcen\^O£Efhsgecjkcm^Oq Ãqr^^
^E««2,=-0>41F«P§MhH{rcih&jkcmlEnUhsg5cen\^w£@fUhHgmcmjrce^wqZhH{r^"ct ^geu0fUqr^ t cmnhsoUo\gmce^ t ]h&jkY\^]h&jkcexwq"hsn t ¢&hs{kcmlEfUq@?U^gt q
lHÃqrxcm^wnUx^ñ"cjkY6hsoUo\gmcixhsjrcelHnUqMjrl^wYUhV¢dcmlEf\{MlslEgmceHlEolEgmciqvjrcix"]hs{A'H^jq Ef\{kUhsnjk{khHnUqrolE{vjh&jrcelHn8n\^jv
!lH{A'pq jr{h;B0xn\^j}!lH{A'pq 5cen@jr^{knUhsjrcelHnUhHgÃjk{kh
t
^H hHH{kcexf\gjkf\{hsghHn
t
^wn\^{kHu]hs{A'H^jkq¤¯qroUh&jkcehHg2o\{rcix^
^O£@f\cmgece\{rcihEªC,s_;1D,E/019,H41S«XZY\^6q}jhs\cegmcmj}ulH!¢&hs{kcih&jrcelHnhsgPcen\^w£@fUhHgmcmjrce^wqYUhEq^^n)cend¢H^wqvjrceEhsjr^
t
du
¢&hH{rcelHfUq©hsfpjkY\lH{qw qr^^^H«U«,>;12,.-w;12,.--1F,;15,@G1S«©¨n jrY\ciq®oUhso^{®!^."cegmg t ^Ohsg"cjkYjrYU^.lEgmgel&"cmnU
xgehEqrq!lH t udnUhH]8cexwhsgqrudqvjr^w]qH
¥Ã^jJILKNMOQP^h6nUlHn\^w]o\j}u xgelEqr^ t xlHnd¢E^yqv^jw«8¥^jSRUTMOQPWV3P ^hHce¢H^wn ]h&jk{rcmy hsn t
XZYMOQP[\MOQPh©n\lEn\gmcen\^Ohs{2lHo^{h&jklH{O«]6\lE{2^"_`acbd`;eFTfMOhgiI4 &!^!xlHnUqrc
t
^{jrY\^Zo\{klHUgm^w]kjl^m_`acbd`;eH
6cen
t
h0fUnUxjkcmlEnn_o[Lbp^m_qer^m_SsN_`0e®"cmjrYtbuThv
`
^cw_`a$x7yuezqMOQPe o{$|
{A}
Tu~@
^"_`ax7yzcMO5Pde®hsn
t
qrfUxY6jrYUhsjGH
b^"_qe2T+Ia_Fs_`
{$|
{A}
^m_qexR9b^m_qexXl^"b^"_qeqeacCnb^"_qeq2salTI8aMh\«^H«;_Fsu_ `
b^"_` e@b `
¤-Oª
*ñ^{k^
a t ^wn\lsjk^wqjkY\^M^wfUxgect ^whsnqkxhHgehH{o\{rl t fxjÃcen7MO5P«XZY\^MxlE{r{k^wqrolHn t cen\Zn\lE{r]Jceq t ^n\lHjr^ t
duk
&« XZYU^ëqrupq}jk^] cmn ¤-Oªciq6hHn ^¢ElHgefpjrcelHn-¢&hs{kcih&jrcelHnhsgñcen\^O£Efhsgecj}u "Y\cixY !^ t ^nUlsjr^)hHq
¥Ã¦M§ñ¨^RJaAIe2"Y\^wnlX\«¨SjMlHgegml&Bq{klH] q}jhsn t hs{ t xlHnd¢H^y.hsnUhHgmupqrceqjkYUh&jñ¤q-Oª2xhHn8^"{k^"{kcjrjr^wn
^O£@f\cm¢&hHgm^wnEjkgmu6hHq!jrYU^ t c5^{k^n@jkcehHgcmnUxgmfqvcelHn
b
_
^"_qe]xRQb^"_qexXl^mbp^m_qeqeQTQCC^"b^"_qeqe ¤>Hª
"YU^{k^CS^"b^m_qece:U4)TtMOQPnY
aq b^"_qeq7¡NdaF88T I ¢8ceqñjrYU^nUlH{k]8hHgxlHn\^.jrlI hsjDbp^m_qe
,.-w;1F«"¨nxwhHqr^JI£Z0b8TMO P YvDbx
s¤3¢lE{ñqrlH]8^]h&jk{rcmyv¥T8MOQ¦
V3P
hHn
t
¢H^OxjrlE{
TMO9¦.
