D e plus, on note ici que la mise en oeuvre d'un tel module ne ...... 3. the model relevance, as %$£& al¨ s d ¨ n 3 ¢ A65. &. If the model is more relevant than ...
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Implementing a variant of the Kanatani’s estimation method. T. Viéville, D. Lingrand and F. Gaspard
N° 4050 Novembre 2000
ISSN 0249-6399
ISRN INRIA/RR--4050--FR+ENG
THÈME 3
apport de recherche
%'
(
! "
" $#&%
)
+*-,
.0/124365 2874789;:=/@?A24B CEDGF;BHIFJBKHML/@NF;OQPKF;DGH RTSVUWX(YZ [&\^]_X`_acb]_dfe6\gSVecWhWXji&WhacbkSVdf\VXcl dfWhacm6XnlpoVe6\q\VrXnlJbe6\q\pacdfnsn_at\VbXn uv`setwxX]zy{e6|qd}ec~d}n yzacqe6`x]ToVX`sXbkSVX`bkSVX\JK^
^t
>Z
zeQ6XW(|V`Xc
6
c
(Z
tVacm6Xn
KGVc^) X`Xd}ndf]]_SVX@V`e6|VfXWecqpac`sacWX]_X`Xn]sd}What]sd}e6\d}\be6WV]_X`d}nd}ec\'l `sXbe6\Vnd}oVX`sdf\Vmac\Vod}WVfXWX\$]sd}\qm Spa]W+aG¡(|XTbac}fXo]sSVX¢ac\pat]_ac\Vd8£¤nvXn]_dfWhat]_dfe6\ WhX]_SVeo'lJV`XnsX\^]_XogSVX`X¥acn{ansdfWhq}Xe6q]_dfWd}nsat]_dfe6\0V`se6|q}XWl;nseg¦4a6§) d¨]_Sqe6q]ac\^¡ oVd}`Xb])`sX©X`X\VbX]_e(aV`e6|pac|Vdffd}nx]_dfbz©`_atWhX Aec`sªh|Vq]«¦8|J§be6\Vnd}oqX`sdf\Vm¦©d¬§v\Ve6\i}df\VXac` d}WVfd}bdf]®WXGacnV`sXWhX\^]"X¯$pat]sd}e6\qnac\Vo°Vac`_acWX]_X`+be6\qn]_`sacdf\$]snlTVfVn±¦©d}d²§`se6|Vqn] Xn]sd}What]sd}ec\0df\]sSVXV`sXnsX\VbXecKecq]_fd}X`sn{ac\Vo-¦8dfdfd¬§AWVf]sd¨iWeoVX³be6Wpat`sdfnse6\Vn´ µ{X`Xclz¦8¶«§a·V`etwxXb]_dfe6\¸acfm6e6`sd¨]_SqW |patnsXo¹ec\¹m6X\VX`_acfdfn_at]sd}e6\qnecns¯$pac`Xi`seec] oVXbe6We6ndf]sd}ec\Vnhac}feQ nhac\¹XºhbdfX\^]®ac\Vo¸\$VWX`d}bac}¨¡¸n]_ac|VfX}ebGat)`sXnse6fq]_dfe6\¸ec a»nsX]®et\Ve6\i}df\VXac`+X¯$pat]_dfe6\Vn´I¼\½]_SVXec]sSVX`+Spac\Vo'l¦4¾T§a»`e6|VVnx]®Xn]_dfWhat]_dfe6\ WheoVVfXecKaSqd}X`_ac`bkS$¡"et=\Ve6\i&fd}\VXac`TWeoqXfn{SVacn|XX\goqXnsdfm6\VXo·ac\qo"tacfdfopat]_Xo'´ ¶¿nx]_XacSqXGaco'lz¦4ÀT§¥]sSVXnsetÁ]& )ac`Xac`sbkSVd¨]_Xb]sV`sX"ec{]_SVXXn]sd}What]sd}e6\½WeoqV}Xdfn oVd}nbVnnsXo± d¨]_S·]sSVX(mce^acec|;Xdf\Vmdf\$]sXm6`sat]_Xo>d}\g`sXGatb]_d¨6X(nsecÁ]& Aac`sX(X\^d}`e6\VWX\^]_n e6`( d¨]_SVdf\½acVVfd}bat]_dfe6\Vn¥ d¨]_S¹]sd}WXbec\Vn]s`_acdf\^]_nl SVdf}Xac\¹XjÂX`sdfWhX\^]kat]sd}e6\½bec\i nsdfoVX`d}\VmÃ]_SVXpac`sacWX]sX`sdfn_a]_dfe6\ecz`sX]_df\pacoVdfnsV}acbXWX\^]_n®|X]& AXX\]& Äe»dfX n®dfn V`se6;e6nXo0acn{ac\"d}f}qn]_`sat]_dfe6\ec ]_SVXXnx]_dfWhat]_dfe6\WheoVVfXc´ Å0Æ^ÇEÈÉ¥Ê Ëc ze6\i&̳d}\VXac`{Ívn]_dfWhat]_dfe6\'lJye6|Vqn]zÍvn]_dfWhat]_dfe6\'l;ÎVf]sd¨iÏÎ0eoVX
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
;
* #%'
*-#"
K *
*
)
h*
"
" $,
