Bayesian Networks
Many techniques for learning rely heavily on data. In contrast, the knowledge encoded in expert systems ussually comes solely from an expert.
###~ e §u " {y
z
| w uv us o n z
8{Hxr#%trqpRx
§rurr§6§{$Hxr#%trqpn
ox |s u s u w uv us o
xuwvwo o)##ru#x6ccz p cx#| 6i~
o
u}q zq
}qs |zvz y wuv us o
c%#tc{$HxE#%trqpn
m lh
h h f
§rExkj i gy
tV i d C SF S Q
pxeEQ Wa b #
G Q F D
SV C
fx§E x`#Hq1EQ %xxWb y
ts iq iV F X e C XV Q TS
Xxi8wSvEur6p8hSgRfdYE6c#Q b
aC XVQ TSQ I F DC
`YW6U#RPHG1E!B
3 @ ¨ ¦ 7¤ 4 3 0 ' & ¨ ¦ ¨ ¦ ¤ ¢
A©9865©%#121)($%$#"!©§¥£¡
d ox|x zvzs zs z }x uqz z gu f z } |xvs | xzs szx o ov|z zs |
ixwuEptrc%6t%!xp) o z cxtR wz xxxpx #pr%tz 6 jc%6tr# )r
rrEt%xu #tq
z x z zv u d v o }v ox zs |v | v ox q ox | o u q zs u u v zss u q zxw
{g r
rtxbrx§{5dx xpx§rurE| c%$Epx&tq #| xxwucx rrvo rzx} t5x§#cc%prx §fpc%r§cPtrEu
v fs u gxz ovz
z s | o vqs | v u z } u d o s | w u
q |s qq |
q o
#R§{1cx)| c#8| xrtwz $c%#| #cz x£xpx {g wx xr#trzE)cEr6dcE| `cxtrzcq ¨z
z }x zv |zsq ux z g u f o }x zv fs u gxz ovz
| o z g u f xsz hz uq
xpgrEt%tx o rg# rz$Bx§rvxp9x #| R§{1cx| c#8| g# rz$Bx§%t669z cxtz
ov|z |q
r
rrEt)tz g x dc#EY##| 6 $#p%§f £{CiE6} tz {Bx} ¦§{Ccx9#| rct| x §Erux z
z dvz |x | x |xs u o u gx v| s z gu v fs u gxz ovz
o
vvzq us z dv fs u gxz |s z ov x | }x ux s ov o v fs u gxz ovz
ov o s |
rccx%6Rx} d¦§{Ccx r6dx x xm6pRr¥#| wo $rvA¦§{Ccx #| rct| x rxSx xr#tz
vv z q us o s | z }x us o u zv zxw u | q z zx u q | zs o z
ddcc§%6 x xr#trz$xY$z %6 rx wxo rxutrE!#t{{g rcrzx cx o #Rrzx} | wock66mrv$ wz xxf gu
xsz h z g dxsz hz z }x w z gu f z }x o vs uss ux xv } us }q | us | z dv o }
%tf z tx} tz td%t66RxY2Eu # rz$Bx§sxp) $k§%rtz $rxb%rvo §%66#!x} dx xpv
ox z v oxq ox gz w ox|q ox z }x v ox u z gu f xsz hz | o os
&xwuE| c%s #| x§rurcx rrrvo x©Eu §rurEt"
rtz o xYAcz rcz rv #| wz xx%tf 1E6 #r%§u
z }x w u x z
z | v q o vzs z dv fs u gxz ovz
gz zs s u z ox |zs z
xp©$#tz x ¨%s Rcz Wcx $rxx6c%Rx} d#R§{1cx)| c#8| xj%xu §ix§u x rEtktq # z
gu f o }x zx ux zv| } |x | zv z z zxv
xsz h ox o } | } us | o
$Bx§rvxpprE| 69rE6&pE| prx{g tx} d rrxrv kt66z rqrrrvrowx&6%6 (x o rxb}
z } g z o v fs u gxz ovz
o vxsz h wu xzv s u xsz hz w z
txiqxxu rvRE| ¦§{Ccx #| rc#8| | Rrkt66z EcrixR%tf g#| Eu wz xxx rwvxz gu f ox o h
z }x uq z z xv o dv g v vz u vvzq us o s | z } v fs u gxz ovz
o
xpgz cxt){g %s d$Brur#Huw E| c§# rccx%6x x#trz)xpx ¦§{Ccx#| rc#8| x rv
d } #t xE| cz | tEc$ w#t tf§§¥ #Rrv%tHw ro §##t wxo E6%tz #$tf§x{
d x s z f q z s z u u | os z ~ v u fvs | szuu
v o uv oxqz z |fs z z } ux gu } zz } | }
z }x x
x E| u z rd o z rcce¨`r
x} 8¦#| ks frg Bxpv tcfuz 6dcxYxb} x o #u z wrrv #| ox
gz zs z
x!%#| 6§rucz z tcfz 6} E6pcxb5x6crx x} bYE| 9 #!# rz$Bx§¢%tf Eg§rurE6 x}
zz } | x| }x vz o }qz z d |x | z gu f xsz hz wu ox| o
u
cq | %uw #¦xu Ccxp#| rc#8| x xr#trz$xHiv xpcz 6§rucz z z 6R%txc%#tc%s r
rtcc%s
us v fs gx z ov z
o s | s uw u }x z | } vsz }qs |zvz x zqz
zs u n | x z s z f q zxv
v xs z h z o z g u f xs z h z o |xs z q u q z s u
%§pd | #tw dAc#| tErcz x'v r§%t66! $# rz$Bxx%t66! Ep%tcx6ux o cxte§w
ox|x zvzs zs s u uqz } v| } fs gxz ovz
z }
§rurEY#trck6t%R#| xb§f | z cc6¢E6)¦xu Ccxp#| rc#8| xpx z tcz r| !xpitz i d #t
|q xv z }x s
%#tz y b#tte ¥Bu xxwuE| xb x| EtrqrrrvrEpRxHuw wzx&prxx6v rxo x #&| A crqr#| rprqrrrvrorx} |
s | s | g ox o | ox ox |xv s } | o of v ox zv ox o
e dxzs szx | xq sxv uq ux
v|
&%s6E| §Hi6} §rurEptrc%6tks xYx §rurrxo 6 | udc%6rt# o #Rcx¦px§c)r9Etz srzx
} u s uw v | ox |x zv zs z z } o
z v x| }x z gu f o|xszq w ox|x zvzs zs | o } |s | o fs u gxz ovz
uc6Axr#u E6p$# rz$BxxS EY%tcx6Eu §rurEptrc%6t%"twqx6r§{rv¦§{Ccx #| rct| ~
d |x | ox ox|x
bp| EtrqrrrvrEYrv #|
z wz guf o xsz h o o u
} z gu f gz s | ux v v g | ox |x zvzs zs z }
xxs E| u %tf z x x x} cq ## rz$Bxxx!r#trz x$BwurE!§rurp#tc%6t%$xpx
r
cz ~ d s u g }x u } w u xv z } z }x | } v vx x | }x | { y wv o t q p o n l j
|iPdv %§{gp#feErc6txpz 62xPrcrzeE6Y#dRz Pxdut slr&mk| rzwtq §rurp#tc%6t%s | ox |x zvzs z
z wz guf | z h s z | o } e d xs z hz u uv v u | v zxv
xs z h
xx¢x o | z z g tf#6 rvxpx uPdkt66!#| %s w w
crz#Acz cq w
rE6¨xiv r§rv %t66z
o z uq z z gu f z } xv|sx uq e d |x u | z } zs o s | s uw v z o } q zx
cxt!# rz$Bx§sxpx Erp§cp 'bp| §pr
ro tx`r
c%px xr#trz{§cxb5x6cr)#| n
¦ev¤
a CQ
A
7 "A "A 9 3 " Q 7 $ H ! Q
¨%48@59@1A8¢@5API0( ¦5PID B5$"sdD y( 5$" 5$" ¢d¦gBPd( R%P&¦ ¢@65@s0%D8CR@¦8) ¦@)
r ! D4 V r Q 7 ID $ H I $ $) 7 DA $ "AA $9 2
@At89 s6yGI&D @yxw5D@AW7 &%2&qb654@8%98C@vdpDu%&15A" 8G5At( 5$Bs¤¦54@Bs¦@9
3 F $ 4 I D 3 I 39 a $ " F " $ ! 7 "A "AA9 ) E 7 r F9 " " H ! 9 "A $ !
548@595"%7"&0@) 2q@0DpiiA¦dB¨¦@) 8¦@B5$"gQ GR4 @8@9 0¦@f@¨e59#d5D@1B¦@R@) ¦8P Pbb@0GI
"A r r D 7 !) E 9 3 V hA 2) A $ A F)A $ D4 DA V9 " $ "AA $9 2) 3 c a H) D
YA $ $ "9 V Q 4 7 I H " A 4 F ED $ "AA $9 2) 7 3 2) ( " !
