Jul 29, 2003 - dopting a vector notation, define. (t) ¤ ¦ ¨= diag(z ¨ - a(t), . . . , z m - a(t)) = z ¨ - a(t) . .. z m - a(t) !" . Then the Wonham filter can be rewritten as.
! #"$&%'( )*+ , .-0/. , 1 2#43567" 8:9!;
;:9@ACBD
E#
lX!/
0 z
U1;a5 F 9 1;n z %> 0 `,>!Nf!-/"%&'°¯£/"jl!(&BNf"&)/("W)/X%=)±(-!>!²!>!c)-#"Nf6¹6O»E ~ -0"c)/(dT!"T!-#'+M>!¼²#c)Y(&$!'( JLT!!0)Y"Q±½º"&)/)YX%r)14«c;K(!>!0t=)/-®)/X%=)6)/X!e$%&-#(0"&$!-/#==)Y" N"U>!'X!&-6)YX!JL"&/N¾"&JÀ¿#-/ v %&' !'T!-£!"&(-/Á ~ =!>M)YX!=)£)/X!®>!-#)//($GTG)Y"M"&J¢1]?#;(-!"U`³±=T!-/-#Â&f$!TG)\-\e©&T!-#-/(&[N*Ãk)YT!#º>GT! )Y"e)/X!£Ä#T!Nf!#"U0-#-/-®Z\1]?#;Q Å @)YX!-MJLY=Nfl£"#i ~ "&!W"&J©)YXGW0'(&-/-#(0t='º#-/TG')Y-MikG"l&-f)YX!SÆhÇrÈGÉGÊ&ËÍÌδϳÐÑÒ0"G0#!-b)YNM=)/( v Z\1]?#;$%&-#>")YX!®"$!-/#==)/("¢1b¬;Q°ÓX!)YX!6=&'T!-\"=JÔ)/X!-#)Y=)Y-q ¨ 5t¬j¬j¬5:q =!> )YXG v !Y=)/"°w»=/\ÕrÈÇrÖ ÈÊ×VÑØÇrÑaØ=&!>±_GÃU> ~ )YX! ÓÙ"!X%&N_!')YCªÚrId!/"jk(>!-Ô)/X!"G)/(Nf&'=_%'*)Y ()/X!/NM&!-\=-|"!6"&J)/X!®#+[JLlÜid!"jl_%!*)Ya`,>!Nf!-/"%&'%_%'*)Y#-\)Y"=`Ý>%=)/&Q1LÞ|X! _%#-#)# v "&/"T!-Ô>!'"!Nc)"=J%!"U`Ý'(!t&¥_%'*)Y/-JL"&>!*¼TG-/("&U`Ý),+kV!#"U0-#-/-l£&-CªßI4Qà%"®N"/ >!):&'(>f)Y/=)YNc)|"=J¥_%')// v !#"$!'N- ~ -#Cªá ~Uâ "&' 0ã rI4äGJL" v !Y&'#JL/G0-"åg8&/i=" !#"U0-/-#-&!>¡-b)Y"k0:X%&-b)Y(0M>!¼²#c)Y(&'ÛdT%=)Y"!- ~ -#ÒC 0~ ~æ I4äJL"&À-/"&Nf[#0c)^/JL/!0-^" _%'*)Y#( v =!>8-#)/(Nf=)Y" ~ -/MC 0 E ~ 0,0 IQç; Å )6-®%=)/T!Y=')/"M):=i&f-#)YWJLT!#)/X!®&!>W0"!-#(>!º)YXGÀ-b)YNM=)/("å!#"$!'(NèlX!W)/X!#e &>!>G)Y"%&'T!G0b):&c)Y(-(h)/X!=&'(TGÀ"&J)YXG-#)Y=)Ye-#%&0^q ¨ 5tststs5:q "&6"&J)YX! v !Y=)/"^1{z ;Q à%"©(!-b):&G0 ~ "!NMt+B0"&!-/>!±)YX!f0t&-#flX!¡q ,é -8êkÈGÕrÈÇrÖ È2Êf×VÑaØÇrÑØ ~ &!>Ò)YX!(©&='(T!