{e6Vn`sXd}ndf]se6\VnAfX{V`se6|q}UWhX{oVX8£¤Xn]_dfWhat]_dfe6\+pac`_atWhr]_`d}¯$VX{X\hdfnsdfe6\ pac`"e6`soqd}\pa]_Xq`l`sXbe6\qnsdfoVr`sac\^]·X]0dfWhq}rWhX\^]kac\^]·bX»¯$Vd;e6V`s`sacd¨]"n£¤acV;XfX`g}a Whr]_SVeoVXo'£ Xnx]_dfW+a]_dfe6\»oqX+¢ac\Vat]kac\qd4l³V`rnX\^]_rX+dfbdvbe6WWhXV\ÃnsdfWVfX+V`e6|VfUWX o'£¤ecq]_dfWd}nsat]_dfe6\'l^oVec\Vb¦4a^§ n_ac\Vnv`r©r`sX\qbXToVdf`sXb]_ X «V\bacoV`XTV`se6|Vac|Vdf}dfn]sXTW+atd}n{¦©|J§ X\ be6\VnsdfoVr`_ac\^]¦©d¬§oVXn¥r¯$pat]_dfe6\Vn(oVXWXnV`sXn¥X]oqXn(be6\^]_`sacd}\^]sXn\Ve6\i&fd}\Vracdf`sXnl ¦8dfd¬§TV\VXn]_`sat]_rm6dfX(o'£ Xnx]_dfW+a]_dfe6\>`se6|qVn]sX(X\gV`srnsX\qbXoVXWhXnsV`Xn«X`s`e6\V\VrXnlv¦8dfd}d²§ X\WhX]s]_ac\^]zX\0be6\VbV`sX\VbXVfVnsdfXV`nWeoVUfXnzac"nsXd}\0o'£¤q\VXSVd}r`_ac`bkSVdfXc´ ¶zoVX «oVXT8£¤Xns;e6d}`voqX)ecq6e6df`vV`rnsX\^]_X`lac\Vd¨6XGat+oVXT8£ d}WVfrWX\^]_at]_dfe6\'l$fXn ]_`_aGtacÂoqXA¢ac\pa]kac\Vd^oqXÄWhac\VdfU`X)acbbXnsnsdf|VfX)X]e6;r`sat]_dfe6\V\VX}fXcltbX]s]_XÄbe6\^]s`sdf|Vq]_dfe6\ d}\^]_Um6`sX¯$VX}¯$VXnAacWr}dfe6`_a]_dfe6\Vnpac`v`sacV;e6`]atÂWr]sSVeoVXn@VnsqXf}XnÄoVoVecW+atd}\VXt´ (£¤q\VX®pat`]Gl)¦ §V\¹at}m6ec`sd¨]_SVWXhoVX®V`etwxXb]_dfe6\ |patnsr®nV`(oqXn(oqrbecWh;e6ndf]sd}e6\qn¥oVX ÀASVe6fXnsª^¡gX`sWX]V\VX(`rne6}]_dfe6\·\$VWr`d}¯$VXfebacfX(n]_ac|VfX(X]«XºhbacbX¥oqX(bX]«X\i nsXW|VfXoqXbe6\^]_`sacdf\$]sXn\Ve6\i&fd}\Vracdf`sXn ´ (£ atq]_`Xpac`]l³¦46§ÄV\"WeoqV}XoE£¤Xn]_dfWhat]_dfe6\ `se6|Vqn]_XoVXnpac`_atWhU]_`XnTo'£ V\VXSVdfr`sac`sbkSVdfXoVXWeoVU}Xna¥r]_roVr6Xfe6V;rX]Ttacfd}oVrt´ uac`@acdf}fXV`nl4£¤ac`bkSVdf]sXb]_V`Xzfe6m6dfbdfXf}X{o'£ V\]_XJWeoVVfX{oE£¤Xn]_dfWhat]_dfe6\+Xn]@oVdfnsbi ]_rX@opac\qnfXÄ|qq] oVXÄ;e6qce6df
` ]_`sX@df\$]srm6`rÄoVac\Vn V\(X\$df`se6\q\VXWX\^]vfe6m6dfbdfX$`rGacb]_d¨pe6 acnsXd}\"o'£¤acVVfdfbGat]sd}e6\qnaQcXboVXnTbe6\^]_`sacdf\$]sXnTfe6m6dfbdfXf}Xn ´ XVfVnlqe6\\Vec]sX«d}bd'¯$VX ²aWd}nXX\geXq`sXo'£ V\0]sXWeoqV}X\VX\VrbXnnsd¨]_X¥Vacnz¯$VXoVXnzoVr`sd¨tat]_dfe6\Vn{\$VWri `sdf¯qXn«Whacdfn«acqnsnsd n¡W|e6fdf¯qXnX\·fdfm6\VXcl;bX¯$VdnX`sa®4£ e6|wxX]«oVXoVrcXfe6V;XWX\^]sn ©q]_V`n´ d}\pat}XWhX\^]GlV\VXÃXÂV`d}WX\^]_at]_dfe6\X\Mbec\VnsdfoVr`sac\^]·V\qX-pac`sacWr]s`sdfn_at]sd}e6\ oV oVrV}acbXWX\^]z`sr]sd}\qd}X\0X\$]s`sXoVXÂVXn{Xnx]V`sece6nrbe6WWXd}ffVn]s`_at]sd}e6\oV©e6\Vbji ]_dfe6\V\VXWhX\^]oVWeoqV}Xo'£ Xnx]_dfWhat]_dfe6\V`srnsX\^]src´ " Ínx]_dfWhat]_dfe6\\Ve6\i}df\VrGatd}`Xcl;Ívn]_dfWhat]_dfe6\`se6|qVn]sXcl;Î0V¨]_d ixÎeoVU}Xn Ê È
! "# $ &% '(' ) *$+ ! &,.-
/
; h*
Y
10@
Í nx]_dfWhat]_dfe6\ecpac`_atWhX]_X`sn³df\be6WVq]sX`xi d}nd}e6\dfna`XbV`s`X\^]ac\Vonse6WXSVeQ 32Ï\qX6X`xi nse6¨6Xo54@V`sec|V}XW ¦4aoVdfopacb]sd}b@df\$]s`seoVVb]_dfe6\(at|e6] ]sSVdfn ]se6Vdfb@WhaG¡|;X@©e6q\Vodf\6 c