!^xhHn6{k^"{kcjk^¤-OªZhEq
{$|
{A}
^m_qe]xRQbp^m_qexXl^mbp^m_qece@¤vo§©¨
¡uª«vDbrx r¬ ¨s
¤¯Eª
"YU^{k^8¨ T MO5¦ ceq6h¬¥ÃhHH{hsn\E^6]f\gjkcmoUgmce^{O "hsn
t
jkY\^ qr^wxlEn
t
gmcen\^lH8¤>Eª8]8^OhsnUq8jkYUh&j6lHjrYª
hHn
t
¨ëYUhV¢E^jkl^nUlHnpSn\^@h&jkcm¢E^H 5hsn
t
lE{vjkY\lHElHnUhHg>«adupqvjr^] ¤>Eªñ^wgmlEn\Eqñjrl6jrYU^xgehEqrq©ls°¥ÃcmnU^whs{
lE]8o\gm^w]8^n@jkhH{rcmj}u adupqvjr^]q0¤>¥
a\ª"cjkYë{k^gih&jkcm¢E^
t
^E{r^w^8^j}°^w^ntª hHn
t
¨s+,.-V019,=-4/01:,.-w;1F«
§MhH{rcih&jkcmlEnUhsg5cen\^w£@fUhHgmcmjrce^wq"hHn t xlH]8o\ge^]8^wnEjhs{kcj}u6hs{k^:'dn\l&"n6jrl^xgelEqr^geu{r^wgehsjr^ t ,Ñ>41@,E41 ,s_;1S«
6³ 4p
D^wxYhsn\cixhHgqrudqvjr^w]qñ"cmjrYfUn\cmgih&jk^{hsg2xlEnUq}jk{khHcmn@jq t lnUlsj©^gelHnU0jrljrY\^xgihHqkqBlH¡qvupqvjr^]q
q}jkf t ce^ t cenDjkY\ceq©oUhHo^w{w«B¨ n t ^^ t cmn ¤¯EªBlHn\^.YUhHq9ªflblx "cmjrYNv lE{ñ]8^wxYUhHn\cixhsg
qvupqvjr^w]8qw«
XZY\^o\{klH\ge^]q{k^gih&jk^ t jklDol@qvcmjrce¢H^wgmu cmnd¢&hs{kcehHn@jqr^jqhsn t xlEnEjk{rlEg2Y\lHgt hsUcmgecj}u ls"qv^jkq¤¯qr^^
^H«U«F,@G1,.-1,;1¿ªPhH{r^Z^Oqrqr^n@jrcihsgegeu t cm^w{r^wn@jP{rlE] "YUhsj¡ceq¡q}jkf t ce^ t cen8jrY\ciqPoUhHo^w{w«¨n t ^w^ t ¤¯qr^^
jrY\^wlH{k^]£-^gel&ñª!jr{h&|}^OxjrlE{rce^wqZlHB¤-Oª"{r^w]8hHcmnDcenI lE{ñhsgegR hsn t hHgmg_5s_`.^wxhHfUqr^jrY\^
t udnUhs]8cixqZciq"]8l t c?^ t lHn6jrY\^lHfUn t hs{ku0lHpI4«
&ñqkqvfU]^jrYUhsj:I GbT+MO P
Y^"be9s3¢lH{©qvlE]^xlHnd¢H^y0f\nUxjrcelHn ^ e«ZXZY\^wn"!I ]hVu
ol@qrqr^wqkq"hsncen3?Un\cmj}ulHxlE{rnU^{q«PXZY\^®{hs]8^!lH{A'cmn¬¤q-Oª°^nUxlH]8oUhEqrqr^wqZqrfUxYxwhHqr^wqw«
XZY\^8oUhHo^w{ceqlE{r@hsn\ciqv^ t hHq©lEgmgel&BqH©cmn)qr^wxjkcmlEnë6qvlE]8^.jkY\^lE{r^jrcixhsg2{k^wqrf\gmjkqhsn tët ^?Un\cmjrcelHnUq
hH{r^o\{k^wqr^n@jk^ t «P¨nDqr^wxjkcmlEnD]hsjr{kcex^wqQR cen¬¤-Oª°jkYUh&jBudce^gt q}jhs\ge^qvupqvjr^w]8qñhs{k^qvjrf t cm^ t «°ad^OxjkcmlEn
_Dciq t ^¢HlHjr^ t jkl xYUhH{khExjr^w{rce±^f\nUqvjkhH\ge^0]h&jr{kcix^wqSR«ad^wxjrcelHn/xlHnUx^{knUqqvjkhsUgm^0hHn t f\nUqvjkhH\gm^
¥Ã¦M§ñ¨^RJaAIe«Mad^OxjkcmlEn0qvY\l&BqjkYUh&j!q}jhs\cegmcmj}u.ciqMoU{r^Oqv^w{r¢E^ t f\n t ^w{¡qv]hHgmg\nUlHn\gecmnU^whs{ t ceqvjrfU{rUhHnUx^Oq«
ap^wxjkcmlEnDhHo\o\gecm^OqZjrY\^{k^wqrf\gmjkq!jkl8qrlH]8^xlEnUx{k^jk^o\{rlE\ge^]q« lEnUxgefUqrcmlEnUq!^n t jrYU^oUhso^{O«
# $
Ã.M&% "Ã/
¥Ã^jPfUq©?{kqvjMqvo^wxcuqvlE]^ZxlEn t cmjrcelHnUq2^wnUqrf\{rcen\®jrYU^"^ypceqvjr^wnUx^"hHn t fUn\ce£@f\^wn\^wqkq2lsjrYU^!cen\cmjrcihsg\¢&hHgmf\^
oU{rlE\gm^w] jl^m_ ` aqb ` e«°XZY\^®lHgegml&"cen\^ypceqvjr^wnUx^hHn t fUn\ce£@f\^wn\^wqkqZ{k^wqrf\gj"ciqBh t ce{r^OxjBxlEnUqv^O£@f\^nUx^©lH
,p UxlH{klHgegehH{ru\\«;1F«
')( ³d· ³ *,+ # I A#<-#/.10f! 2;#A!3;44#576d#98 MO9P ; .# R T8MO5PWVP $#r< c#$