±id!"jlW"&!'+MT!8)/"M^0#):=(>!(-b)Y#($!TG)/("QÞ|XG(-!/"&$!'(NÍ&/-/-JL#ÛdT!d)/'+åJL"|aÃG&NfG'( ~ ¯\t+-/(&W-#)Y=)Y-#)/(0- ~ lX!#À!#("#-K0"T!'>8$VGYtlhJL/"&N >!-#)//($GTG)Y" Q 6!±V"-/-#($!'±-#"'(TU)Y("& (-\)/"&!!'*+g8"c)Ya` \'("^&G!/"c=0:XålX!0:X8c):&'(-£)/X!©/G'Â&0Nc)"&J-#):r)Y-)/X!Ó"&!X%&N _%'*)Y$c+)YX!(-/NT!'(=)Y>å"&º=!!/"tÃU(Nf=)/>&='(T!-QRUTG0:X &!!#"c&0:X8Y&-/-NfV"#)Y&c)ÛdT!-b)Y("&!-/TG0:XM&- )/X!|Y=)/|"&JV0"c& v !06&!>^//"& -#)/(Nf=)Y-QÞ"©-/"&Nf|aÃU)/c) ~ Nf&c+"&J)YXG-/K!#"$!'(NfNfj+M$²k(l£>W&-Ke/"&$!T!-#)/!-#-º-/-#T!- »)YXG(-(-\)/X!©0c)/Y&'¥)Y"&!(0"&JÔ)YXG(-|%&VQ
6T!K_!/-#)KNf&(#-/TG')K(-|)YXG!)/("!-Q Ó6&'(-#"!( v $V"&)YX[Nt=[-/ÛdT%^1{"&|$V"T!!>!-Y;£&-l£'('²&-£$V"T!!>G-\$%&-#> "åX! v X!N"Nfc)Y- ~ !/"jk(>!±/-/T!'*)Y-")YX!±Yr)Y©"&J0"c v !0&!>å%&$G'(©"!©)Y"&-#-/-#-®)YXG ÛdT%&'),+["=J)/X!±&!!#"jÃUNM=)/("G-Q
!#"%$&'("%)*+ UR 0)Y"å0"&d)Y&(G-©)/X!NM&B/-#T!')/-Q-, /"k"&JL-©"&J)YX!NM=( )YX!"/Nf-A@4B+C
DFEHG'I#J
)Z£1L?#;$²|K_%!)/`Ý-#):r)Y£0"c)YkTG"T!-°)/(N\gh=/i&"jÀ!/"k0-/-l)/X-#)Y=)Y£-/%&0\m &!> v !/=)Y"w ny1{z ;|A8} z ~ &->!_%G>h&/'(Q ©* 1{«c; ~ >G_%! K 1]?#;ny1 K ¨ 1]?#;5tssts5 K 1]?#;/;\Ah} ¨ 5 l)/X
K ³1L?#;n9M1{Z\1L?#; nq»!)/("!&'d>!!-#),+1{V"-#)//"°G/"$%=$!('),+G;G/"jk(>!-)YX!\N(G(Nf&' Nt&-/ÛdT%=/±/#" ~ &!>å-Y=)/(-#_!-|)YX!JL"''("jl( v -#+k-#)/N "&J-#)/"U0:X%=-#)Y0©>!¼²#c)Y(&'ÛdT%r)Y("&!¤ K 1L?#;n
K =1]?#;bzZ ¤ ? ¦ S 1]?#; Z£1L?#;CFq Z1L?#;³I K b1]?#; ¤ ? ¨
6¦ S 1]?#;CFq \ Z 1]?#;³I K 1]?#; ¤ ¢1]?#;5|n 0 5ststs5QP 5 «
1ß&;
lX!/
K 1L?#;a5:qn q K ³1L?#;5Üqn ¨ &!> >!G"&)Y-K)/X!)YY=!-/V"-/©"&J Q >!"&G)Y v e&0)Y"K!"&)Y=)Y" ~ >G_%! q ¨ 1L?#; n >!( v 1{q ¨ Z1L?#;a5tststs5:q Z£1L?#;#; n Z\1L?#;n
Þ|X!8)YXG©ÓÙ"!X!&N _%'*)Y|0&$²©#l/*)/)/8&-
Z£1]?#;
QQQ
s
q. Z\1L?#;
¤ K ]1 ?#; n K L1 ?#;bw ¤ ? ¦ S ]1 ?#; Z\1]?#; K 1]?#; L1 ?#; ¤ ?