7Á§jl nsdf\VbX«Whac\^¡®oV9d 8X`X\^]acnXb]snTac`sX{]_e¥|;X]_acªcX\d}\^]_e¥acbbe6V\^]TnsqbkS0atn¦8d²§@\qe6\Vfd}\VXac` X¯$pat]sd}e6\qn)ac\Vo+be6\qn]_`sacdf\$]snl'¦8dfd¬§acVV`eGÂqdfWhat]_XzWXGacnV`sXn)ac\Vo+e6q]s}dfX`nAXfdfWhdf\pat]sd}ec\'l ¦8dfd}d²§Ansdf\Vm6V}ac`df]sd}Xnzdf\]sSVXX¯$pa]_dfe6\Vnzac\Vo"`sX¯qd}`XWX\^]_nz]_eVnsXoV:d 8X`sX\^]zWeoVXfnzacn acf]sX`\pat]_d¨6Xn´(ÌX]Vn`sXd}X ]_SqXnsX]sSV`sXXe6df\^]_nac\qo>d}f}qn]_`sat]_X]sSVXnXacns;Xb]_n|^¡ ac\"XÂqacWVfXc´ ;=A@dfn"]se 2xaG6X`_acm6X 4·]sSVX>opat]_aq´ ¾Aq]]sSVdfndfn\Vec]a¹m6eeo°]_SVdf\Vm d}\±]_SqX+V`XnX\VbXec)S$VmcX+e6]_fd}X`sn Sqd}bkS WhaG¡±;X`]sV`s|»oVXXV¨¡Ã]sSVX+aQcX`sacm6X Xnx]_dfW+a]_dfe6\'´ ¼«\½]sSVXget]_SVX`hSVac\Vo'l¦©d}d²§¥]_SVXoVX©X\VbX·acm^acdf\Vn]he6]_fd}X`sn®dfn]_e 2ÏnXfXbd] 4e6\V¨¡a«©X nsX]ÄetEm6eeoopat]kal$ Sqd}bkShd}n\VeQ \qec]m6eeo¥©e6`aGcX`_atm6d}\qmV´ RTSVdfn]_`d}bkª^¡Ãnsd¨]_Vat]_dfe6\-dfn(X6X\- Aec`sn](|XbGacqnsX+ ÄXclKWhecn]ec)]_SqXh]sd}WXclKSpaG6X C )hWXGacnV`sXn ´ eg]sSpat]lKd¨]¥dfn¥\Vec](XGacnx¡»]se·VnsX®n]kat\Vopac`o n]_at]_dfn]sd}bac ]_XbkSV\Vdfb]se8atbX]_SVdfnoVe6V|q}XV`e6|VfXW"´ RTSVXnX(atns;Xb]snat`sX« ÄXf oqd}nbVnnsXoEl;©e6`Tdf\Vnx]kac\VbXclJdf\ 6 $ 74´
Ri h
Æ ( h Ë Ák i È Ê Ë Æ i h[lT¶ }acn]acns;Xb]d}\ ]sSVd}n(ªdf\Vo¸ecXn]_dfWhai ]_dfe6\¸V`sec|V}XW dfn]sSVX8acb]]_Spat]ne6WX"nsX]heczopat]_a>W+aG¡¹|;X+' 9(Xd¨]_SqX` |XbGacqnsX p ¦8d²§]sSVX¥pac`sacWX]sX`«dfn«\Vec]©V}¨¡0oVXp\qXo±d}\±a+m6dfcX\±nsd¨]_Vat]_dfe6\½¦8Xt´¤mq´«]_SVXa Âqdfn ecKa`ec]ka]_dfe6\"W+a]_`sd Â"dfnV\VoVX p\VXo0dfKdf]sn{ac\Vm6fX«tac\VdfnsSVXnk§l ¦8dfd¬§']_SqXAopat]_aznX]vdfnK\Vet]=ac|q}X@]_e«V`eQdfoVXTa{`sX}Xcat\$]KXnx]_dfW+a]_X¦©Xc´ mV´KXn]_dfWhat]_df\Vm aV²at\VXd}n\Vec];e6nnsdf|V}Xd¨vacf';e6d}\^]snzat`sXbe6ffd}\VXac`k§j´ Re>8acbX]_SVXnsX"²atn]hV`sec|V}XWnlÄ ÄX"W(Vnx]®|;Xac|VfX]_e±oVX]_Xb]+]sSVXnX"nsdf\Vm6V}ac` nsd¨]_pa]_dfe6\Vnac\qo Xn]sd}What]sX>d}\qn]_Xaco ac\Vet]_SVX`We6`sX·nXbd pb>WeoqX8´ RTSVd}ndfn XÂ]_X\Vnsd¨6Xf¡0oVdfnsbVnsnXo·df\ 6¤clJ6Y 7³©e6`Tdf\Vnx]kac\VbXc´ pV`]sSVX`Whec`sXclXcX\df\\Ve6\i&nsdf\Vm6q²ac`Änsd¨]_pa]_dfe6\Vnl}ee6ª$df\Vm©e6`AaWeoVXJ df]sSa )\$VW|X`=ecppat`_acWX]sX`nK SVdfbk S V]K]sSVX)opat]_azdfn=ac¨ AaQ¡nv`XbecWhWX\VoVXo |XbGacqnsXcl]_SVX«fXnnTpac`sacWX]_X`snA]se¥Xnx]_dfWhat]_XtlV]_SVX«fXnn)WXGacnV`sXn{ac`sXz`sX¯$Vdf`sXo'l nse]_SVat]up ¦8d²§Ä]_SVXbkSpat\VbX]_ensX}Xb]ansX]zecWXGacnV`sXn{ d¨]_SVecq]{e6q]_fdfX`sndfnSVd}mcSVX`l ¦8dfd¬§]_SVX\$VWX`d}bacvn]_ac|Vdf}d¨]&¡>ec]sSVXXnx]_dfW+a]_dfe6\»dfn|;X]s]sX`l³Xns;Xbd²at}¨¡±d}\·]sSVX V`sXnsX\VbXec\Ve6dfnsXcl df]T]sS$VnzSqXfVnnse6¨d}\Vmh]_SV X 2ÏacVV`eQÂdfWhat]_XWXGacnV`sXnat\Vo0ecq]_fd}X`sn 4V`sec|V}XW"´ µzeQ ÄX6X`l{]_SVdfndfn\Vec]®¡cX]"VnXo df\ be6WVq]sX`Ïid}nd}ec\'lzXjÂbX]©ec` 6¤clA6xY 74l |XbGacqnsXdf]{WVn]z|Xdf\^]_Xm6`_at]sXo df]sSVd}\`sec|VVn]zac\qo0\Vec\i&fd}\qXGac`TXn]_dfWhat]_dfe6\'´ RTSVdfn{nXXWhnz\Vec]T]sehSVaQcX|;XX\¡cX]zoVe6\VXt´[]d}n]_SVXmce^ac'ec ]_Sqd}n{n]sVoq¡6´
8qxiÁki
~} !