.l; :5; 8) c# <>=946?0@0A4#SCBd; X YMO5P)[£MO5P !$n$#ED #;
XNXGF xIHKJ
DLBd# A#
X F + 0W!3B NM!3;dA6AO6 S;
HT8v
F
^"MO P zcMO9e
C!A;#5P=
+
#
_`ST+MO
;
bW`STI
$#
C;#Q=SRQBd#CBd# c#r#5ST63dVU/6d#
b+Tv
`
^qw_`ax7yezqMO5Pe
76d!B+CBd;
b
_ Tf~
^qw_`Ea$x7yuezqMO5Pe ¤_@ª
b 7 :?B3XWqY9# c#W" .# w_` a$x7yue ¤/Hª
b^m_
`
ei¤b
`
¤¯Eª
b^"_qe2TfI8a_@sh_` ¤Fsª
b
_
^m_qe]xRQbp^m_qe]xXl^mbp^m_qeceaqrnb^m_qec5shaplT+I8a =# = _Fsh_` ¤¯Eª
adfUo\ol@qv^jrYh&j®jrY\^8hHqkqvfU]o\jrcelHnUq©ls°XZYU^lH{k^]\-8hs{k^qkh&jkceqq?U^ t hsn t t ^n\lHjr^@u+bp^ zq_ ` aqb ` eñjrY\^
fUn\ce£@f\^qrlHgefpjkcmlEn6lHzM{klH\ge^] jl^m_ ` aqb ` e«°apf\o\olEqr^®nUl& cenh t\t cmjrcelHn6jrYUhsj9TfI hHn t
QXl^eFT ^"Eea ¤">Eª
jkYUh&jBciq
Xl^ea 2suda TI
XZYU^n
bp^m_zq_`EacEei¤da©_@sh_`a
cF«^H«2jrYU^jr{kcm¢dcihsgqrlHgefpjrcelHnceq!jkY\^f\n\ci£@f\^qvlEgmf\jrcelHnls2o\{rlE\ge^] jl^"_`acEe«
6³
4p
XZY\^P!^gegmolEqr^
t
nU^wqkq5{r^Oqvf\gmjkqlspXZY\^lE{r^w] -MxlEn@jrcen@fU^2jrl"Y\lEg
t
lH{h"xlHn@jk{rlEgmge^
t
¥¦M§©¨^"RSa)aAIe
t
^?Un\^
t
hHq
{$|
{A}
^m_qe2x RQbp^m_qe2x©^m_qe2xXl^"b^"_qeqeac+b^"_qeq8s aT I °"cmjrY LTNMO ¦ V3P5
hTuv
`
^qw_` ax7yezqMO ¦ ehsn t {
{A}
T~
F
^qw_ ` a$x7yuezqMO ¦ e qr^^,41F«XZY\ciqciqcm]8olH{rjkhsn@jcen ¢dce^ lH
xlHn@jr{klHgegihs\cegmcmj}u®ceqkqvfU^wqw«Ã¨n.{k^gih&jkcmlEnUqrY\cmo."cjkY6¤>EªÃhHn t ¤>Eª Hgm^jfUqn\lHjrcix^¡jrYUhsjcmWªr«vDb©x x©^m_qe
cen ¤>Eª jkY\^n jrYU^{kcmEY@jvSYUhsn t Sqrct ^lsñ¤FHªñ^OxlH]8^Oqñ^O£Efhsgjrlf
}
^"b^"_qeqe Ãc>«^H«jkY\^xlHnd¢H^yqr^j
Iu^©^m_qeceQ 0b TtMOvDblx x©^m_qe7s ¢ciqñjkcm]8^¢&hs{ku@cen\«®¨SFRZkhsn t Xl^ e: jkY\^n jrY\^
lEpjkhHcmnU^ t qrupq}jk^] ?UjkqZ"cmjrY\cenlH{k^whsfqZqr°^w^o\cen\o\{rlpx^wqkq9,Ñ/01S«MXZY\ciq"xhEqv^®ceqZnUlsj"q}jkf t ce^ t cmn6jrYUceq
ohso^{O«©*ñl&°^w¢H^w{!qrlH]8^^ge^wxjr{kcexwhsgxce{xf\cmjkqZolEqkqv^OqrqZh{k^gih&jrce¢H^ t ^wH{k^^^j}!^^wnªhsn t ,.-w41S Uqrl
jkY\^^ydjk^nUqrcmlEn6lHÃjkY\^o\{k^wqr^n@jr^ t {k^wqrf\gmjkq!jrl&Zhs{ t qZxlEnd¢H^yqr^jq5I^"_qe!ceqZ¢&hsgefUhH\gm^E«
ë^]8hVunUl& t ^?n\^®hEq!cmnn,;1jrY\^qvjkhsUcmgecj}ulHÃjkY\^ñjk{rce¢dcehHgqvlEgmfpjkcmlEn«PXZY\^q}jh&jkcmlEnUhs{kuqvlEgmfpjkcmlEn
6ciq®xwhsgegm^ t qvjkhH\ge^cm!qr]hsgego^{rjrfU{rUhsjrcelHnUq®lHMjrY\^8cen\cmjrcihsgMxlEn t cmjrcelHnnb^"_ ` eo 6ge^wh t jrlDqrlHgefpjrcelHnUq
"YUcexY{r^w]hscen6cenjrY\^n\^wcmEYdlE{rY\ldl
t
lH©lE{Bhsgeg _@sh_
`
\oU{r^Oxciqv^wgmuH
³ ¯· RQBd#)#3U63 " C6 . 0A;W b C;"A#$ =# NB#C## 98 + 0-63Q <8
8 #/;# "!$# CBd# A#+#5"&% % ^! e # 76d!BNB;8; +;d bd`tT«I DNB bW`E8¡ %NB#
/ 63V bp^ .zq_` aqb ` e 98K0 .#. jl^m_` aqb ` e '@# bp^m_zq_` aqb ` eGD¡ ! a_Fs_ `