`¦ XW@¦0¨UT#SR%5776'0( Q¦5PD $B$5C@)¦¦&$ G05D@CB¦@¦8) ¦8¤654" &10¢'&%$# ¦
¥ ©§¥£ ¡
¨¦¤¢
x{X #cq xYAE6px #tz z xpx rx f Eu %rxrorx} 6%6 | §rrE9r
cEWfwo x{'x} #cq jx§cz rv
u g o u z }x x| } x z } u i w
o | } us ovv| z u g z o u | z u u
o ux zsz g z g | hz s u
o | } us x | } v us u } g uvsz z }x wu z gu f w
z # r%t{{ ow rzx 6{§1'd %rxrorx} 6%6 6px cz o %6 xi§rkt6 xpER# rz$BxxiEu
zx|x z }x z v
| o g w z } s
o | } us ox|xzs szx o ovz
z }x
rEprv xpg§u tftz x8$%g| rr$kYrzroc6g§u %rxrorx} 6%6)| §rurEpc%6tr# g#| rc#8| xpp e
d ox|xzs szx
ixwuEpc%6rt# o
ovz
z } w zv |q oqz v o ox |xzs szx o x ox z zs z } oxq
#| rc#8| xpx u rt$E| cc6pg| rv5§rurpc%6rtr !rrvr#txb%uw xpx " xwuccz o cr$rE6Yv {g zzv | } z
ofq vz
z q zs zw o ox o | } us w u
s u z }x z } s z z o u z z
v ~ d £ t' x E| b#t c#8| cxt%t `rqrwvrorx} 6k6 EP%§cxp)xpx tcx§rux rx 6 cx}
u g z } us x ox oqv vz
v u zs z y z }x wu s u u
x} yv # £ o xpx %uw rrvrtwzc| c#8| | x} ) t%tz {ixpeE§xxx} o xwuEpc%6rt# o ox|xzs szx
t q p o l s o qv X o VI e z } |q w z } w u zzs | v
o | } us | w u ox|xzs szx
&plBn j §u 0a`x0YWhgp xpx wzrEt)rvo Yrzroc6q`ck§cz )E| %rxworx} 6x%6£xwuEpc%6rt# o
z } xv |sx u q d ox |x zs s zx o v qv t o e coz G s u o qv Xo I y z }x v u zss wzs | o |s
xpx rrp§c5ue i§rurEpc%6tr# p xwdxfdCrb§!0a`x0YWVUxp!E| rx krtHzYkw
rE6xwuwxo rpx rvo
vx os z hz x | z zs w u v os z | o
q z zsw | v
o | } us | w u ox |xzs s zx o z
r#tz kt66)Et6t%£)cwzktrv ( cxtxb%up)E| %rxworx} 6x%6£xwuEpc%6rt# 9x}
ds qqu o g 9 xu su sz}xz
6dcx©rr$!#x$§¥txpcx} g
x u zs v zzs
xf} | %6¨x6Sc%§cz z r)rx wvo x} txpx Trx #| tcz Ccf} %wxrorx} 6k6)£x§rrr| x} we
uv u z z } 9 u z gxz
o | } us | v ovv z
dit66#6R#x{rwo sE6pg Ep%tcgprx$cz rzwocfux} txpx §x Eu %rxrorx} 6%6)Rx§rrE| x}
z | } x u g 9 x | }x
x o |xszq } o g v z } z z } 9 u w
o | } us | v ovv z
w¢6dcxwr$#!6p)%# Epktc9Ywxo cz rzroc6ux9txYx §rx Egrxrorx} 6%6 x§rrrEp§rkt6
e ds qq u o g 9 x | }x
x o|xszq } g v z } z } z } 9 u wu
o | } us | v ovv| uvsz
dx osz hz ov | s qq u o g 9 x z }x x| }x uvsz
z } G PoI Gy ooz E
| we d#tz kt66)wzx )5 o 6dcxArr$XStz z xYRE6pd§r%tf9| #} cxRso%qQ¦¤HS¨CFo D
z } vx zvzs zs 9 wu
o } | } us z }x x| } o ox u x zsz
xpx #trck6t%)CE%rxrowx&6%69xp!E6px wv5xwu#x #t%teo ~ d Bx #9¦cz crxu 9 x u A9 | 9 v u q x
rzx} r#6Pprx$utz %t66p#| cz rg##| t6t%s {tx} g %6dcxu @cwqxiprx$cxtx %uw
ovv u } o g x osz hz v ox
x |z z z g z vs qq 9 } o } g } o g
q z zs
}x wu zs v| | o o x | }x o
o | } us v w ox zq u x zs z } 9 x |
zxpE{%66Etz {rvwx6pArv!%wxrorx} 6k6Arrxo Eu §rurxtcx§cq #trzE| %6$xpx ##tz z #!tz o 8
d b#6# k#6§7§Rcx6x$tf § ¤#6pk§u E£#ruc©rr$g
s | | 6 u zq u sz 5 | }x zs x| zv q o
##$6prv$#tz z x rrcktr# o %§u x#6rtf ~ dv tx`6z crwo #cq | Eg "4#| xdwq%#6
u x | }x o x oxvzszx zs v | }sz d |z } uq g o u wu o 3 s oxs |
x| }x o x wu hz ovv zs x w s x zvzs xv | z } o s zx
|{E6p{rvAtz z | wzx | rqrE| cq ~ d %66x@§u trc%6 rE6xpx E| tr o z rx z rv o o u
s u g s u wu xs | uv w zx |x | | z x z dx z z } z o gsz }x u s ovz
%§{t6E$k#6£z r2u rprv )#tz {g tz )
0#tz xYx rvo rrv$Ctxp#¥§u #| rc#8|
o | } us wu z | z } w x
s os
o | } us w ox|xzs szx ovz
z }
%rxworx} 6x%6 E{#6x#| {xpx Eu #tz wzcz %#| %6 ~ d %rxrorx} 6%6 Eu §rurEpc%6tr# o #| rc#8| xpx
g zs u z } o g |x us z }x s | ux gu | v fs u gxz ovz
vv q
wzo %rx cx"rr$ywxo pE| %uw xp!r#trzirBx} #2¦§{Ccx #| rct| rxdrrvo z t%xHYz g zs uw
0 " ( % "
21!i)¦$'&k$i#! ©
o zs | vz o }qzx |sz z zs u n dvzx |x
d } ##t 'xE$cz #| tEc$ #| Bt Sx r6 o tz # %#cx 5x6ccr"Etxt#$%§pdcrprv
d | x s z f q z z ox
zxzsq u z |x v os zsz g v o } us ux ovv q s u z u
c%trrvo §f pcrzx} | %#| %tx} ¢x E| u rzxk6 rp§rurxdrrvo 6rxo roR{g rrv ~ d ¨t
¡
dxE{cz c%s x § #| dbt | tz ¦ "%#tz Stz Arv!cE§%66#| #| rc#8| &§xz rcce¨!trEu
| x v zx o s ¥ | s |
} o o } q | us ov z
u ox q z z zxw
| oxvzszx o d o s| s u u }x ovz
ov| | ovz
ux ovv q s
#x rc%tr P ~ wx xr#trz§w v xYcz #| rc#8| rE6b #5#| rc#8| 5§rurrxdrrvo 6u
osxvz z d fs u gxz ovz
ux v oxq ox zvz }x ox|s zx s u g z }x x u
xcrq%pc%s P9¦§{Ccx| c#8| | r o x§rurcx rwvo cxppx Er§cr o | k§{Sxp!xf} |
ox q ox g z o
ox s uw u }x vv q z v ox q e d fs u gx z ov z
vx§rurcx rrrvo x)x xw #tz o §{v xYcz rxdrrvo {g f #| xxwuccz uPwR§{1cx #| rc#8|
w u zs x q sx | v o o | } us z } o s | s uw u }x z os qv z £ } us } v ox q