2¦ S ]1 ?#; K 1]?#; L1 ?#; ¤ ¢1L?#;a5 K 1{Ec; n K R s
F
7987
14q\¨5tstss5:q}|; ]5
4J!= ;C
B G I < =?>A@4B+C
1 ;
DFEG'IJ"!$#%>$&('*)+-,/.
½ "jl ~ ')|TG-|&-/-#T!N6)YX%=)|q ,é -&/6G"&)t=&('(&$!'( ~ &!>[)YX!=)|"!'*+f)/X!£!"&(-/®0"#/T!G)/>Nt&-#T!/a` º Nc)Y-K"K"$!-/#==)/("!-K">!-#)Y#($!TU)Y("&%&'GJL"/Nf=)/("Àr)º"&T!º>G(-/V"-/&'QÓ1 1 1
1 1
¤ K !1L?#;n K %1]?#;#w ¤ ? ¦ S ]1 ?#; Z %1]?#; K !1L?#; 1]?#; ¤ ?
2¦ S ]1 ?#; K !1L?#; !1L?#; ¤ ¢1L?#;a5 K !14E;n K R 5
1
?1 @ K 1%1]?#;5 qA15 1!1L?#;n>!( v 1 q±1¨ Z1!1L?#;a5tststs5 q³1 Z1%1]?#;/;as Z !1L?#;n
.
1æ ;
1
UR !0Mo K %1]?#; u (-6M-/ÛkTG!0f"&J=!!/"tÃU(Nf=)/("!-K"&J )/X!e²"&-#)Y/"®>!!-/*),+ K L1 ?#; ~ l£eNft+W&G!/"=` !#Â=)/'+f!"#NM='( 6)£)Y"!-#T!/±)/-|$²"TG!>!>G!-#-CFÚ=I4Q _%G !1L?#;n K !1L?#; K 1L?#;s
9
1
1
Þ|X! ~ %1]?#;|-/=)Y-#_%
1
¤ G1L?#;n
S ]1 ?#;C Z?1!1L?#; Z\1]?#;³I K 1!1L?#; 1%1]?#; ¤ ? ¦S 1]?#; Z\1]?#; 1!1L?#; 11]?#; ¤ ? ¦ S 1]?#; Z\1]?#; K 1]?#;C 1!1L?#; 1L?#;³I ¤ ?
6¦ S 1]?#; 1!1L?#; 1!1L?#; ¤ ¢1L?#;
6¦ S 1]?#; K 1]?#;C 1!1L?#; 1L?#;³I ¤ ¢1]?#;5
1
!1L?#;bw ¤ ? ¦
1
!14Ec; nEGs
1
1
14Ú;
Þ""$G)Y&([)/X!©>!-#(#>h'(N)/-/T!'*) ~ l!)/("!-Q 0
021
3 021
; o q u (-£!(0K-/ÛkTG!0©)/X%=)-Y=)/(-b_%- q [(-T!!*JL"/N'+À$²"TG!>!>Q Þ|X!©-#ÛdT!G0^o q u (-\!>!²!>!c)K"&J)YXGÀg8&/i="[0:X%&(Z£1b¬;£&!>)YXG©¯£/"jl!(&Nf"&)/(" § 1b¬´;aQ
021
Þ|XGfT!GJL"#N $V"T!!>!>!!-/-À"=J£)YXG-#ÛdT!!0ho 02q 1 u -©!"&)±/-b)Y#(0)/("B-#(!0f"G Nfj+åT!-# ~ JL"ºaÃG&NfG'( ~ )Y#T!!0=)Y> !"/Nf&'Y=!>!"N >!-#)Y#($!TU)Y("&!-Q Å )®0"c!(c)Y'+h&''("jl- K 1%1]?#;