¨SPcenh t\t cmjrcelHnjkY\^jr{h&|}^OxjklH{kcm^OqZlsjrY\^o^{rjrfU{r^ t qrlHgefpjrcelHnq"hs{k^h&jvjk{khExjk^ t du<jrYU^nD!^qrhVu
jkYUh&j"jkY\^qvjkh&jkcmlEnUhs{ku0qrlHgefpjrcelHnceq"hEqvud]8opjklsjrcixhHgmgeu0qvjkhsUgm^E \o\{k^wxciqr^geuH
³
¯·
RQBd##3U63 " C6 . 0A;W
bnZ
;$ . 0;"!$; =#8rQC$ =#)NB# c#
#5" #
76d!BNB 8; fd
b ` TI
DCB
b
`
¡
NB#</; 63V;
bp^ .zq_
`
aqb
` e
8E0 =#/.
jl^"_
`
acb
` e 8363 '
}
b^"_zq_`EaqbW`0eQ
XZYU^®nUlsjrcelHnlHf\nUqvjkhH\cegmcmj}uciqZn\l& Ecm¢E^n«
³ ¯· RQBd#f#3U/63 " C6 . 0d bh T63 =#<8loQ;D .#7oV=# =CBd# A#<#5$
!# 76d!3BfNB;Q8; Sd %"# da ;#E.l; ' bW`JTfI DCB bd` D¡ %;_Fs_` 36d!3BfNB@NB#
/ 63V bp^ .zq_`Eaqbd`4e 98K0 .#. jl^m_`aqbW`0e ;# '@#
bp^_zq_` aqb ` eG #$!
¥Ã^jfUq®n\l& Ecm¢E^.H^wn\^{hsg2hsq}jk{khExjñjkY\^lE{r^w]q©lH°qvjkhsUcmgecj}uE hHqrud]o\jrlsjkcexqvjkhsUcmgecj}uhHn
t
fUnUq}jh&
Ucmgecj}u8cen0jk^{k]8q°lsH^nU^{hsgecm±w^
t
¥u@hso\fUn\l&¢f\nxjrcelHnq Tv
F
^mMO9PzqMO:e«PXZY\^©lHgegml&"cen\{k^wqrf\gmjkq!hs{k^
ohs{rjrcixf\gihs{"xhEqv^Oq!lsjrY\^lEn\^wqZo\{kl&¢H^ t cent,41S«
')(
³d· ³ -6?0@0A4#NB;9CBd#)4$76 .10V98"R-Bd#3; c#/.fE#NB# DCBt!3;;V;TB =@=
-6?0@0A4#SCBd;FCBd# c#C#5 # ; T+v
F
^"MO P zcMO9e 36d!3BfNB
)^"be2s! ^cb©eab+TI8a9b©9¡ a
DCB )YWwda #" [£MO ;C8$;P ^"_qe # _@Tt^a ez
%$& )^"Eei¤dz
%'& b)(
J
^"beQTfI8ab+T !I8a5bpD¡
*)+
RQblxXl^"bea, J^"beq5shdapb8TfI8a9bpD¡
=
RQBd#CBd#J CG" /; :63V 8-,./ W021r7 =#?=
')(
³d· ³ -6?0@0A4#NB;9CBd#)4$76 .10V98"R-Bd#3; c#/.fE#NB# DCBt!3;;V;TB =@=
-6?0@0A4#SCBd;FCBd# c#C#5 ¨ # 3 # ; T+v
F
^"MOQPzcMOQe 36d!3BNB
^mbe2s4 ^AbpGea 8 S; bTIa9bpD¡ a
DCB )YWwda #" [£MO ;C8$;P ^"_qe2s65_87 _@Tnwa #"X-8; o/ .l#C!3d 5 # 39 # dz
%$& )^"Eei¤dz
%'& b)( J^"beQTfI8a 8; S;
b+T;!Ia9bp:¡
*)+
RQblxXl^"bea, J^"beq5s¨#)^"bea 8; C
b+TI8a9b©9¡
=
RQBd#CBd#J CG" /; :63V 8-,./ W021rC; .10"!$; ) .# =
¥Ã^j©fqBn\lHjr^jkYUh&jxlHn t cjkcmlEn4¤¯@ª"ce]oUgmce^wqS J
^mbe:Tr^mbe"lE{©hHgmgbT !I pbp7¡ "YU^{k^
r^mbe8ceqjrY\^Djhsn\E^n@j0xlEn\^jrl I h&j)b "hsn t J
^mbe t ^wn\lsjk^wq8jkY\^DH{h t ce^n@jls )^9e8hsj)bk,.-wp
oU{rlEol@qvcmjrcelHn/p«Ñp«.-1S«
ë^lH{k].f\gih&jk^n\l&JhHn6f\nq}jhs\cegmcmj}u{k^wqrf\gmjw«
')( ³d· ³
-6?0@0A4#NB;9CBd#)4$76 .10V98"R-Bd#3; c#/.fE#NB# DCBt!3;;V;TB =@=
-6?0@0A4#r; /CBd;
I943¢S
= V87NB# c#S#5$
Tv
F
^mMO5P zqMOQe
#
36d!3BNB
^mbe2¡^cb©eapb8TfI8a
DCB
9Ydwda$x7yuei[£MO
N8$;
;^"_qe2¡3_
_@su
A8 7/ .l#C!3d
# #
z
%$& )^mbe # a©bTIab ¤ #$ dz
%'& J
^mbe2TfI
ab+T !Iz
*)+
RQblxXl^"bea,
J
^"beq5¡«
)^"bea b+TI
NB#NB#S C0"; ]/; 63V;6,./ W021l 63d =#?=
XZY\^{k^wx^wqkqvcelHnxlEn\^7I
"cegmgÃ^ t ^?Un\^ t cenjrY\^nU^ydjñqv^OxjkcmlEn«
ð "$%. ! %à " °%., !