|2%66cx¦pv #Rcrzrrxworx} 6x%6Rxpx x x#trz{§{v xYcz f} ktrcz {g ¤§x%6px x§rurccz
ui§rurEptrc%6tks xYx #6§r#rurx6p#| rc#8| xp!rxdrrvo {g ¢ #| x§rurccz qpE|
e d ox|x zvzs z z } |
} uv o } ovz
z }x vv q z ¡ v oxq e d |x
us z }x o s | s u u }x | v fs u gxz ovz
u os ux x w os } | sz | o
%uw xp!x x#trz§w v xpcz #A¦§{Ccx #| rc#8| §"| k§rx6©Yrz%6#$wvo tf#6$wvx}
¡
g D
T
XU C S EU X E QU S I EU S XU D X D C S D e T x S Q E Q D
VV#b¨6gWfRb6©W6Bb!B#6!vRYy©d¨!HA
a SU X E D a SU`U h T h Q g
D U` T g D E D T D`` T I X D xU S D x Q X XU u s Gq p i X D` h TU g T f X d Q d EU S E Q I E T D S D g I XU C S Q h X EU T S E Q
yb6#F¨6bWWR©RF¤bWVF©yYcbWVb6Bb#et 3r¦yb¨VbBRV#V#eW6V©RBFBb6y©WRBVI
G E D C A a SU X E D a SU`U h T h Q g
T D`` T I X D xU S D x Q X XU u s Gq p i X D` h TU g T f X d Q d EU S E Q I a` E Q X EU T S E Q I G E D C A
1F#3yb6#H6WW¨V#VF¨!bWRb6yBYbwvt 3r¢¨bRbBVV!#V#eW6VcbRY#WVBRPHF#3B@
d 0 w v z x | x v s u ( 0 v zo xoo | } u s w u x z v z } v ¡ 0
9u cEprerE| §Hw ¡£ 8 6 crrrrrx} 6%6AE$cxpx ro c £ 76
zx u 0 p I q l ` Gy v o p l z o y qv qzv n q l yz " z d o o v os w u x z s
#xtz 6 55oP Upl¨z d¦Hyd#dd` t syxe I ¨xr qp D xpv5qWPI RI Cex} drxcrqrox Rcrzx} | %#| E$crv §u
os | wu zx|x z } | z v ox ( 0 z o 0 wu zx|x | v ox szv }
rzx} | %| $E!rEpv xpx z trz!{g cz rcz u d 4 3wxks g #| 2£Eprv !x§rurE| trxu
w xzv o }x |q z 0 xzv os
s z s zx|xv z }x szv } u z g z
Eu cRrvxprEt!{g 1crg o rzx} | %| ktz $xHuw rEpr!xp!z trx!{tx} d ( rprp rvp& zx|xv o o
os x | } zx u u ( & z o g d v } os w vxzv x zvzs zs u vs zxx zv | qs z
rzx} | %| 6px #xtz rx ) 'rrx%s z 90cwzx&| k#| Eu rcrRtrc%6tk`rx %trrcrz)rEtu1t666
v os o x zv zs zs u x z | } z } w z }x s | z | v vs zxx zv | qs g
#| crzx} | %#| rz#x rv #trck6t%9rx c6} 66 E| xYx Eu tz xpi#txr
rE66xx%trrcrz!rEtu1tz Bru
zv s z | o }x e d o uq z }x w x } oz g z } x zvzs zs u zv z | q os v u ox u
rxsz g t6#6Rrvxpgugi #c!xp2u §rc{qxYx trc%6t%)rx rxu6} #t!rzx} | %#| xxx r§cq
| v|zsz
Et%tx} g "§ cq | Eu cz crxu wzxW}r#6!xpx trc%6tks rx rxqf#tq wzx&| k#| ¨z pt§u
o 3 o u w v uqx ovv u z } x zvzs z u zv z } | } os n l qI s
zx |xv u gx | h z s u d p e y qv y z }
o s v zx |xv w s z |x u s u z o
rpruB{Cg| rzx 6Rx" r&¨xe stxwt ¨X 68| rxRxu crEpr$Eu t6} )rzx} p6cq §)rrxx
| | ov oz z}
} os dx z u ux u vzss u zx|xv }q|z zsz
9x o 6} x0CdX Wpq D 68| wzx&| k#| ~ 0#tz !z rv Rv §fpc%r§cq rEp9cEt!%tx} g crprv vzx|x
oxv | } h oxq u ov q h | x wu oxq u usw vz u vz |x q l
z rx 66z r
cz rccrzwcq | z rxWc§z r
w66x E!xwuccwzr#cq | %ucxWE| §cEf Y©5oP I pl¨z 0` ~
dvx z | }x sz }x| v os wu sz zvv zs h z zxw zs | v zv
drtz !#6YtxpEs crzx} | %#| EAv trx o rrck6 !tHEu %#$crzx¦s x r
x§u ctxYx uq sz}
d w£%tz #x¦Yx%s#9 | #2E6pgrxrorx} 6%6RxYx crxtz A £ #d#R %tx} g
o z s z | § 9 x| }x
o | } us z } vzx u ¡§99 zsz
¡
¡ §
£ #
R9 $£#9 #R9 ! £ ©¨YR9
¡ § 9
9 vx z g
| s uw x | }x v
|v } o } ez vX yz " z }
§ 9 #| !rtz !u Cx #$§A6p$xtY)cwqxig 5oP dtdUe D Cexpx #|
¡ ¡
! £ ¢ £ ¦
A9 R9
x uq v | 9 x
| su
A 9 #tz wzx c$rrxo #!!tz z #$§w
x| }x v
|v } o
E6p$x8p)crqx} g %oUdz ¢e uxYx %| e z %tz 68| crzx¦s txp#)crqx} g %uw cwzxR£rqrE6u{g
P e ¥ p z } zs os z }
v sz }x u } o us v s ov| } u
o | } us wu v s z }x v |v z} os | } vsz }qs |zvz zvz } v oxsz us wu vx z }
d rxrorx} 6%6"Ecrzx¦{xpcrzx¦s z pxpx z %tz z 6©ktx%trc%s cxpx crzr%tf§%6"E©rrvwo xpx
wu }q| u oxxz o z z
E!cEtz ks & £ t rrcx w#t #| | b#t xu Ub¢Bt B{ d zkYrzroc6GE{cc%§cz }
u 8 hu d w z } wu vzzs
z ox|v z u }v x| } v oxsz us wu vxzv x zsz g zx o g | } vsz }qs |zvz
"
wvEpi6} xxYAE6px cwz%t6§k62E{rcr{t%te o Bu trrrx%s gz 6$%txk#trc%s #| n
d £ z gu us fq| o | z sx 9 x z x| }x to q
w# rz$Bx§f 6k§#E6} tz # #Rx¦pirvo !tz $6p!d0a`xE § 9
x z w
o | } us z }x zx u u £ ¡§9 z os g dvzvv u zx xv
z }x w }q| u |z
tz ©Eu %rxworx} 6x%6jxYr#xtz x 9 ©¨R rrx%i'z dcr#rx tr{r%s fxp©Eu cEtz x$v tx}
v u ou | z }x x| } ox vv| z }x s vvu }x z } |z gu } u
6cz cq cq z pv xYAE6px xwux 6rExp{tz 6 #rx ptz rzcz xYx §u v tx} Bxpv x{g
o u z }x x| }
o | } us z } vvzvv |q szvv u o uq s | hz s u z sx z } ux po ¥ ppl z
#cq xpAE6Yx %wxrorx} 6k6jxpx rcrr| #ttr#rx #c6u rzx 6x"vd x¦pi6sr©q¦e 6Bsx}
x| } ox s w zv| }
o | } us | vvzvv | uvsz ox|xzs szx o o }
E6px §rurE| §Hu o §u rE6%rxworx} 6x%6R$rcrE| tq §%t6!| §rurEpck6rtr {rvxpx o rrv ~ u