)Y"®X%t&!G/"tÃU(Nf=)Y>²"&-#)Y/"G/"$%=$!('),+0)/"(c)//G/)Y=)Y"Q '*)YX!"T v X!"6!>!²!>!G0 (-&-#-/T!N>MJL"&)/X!®-#ÛdT!G0eo q ud~ (f-/NT!'Âr)Y("&e"!®"=J])YMT!-/-\QªQª>Q°-#ÛdT!!0-JL"&-#(N!'(0),+&Q v "k>!0),+(N!'(-)YX%r) q q l©QªQ 0 Q Þ|XGÒ0"!>!*)Y"!-[0"&8¡'Â& v W0'(&-/-"=JÀ!#"U0-#-/-Q ÃG&NfG'(-º"&J(c)//-#)/-6(!0'(T!>G±)/X!0t=-/ÀlX! o q u -®f-#):r)Y("&%+ !`,N*ÃU( v -#ÛdT!G0 ~ lXG(0:X (8)YT!# (-® v "k>!01{-#C . ~ GA Q . ææ H` . æ Ú=IÂ;QKÞ|X%=)6(- ~ q f q[l©QªQ 0 Q Å B&>!>!*)Y" ~ J)/X!N*ÃU( v Nt&-#T!/ [-Y=)/(-#_! - ¨ ~ )YXG 1 q qc;60"c& v -±(B>!(-b)Y#($!TG)/("8)Y"å!"/Nf&' Y=!>!"N =Â&$G'(ºl*)YXåNf&åE^&!>å0"j=&/(&!0
;1
021
021 ;1 < 1
1 1
1
3 0q R 0q R
n
¨
3 0q R 0q
¨
3 0q 0q Rj s
1 0 cE ;
;1
Þ|X!-º=-/0#)Y&(!-|)/X!©0"c v !0À&!>åY=)/"&J0"c v !0Q
0
) # È!kÐÑ 0 ; ~
3 1
0 ~ -R%#$'T!&($* ) 1L?#; n U 1 0 ;5 E M1 0 ;a5 n 0 U5
G-JL"&|X! v XGNf"&Nfd)/-Q
)
+#+êkËMÐÀ1
; 0
1{];ÔÇrѱÊ&È©×%Ç +Ø]Ï{Ø &ЩØ]È%Ï,Ð"!kÐÑ$#©O 0
"
-#T! 3 1 & % n %R $'&($*) 1{];(ÔÇrÑ
n
0)
1
U1 0 ;a5 [1 0 ;5
E ' 0 '" n 0 '"
A@4B+C
1
ÃUÔ1a * %1]?#; ; n/[1 0 ;5 Ê,+
DFEG'IJ"!$#%>$&('
2
<
s
) ,>.
01
½º"jl ~ l©&-#-/T!N6T!!0b):&d),+f( 1{z ; l)/X)Y--/ÛkTG!0±"=J!"(-#60"&//TGG)Y>å"&$!-/#==)Y"!- w ! v '*+^$d+ >!_%!( v 3 0 w n 3 w 5 1 0 ; ¨ &!>å$c+/>!_!!( v e-/ÛkTG!0"&J°&!!#"jÃUNM=)/("G- K !1L?#;£l)/X
01
1
!( v 14q ¨ Z>1%1]?#;5tssts5:q Z?1!1L?#;#;s ) 1%1]?#; n K %1 1]?#; K 1L?#;aQ Þ|X! 1 1]?#;n !1 1L?#; w 1 ¤ ?|
K 1L?#;1 w 1 wÀ; ¤ ? ¤ % ¦S 1]?#;C Z?!1 1L?#; Z£1L?#;,I K 1!1L?#; 1!1L?#; ¤ ? ¦ S 1]?#; Z£1L?#; !1 1L?#; !1 1L?#; ¤ ? 1 .d; ¦S 1]?#; Z£1L?#; K 1L?#;C !1 1L?#; 1L?#;,I ¤ ?