XZYU^hHcm] lHBjrYUceqqr^wxjrcelHn ciqjrlëcmn@jk{rl t fUx^hHn t q}jkf t u)j}!lëxgehEqrqr^wqls©qvjkhH\cegmcmj}u¬]h&jr{kcix^wqw« XZY\^
{k^wqrf\gmjkqlH\jkhscen\^ t Y\^w{r^"cegmg"^DfUqr^ t gehsjr^w{cmn jrY\ciqoUhHo^w{jrl¬xlEnUq}jk{rfxjH^wn\^{hsgecm±w^ t ¥uEhHo\f\n\l&¢
fUnUxjkcmlEnUq"n\^w^ t ^ t jkl0hso\o\geujkY\^hsUqvjr{hHxjZqvjkhH\cegmcmj}u{k^wqrf\gmjkqZHce¢H^wncenDqv^OxjrcelHnDp«
¥Ã^j0fUqr?U{qvj8{k^wxwhsgeg"qvlE]^UhEqvcixjrldlHgiq{rlE] xlEnd¢H^y hHnUhsgeupqvciqf,=-O41S« ¥Ã^jv ^Dhën\lHnU^]8opj}u
qrf\Uqr^jBlHMOQP5« ^qrhVujrYUhsjDv ceq©hxlHnU^c ¨v¥KvDa ¨ #
&n\lEn\^]8opj}uxgelEqr^ t xlEn@¢E^y6xlHn\^
ciq"xYUhH{khExjr^w{rce±^ t dujkY\^{r^wgehsjrcelHnUqGH
¨vkKvDa ¨ #
znvxuvkKvrztTv
¥Ã^j K«MOQP^hn\lHnU^]8opj}uxgelEqr^ t xlHnd¢H^yqr^jO«©XZY\^{r^Ox^wqkqrcmlEn4¤lH{®hHqrud]o\jrlsjkcexOªBxlHn\^
lH
+ciq t ^?n\^ t du
`0¨^V nbd`4ea
"YU^{k^Sbd`ciq©hHn hs{k\cmjr{hs{ku)?\yp^ t ^ge^]8^n@jls>
¨n lHjrY\^w{©!lH{ t q"jkY\^.{k^wx^wqkqvcelHnxlHn\^ls> ciq©jrY\^
qr^jlH t cm{k^wxjrcelHnUq®{klH] "Y\cexY)lEn\^xhsn)Elqvjr{hsceHY@j{klH] hHn@u olEcmn@jSbW`fT jrlDcen3?Un\cmj}uH "Y\cegm^
qvjkhVudcen\cmn£,=-Op A& \«;1F«PXZY\^qr^j
ceqBh8xgml@qv^ t xlHnd¢H^yxlHnU^H«©n\^YUhHq
kx
KI
hHn
t
jkY@fq dcmrT çjrY\^wn K
¨SL$ciq!qvud]8]8^jr{kcixs @c>«^H«b+T 5b+T çjrYU^n6xgm^Ohs{kgmuS
ciqZh8qvf\qvoUhEx^®ls]MO P
¨S +ceqZlHfUn t ^ t
jrYU^n
N03¢@«p6UlH{2bTfMO P
°^
t
^wn\lsjk^®du)jJ^mbe°jrY\^
fUn\ce£@f\^qrlHgefpjkcmlEn6lHÃjrYU^¢VhH{rcih&jkcmlEnUhsg5cen\^w£@fUhHgmcmj}uH6cen t
T (qvfUxY6jrYh&j
nb]aqªC Fsa)ª T&
XZY\^ñ]8hHo\o\cen\SjYMO P [ +zcb[\jJ^mbePciq¡xhHgmge^ t jkY\^ño\{kls|}^OxjkcmlEnlEn D«¨S ceq°hqvfUUqvohHx^"lH
MO P jkY\^nlj4ciqPgecmn\^Ohs{Phsn t qrud]]8^jr{kcexHǬnjrY\ciqMxwhHqr^H &!^!"{kcmjr^5j7^"beFj5b8"Y\^{k^5j TfMO PWVP
t ^n\lHjr^wq!jkY\^qru@]8]8^jk{rcix®]h&jr{kcmyls2lH{rjrY\lEHlEnUhsgo\{kls|}^wxjrcelHn6lHn
XZYU^6f\nUcjqro\Y\^w{r^6cmnhMOQP ceqY\^w{r^
t
^wn\lsjk^
t
@u F aPcF«^E« F Y\0bNT«MOQP«Y:fb G ¢
¨ n jrY\^
qr^w£@f\^wgRTMO5PWV3P
t
^n\lHjr^wqZh.{r^Ohsg]8hsjr{kcylHÃlH{
t
^{
<
hsn
t
I\KuMO5PWV3P0ceqZh.qrf\Uqr^jZlsMO5P
¥^jZfUq
hHgeqrlolHcenEj!lHfpj°jrY\^ñlHgegml&"cen\nUlsjkhsjrcelHnUqGH ^R:e t ^nUlsjr^OqMjkY\^©qro^wxjk{rfU] lH]R ^R:e¡ceqMjrY\^qro^Oxjr{hsg