o | } us z }x v us u g uvsz z }x wu z gu f w zx |xv z }x vx zvzs z
d %rxrorx} 6%6Rxpicz o %6 x} §%t6RxpE# rz$Bxxuu rprRxY$rtrc%6t%s £
#6} r$x} w¤d0a`x29 Eu rxrorx} 6%6$xp| t%s rv!crqx} g c £ ¢9 E$9 E!rxrorx} 6%6ixp{rrx%s g
u
v z d £ to q E w
o | } us z }x v |z o } o ¡ v| wu
o | } us z }x z o
z v dx z }x ux
o } | } us sz } o } | ovv u g z | z } w u s |w
{g x} dtz z xp9%rxrowx&6%6 tx§rxp5§rrrE| x{Sx} v txjEi§u uP o #§rc{g zx} oz
v| o uq z } x | }x uvsz x | } zq uq z s gu e dvv u x hz z } |z gu }
E$g c9xpx 6p§%t6 6px cx o §c9{g tz z Bx} Hwdr#x xx`xpx §u v tx} Bxpv
z z} 7 8 |
fvs z } zx zxw u z x | }x g u }v |
x} d £ t #| x6#| 9#6ktz { rzx¦s n xpx rE| #ruo trEu rzx§cfRE6pg Bxp!z 6}
vs z }qs | zvz xq | e d fv |x | z } |q
x o|xszq s o
%txc%#tc%s cEuw u¤6Eprxxdq o $f¢#t%# Epktcx6Gtz 6¢x #f | xwuwvccz E crqrcr6R e o oq z oxq|s
| ~ d z o h | z u q w
d xB#t¤ E| | h £ B8 rtrxt#%§pn #g6#| dz §u x w d qv ruxB9x rowcf cEu
z szxv z s u
vxz usw g u s o }x x | } g u }v | } vs z }qs | zvzs |s
ox zxqz hz o } vz
rcv %u$v rur#w wzxRRwvxY$E6px Bxpz 6jktx%trc%Ertz z d rxrorrx rccf rvxRcc5o o
h x| }x ox| sz | z }x zvu u } ox| sz | ovv u
s o
&B| 6pz rE6rtwxjxpir#xxcq ¡ #| z E6rtrrxE!wzxW}r#6 ktz z tz z crxRrzxW}rr6 uqx u ovv u
s ux v o o | } us ovz
ovv ox | sz ovv u
s z wu uqx ovv u
%tz z r!crzrrxrorx} 6%6 | c#8| xwrE| z r6rtrrxE| rzxW}rr#f9%tz ERz crxu rzxW}rr6
s ux
ox | ovv u }v sz o oq v ox| sz | oxv | } h ov q h
%tz z rg%wxrorrxug§rrrE| d xxY{tEf | §rurrvccz | cz rE6rtrrxE!z rrx 66z | z x cxz
| x wu xzv | o x| }x v
| v o n qv ov X " o o q q l ¥ s z
r
rE66x ERcrg5tz # E6pRx8pv crzx¦s rvx} d n xpv5qWPxe D xddo V s6¥ s' rzx¦)x§u 1 2 $ " 1 6 £ 5
ox zvv z v | }
s u z } o o q z d v z q zs zwzs s z o oq
x zv zs zs ux p q qv
r
rE| rtrrc!E6%§cxpx §rurrvccdccxt%tY%6!v tEf | xwuwvccz | trc%6tkrRpoxsv5qaPxxe #|
vw z } s z o oq | x zvzs zs ux v o o | } us ovz
v ox | sz oxv | } h
Yrzwocf'v tf | §rurrvccz #tc%6t%)r!cwzwxrorx} 6k6`| c#8| i cz r6rtrrxE| z rrx 66z #|
ov q hz | x wu xzv | x zvzs zs ux q l` q qX zv z
s uz } o oq e po t
z rxWc§!r
rE66x EcriAtrc%6tkRr5oP I sl¨z d7t syrp ddo D | rx{g %§cxpx §rurrvccz u¤d 6X do
3 4 z o Goz " o vx | g z } x |
dRCewvx} 'r#¥gx$E6} g #| c ¨Rs5qfRSrvxkv xx¢x} E6} g c dWxv 60x%vP krvxu #ttf |
p Go P oI o } g u f z x | p o `q l t z o l o } | q s z
£
o oq | x| g vx z u u zzs }x v| } o oq |sz z e dn yo v q qX v| gu
§rurrvccz £E6} rtx§6 cq ck6p!E6§rurrvccz | Ertxt#5 ¨z ¨ t syrp ddo D Eixxf ¡ ¢
z oq o
x o|xszq s o o oq ux zx hz
} uv o } ovz
z
xhrox crrvo | 9%# EY%tcx6tz 6x f | §rurrvccz rv t§p6§r#rurx6p#| rc#8| x}
¡£ ¥ ¢ £ ¡ 0
¥ 76 & '% ¡ 0
£ 76
£
%oUd&pybt bV uxpz 6R{g r
rE6 Pdxxx r§c%#
P ez t qp l " o z }x | } z | o dv u ox uq zs | 1 2 ¥
o v os z }x wu | s u uv z g |s zx v q o x| } z |sz z |
icrzx} | %#| xp©ErE{§z )tx} rvE§cr o cz Wcx {E6Yx 6v c5roErtxt# rvo zsz
%tx} g ) 0
&
¡ 0
£ 76 ! ¡£ ¥ ( 0
6 & '%
e ¥ e o P lzo to z }x |
5oP dz ¦gp D 5q¨C0wdxE xpz 6} £ $ "
z u dv fs u gxz ovz
wu o o
z }x o x |xs u o s o } x| } zz | }
{g rrv ~ d¦§{Ccx #| rc#8| E5§rurrxx ¨z xpP R#p%§f !wvo rzx¦£rvxpx E6px cv rE6Yv z
! "
# ¢
£
& & &
W¡ B ¡ & &
! £ B
£ 5oP dz pt&¦xpirvRrzx¦$txY#x ~ d#px§c)§rurt%roE| §x rvo
e q l ¡X z }x o s sz }xu dx |xv uq ox| s u | zsz
%tx} g
¡ 0
£ 76 £ ¡0 ¥ ¢ £ ¡ 0
¥ 76
zx o g zs uz }x vz
zv | q o } e d xvzs zx o w u
trrrx%s grvo %§cxY§c#8| rEt$rvxpx udc%tr Eirvo 0
wu oszxv ox z }x v zv |
e ox q z v z 0 w p qz ov p y | pz qz " z }
Eis§ru%trru6 z r| cks zxY`r
x§u crEtqg#| ud r
cz rcc6pcks 2u Rz py¨dxBb" #R¦&py¨expx
| v o z v ox sx zv d ¥ g u f z g s zxw 0 w u ox osx
o } | } us
rzwtqRcz rxcz urv %s#| x§rurxbW}o%prrvo rczx} X©BxxS{¢tr8| 5§rurxbW}%prrvo %rxrowx&6%6
z gu f g zs w 0 w ox osx
o | } us z }x
x}px wvo £$2¥ ¡ 0 #| ¥¨Bx§uz{u%xuHYzf} Eu xwuxb} kprrvo %rxworx} 6x%6 xpRrvo ¡£ 0 %tz zs
¥ ¢
u ¡ £
¡
g¦§ ¡£ ¢¥ s§w £ 760 $£ ¡£ 0 '¢¥ $2¥ ¡ 0
£ ¤ ¥ o
¨Cz
yo ¡ pon l j o
o | } us w u z
6x¢v &mwvg%wxrorx} 6k6 Eu rzx¦s xu cq x
z} o v u z zs xq sx fs gxz ovz
z } z
v oq z o | o uq zvz
xpx icz xRx} d %66cx¦pv ¦xu Ccx&#| rct| xpx x ¨z cz cxtz tftz ©E6xwuwxo xcrcx}
# ¢
£ G Q¡ & £
B & & &
yW¡ B
G o x z o | o uq zs
rvo{xE|6} d Ptz #Rtz t6tz gw
rE6xwuwxo xc%#|
&
yV & I
#| & x | } x } q
9E6Y!x¨v &
V & H 0
G xzv } v uv z } o g zsz }
s s g
cxb6{z r$ferr$t%txpx & %tz z §Huw u ~
!