! "# $ &% '(' ) *$+ ! &,.-
KH
@d`sXns;Xb]]_e®]sSVX(WXGatnsV`XWX\^]X¯$pat]sd}ec\±ac\Vo oVX p\qXo"V]_ea¥nbGacfX«8acb]_e6`´=RTSVXdf`TXnx]_dfWhat]_dfe6\"WhaQ¡+]_S$VnT|;X«W(qbkSnd}WVfX`T]sSpac\ Xn]sd}What]sd}\qm-]_SVXgVS^¡nd}bacVac`_acWX]_X`n´ J`e6W aÃ]sSVXe6`X]sd}bac;e6df\$]®ec«dfX lT]_SVdfn be6``sXnec\VoVn]_ehac\pac¨¡nsdf\Vm]_SVXV`etwxXb]_d¨6Xn]_`Vb]sV`sXec ]_SVXnbX\qX¦©nsX X 6¤6lV^Y 7Á§j´
}~}L&
q- zOF,, n- A' LF,
z- R j
R Sqd}npac`sacWX]sX`sdfn_a]_dfe6\±d}nV\qoVXp\qXoÃd}\>]_SqXbGacnXec)a)2&V}ac\pac`4(oqd}nV²atbXWX\$] T ¦8d8´¤Xt´Äat}';e6df\^]_n{ac`sXdf\]sSVXn_atWhXV}ac\VXe6`Td¨]{d}n{aVV`X`ec]ka]_dfe6\J§Ä SVX`sXGatnac\qec]_SVX` X¯$pat]sd}e6\®SVe6foV n p ( ' ):*lm6d¨6X\"ac\Vec]sSVX`ÄWhat]_`d¨Â 1 lacfnseoVX p\qXoV ]_ensbac}X8acb]_e6`lp|Vq]\Vet]znV|wxXb]{]_ebe6\qn]_`sacdf\$]´ µ{X`XclJd}\qoVXXo'l;e6df\^]_nWhaQ¡"|;Xfe6\Vm]_e+ac\Vet]_SVX`{`d}mcd}oe6|wxXb]_n{e6`WhaG¡"|Xdf\Vbe6`Ïi `sXb]_¨¡>What]_bkSqXo»ac\Vo>]_S$Vnacb]acne6q]s}dfX`n«©e6`«]_SVdfnXnx]_dfWhat]_dfe6\'´ye6|VVnx]Xnx]_dfW+a]_X d}nT]_S$VnWhac\VoVat]_e6`x¡6´ pV`x]_SVX`sWe6`Xclz]sSVX>`sdfm6dfo oVd}nV}acbXWhX\^]ge6`]sSVX>bGatWhX`_a¸d}\^]s`sdf\Vnsdfb±pac`_atWhX]_X`sn W+aG¡±|;Xns;Xbd pb 6¤cxY 7v]_S$Vn¡d}X}oVdf\Vm0pac`]sd}bV}ac`©e6`sWnec % 1 e6` 1 ´ X6X`sac WheoVX}nW(qn]{]_S$Vn|XXcat}pa]_Xobec\VbV``sX\$]sf¡c´
1\.IL@FZ]a
IL@FEHG
N KHUbZ
UWGW6DCFE % GH ?'EUTR8;:BE>N%NV2K:9:92'6BC'WYXZSR2
8
8 G 2
8d:DEUNV8V?>P(:9S_2
:B8d:ut H
EI:B698J?K2*C18 M L A>N G
G [ EUNJC1A>\]2*?@:9A/6BC1EU6B2^6B2!TR6B2'C92 (
G AU:9efTR6BA G([ ?K:
L 2'8 R Q
476B8d:9:92
E>CZg]h]ijE _ G
EI:B698;v38JCc476B8;:O:92 x w W#032M6B2!TR6B2'C92
C [ T`2!6DC9?!698VT(:DCs\+6BA H
}~}L&
:B2 G
: :BSR2y?!A H
N;2!:O:92'6BC'P H
E>CF:9S_2^:B6BE
EI:96B8J?K2'C
L 2!8 R Q
47698;:O:B2
COT`A/C92aA>\bEc6on gpOqrisW1XZSR2 T%A
2
:9A}|(P~2>W Q WVg
`>9UO`Ifh1WYa2'692=gi
:DCcAU\aE H
2'E
H
EU:96B8dvzA>6oE{2'?K:9A/6
Cag{i\+A>6ZCOA H
C 8 RQ [ 9
2 m RW
Q
q- zOF,, n- A' LF,
z- R j
ca \ . O) o z' ) Ql d4´ Xc´v ÄXbe6\Vnd}oqX`]_Spat] ±dfn{b}ecnsXo]_e ©e6`am6d¨6X\0oVdfn]kat\VbX l
a nsX]ec= ( d4´ Xc´
.O) ' 5 ' 8
8 d¨]_S a
ÄX®bec\VnsdfoVX`]_SVat]]_SVX1 * WXGacnV`sXn Äac`X+b}ecnsXoÃ]_e"]_SVXhe6|VnX`x6Xo WXGacnV`sX n ©ec`amcdfcX\oVd}nx]kac\qbX ! SVdf}Xtl©ec`'XGacbkSWXGacnV`sXtlcaTnX]ecR ' R-, L $L'Z/ ) * oVX p\qXnz]sSVX`sX²at]sd}ec\|;X]& ÄXX\·WXGacnV`sXac\Vo"pat`_acWX]sX`l
nsVbkSgacVV`eGÂqdfWhat]_XWXGatnsV`Xn{SpaG6X]_e|Xw
w ,|^¡]_SVXacfm6e6`df]sSVW"´
acnnsbkSVXW+a]_dfnsXogd}\ K dfmV´JYq´ q0 m1 ... mi ...
l
Initial Estimate
Q1 Qi
mM Q Measures M
c (m , q)=0 i i
Q0
?q
Measurement Equation c(q)=0 0
Parameter Constraint
Kd}mcV`sXYLp Xnsb`sdfq]_dfe6\get]sSVXXn]sd}What]sd}ec\gV`e6|VfXW"´
RTSqX«\Vec]sd}e6\+ecCx2 atVV`seGÂdfW+a]_X { 4 oVat]ka(dfnÄ©ec`sWhacfd}nXoSVX`sXtlqVnd}\Vm ,' Cw'lqacnoVd}nbVnnsXo·d}\0acV;X\qoVd¨Â0ÍIlVd4´ Xc´Rp "$#%!
) &"# #(' &"#
, L.,F *$wH'j . ¦ §
©e6`)" at\Vo# ( SVX`sX ' d}n)a¥e6ndf]sdfcXnsXWhd i&oqXp\Vd¨]_Xnx¡WWX]s`sdfbW+a]_`sd ´ RTSVXWhat]s`sd  ' WhaG¡+|;X{bGacf}Xo+]sSVX , L.,F *$wM ) *$ ) *6´=[&\an]_at]_dfn]sd}bac ©`_acWX Äe6`ª·¦©nsXX«acV;X\VoVd ¾ ©e6`Äa(oVdfnsbqnsnsdfe6\J§Ä]sSVdfn)be6``sXns;e6\VoVnA]se(]_SqXdf\$cX`nsXec ahbe tac`d²at\VbX(ac\Vo"]_SVXoVd}nx]kac\qbX(be6`s`Xne6\qoVn{]sea+ÎgacSpat\pacfe6|VdfnoVdfn]_ac\VbXtl|qq]z ÄX
~} !