{h t cmfUqBlsR hsn t lE{:¨8T ^"RDe 5^¨e t ^wn\lsjk^wq"jkY\^.xlH{k{r^OqvolHn t cmn\^ceH^wnUqroUhHx^H«°XZYU^jr{hsnUqrolEqr^
lH9Ráciq t ^n\lHjr^ t dutR:§¡ 'E^{G0RJ¢ceq.jrYU^6ndf\geg!qroUhEx^0lH:RáhHn t jr{G0RJ¢6ciqjkY\^6jr{hHx^ls:R.«ëXZY\^
cen@jr^w{rcelH{"hsn
t
lHf\n
t
hs{ku0lsI hs{k^©{k^wqro^wxjkcm¢E^geu
t
^wn\lsjk^
t
du
I
hsn
t
!I4« ^hEqrqrf\]8^®jrYUhsj
F I ciq"xgelEqr^ t
I ciq"xlEn@¢E^y
rT+I
©nUgmujkY\^olEqkqvce\ge^h t\t cmjrcelHnUhHgxlEn t cmjrcelHnUqZn\^w^ t ^ t lHnI "cegeg^qro^wxc=?U^ t cenjrY\ciqZoUhHo^w{w«
³ ¯· RQBd#. :5 R TMO PWVP + 0-63Q 0A4C4##/.rCW$ =#T I 8CCBd# c##5$
. :5
T<MOQPWVP
36d!3BfNB
|
!
baqb
#
da
%$& RQbaGw x § "b2shabTI8a
%'& bT;!I" w#7w x § ""b+TI
³ ¯· %$ RQBd#".l; :5 R TkMOQPWV3P + 30-63Q 0;C;#+ =# ; I 8CBd# c##5+
.l; :5 TfMO9PWV3P 76d!3BfCBd;
|
baqb # da
%$&
|
R9b]aGw x § "b # a
%'& bT;!I" w#7w x § ""b+TI
6³ 4p
lHn
t
cjkcmlEn¤-OªMls
t
^?Un\cmjrcelHn0_6¤¯hsn
t
/HªMceq¡^w£@f\ce¢VhHgm^wn@j¡jrljrY\^©^ypceqvjr^wnUx^©lsh.xlHnUqvjkhHn@j
5 #
qvfUxY6jrYh&j
b]acbQs457@b
apb T I
B^wxhHgmg5jkYUh&jñh]h&jk{rcmy TMO5PWVPciqBqkhsct jkl^xlEol@qvcmjrce¢H^lEnfI cm
baqbQsudaplb T I
& ]hsjr{kcy TfMO PWVP ciq"qkhsct jkl^qvjr{kcexjrgeuxlEol@qvcmjrce¢H^lEnfI cm
baqb
#
da]b T I E43¢
XZYU^wqr^.xgihHqkqv^OqZlsP]h&jk{rcix^Oq"o\gihVuhHnDcm]8olH{rjkhsn@jB{klHge^cmn xlH]8o\ge^]8^wnEjhs{kcj}u0jrY\^wlH{kuë¤>qv^w^^H«U«D,H41ª«
XZYU^8qr^jlH!xlEol@qvcmjrce¢H^]h&jr{kcix^wqqvjr{kcexjrgeu xlEn@jkhscenUq©jrYh&jls!ol@qvcmjrce¢H^8qv^w]8c
t
^?UnUcjk^]8hsjr{kcex^wqr,Ñsp
o=-&V_1S«
lEn t cmjrcelHn ¤¯Eªñls t ^?UnUcjkcmlEnUq®_6hsn t /6xlH{k{k^wqrolEn t jrlxlEn t cmjrcelHn ¤>Eªñcmn jrY\^wlH{k^]q0hHn t U«¥^j
fq©YU^{k^ t ^wn\lsjk^du5 ¤{k^wqro«
eñjkY\^qr^jlH°xlEol@qvcmjrce¢H^¤{k^wqro«q}jk{rcixjkgmuxlHolEqrcjkcm¢E^Oªñ]h&jr{kcix^wq
lEnI
¥Ã^jZfUqZhsgiqvl t ^n\lHjr^®du
jrY\^qr^jZlsÃ]h&jk{rcix^Oq°qkh&jkceqvudcmnUxlEn t cmjrcelHn ¤q-Oª¡ls t ^?Un\cmjrcelHn6_U
jkYUh&jBciq
¥TMO PWV3P Y
|
Jb]acb #
¨SjBciq"xge^whH{ZjrYUhsj
K
K5
I;FQKI
K
· ¡· ¯· V8 I S<!3#7NB#
·· ë^2'dn\l&¬jrYh&j
K
¨SjMqrf3B0x^OqÃjkl®xYU^wx$'jrYh&j
K
¥Ã^j ¥T
aOjrYUhsjPceq
Jbaqb
#
da]b T I E43¢®hHn t gm^jBfUqZ¢H^w{rcmujrYh&j"jrYU^{k^®^ypceqvjkq5
#
qrfUxY6jrYUhsj
Sb]aqb5s45o
b8
alb T I E43¢