# ¢
d £
$v & &
yVeW¡ & ¡ & &
! £ yVeB
£ v g w v|
o | } us w s o| }q z } ov wu ox osx
$Brur#Hu¥E9%wxrorx} 6k6 Eu rzx¦9 E6cxpx x x FEg§rurxbW}%prrvo
o | } us x o u z } z o | z
&
o |
%rxworx} 6x%6 # #%Expx rrx%s g tq {g yV & D C | u 5tz o 8 BCR0X dxrRz Px0wt A o z e v e z v p { y w v o
3 lq p o n l j z } x } |s o } x | q z z q z o | o u q w u v oxs zvv | v u q z x | } x } |s
t sr&mfxp6r§rvxp6rEtAP{d cxtz t6tz "E6xwuwxo xc"E©xxwu%trrEAcz cxtE6p6r§
q
q zxqz | xq sxv uq ux fs u gxz ovz
| oxq sxv uq o zx uqzv z
rqwocxcE| cc% os Rcx¦px§c)rRrvo ¦§{Ccx #| rc#8| `x rcx¦Yrx§cP gtrv §cc£x}
d @#t
8
u 8 u o |s vzx|xv } o g os v u ox u z } o E
rx 9 %s w x #x#ricrEprgprx$srzx} | %#| xxx #§cq | 6xfe l & crz xc{g rzx 6$x" x uq z |hz su
d o|x wu
rEYcz Ecz wz tx
jERcrzx} | %| cxpAERk§u §!x§EicrEpRxpcz u d xcq {g wv ~
sz | x| v os zvz }x wu zs s u z u wu vzx|xv z }x u z u
h s g |zs u g z g v v os zs
q uq z zvs uq d u
d rzx | z %xu @Etk| o x{{GE| crzx} | %| %§u #| z Wcx o xc{{g r%6cew wx
#| c$crEp)prx$g !¨z xv 6 #| x #| c#{crEYr)prx$g 430d22¨xe 0 %x z #)%x z
v z
v zx |xv } o 7 v l 5 u v z
v zx |xv } o z o ` 1 tz )
x |
x
x u vzx |x } o o Ee &
x
#x$crprv prx$g ('sQ¨l %x z #| x $#x$crEpv prx$g %efxe #e 6} #| §#{crprv
x z x u vzx |x } o $ P o " | u u vzx |x
} o nz ovv l j o o o }x s v os w z o u } ovv u z d
prx$g !¨dxx&mXrvp E| u rvxpxHuw crzx} | %#| Eu crq#xq rzxW}rr#f x xcz u rcrEpv #| ux vzx|x
v } os x| g oq ux fs u gxz ovz
| oxq sxv uq o zxv xv
z dxs |xv u
cwzx&| k#| E6} Xz ccz rrvo ¦§{Ccxp#| rc#8| 9x rcx¦Yrx§cp )trr%s #x} d%#p$x §{g
| } s |q | ox u u }v } us w u o z } s ov u v x ox |x zvzs zs z }x zx|sxv o
xE6px #ti£x r#xxpcrzxb%Yx ! E| u xpx tz rx§cq xicrz §rurp#tc%6t%$xpirErpx rru
dv ox osx |q z } us ox osx x o u | } z }x xq sxv u u
0x§rurxbW}%prrvo Et§ruxpx %uw §rurxbW}%pwvo # #%E6ru# xp{cx¦prxxcq rx
g | x| } zq z o | o uq wu v oxszvv| wu xzv | }
zx§u BrurE$E6px cxtz tftz eE6§rurrxo §cE{x§rur%trE2E$cR)Ywxo g x x} cq x§rurxbW}%prrvo z o u v ox osx
o | } us | o uq |q w xzv | w vx ov u ox|x zvzs zs z d s ox osx
%rxworx} 6x%6RE6§rurrxo §ciEtxwuRu crP£Eu rrrvrx§cq §rurEptrc%6tkdx} q§Huw §rurxbW}%prrvo
o | } us x o u | vx zvzs zs s u fs u gxz ovz
d wu vzx|xv z }x | s ox osx
%rxworx} 6x%6A# #%Artrc%6t%(§w ¦§{Ccx!#| rc#8| ~ q©EcrEpr{xp6rEtz u §rurxbW}%prrvo
o | } us | y G qv qzv n q I l yz " v y z } & v os w o
%rxworx} 6x%6Arvo z rbt syxe I ¨xWpq D xsv%qWPU¦I Cewwstq rV xpx V v & crzx} | %#| Eu | u
| o z oqzs zs u d o | o v os | v o }v ox z o |xs z q | v z }
gtz # r
crrvcc%6R%§pn i | u g crzx} | %| x§u Rx xpx§rurE| c%s Ep%tcx6r
rE66xxxpx
u | fs xz o z
d s w xz v opzo q t e s l ¥ ¥ yz
wE"cz u $wvo ¦xu gCcx #| rvc#8| ~ dvcrzx} | o%#| Eu{crv |$xrx rvo rRd0a`b§ustq sy D 5oP I Ce" ~ ©
"
f P g e" ! '
§ ¨ ¥ ¦ £ ¤ ¢
d g s zxx z } x v | s u } x | o } x }
zs z } x we s | g x | xs u o zs z }
rzo trE| Rxp$6} xxpx wvxYx xbu #| v %txpvd #t #$u xq#pk§6 %xu xpx 5
| v ox |x zvzs z | vx zq uq oxzs uz }x o oq w zv z } z z } usw v ox
rE$x§rurEY#trck6t%s ¥xtcx§cRrqrc%xcxpu&§rurrvccz Eu xkxpx Ef | rzx¦s xYx %u{x§rur o| z
5 uz x | } s z }xs w z s xqz zs ux z u u ux zs n z } os u zv
v rzx§c6E6px txp%6@xk#| #| cc%¡%)r9x rorc6 cq xrR%| rzx¦s yRxpx z ktz rx rx
v wuxB9xpx E6p)x%| tz {Bx} %txk#trc%s txY#u #| d ##tg xE| cz #| x6#| rzx¦s
o h | z } x | }x z s s z g u vs z } qs | zv z s z }x
n d x z } 7
z }x xqz z ux uq | } vsz }qs |zvzs uv x | }x |x zs | x |q o o uv zs | v ox
xpicc¡ks Rz cz 6i%txk#trc%Rz r$E6p!rzx} pcrqo %6 ###t"
x§rrv rR%jx§rur o| z
rE|$xrv#u |)ueddvxcqcz ¨zzxE o| z o$s oczx}px!urx vczwx}&| oks#| zrvx&|tq u%s w vcq%s| g0|rs z{g vczwx}&| oks#| wEu{xczrv
tz o$|s§uw f¦s§u{gCxczx #| orvcz
t| |xcqx¦spxrvxxucqurx
rcz |i~ddvczrx} | o%s| zx}px x o%stz s§ucz%s6Axxxux}pxro$gtz%s66x
¨qx¦spxv!f¦s§u{gCxczx&#| orvcz#
8| | xcqx¦sYxrvx§ucq urx vx§urorx%stzrvrv|£zrvczx}pxzvx#|tq #| o| u |g ovczrx} | o%s|
x§u |$vx ox}pvx§urorx| czks"E|pvx |tqx%stzvrvE|
rro |tz%s!tzrxwEu!#|tq{z{g zcqrorxcqE|rs6 o
wczxE|666x%s§u1wd $ ' 3 7!