! "# $ &% '(' ) *$+ ! &,.-
d}fJ\Vec]©e6f}eQ ]sSVdfn@]s`_acbkªSVX`sXtlnd}\VbXz ÄXzbac\®\qec]@m6pac`sac\^]&¡¥]_Spa]@]sSVXzacnsnVWq]_dfe6\Vn `sX¯$Vdf`sXo0]sehoqX6X}ecgnsqbkS·a¥©e6`sWhacfdfnsW¿ac`X6X`d VXogdf\e6V`TbGatnsXc´ [Ä\Ved}\qdf]sd²acKXn]sd}What]sX+dfnaGcatd}}ac|VfXe6\VXbGat\Ãnd}WV¨¡> `sd¨]_
X ) ' ) *ql']_SVdfn pac`]et]sSVXns;Xbd pbat]_dfe6\gdfnT]_S$Vn{\Vec]{abec\Vn]s`_acdf\^]G´ f
_ac\ atVV`seGÂdfW+a]_X nse6fq]sd}e6\ElpX]_bt´}´f´ zi h i h Æ p Æ É i©Ë~i Æ Æ h ;Æ$Ê Æ Q Ç½Ê Ë Ç[h i4^ l¾Ä¡ÃVnsdf\Vm Ê > \Ve6`W+at}dfnsXogoVdfn]_ac\VbXnlacnoVdfnsbqnsnsXo>d}\gacV;X\Voqd¨Â0ÍTlp AXbecW(|Vdf\VX(df\0ac\gatoi oVd¨]_d¨6XW+at\V\VX`lAoVdfWX\Vnd}ec\i&fXnn¯$pac\^]_d¨]_dfXn´ e6df\Vm±]_SVdfn+SVacnnsXcX`saczmceeo V`secX`]_dfX n p{¦©d¬§Ä ÄXbGat\Wd Â"WXGacnV`sXnT SVd}bkS0SpaG6XoV:d 8EX`sX\$]qS$¡nd}bacV\Vd¨]_n e6`oq9d 8X`X\^]e6`soqX`«ecWhacmc\Vdf]sVoVXac\qo¸¦8dfd¬§ AXbac\·6X`¡·Xacnsdf¨¡>acoVo±) a 2&\VX 4 WXGacnV`sXat]vac\^¡]sd}WX ´ X)X6X\+bac\be6W|Vdf\VXWhXacnsq`sXndf\oV:d 8EX`sX\^]v©`sacWXn ec`sX©X`sX\VbXtlqnsdf\VbXz]_SqX{\qec]_dfe6\®etEoVdfn]_ac\VbXVnXo®SqX`sX{dfnÄdf\VoVXXodf\VoVXX\VoVX\^] ecK]sSVX©`sacWXetv`sX©X`sX\VbXt´[&\g8acb]lJWhXacnsq`sXn«ac`sX}df\VªtXo·]_eh]_SVXpac`sacWX]sX` ]_eXnx]_dfWhat]_X|^¡ac\^¡\Ve6\i&fd}\VXac`d}WVfdfbd¨]zX¯$pat]_dfe6\'´
(
Hf
® K@\
%
0A " A0Ä
(
@\ca]SQ5U .
N;8JCBEI:98VA
}~}L&
TRNV8%2'C=:9S_2
2*Cu:B8 H
EI:B8;A
A>\1E
A [ :aA>\ :9S_2cC9?!A>T`2=A>\b:BSR2 TR6B2'C92
G t
E H
:aCu: [_G t
8J?oT_E>6BE H
2K:92'6'P E>Nd:BSRA [RQ S42
?!A
C98 G 2!6=:9S_8VC
G
q- zOF,, n- A' LF,
z- R j
)
]_SVXnsXX¯$pat]sd}e6\qnzat`sX]& d}bXoqd98X`X\^]_d}ac|VfXcl SVd}fX '
'
'
d}n{a|VfebkªoVd}acm6ec\pac'What]s`sd ÂE´
¶znvnsVbkSEl]sSVXTV`sec|V}XW dfna«nsdfWV}X jw $q`se6|VfXW"l$d8´¤Xt´K]_SVXTb`sd¨]_X`sdfe6\m6dfcX\ d}\-¦/ ^§AWXac\Vn p\VoVdf\Vm]_SVX¯$pac\^]sdf]&¡ " ¦8d²§Abfe6nsXn]{]_e "7©e6`)]_SVX¯$pacoq`_at]sd}boVdfn]kat\VbXpac`sacWX]sX`sdfnsXog|^¡ ' ac\Vo ¦8dfd¬§Adf\]sSVXnsX ] »oVX p\VXog|^ ¡ &" ):*qlpacnnsbkSqXWhat]_dfnsXo·df\ KdfmV´Vq´ x0
x c(x) = 0 Kdfm6V`XPpze6\i&fd}\VXac`Xnx]_dfW+a]_dfe6\gatnzaV`etwxXb]_dfe6\V`se6|q}XW´
[]{dfnT AX}ª$\VeQ \ ¦©Xc´ mV´H6¤YcqlJcYx7¬§Ä]_SVat]op p ? ' L' 5 1, 'j 5 $ x ' w )vC ('j 'j u [L'#jw L'j $ 5 'z'j 'j L'j~ *59 AL' Cw A ! 5Cw $ " " 'H e$wM, Y e 5, ,'jw,/. , , ' | C :x 5 j&, "7w $ !' jw $p´
(
Hf
;=bGacnXnl ]sSVXbe6\^6X`sm6X\VbX+ec@]_SVXWX]sSVeoEl \qec]\VXbXnn_ac`d}¨¡±]_e ]_SVXe6q]sd}Whaccat}VXtlp|Vq]zat]fXGacnx]]_e+a`XGacfdfn]_dfbnsV|ie6q]sd}Whac'Xn]sd}What]sXc´ µ{eQ AX6X`l ]se"at]s]_acdf\±]sSVdfnoVe6V|VfXm6e^at4lE ÄXW(Vnx]acfnse"`sXdfnsd¨]a®6X`¡>nx]kac\VoVac`so \qWhX`sdfbGac acfm6e6`df]sSVW"´
( )( Hf
\ Z
HaWQL
C98VN;t
E>N WaXZSR8JCa8JCr2'E>C98VN;t
~} !