¨S2°^qrf\o\olEqr^jrY\^xlEn@jr{hs{ku8jrY\^wn!^xhHn?Un t h8qr^w£@f\^wnUx^rGb
P
¢JKuI E0¢
qrfUxY6jrYUhsj
Sb
P
acb
P
F
P
Fb
P
¥Ã^j P Y |
|
ë^YUhV¢E^l P
G hsn t jkY@fq"jrYU^{k^®^ypceqvjkq
h6qvfUUqv^O£@f\^nUx^
P
¢8qrfUxYjkYUh&j
P
[ a0 0 8hsn t a Q
P
P a
P
o¡
XZYUceq"xlHn@jr{h t cixjq!jrY\^qvjr{kcexjñxlEol@qvcmjrce¢dcj}u0lH
6³
4p
¥^j9RT<MO PWV3P
^holEqrcmjrce¢H^q}jhs\ge^]h&jr{kcmy5 pcF«^H«
^¨e # a ¨fT ^"R:e
^
0e
XZYU^n jrY\^w{r^^ydciqvjkqhë]h&jr{kcmy
TNMOQPV3P qrhsjrciq}udcen\¬xlHn t cjkcmlEnUqD¤-Vªhsn t ¤>Eªls ñ^?Un\cmjrcelHn¤/p«
¨ n t ^^ t "gm^j TZMO PV3P ^ hsndu olEqrcjkcm¢E^ t ^?n\cjk^]h&jk{rcmy« 6U{rlE] ¥u@hso\fUn\l&¢ qjkY\^lE{r^w]¤¯qr^^
,Ñ&_1¿ªjrY\^w{r^^ypciq}jq8h olEqrcjkcm¢E^
t
^?Un\cmjr^]h&jk{rcmy
T«MOQPWVP4qkh&jrciqvu@cen\ jrY\^¥u@hso\fUn\l&¢)^w£@fUh&jkcmlEn
RhxR:§
¬«MXZYdfUq
RQbaGw
x § "
bi
+b]acb
#
abTfMOQP E43¢8«
6³ 4p $«&«?U{kqvjBq}jk^ocmn<?Un t cmn\h]h&jk{rcmy qkh&jkceqvudcmn\xlHn t cmjrcelHnë¤>Eª¡lH©^?UnUcjkcmlEn_¤{k^wqro«
©^?n\cjkcmlEn)/HªÃ]8hVuxlHnqvciq}jjrl t ^Ohsgp"cmjrYjrYU^Z¥ÃuEhHo\f\n\l&¢^O£Efh&jrcelHn Rx)R:§ hsn t dujh'dcmnU
hHq"h]h&jk{rcmylH 5$¤{k^wqro«
e«¡XZY\^¥u@hso\f\nUl&¢^w£@fUh&jkcmlEnxwhsn^"{kcmjvjr^wnDhHq
^R
§
#Dx# R § e
a ^
e
"YU^{k^>hsn t8t ^wn\lsjk^wqjrYU^ZxlHgef\]8n <
¢E^wxjklH{qlE{r]8^ t {klH] jkY\^Z{rl&Bqls hsn t ¬ H{r^Oqvo^wxjrce¢H^geuH
jh'E^ncmnDlE{ t ^{O«BlHjr^hHgeqrl8jrYUhsjñdu6xY\ldl@qvcen\ hsn t qrud]]8^jr{kcex®jkY\^n {k^ t f\n t hsn@jB^w£@fUhsjrcelHnUq
hHn t ¢VhH{rcihsUgm^Oq!xwhsn^{r^w]l&¢E^ t jklHce¢H^h8qvupqvjr^w]$ls2lH{ t ^{
F
< ^< x 4e
¥Ã^jfUq®n\l& t ^wn\lsjk^duF jrY\^qr^jls°¥ÃuEhsoUf\n\l&¢ol@qvcmjrce¢H^8qr^]8cqvjkhsUgm^]8hsjr{kcex^wq®lHnI hHn t du
jrY\^qr^j"lsP¥u@hso\fUn\l&¢ol@qvcmjrce¢H^qvjkhH\gm^]h&jk{rcix^OqZlHnI
ë^qr^^®jrYUhsj
@ RNT<MOQPWVPY T
^#Jw x § "e^X!IneFKuI
RuxR
§ T2
hHn t RNTfMO PWVP Y T
^#Jw x § "e^X!IeFKuI
RuxR
§ T
¥Ã^jfUq.n\lsjk^8jrYUhsj n\^^ t qn\lHj.^qvud]8]8^jk{rcixs«6¨]olH{[email protected]^OqlsZ]h&jr{kcix^wq.qrhsjrciq}udcen\jrY\^
xlHn t cjkcmlEnUqZls t ^?UnUcjkcmlEn_hHn tt ^?UnUcjkcmlEn+/hH{r^®n\l& Ecm¢E^n«
· ¡· ¯· -6?0@0A4#SCBd; RT iV=#
R9b]acb2sab T I
RQBd#
RTF
=
·· ¥^j F
# lHn t cjkcmlEnUq¤-Vª"hsn t ¤>EªZls t ^?Un\cmjrcelHn_0hs{k^xge^whs{kgeuqrhsjrciq?^ t «¡lH{k^l&¢H^w{
^#Jw x § "ebf¤TfI
· ¡· ¯· !