¦#S 1L?#; %1 1]?#; %1 1L?#; ¤ ¢1L?#;
¦#S 1L?#; K 1L?#;C %1 1]?#; 1L?#;,I ¤ ¢1L?#;a5 ! 1 14Ec;nEUs 1 &; o w0 1 u (--b):=)/("!+® v "U>!0-/ÛdT!!0)/X%=)-Yr)Y(-b_%-?3 w 0 ± 1 nw@&!>±(-TG!JL"#Nf'*+K$²"TG!>!>Q Þ|X!º-/ÛkTG!0o w 0 1 u (-(G>!V!>Gc)|"&J)/X!®gh&/i="jM0:X%=([Z£1b¬;&G>f)YXG6¯£#"lGÂ&fNf"&)/(" Z %1]?#;n
0
§ 1b¬´;aQ
Å h^-/Nf'Â&J{&-#X!(" ~ l£©0&8>G/*)YXG©JL"&'('("jl v /-/T!'*)Y-µ
+#+êkËMÐÀ1 &;-É%ÐÈ
)
-#T! å 3 G1 1L?#; E·Ê,+ %R $'&($*)
!>Q %à " (G-#):=!0 ~ Þ|X!"#N eX!"&'(>!-\lX!8)/X!©T!!JL"&/N $²"TG!>!>G!-#-®"&Jo w 0 1 u (-|/!'Â=0>$c+ 3 w0 1²
Q Þ|X!(-®/Nfih&G!'(-º)/"M)YXGJL"'('"l v Þ|X!"#N-©&-®l''°lX! )/X!T!!*JL"/N¾$V"T!!>!>!!-/© (-|#!'(&0>8$c+=!!/"&!/(=)YX! v X!|Nf"Nc)0"!>!*)Y("&!-Q
+#+êkËMÐÀ1 &;
)
1{];ÔÇrѱÊ&È©×%Ç +Ø]Ï{Ø &ЩØ]È%Ï,Ð"!kÐÑ$#©O 0
"
G1 ;5 E '" 3 1 [1 ;5 n U5 kÐÈÇrÏ,Ð+* %1 1]?#;n 1 ¨ 1L?#;,.-É%ÐÈ R%-/$'T!&($* ) 3 ÃUÔ1a * 1%1]?#; ; n/[1 ;5 Ê,+
æ !/"jk(>G8 /=)Y"&Jº0"c& v !0W/-/T!'*)tQ Å )f&-/-##)/-)/X%=)^)YXG 0"&d& v !0[-/V>-±"=J)/X!f"&/>! < ¨ QMà%"©=d+ 0 ~ )//k(&'°'(N)6-"$G)Y&(!>Qf½º"&)/ )YX!=)^)YX!0"&d& v !0W(-^.)/X!å-/G-/h"=J®Nt&2-/ÛdT%=/å0"c v !0=Q»Þ|XdT!- ~ Þ|X!"/N . =!>
9
Þ|X!"/N æ )/''T!-X!"jl)YXG±Nt=å-#ÛdT%&/©//"&K>GV!>!-K")YX!©-# "=J°)YXG±-/&N!'(=Q à°(!&'('*+ ~ )YX!^-Y=NfÀ)/0:X!G(ÛdT!-±0t=Ò$VeT!-#>B)Y"$!T!'(>WÓÙ"!X%=N _%'*)Y#-6T!-#( v $V"&)YX o q u =!> o w u Qà%"/Nf&'('*+ ~ )YX!!-# v !>8X!j&»o w ud~ )/X!.)YX!0"!0'T!-/"!-e"&JºÞ|X!"/N æ 0"&d)/(dT!)Y"^X!"&'(>Q
0 1
08;:
0 1
021
y&3 =+G'B G%=?>
021
Þ|X!#"T v X!"&TG)º)/X!©/-#)º"&J°)/X!!0t=)/>eÛdT%&k` )Y*)Y-Q8Þ|X!-#0"G-#):=d)/-e v G/0M)YX!M-/G-/[)YXG(©=&'(TG-Nft+Ù$VM>G¼²/c)JL"À>G¼²/c) T!-/ v &Q Þ|X!=)|(- ~ )/X!60"cc)/("
Dn P=!> Dn D(-£TG-/>Q¯JL"# v " v )/X!/"&T v X[)YXG !#"U"&JL- ~ X!/åkÂf#Vt=)/> =!!'(0t=)/("G-K"=J)YX!±JL"'('"jl( v (GÛdT%&'),+Vµ|à%"º&c+8#t&' dT!N$V#-/. ~1j0 ~ &!>2 % ¸ 0~ 3® .