! "# $ &% '(' ) *$+ ! &,.-
%
R SqXnsX"oVXp\Vd¨]_dfe6\Vnhac`XoVd:8EX`sX\^]©`secW ]sSVXb}acnnsdfbGacTVnXVoqeti&df\^6X`nsX T +¦8Xt´¤mq´ 6 7Á§et)aWhat]_`d¨Â l³ec|q]kacdf\VXoé`e6W ]sSVXnsdf\Vm6V}ac`tacfVXoVXbe6Wecnsd¨]_dfe6\'l©e6`«df\i n]kat\VbXt´ RTSqd}n)WXbkSpac\VdfnsW dfnÄcX`x¡VnX©Vd}\ecV`AbacnsX«|;XbacVnX«df])acf}eQ nA]se¥be6\qnsdfoVX`A]sSVX bGacnXn SVX`) X p
%
]_SVX# ) $ ) *$w'Y) **q #'j .d, W l$SVX`sX«]sSVX«oVXp\Vd¨]_X What]_`d¨Â 2ÏacnTbfe6nX]se ' acn;e6nsnd}|q}X4d}n{ac]_e6What]sd}bac}¨¡VnXo'l
]_SVX3-, P $L' C Y, , ac`sX+\Vec]df\VoVXX\VoVX\$]ha] " lvd8´¤Xt´ X¯$pat]sd}ec\Vn{ac`sXXfdfWhdf\pat]sXo'l
¦8df\
]_SVXnX\VnX]_Spat]]_SVXd}`(}df\VXGat`pac`]sn dfn¥\Vet]¥ec©VfÄ`sac\Vª§lvSqX`sX`XoVq\Vopac\^]
AXTSVaQcX -, L *$L'A L C eL'l6nd}\VbXcl$df\¥]_Spat]=bGacnX bac\e6\V¨¡¥|;X ec;`_ac\qª¥at]We6nx]c Kl6]_S$Vn\VeWe6`X)]_Spac\j X¯Vat]_dfe6\Vn@ac`X)]kacªtX\hd}\^]_eacbbe6q\$]l
©V`]sSVX`We6`sXtl@d¨ac\T-, P $=' ' 59 zdf\¸]_SVXnX\VnX"]sSpat]d¨]_nm6`sacoVdfX\^] tac\VdfnsSVXnlp]_SVX\]sSVXacfm6e6`sd¨]_SqWoVdfns`Xm^ac`oVn]_SVXX¯$pa]_dfe6\ga]T]_SVdfne6df\^]G´
( .
Hf
3UbZ
S AI5a IL@dUbE
UW`)ILKM8 C98;:98VA
2 GlL tMCOA/6O:B8 _ Q W
}~}L&
:BSR2oC92K:aA>\ 2
[ EI:98VA
C
L 2!\+A>6B2cEUTRTRNVt~8 _ Q
:9SR2 6B2 G([ ?K2 G
C
[ EU6B2Ke69A~A>:
¦GY^§ G 2*?KA H
T`AUe
)
q- zOF,, n- A' LF,
z- R j
¶ ]]sSVXacfm6e6`df]sSVWd}bfXcX8l@ ÄXnsdfWV¨¡¹be6\qnsdfoVX` {l]sSVX)2&bfe6nsXn]F4ns¯$pac`Xi`seec] ) oVXbe6We6ndf]sd}ec\0ec ' lV SVdfbkSgdfn{ahfeQ AX`T]_`sd}ac\VmcV²at`TW+a]_`sd Â|p
) '
# df]sS
#Z
) #
0)
"7Aat\Vo
ac\Voacf}eQ n]_eSpaG6XX¯$pat]sd}ec\ ¦ 6§AnsdfWVfd pXo·acnop
#
#
) "
#
#Z)
#7
#
#
¦$§
%
]_S$VnXGacnd}¨¡ be6WV]_XoIVnsdf\Vm½]_SVX+2Ï`XoVqbXo à 4 ns¯$pac`Xi&`eet]0oqXbecWh;e6ndf]sd}e6\ ) # ) #0©`se6W p
% % % %
SVd}fXclp©`e6W
#
)
.
0 d¨]_S #
#7
¦QY^§l AXSpaG6X)p
)
d¨]_S
%
)
) "
#
#7)
/
"
¦Q6§ ec ¦G^§
.
¦Q6§
&[ \"e6q`TbGacnXclq ÄXbGac\"XcX\"8acn]sX\]_Sqd}nbecWhqq]kat]sd}ec\|;XbacVnXacnToVXV\VXod}\»¦4 ^§ ]_SVXTWhat]s`sd  ' dfnv|V}ebkª(oqd²acmce6\pac8´KRTSVXToqX`sd¨tat]_dfe6\dfnvm6dfcX\df\+atVX\VoVd ¶´X6X`sac ec]_SVX`AdfWV`seQ6XWX\^]_n{ac`X«acfnse¥q`sXnX\^]df\®]_SVXd}WVfXWX\^]_at]_dfe6\'lq©ec`Ädf\Vn]_ac\VbX« SVX\ aWhat]s`sd  ' d}noVd}acm6e6\Vac4´
( *
UbE XF@dEM6 G C^E H
:BSR2cEUN Q A/698;:9S H
?K2
EIv(8 H
[ CO8 R Q [RH
8J?=C9?DSR2 H
A/6 H
E>N 2
A>6 ElC9E GRG NV2
T`A>8
E
:BSR2
G 2'CB?K6B8 L 2 G
[ EU:98VA
C^AU\Y:BSR2
: AU\s:BSR2}?K6B8d:B2!6B8;A
?!698;:92'698VA
P%412
WoXZSR8JC58
H
E tye8
:BSR2!A/69te1?!A
\
E>?K:54A [ N GL 2
2'6 Q 2
G 2!:92'?K:92 GL t
SR2!6B2>W
~} !
! "# $ &% '(' ) *$+ ! &,.-
8¦ |J§Äfee6ªh©ec`Ta¥ecd}\^]bfe6nX`lV]seq2ÏnWheec]sS54{]_SVXXn]_dfWhat]_dfe6\'lpd¨]_SVXq`sXdfe6VnTXn]_dfWhai ]_dfe6\"|Xbe6WXn{V\Vnx]kac|q}XtlJ ÄXV`se6;e6nX«]_SVX©e6f}eQ df\Vm+ac}mce6`sd¨]_SVW p "78 '
h y ³0
[&\Vd¨]up ̳ee6|p [ RTSVX\ ÍfnsX {\$]sd} Æ
):* )
I
&" " ) ) " "&" " ! " " ! "
h
¦ ^§
XgSVaQcX·bkSVe6nX\°]sSVXg\Vec`sW " ) " ]se-Xcat}pa]_X df\ e6`soVX`)]_eh|XnV`sX]_SVat]qX¯$pat]_dfe6\Vntac\VdfnsS'´ d¨]_S]_SVdfn{WhXbkSpac\VdfnsW"l; AXXGacnd}¨¡nsXX]sSpat] AXbe6WV]_X " ) " " ©e6`ne6W X 0) ´ pV`]sSVX`We6`sXtl@]sSVX"}df\V XGat`sdfn_at]sd}e6\½ec &" |;Xdf\Vm°;X`©ec`sWXoMat ] " lnd}\V bX
&" ) *½©`e6W ¦ 6§"ac\Vo &" ) " »©`secW!¦ ^§jlq `sd¨]_df\Vm©e6`sWhacf¨¡ p
%&
!('*)$# #!"