x o%stz sxuzx}px x orvx oE| u stzrxu§ux}pvczrx}bukspxzrwox}xu urxx |Rzx}Yxs§uw f¦s§u{gCxczx #| orvcz#
8| |$xcqx¦sYxrvx§ucq
xux}Yvistz |tz%s zx}px zrvrocq%stzxhz9|£v ~ di oE| u zx}Yx o vcz ocqxtz tzftz oAE|6§urorxro §ucq)
#| |tz z%s
urx$roE|uwp
8| z%s66xcqx¦spxvpf¦s§u{gCxczx x orxrx6vczks9zx}px
rrvrvczrcz%s#|tq5tzrvux}q vro stz s§u)zx}YxjwHe dstz sxu9zrx} |
o%s| §u v tzftz zks66xcqx¦spxrv f¦s§u{gCxczx¥x|6}px{vwo zx
¨z vE|$v#f¦sxu gCxczx #| orvcz#
8| wEu!fqE|6}'g0|rs ~
dq sxuHw §urorxxb}Wo%spxvwo
%xrorrox} |6}u%s6 x o#u% zx}pxivcz ucqxtz{vx
8|¥g5E| s§uw f¦s§u{gCxczx
#| orvcz#
8| | xE|6}px)zczv)z g 6 #| vxxuwoxE|6 u x ox ox} u{d z%s6xwo o5 gBux}pv zks#|`zrx |6hz
zrrox}u urxx |is6u$sxuHw vx§urorxxb}Wo%spxvwo zrvczx} d G wEu zrxE|pxrvg
%stz z s§uwg§urorxxb}Wo%spxrvro zx§u £$ G ¡ &B
vx§urorxxb}Wo%spxvwo E|tqxur)zx}px!vrvczrvrv|dux vropf¦s§u{gCxczx| ovcz#
8| |x orxcqxRspxrvx§ucq oPtzrxrv E|6
uzx}
d z%s6ro o gBux}pvz%s6¨xcqx¦spxrvzx}px oE|Yxx}uz{g
rrxtzx zvx§u{
¡ £y3 $Q¡¢7! £$3¡'¡$ # Q¡¦7! £# Q¡e34 £'¡$ # ¡v34 £ ¡9$% Y £# ¡9$%
vczrocqxtz
&tz6tz oA|6§urorxro §ucq!zx}px!z |6} z{g 7 #| 3 ' $ x o%stz sxu£zx}Yx9x orvx zrx | hzis6ug e
d G
xczrv!zx}px)ux §u6Yvcz%srs§ucq &5wEuvrxtz%s#|6
zx} di oE| u zx}pxp o!vczrx} | o%s#| ux §u6Yvcz%srs§ucq!z%s66xcqxRspxrv
d z ux£zx}px!urx$xtzcqE|r |
gBux}pv$zks#|jz uxR| }pxro$g zxE| ocq§urvvE| v¤§urorxxb}Wo%spxvwo
%xrowrox} |6}xu%s6 E|tqxur zx} d0xcqcz ¨z urx$zrvx&|tq u%suw
g0|rs z%s#|Rvcq%s ~ ddx%s#|pxv$x §u{ggxE|6}pxis#|tq |`x orx#uxux}pvczrx}bu%sYx$s§uw f¦s§u{gCxczx&#| orvcz#
8| ~ z%s6ro £
p(s=no | t=no, f=empty ,ξ) = 1.0
p(s=no | t=no, f=not empty ,ξ) = 1.0
p(s=no | t=yes, f=empty ,ξ) = 0.92
p(s=no | t=yes, f=not empty,ξ) = 0.01 p(t=no | b=bad,ξ) = 0.98
p(t=no | b=good,ξ) = 0.03
Start
Turn Over
p(g=empty | b=bad, f=empty,ξ) = 0.99
p(g=empty | b=bad, f=not empty,ξ) = 0.10
p(g=empty | b=good, f=empty,ξ) = 0.97
p(g=empty | b=good, f=not empty,ξ) = 0.04
Gauge
p(b=bad | ξ) = 0.02
Battery
Fuel
p(f=empty | ξ) = 0.05
£
sz u u s | } ~ o fs u gxz ovz
s |s o }s | zq zs w o xq| h zq zs w o ox o } | } us
t6x§{ #6 vwv¥¦§{CcxR#| rc#8| %rprxx¦##| o cxtktHz ecE6z cxtktHz {rqrrrvrowx&6%6
s uw fs gx z ov z
| o z q z o | o u w u v oxs zvv | o h z | q z g } u }
§{¦xu Ccx#| rct| R $8xtz t6tz §6§rurrxo §cq ex§rur%trEArx#rux i#t{§xxprx ~
ox| u ox|
d §rurE6bPSrx §rurE6bP
usw ox s uwv |sx z }x o v | u
v vx q us
%ug§rurE| §%x#rp)xY5 !E| r
wtwqro#f} r!rcx %6 #| v ¨)c"
rox r!E6Yx Ywxk§#rE| v vz ov x| } } os u
z q zs zw o z ov us x z q zs xv u n z q zs zw ox o | } us s ws z
cxt%t g#| 6§rucz z {0b#t rur#%6} ~ r
rtcc%r#p!d cxt%t o rqrrrvrorx} 6%6 §Hut6
u zzsx o }x w v oxsz us | ox z }x |s zv v o hz z } } os u | z d o
rx c%p!rvxp$Eu crzr%tf§%6 twqE| xpE| Ertz r!rrx#rux 5txpx prx%§#rE)x} i E| u xpx z}
v os w xzv } v | u u vzss uq zzsx z }x o u }q|z zsz g zzsx | ux o fs u gxz
o crzx} | %#| Eu cxb6prx v §6pckr§c)c%pgxp )z xcEt)%tx} ckppr p¦§{Ccx
ov z
z } s uwv |s xv
x | } } os u | zx | zs s z | z o | z os |
#| rc#8| xpx v §%x#rYx %s yE6px prx%§#rE)| rt%tq #t utrrxE6} c#crzx ¤ #9tcRwxk6 e
dv os zs s u z u wu v ox szv } ux zv u vz
dcrzx} | %#| %§u §!x§AExxwuE| txu £x§6pcks o ¦xu Ccxp#| rc#8| | £z xpt$§w fs gxz ovz
o u }q|z su
v ox osx
o } | } us z }x vzx x | }x z }qv ovv | z |vv
x§rurxbW}%pwvo %rxrowx&6%6 xpcE| 6E6Y$z xcrx rrE6¨#prcz | 6§rucz z t ¤%#tz z s |
zs uz }x vz
w ox | | ux u vzss uq |vs z qs }q| } os u | o }x e d } |s
d %§cxYE c#8| u §rurtwqrox6#| #RrAv x6pc%§c6Ep%tz %s %#| Etz prx%§#rE$rvxp! Ui6r§
z } us xqz |zs z } |
sz ox o | } us o z }x ux sz gv z }x ox zs xq sx
xpx %uw r
rcc% os t%96tq %txbrqrrrvrorx} 6%65tz # xpgrt{¦x| xp{rr6S%66cxRprv
fs gxz z } o vqs | vzvs z x| } } os u z szx }q| ¡ zx
¦xu Ccxxpx {c%#$cr%tz ks E6px prx%x#rE| | 6xwucz z ##t kt#cE6} T #| { ¨t rrv
s| g
Ecd#t §rcxYE| n | #$u rzx | §1¤drrv$CAt%te o prx$#§xxprxE| e fW}%trcz
uvz }x hz s u dvx o gx x zsz } o g } u } z osqv
| z g v | } us z q z o | o u q o h z v fs u gx z ov z
o z q zs zw ox o
z 6} {vE£r
x§xx%Rcxtz t6tz "6§rurrxo §crx#rux #R§{1cx #| rc#8| $cxt%t o rqrrrvrorx} |
} us s uw } os u | x q h z d o t oz o q Xqv q l yz
&%6 §Av prx%§#rE{cE| r ~ d¨X dC0rG pt¢Wxrp 5qaPI RI Ce" rzwtq rvo §rurxbW}%prrvo rxrorx} 6%6{# #% | ox osx
o | } us x o u
o o ovvu usw xvzs zx o w v o o | } us ox u w
rxcrqrox w
xW}r#6 | %uRc%tr iEu crzrrxrorx} 6%65x xb cq Eu rzx%6$Etxt# x} } us |sz z z
dv ox|x uq z }x w
dx§rurEYxb cxpEu
| ov z }x zq zs ux g ox osx z }x } o g oxq u
%rxroE6§rurxtz o xpAcx %ir0| {z rxbW}%prrvo xpprx$#§rurcx6¦ §cq o rx6##teE6px §rurxb} zv z } |q x| } ox
osx
o | } us x o u z }x w o ov u uq vzq us zq z o | o u o x|
%Yrrvo rxrorx} 6%6i# #%Fxp©Eu §rurrxr#f ccz | ccx %6 cxtz tftz ©E6xwuwxo xcq rv{E6}
¥
)
#¡ £ £ £ y¡ ) 7 ) ¡ )
¡ $ ¦
£ u ¡ $
) #¡
¡ 3 ) 7 ) ¡ ¡ $
£ $£ $ QYQ('Y(' £ $ #v#3¡£Q Q e4 $£ $3 x¡u3 x ! ! ¥ £ !£ ! £ !£!9% ! x Q7!!
y u
v uqz ox| ox| o v oq z o | o uq z }
cz cc6} §rurE6bP 6¡ xwuE6 u Rcz cxtz t6tz ©6§rurrxo §cxpx
o zv | o } e d x o z zs ox |x u o } z f u fs gxz ovz
|
tz rEtq wvxYx udtrzcq ¨$%xu xwuEpxb cq wvxYx E&| rx ¦xu Ccx #| rc#8| ) o z cxtz uq
v oq z o | o u z}x o h |q zx | xs u d szx zs s s
cz cxtz t6tz "E6xwuwxo xcq xYArx#rux z #t{z g r
cr666%§1¤dv tr{%§u §u tz u x o 6v
o |x zv | q z ov | zw x u o } q | us o } v os ¨ } o
wvrEY#tz wxo rx tcf} rzxW}rEt#x!wvdEx%66#| rvxpx crzx} | %#| ©prx$g rzx%6 %§{@Et%)5ue } us s u g |zs |
¡ ¡ ¡
'
£ x 7 y3 ¡$ #! ¥ ¤£ §¦ ¢
¡ u ) £ x !