-6?0@0A4#SCBd;
RT
iV=#?=
|
RQbaqb #
RQBd# RT
=
··
&©q"cen6jkY\^o\{kldlslHzM{klHolEqrcmjrcelHnDp p!^qv^w^©jkYUh&j"jkY\^xY\lHcix^
F
#ciq"xlEn@¢E^n\ce^n@jO«
6³
4p
6\{klH]$z¡{rlEol@qvcmjrcelHnUq"8hHn
t
U p°^
t ^ t
fUx^jrYUhsj
2 K FCa K
ë^qv^w^8n\l&jrYh&jw "cjkY¬qvlE]^8h tUt cjkcmlEnUhsgMxlHn t cjkcmlEnUq®cm]8olEqr^ t lHn jrY\^0qr^jJI4 Ãcjciqol@qrqrcmUgm^jrl
xlHnUqrct ^{Zgihs{kH^{"xgehEqrqr^wq!ls2]h&jk{rcix^Oq«
· ¡· ¯· -6?0@0A4#SCBd; I S!3;#776d!3BNB;
bT;!I"£b
©TI ^ a
.=
a < e
DLBd# A#
#Q;#7NB# A NB!$;Q;d"!$ ;#A!; E 8 MO P
V8oCBd# c#C#57 0;$C;#C"/ ; L.l; :5
36d!3BfNB
RT 5
NB# RNT@ =
·· ë^0qv^j Y F
+a"Y\^w{r^ Y
F
P
¢ XZY\^8]h&jk{rcmy ceqqrud]]8^jr{kcex8hsn t
olEqrcmjrce¢H^ t ^?UnUcjk^H« lH{k^l&¢H^w{w
RQbaGw x § "b
F
)RQbaqb8hsn t jrYdfUq
R9b]a0w x § "bs
dabTuI
6cenUhHgmgeuH ^#w x § "eb
F
P ^ D {
eb
¢l
P
LF
^9D {
eb
XZY\^wn
fqvcen\jrY\^hEqrqrf\]8opjkcmlEnUqZlHnIap!^qv^w^®jrYUhsj"lH{5b+T!I !^YUhV¢H^^#Shw x § "ebTI4«
· ¡· ¯· $ -6?0@0A4#SCBd; I S!3;#776d!3BNB;
bT !I b
TfI ^ a .=a < e
V8oCBd# A#C#5$J 0A4C;#;" ; .l; :5 76d!3BNB
)RT
NB# RNT
=
·· &©qñcenzM{klHolEqrcmjrcelHnD_!^.qr^j Y
F
"cmjrY Y
F
P q¢E«:*B^{k^
RQbaGw x
§ "b7
F
)RQbaqbhsn t jrYdfUq
|
RQbaGw x § "b #
XZY\^8o\{kldls¡ciqhHxY\ce^¢E^ t hHqcen
z¡{rlEol@qvcmjrcelHn_U«
6³ 4p ¨S9Rçciq.hDn\lEnUqrcmn\Ef\gihs{ "]h&jk{rcmy cF«^H«R #ljzA # ^"jJe j(ceqqvfUxY)jkYUh&j
7sadlH{BhHgmg $a"!lTa
=.
a< ¢E @jkY\^njrYU^{k^^ypceqvjkq"holEqrcjkcm¢E^ t cehHHlEnUhsg5]h&jk{rcmy (qvfxYjkYUh&j
£Y,)RuxR
§
ciqMolEqrcmjrce¢H^ t ^?Un\cmjr^¤¯qr^^B^E««@,.-O01ª«2¨Sj!{r^Oqvf\gmjkqMjrYUhsj
R9b]albF
F
R9b]aGw¤x § "bi
F wR § x
R "b]aqb8
F
b]aqbs
F ¨ ¦ P
^$# #&%
e b
XZY@fq
|
RQb]acb # ¬hsn t jrY\^
xlHn t cjkcmlEn6{k^w£@f\ce{r^ t cenzM{rlEol@qvcmjrcelHn+/lHnjrYU^]8hsjr{kcyfR ceq"qkh&jkceqq?U^ t «