$# d¨]zacV;XGac`n ]sSpat] &" ) " + &" $" -, . ) " /0 " 1 2, 3 ) &" -, . 4 ! &" ! " ! , 3 ¦ t
^§ [E AXzbkSVeecnsX5· d¨]_S6! , ! " tac\Vo+nsqºhbd}X\$]sf¡®nsWhacf;©ec`@Sqd}m6SqX` e6`soVX`)]_X`sWn{]se|X\VXm6}dfm6df|VfXclV ÄXe6|]kacdf\ &" ! " $atn{oqXnsdf`sXo'´ [&\±V`sacb]sd}bXcl']sSVd}nbe6\VoVd¨]_dfe6\> bac\±\Vec]|;X¥ `sXacbkSVXo»d¨]_SVX`X¯$Vdf`sXo7 dfnnsWhacffX` ]_Spac\½\$VWX`d}bacX`s`e6`snl@©ec`hdf\Vnx]kac\VbX0d¨ " !|Xbe6W Xn+\VXmc}dfm6df|V}XtlA|V]h ÄX ]_S$VnSpaG6Xbe6\^cX`smcXo'´
op
:9
}~}L&
9
9
:9
c
q- zOF,, n- A' LF,
z- R j
R Sqd}nbe6\Voqdf]sd}e6\»bGac\»\Vec]|;X+`XGacbkSVXo¹acfnse0dfÄ]_SVXhb`df]sX`sdfe6\»Spacnn]_`e6\Vm0d}``sXmci T ²ac`df]sd}Xn¦©be6``sXnec\VoVdf\Vm·SVX`sX®]se0]_SqX+8acb]]sSpat]¥Sqd}m6SqX`(ec`soVX`]sX`sWn¥WhaG¡Ã|X+V`sXji e6\qoVX`sac\^]j§T|Vq]]sSVdfnWXGac\qnz]_SVat]z]sSVX(q`sXnX\^]acfm6e6`df]sSVW¿dfn\Vec]acopatq]_Xo0]_e+nsVbkS andf]spat]sd}e6\0ac\Vod¨]{ac}ne+WVn]{nx]_e6'´ ¶znbe6\VnX¯$VX\VbX¥Xdf]sSVX`op
*ac\Vo
/ "
fd nn]s`sdfb]_¨¡oVXb`sXacnsdf\VmVlnse]_Spa]v]_SVX{acfm6e6`df]sSVW bec\$cX`m6Xn
©e6` ) l^d4´ Xc´ SVX\]_SVXTbe6WVq]_at]_dfe6\ec &" dfnvn]_ac|VfXcl^ AXbac\VbX ]_SqXy " q]se]sSVX p`snx]@e6`soVX`l$acnv©e6`a{X T]_ec\acfm6e6`df]sSVW ac\qo]sSVX bec\$cX`m6X\VbX(dfn¯VacoV`_a]_dfbcl ©e6` nsWhacf}X` *lt|V]K d¨]_S ! " " ! lt ÄXAec|q]kacdf\¥afd}\VXac` bec\$cX`m6X\VbXclV]sSVX«acfm6e6`df]sSVW|XSpaGd}\Vmatn)amc`_acoVdfX\^]ToqXnsbX\^]TWX]sSVeo'l
e6`
df]sSg*at\ac\VXjoÂe6\qX\^]_d}ac`_at]sX) ac\Vo ]_SVX acfm6e6`df ]sSVW¯$Vdfbkª$bfe6¡\^6nx]_Xe6`sVm6XnnÄ´ ]_eQ Aac`soqnX`eVl
( Hf
"
`]_SVX>b`sd¨]_X`d}ec\ q`se6;e6nsXo |$¡ 6¤Y^j 7« SVdfbkSISVacn|XX\ nsSVeQ \"]_eh|Xq\|qd²acnXo·|^¡]sSVdfnzatq]_SVec`lpbec\$]s`_ac`x¡]_eec]sSVX`T©e6`W(V}at]sd}e6\qn´ [&\ ]_SVdfn"bGacnXcl«XacbkSIWXacnsV`X-atoVo ) oVXm6`sXXnec©`sXXoVe6W ]_e acn oVdfnsbqnsnsXog SVX\0oVX`sd¨d}\Vmh]_SVXoVX p\Vd¨]_dfe6\m6dfcX\0d}\-¦ 6§j´
{ y *i8.i©
[&\Ã]_SVXhnsX¯$VX@ AX+ac`sXhm6e6df\Vm"]_e0VnsX]_SVdfnXn]sd}What]sd}ec\ V`sebXnsn©e6`]& Ae0ns;Xbdpb VV`s;e6nX&n p
}~}L&
6
q- zOF,, n- A' LF,
z- R j
i h i - @
)i h ©i ji8 Êh ËziÁki Ê Æ Ê ³ki Êh½É ©i Ê ³
h
[&\]_SVXbGacnX SVX`X ' )+*¦8d8´ Xc´vdf\Vdf]sd²atEbec\VoVd¨]_dfe6\Vnac`X\Vec]A]_e¥|;X]katªcX\"df\^]_e acbbe6V\^]j§jl Sqd}fXh ÄXhSpaG6X+a2&Whdf\VdfWhacvnsX]et)becSVX`X\^](X¯$pat]_dfe6\Vn4g¦8d8´¤Xt´h ÄX acnsnVWXÄ]sSpatn ] ! H O' !' 'j 5 $ Y M-, L $L'5 ' ) 9 1 I/ ' 9 ) *|c C :x j&, # ! 'j , '5 s§jl ]_SVXb`sd¨]_X`d}ec\0nd}WV¨¡"Wd}\VdfWd}nX
n p Wdf\ ! SVdfbkSgdfn{df\VoVXXo0Whdf\VdfWhac'©e6` ) d}``sXn Xb]sdfcX¨¡0et]sSVXbe6\Vnx]_`sacd}\^]sn´ RTSVdfnvWhXac\Vnv]_SVat]=]_SqXTn¡n]sXW dfnvnse6¨6Xo+ec\Vf¡ df]sS`sXnXb]]_ e at\Vo\Vec]= d¨]_S `sXns;Xb]]se 4´ []T]_S$Vn{be6``sXns;e6\VoVn]_e]_SqXq`setwxXb]_dfe6\V`sec|V}XW p
%9
4
!
!