¡ u 7
¡ ¡ £ u ¡ $
)
£ x 7 3 ' $ #! ¥ ¤£ ¢
¡ u $
£ x 7 ! ! $ x 7 9%
¡ u
| } z g
o } | } us w v s z } us dxs |x vz s |q z }x x| } o
z 6R{%rxrowx&6%6AEu crzx¦RxYx %G0%#prv x pcxu #txp{E6px tz #
Po wu ox sx o | } s z }x zx u ux x | g z g zvu | hz s u dxv szx o w
Qe " Eg§rurxbW}%oYrrvo %
rxrorx} 6%u6!xpRrxb cq r$#${sr#f666v rzx 6{§1tdrc%ztr AEu
o | } us
| zx uq ux fs u gxz ovz
zv oq os o |q z o
%rxworx} 6x%6 #jxb cRRR§{1cx #| rc#8| | rx yrzx cx %6) #ti{g | u 6p§w x| }x su
ox osx
o } | } us x o u | vz szx o
§rurxbW}%prrvo %rxrowx&6%6 # jcx o tcz | u ##{§w ¦xu Ccx)#| rct| Rx tcz
| s u fs gxz ovz
| zv |q
5dfxe 6 #{dd266xe ) E$cce¨Epx ticc% os xpx wvo 6&xv 5 #| ¨dxxv tE$cce¨z
P o " | z o ` 1 tz w u x q z z |v | q x q z z } vz l nz ov l j w u x q z
Epx t!cc% os xp!rv$0d21 6xe ) Qe " #| ¨dxx&m¢Ecce¨EYx tRcc% os xYRrvRxfe l & E6px
|v |q xqz z}x o zo` tz Po nz ovv l j w u x q z z |v | q x q z z }x o o E x|}
oxszvv z }x ov zxq sxv uq v|
vx§rurktrrE| xY`x rx rcx¦prxxcE$g %6xw )¦xu Ccx xYx rzx 6i§"d rEr6dcE| %#| zs o o fs gxz z } | hz s u zx|s qq zs
v ox|
x§rurEtrqrox o cxWz t1tz u 6§rurrxo §cr#x} ¦§{Ccx9| c#8| 9 o wxx¨c%s v x #u 6 crEtq
zq z o | o uq zv u g fs u gxz ovz
| v vz u o vzv|
|sz z dvxs |x s |q z } x u s sz }xz } gu
Ertxt e 0r%#pv #tgxpx #x xu txpcxig Bx§f z g §rurrvccz xp9E&| {z `xYx E| o oq z }x zf z g ox z } x
x | } vxs zvv | z q zv zs vxe qs | ox s uw ux v l 5 us qs z dvqs | zq z
E6px r%trE9cxtrc%6!rd k#xwuE| § o | rvo A¨z xv ¤ %uw k#| x} dc%#9cx| rzc%s
zs | v u zq | } z } ux ox o u vqs | z u
ox z }
%#cz x E| Hu cx6q xpx r)x r #6c%#!x} d z x rxrorrxqxYx rvo ¡ z x §u o| x} u z
dv ox| sz | s u vx zvzs z u o oq | u zs | v z
dcz E6rtrrxE6#trck6t%s #| z x§rurrvccz Rrvo z x %#6b¦!x} d %6r g Bxpv zs o o gu }
o o oq o } s u |s zq z o d o }x u s s | z }x s z xz
szxx | } z }
wvP§rurrvccz rvxpx §w r§E o| cxtxe3 p ~ wx xpx`u xu #tq xpixHuw cx`w c# %trr6Sxpx
zq zs ux v ox z } | } z g zv u o ox u u }v } us s u
c| xtkd£xxwux§u xYx z 6){r#666¨v E| u x r#xxpcrzxb%px 65 o rzx 6§1 |hz su
o oq ox z }x x| gu f o x| } g zx|
d z | rvo §rurrvccz | z r$xYAE! BxxmrvE6i'rtwqo o rqx} b¨Hz t sxv syz rG ptq p#xcR8|
} o g | p X l yq l ¥ y o | x u q
|s zq z
u d v z q zs wzs s z f o o q | vx zv zs zs } o g | y t n qv e z
v r§E o| cxtxe3 o wv ~ 0ccxt%tHzYk6 v tE&| §rurrvccz j#trck6t%prqx} io D wXxpv5qWPx7x§u
xv x v os o oq x zvzs zs } o p y q qX o|x u
r#u E| | crzx} | %| xwuwvccz #trck6t%9crqx} g o D wt t pyp ddo D Ep§cq 8| v rxE o| cxtz |s zq
o e oxqz vz pX l o tl` Po | p y t o tl ¡ |q zs vxq sxv uq zvz }
&e3 o xwuwxo 6 | d w
cz cc6pc%s Hz '¨X &df5oQ1z #o D w¨X & X rzrEt$%| rcx¦Yrx§circxpx
|s zq z o e zq z ox o | } us ox zvzs zs vqs | v os o |xs z
) rxE o| cxtxe3 )| usd cxtz t6tz rqrwvrorx} 6k6`x rtrc%6t%c%#| #£crzx} | %#| p%tcq
ox zvzs zs v u v o|x u |s zq z o fs gxz ovz
z }x z o d } us
&6sx r#tc%6t%$cz xAx EY#§cq r§ o| cxtxe3 !| ¦xu Ccx | c#8| xp$EWf0v rzx%6
o oq u ox |x zvzs z fs u gxz ovz
z }x w ov zx hz | o ¥ lz
§rurrvccz rx §rurEY#trck6t%s R§{1cx&| c#8| xp"Eu §rurxtrxAwvgCE plq D ¨X 02£st'x} o toe ¢ q z
d &##t tr%tz ) #9trxt6 ##t xEic{trE6} hb#t
zvs ~ | zv z d | x z s zx } q |
u ou | o }xs | y v os z z q zs w o s oxs | s s z u u | s z
x ## ~ 2xpk6 | $crz%txbScxtktHz | xdrqrk#6§u cdb#8 tf§§¥ #£x xu tx
b##8 #| tErcz xcwz#ru#6§5¦§{Ccx9#| xdrqr%#6x %§rurEpx rxdp%#)E6ppcx 5x6ccrx
s z f q v o u ux fs u gx z s oxs | u zs o | uxv q zs | x | }x v z o } q z
o zs | vsz }qs |zvz | oxq|s o zs u }x zq zs w o | v z }x zsz g v ox|
x x§rucz z %#i%txk#trc%s EtrqrcEr6 %| v xYcz cxt%tHz e66xqxpktx} ¢x§rurEtrqrox6#|
v u }x s u d |x x u zs | v v zs
o h u q zv z }x x | } u x o z ov z | s
zr#xY$§1xEp| w #x£k#Rrrxx6c%prxxrzx c!rcxpiE6px rv w
#trzcq &6v "
rox r!6} #tq §u
}§xxtrE| k#$#¦xu Ccx!xpx tz {Bx} x§rurEtrqrox6#)##| §"ud B#8G b¤ | xER
u z v zs | v fs gxz z } s z gu v ox| |
s u
} |
s|} ~
#6 rvo v xpcz ru%#| ¨r#x`)x rx rzx 6$xHuw cxt%t Rr| §B%66#gtz td #t
u }x s zx u n ov | h z s z q zs zw o zx o h us |
d
o oq z
§rurrvccz Ef | z g z g vxs |x s | z } x u s sz }xz g gu f z g x| } oxszvv| z }x vx zvzs z
{tx} rk#prv #tq xYx xA§u txpcx} Bxx'{E6px §rur%trExp{r#tc%6t%s
ux v l
re¨z xv 5 u qs | z } z d v uqx ovv u z }x w v o ox s u vx zvzs z
ks w %#)x rou¨rzxbu x} dcz crxu rzxW}rr6£xY©rE| Eu crzrrxworrxg6irtrc%6t%s ¡
u
z x xu o| z dv ox| sz | s u vx zvzs z u zs | z d o }x u s z w xz
x} dcz rE6rtwx$6$rtrc%6tks z xR%6 ¦v x} wx xp#x u xu cx@{c#
szxx | } z }
%trr6qxpx z | } u sz }xz g wu o oq | s u zs xq sx |s zq z
#x#6cq rx txpcx} PEpxwuwvccz $§w %6¨cx¦prv rxE o| cxtxe3 o ~ %6r zs o £
u d
after d before d
Start Start
Fuel Battery
u 3 1 0 ( q g T & Q $ x Q # E D e T S XU D`
x T " D XU C
e42!)HFR'%Fg ¦FeRBYbfbde!b!