0 * N4* SÕ¨ 1a3. Ô*
0 a* ;as 0 0810
5
J!= =-=
26
@4I= J!IC
7
1
ÓÙ/)/( v 1{Úc;£(å=&/(=)Y"%&'JL"#Nè&!>å!"&)/( v %14Ec; nE ~ l±"&$G):&
1
%1]?#;n
( (
&
1
1 1
& ¦S 1 L;C Z %1MLr; \ Z 1 L;,I K !1 L; !1 L; 879 S;:< ¤ L R& & ¦ S 1 L; Z\1 L; %M1 Lr; !1 L; 79 S;:< ¤ L
1 1 ( & ¦S 1 L; Z\1 L; K 1 L;C 1!1 L; 1 L;³I 879 & S;:=< L ¤ R& ( ¦S 1MLr; 1%1ML; !1 1 L; 87>9 & S;:< ¢1 L;
¤ R& ( ¦S 1MLr; K 1 L;C !1 1ML; 1 L;,I 879 & S;:< ¢1 L;as
¤ R ) à%" 6-/TG):=$!'(JLT!!0)/("1³¬´;£1L&Q v Q ~ 7 & `ÝNf&-/TGY&$!'\&G> ! R å 3 1L?#; ¤ ? ; ~ $c+)/X! RU0:Xcl£&91%1MLr; R
>1
( & å3 1%1ML; R
Z\1 L;j ¤ L£
@ K 1G1 L;
(i=l(-# ~
( & 3 Z>1%1MLr; R
Z£1 L; ¤ LFN*
( & 3 1%1MLr; R
)
s 1 0 cÚ ;
K 1MLr;a5 q 1
K 1ML;5 q 1 qs
Z !1 L; Z\1MLr; n Þ|XdT!-
( & å3 1%1MLr;j L ¤ R
1MLr;j ¤ L
( & å3 1%1MLr;j L
( & å3 q 1 ¤ R R
( å3 %1 1MLr;j L
1 L; ¤ LFN ) ¤ R
( & å3 q 1 R
&
²q ¤ LÔs
1&Ec;
²q ¤ L s
1 0 ;
RUT!$!-b)Y*)YTG)/( v 1=Ec;\&!>1 0 £ ; (c)Y"å1 0 Úc; ~ $d+)/X! #=Q Þ|X!(-Ô(GÛdT%&'),+ ~ )/" v )/X!l)/X±)/X!J{&0))YX!=)Ô¦ S 1b¬; ~ K !b1 ¬´; ~ =!> %1³¬´;¥&/T!GJL"#Nf'*+®$V"T!!>G> ()/X!©(c)Y#=&'CFEG5/HI ~ & !>)YX%r) 7>9 & S;:< (-|$V"T!!>!>8JL"E NOL N@?N@H ~ -/T vv -#)/-
1
1
& ( R < % 3å ¦S 1MLr;j &% Z>1%1MLr; Z1 L;j &% K 1!1 L; &% 1G1 L; &% 879 & S;:< ¤ L & ( N ) % R < % 3å Z1!1 L; Z£1 L; % ¤ Ls *
3+ ¨ &% *N
) %
(i=l(-# ~ l1 0 ; ~ l±&/#±=)
3 1 &% *N
½º"=)Y)YX%r)
& ( ) % W)/XdT!-J{&&!>Ò-/%&/=)Y v
E ~ 0
qå&->!"!^ 1á;
q² &% s
8&!G'((0=)Y"["&JÔ)YXGÀ/"&dl£&'' é -\(!ÛdT%&'(*),+M+k('(>!-\)/X%=)
3 1 1L?#;j &% *N ) % 1 ÃUÔ1 ) %ÝH®;5
&!>å(=>!>!)/(" ~
-/T! å 3 1 1L?#;j &% N* %R $'&($*)
lX!/
) ( 1 n R < % 3å q;1
Þ|X!/JL"&/ ~
#
1
) % aÃGÔ1
1
4 ( "M"
n
1
) %ÝH®;a5
q² &% ¤ L s
[1 0
; 5 n 0 ~ U1 0 ;a5 E 0 UQ
n M1 0 ;&!>)YX%r)\)YX!©$V"T!!>-|T!!*JL"/N ([?A2CªEU5/HIQ Å %&b)±1{Â; ~ l©X%t©-/XG"l)YX!=)e * G1L?#;j &% / &% &% SÕ¨=< &% < * !1L?#;j &% n [1 0 ;ºT!!*JL"/N'+W?ACªEU5/HIQ Å RUNf'Â&|)Y"ÒC ~ Q 0 .dI ~ * !1L?#;j SÕ¨ N 9 9 & % k(l"&J\1&«; ~ l!'"V>(e)YX!- l£"#iQà"&-/Nf!'(0),+ ~ )l£&--/)/T![=f [-/0&'Â=6!/"&$!'(N8Q ÃU)/!-#("G-©)/"[0)Y"&b`Ý=&'T!>B!#"$!'N-&/e-b)Y/& v Xc)#JL"#l£&/>QÀà%"6aÃG&NfG'( ~ "!©Nft+[0"&!-/>!|)YXG±"&$!-/#==)Y""&JÔ)YX!JL"#N ¤ ¢1L?#;°n 14Z\1]?#;/; ¤ ?