# .
' d¨]_S ' )0O ' I/ 1
[&\°]_SVdfnbacnsXtlzXacbkS WhXacnsq`sX±acoVo \qe¹oVXm6`XX>ec©`XXoVe6W be6SqX`sX\VbX d¨]_S" Spat]{Spacn|;XX\oVdfnsbVnsnXog©e6`¦46§´ ki -qki h Æ y Æ .i4&i Êh½É Ái
Æ &y Æ c Ê
]_e
#
¦ § l{acm6acd}\ df\
Æ p Æ
̳X]zVnzbe6\Vnd}oVX` C q ' % SVdfbkS>Spacn{\Vec]z|XX\gqnsXo0]_e®ec|q]kacdf\ am6dfcX\0pac`_atWhX]_X`TXn]sd}What]sX ´ XzWhaQ¡+ )at\$]A]_e¥Xn]_dfWhat]_XSqe nVbkSa(WXGacnV`sXM2&W+a]_bkSVXnd4z]_SVdfn)pac`sacWX]sX` Xnx]_dfW+a]_Xc´¶ becSVX`X\^]z AaG¡ecnse6¨d}\qm+]_Sqd}nV`e6|VfXW dfnT]_eoVX]sX`Whdf\VXxp
¦ c6§ # d4´ Xc´v]se V\Vo]sSVX Ïbe6`s`Xb]sXoWXGacnV`sX m6dfcX\"]_SVXpat`_acWX]sX`Xnx]_dfWhat]_Xt´ [ AXacVqf¡»]_SVX"`sX²a]_dfe6\ ¦ QY6§]_e>]_Sqd}nb`sd¨]_X`d}ec\½ ÄXSpaG6XtlAV¹]_e·]sSVX p`n]
%B
4 !
.
-
4
2
e6`soqX`l;ac\0Xtacfpat]sd}e6\0ec=]sSVXoqd}nx]kac\VbX(|;X]& ÄXX\·]_SVXbe6``sXb]_Xo>WXGacnV`sX(ac\Vo ]_SVX]s`sVXh¦©V\Vª$\VeQ \J§TWhXacnsq`sXclJd8´¤Xt´v]_SVX2Ï|qd²acn4`X}at]_Xo0]_e]sSVd}nWXGatnsV`Xp
)
!
¦ tY^§
~} !
cY
! "# $ &% '(' ) *$+ ! &,.-
df]sS ) l SVdf}X ) Xtac}Vat]_Xn]_SVX(oVd}nÏi
]kac\qbX|X]& AXX\h]_SVXe6|Vn X `x6X oac\Vobe6``sXb]_Xo®WXGatnsV`Xcld4´ Xc´=d¨]_n 2&d}WV`Xbdfnsdfe6\54_´ ¾Aec]sSX`s`e6`sn at\V o SpaG6X]se+|;X«]kacªtX\0d}\^]_e+acbbe6V\^]´ df\VbX©`se6W!¦46§Tdf]acV;XGac`n{]sSpat]{ AXSpaG6MX oVXm6`sXXnzec=©`sXXoVecWlJ ÄX(oVX p\VX acn n 2ÏWXacnsV`XWX\^]X`s`e6d` 4 p
(
Hf
.EbI5X``se6`oVdfn]s`sdf|Vq]sd}e6\ÃdfnnbkSVXWhat]sd}nXo df\ KdfmV´J´ [] d}nXÂXb]sXo(]sSpat]nsWhacfX`s`e6`sn be6``sXns;e6\Vo(]se{]s`sVXÄacVV`eGÂqdfWhat]_XÄWXGacnV`sXnl SVX`XGacnSVdfm6SVX`X``se6`nbe6`s`Xne6\qo»]_e0e6q]s}dfX`n´RTSVdfn dff@|;XhoVd}nbVnnsXo½df\ ]_SVX\VXjÂ]znXb]_dfe6\'´ Yq´ p`se6W nVbkShaoVdfn]_`d}|qq]_dfe6\'l^df\¥e6`oVX`K]se«Xnx]_dfWhat]_XA]sSVXAtacfd}oqdf]&¡ecp]_SqX)Xnx]_dfW+a]_X K l ]& Ae«Whacdf\(nx]_`sat]_Xm6d}XnT¦©nsXX@©e6` d}\Vnx]kac\qbXY6 $7$©e6` a{`sXdfX z§ ac`sX@VnsXo'l6Xdf]sSVX`np
¹.i Æ h h ± Æ Ê JÊ'Ê Ë Æ p Æ be6V\^]sd}\VmT]sSVXvX`xi bX\^]kacm6XTetJWhXacnsq`sXn ( SVdfbkSX`s`e6`=dfn=|;Xfe a qÂXo]sSV`sXnsSVe6fo ¦8Xt´¤mq´ 6' x7³]_SVdfn|Xd}\qm+ª$\VeQ \0acn 2Ï`_at\Vn_acbji&fd}ªtX 4WX]_SVeoVnk§jl p\Voqd}\VmÃ]_SVX"`sac\VoVe6W Xn]sd}What]sX SVdfbkS°at}feQ nh]se»WeoVXT]_SqXWhaÂdfWhac \$VW(|;X`{ecWXGacnV`sXnJe6` h ~ Ë i h » ¹. i 5Æ h Ç - Æ Ê be6\Vnd}oVX`sdf\Vmg]sSVX+WhaÂdfWhacÄX`s`e6` X p`snx]@WhXacnsq`sXnlqd8´¤Xt´=]_SVecnsXT df]sSansWhacf}X`ÄX`s`e6`z¦8Xc´ mV´K]sSVX ecE]sSV WXoVd}ac\>X`s`sec`d¨ ) / * 6 tx
7 l;]_SVdfn|;Xdf\Vmª$\VeQ \±acH n 2]_`d}WWXoi}Xacn]xi WXoVd}ac5\ 4WhX]_SVeoVn_§l p\Voqd}\Vm¥]sSVX«`sac\VoVe6WXn]_dfWhat]_X« Sqd}bkSSpatnTa(Wd}\qd}WhacX`s`e6`)a]A]_Sqd}n);X`Ïi bX\^]kacm6Xt´
Ë ih h ~
µ X`sXcl³ ÄX d}fvbe6W|Vdf\VXh]sSVXnXh]& Äed}oVXacnd}\>]sSVX\VXÂ]nsXb]_dfe6\'l oVXp\Vdf\Vm]sSVX z 2Ï`XfXtac\VbX 4ec ]_SqXXn]sd}What]sXc´ [&\"|ec]sS0bacnsXnlp ÄXWhaG¡"Xd¨]_SqX`op
bkSVee6nsXa ÂqXo·\$VW(|;X` ¥ecKdf]sX`_a]_dfe6\VnlJ|patnsXo0e6\0a+bkSVe6nX\·q`se6|pa i |Vdf}d¨]&¡"ecX``se6`lpacnm6d¨6X\0d}\-¦ c6§Aac\Vo"]katªcX]_SVX|;Xnx]zWXacnsV`Xec` `X;XGat]V\^]sd} a 'Xnx]_dfW+a]_Xd}nT©e6V\qo'´ X p \Vac}¨¡SpaGcX]seh`Xp\qX]sSVXe6|q]_acd}\qXoXn]sd}What]sd}ec\'´
}~}L&
c