.¦1L?#; ¤d§ 1L?#;a5K¢14E;nÜE l©QªQ 0~
lX!/6¢1L?#;£Ah} * ~ 1b¬;£µm ¶·} * ~ ¦ 1b¬´;£µ} * * ¶ } * ~ § 1b¬´; (--#)Y&!>%=/> %j`,>!Nf!-/"%&'!¯£/"jl!(& N"&)Y" ~ Z£1L?#; (-±0"c)YkTG"T!-b`)YNfKgh=/i&"j0:X%&)Y&id( v =&'(TG-(m n o 0 5tststs5QP u QÞ|XG["G 0t=f!#"U0>l*)YXe)YX!0"/#-/V"!>G( v Ó"&!X%&Ny_!')Y&!>&!G/"tÃU(Nf=)Y"ÀlX!f)YXGK-b):=)/|&='(T!±"&$!-/#>8l*)YX!"-/&QÞ|X!©#-/TG')Y-0&8$V©0t/>"jl)/XJLlN"k>!_%0=)Y"!-Q
#) %
G0-Q
* Þ|X!±&TG)/X!"/-|)/X%&!i
Nf NÀ$²"JL"|-b)YNT!'Âr)Y( v >!-/0TG-/-/"!-º&!>/JL³`
2 6 2 +26 2A3
+ ÑYÇ8:Ð#+#+jÐ#+ ~ Ó'(+ £'(&-/-#(0 $!Y&b+ >G)Y" ~ Ó('(+ ~ ½Kl"#i ~ 0 ÚÚEGQ Q â QRUi="/"XG"U> ~ Ï,Ç8:ÉGÊ,+Ï4Ø©Ø 6ÐÑYÐÈ%Ï{Ø{Ê&Î ê!Ê&Ï{ØÇrÈ + ~ RU!/ v b` â /'( v ~
C 0 IGQ Q "U"$ ~ ϳÇ8:ÉGÊ,+Ï{Ø CªrI Å Q Å Q®(X!Nf&&!> ¯£#'( ~0 ÚáUQ
0
«
CF«=IGQeQº&'( ~ Ñ &Ø]ÈVÊ&Ñ gh&'(&$%& ~0 Ú æ EGQ
©Ø 6ÐÑYÐÈ%Ï{Ø{Ê&Î êGÊ&Ï4ØÇrÈ + ~ Q Q/ v , T!$!'(-/XG( v £"GQ ~ =!>
C .&IÀR²Q©'((=!> !)/("%='kG/"$%=$!('),+±>!G-/)/("&Jgh&/i="j!/"k0-/-/-Kl*)YXå&!G'((0=)Y"!- ~
4~ 1 0 Ú .d; ~0 E ` 0,0 ÚUQ
C =I åeQ 6( ~ ϳÇ8:ÉGÊ,+Ï{Ø ×c×VÑYÇ"!Ø]ËÊ&Ï{ØÇrÈ >Q ~ Rk!/ v ³` â /' v ~ ½Kl "&/i ~ ½ ~ & EE«GQ
CªárI Q R²Q ( G)/-/^=!> Q ½ ~ Ï{ê &ØÐ#+±Ø]ÈhÏLÉ%Ð - É%Ð:ÇrÑ Ç +#\Ê&È!kÇrË
RU!#( v b`
"& ~ ½ºl "/i ~ 0 Ú æ UQ
CFÚ=I©Ó Q gÒQ²ÓÙ"!X%&N ~ RU"N&!G'((0=)Y"!-"&J-b)Y"k0:X%&-#)/(0>G¼²/c)YÂ='ÔÛdT%=)Y"!-®)/"["G)/(Nf&'¥!"k` '(!t&_%')/#( v ~
,-./~ 1 0 Ú cß; ~ «.dá`,« ÚGQ
;
C 0 E=IÀ^Q»&!>RVQ + ~ ÓÙt=i 0"&d& v !0B"&J±Xd+k$!#(>@_%'*)Y/( v !#"$!'(Nf-M(c"'*k( v ! t'+ 0"N!')Y'+>!0"NV"-Y&$G'(X!>!>!Ògh&/i="jW0:X%&!- ~0
, 1234657.8:9; ~ 1& EE&«c; ~ E ? 0jæ .dkQ 0jæ &8
C 0,0 I Q=