l qpn " v ux s w | } z sz | o } e o | } s w v z }x ox| z v oxq|
P 6WXr0¡ c| | rtzY%zs rE6Yv {g tf#6 rvxpx ud %
rxrorx} 6%u6©Eu cwzxRs xp!H
kwwvEpv EWfwo x§rurcErusw
s w v oxq u w z } w u zzs | x zvzs zs x u vz
6RBx§ru Eu x§rurccrzr#cq YwzrocfmE!c%§cz Rtrc%6tkR#xRc§u §xxprxE| E6p!rx P } u } x| }x zx u z
wEpx} xpxpEix ")z trx{g
d fq|x }x z }x wu v o 3 szv } u z
ox osx
o | } us | }
Ep§rurxbW}%Yrrvo rvxp!rE| 6 #| c ¡£ §rurxbW}%prrvo rxrorx} 6%6 9Ywxo g xx6} 9% p%tcx6
v| ox osx o }x zx x u |
x o |xszq
s u vvzs hz | d o|xszq z z s zv u g o |q os | v oxq| o }
6!rck6 ptq z gi Ep%tcx6urvo x | x¦px r#x} rx$rEtyrzx} | %#| !E| §rurcEs w rvxpx
w vz ovv u z }x z o uqzs z oxqz vsz ovz
z } us xv |sx uq e
o } | } us
Eu cxWE| rzxW}rr#fRxpRc5x§cc%R{g z rccfp%tf)#| rc#8| xpx %uw rrp§c) id %rxrowx&6%6
o }x zx oxvz u fq|x }x z }x wu v o szv }
o | } us | oxq |s s
rvxpirE| rcRrx rEYx} xpixpeE$x "3 z trxu xxu g #| %rxrorx} 6%6 ¥rvo §rurcEruw 6¦Bx§ru
o }x
| g x ox z z d |z v u fq|x }x z } v o w u oxq|s z }x vzs v|
rvxp!8pv xxu trrvrtxb%s w ~ dv tx} 6cz cq rEYx} xp$xYx cz x !§rurcEruw xpAc%6¨Etz
v o
o v o 3 z } u } z u uv ux fq|x }x z }x o z g zv u d zs o
#| cz rx #| rxix "Btxpx xig xxcz r!r!Epx} xpixpz #{¢r#f66 § | ¡ %6r
o g u }v v lv | z } v o u s lo x o u v o u sz } oz xvzs ux uq g zq| s
g BxpE| U pWPq xC txRwxd§i§u p D 6¡ #6Rwxd§txprxcrck9r!z c{rwo ¢wxo cEuw 66v
x s|} | x o| z } o fq|x }x z } gus }x z g e dvxz fs sz
E| 3 e #6P§u # | o cwz #| s E9xpx 6Epx} xp)xpx B%6p){wdrc¦#| tf66v
xv uw z } | q x | } | z } x us | } g z u f q |x }
r#u o 6i6X#t{E6px tx$E| 3 e 6%R)Ywxo x§rEYx} xpx §u cR{tz rx§¥ uq | s ov u
zv|q o }x z | h
d rEtirvxpRx o 6z
z oxqz o } e } os o w u ox osx
o | } us z }x o s | w u x hzx u z }
{g xwuccrv rvxpx ugd wzx&| k#| rz#x rv | Ed§rurxbW}%prrvo %rxrorx} 6%6!xp)x xr#trz2$§#§cq xpx
zvv q z } | zz z g x| }x vz o }qzx z }x wu |s dsz | z }x wu s o zs z }x
o rxdrrvo ftq cxR{gE6pcxb5x6cr!xpEErtz z t66£xpAEitz E| %£xpg o
vz o }qzx zvz }x vv q zvz }x s | ux v ox ox|xv ovz
cx 5x6ccr{rcxprxdrrvo z ebYE| ( %urvcz u cxprtwzircrqrrrvrEp#| rc#8| %ucx 5x
d |x usw usw vz o
}qzx | o |sx zv |q z ox|xzs szx ox o | } us | | } v fs gxz ovz
zv |q
&ccrE6§rurrxo rpxS#ti{g §rurEpc%6tr# o wqrrvworx} 6x%6!jz 6{#¦xu Ccx #| rc#8| rx tcz
b$( m ©# eC¦( q§S¦¤% ¤¨vt ¤¢
" ¥ ¨ " ¥ ¥ £ ¡
dv u
dcz x
zq | } ux x o u vqs zq zs v|zsz v u o oq ux u x o u vqs | ox s w
cx6q )w
xxu #6 ck#| cx#| rzc%Et%tx} g cz xp§rurrvccz r)r
x§i# #f c%#g§rurE| xHu o
d |z } wu
o | } us | ov
}
dv txAEgrxrorx} 6%6Etrqr§6
z } s uw ox osx
o | } us ~ } d o 3 f q |x } | w v u qx u z | zs o
xpx § §pxwuxb} kprrvo rxrorx} 6%6 i xi "1Epx} xpx ¥u cz crx!x} s ¡ %6r £
(b) (a)
θ
1 0.8 0.6 0.4 0.2 0
“tails” “heads”
p(θ|ξ)
t
a U`U h T h Q g
D d g S E T i a U`U h T h Q g
D fU S I D 5 h Q i a I E D d 3 D T X T Q S D g g D D g Q X` T XU 1 D` h TU g T f D C
yS WWR©RF#B61©R¢yS WWR©RFfb6BV#y©©y4Fg # BcFBFr# FBbRYbd2bRbBRV!©!0
vwox} dwx oc5ow| s§uxtz%s #| 1B P$ §urorxcqx6@w!zx}pxp
#}xuwoxxb} okspxrvro s§uro%s6£vrxro x ox
rx oxwx
}
s§uwp§urorxxb}Wo%sYxrvro s§uro%stzrxv#u6 zx}pxp oE|Yxx}u!z g vroxE|6} d0x##|Yxrvx§ucqp§urorx|t%orE| s§ux z urvvro z%stzx} g
¡£ ! ¡£ £$ ¡¢7 $9 ©# & ! £ 7 9 ©) &W¡
vcz ucqczf} s§uw)xuwoxxb} okspxrvro
%xrorwox}&|6}u%s6$s§uro%stzxrv#u6Rzx}Yx ) z%s§uczx}Yx§ vcz#
8| x orv ddv |tzx}Rz stzrvx}u
#| zcqxxufqE|pxx} }Yx$zx}px o"3 z{ggzrv#u666¨v z%s§u stzx}Yx%s6ePd wEu xuwoxE|pxcqcz66hz{zx}pxAxvx vwovv#urxAxxhzx
zx}px!xuAv |tzx} s§uHw
xrorrox} |6}u%s6 s6u vwo xE|6} dw£tz o# wEu §urorxE|pxcqczf hz zx}pxAvczrxuxtz ¡£ ( z%stzx} g
¡£ (#&' ¡£ %#1 ¡£ £ ¡¦7 9 ©# &B %# d £ ¡¢7 $9 ©# &B
£v |tzx}96z ucq©rro$gsfqE|pxx} x}pxRzx}pxwEu$vrv#ux$x§hzxRzx}Yx$xE|6}px)
%xrorwox}&|6}u%s6$s6u zx o stzrxcz uxRzrx¦s
xuwovx#|6 hzizx}pxzrvx|tq z{g zrvE|tq$vrox}px ed wEuzxWE| zx}px{xxu6} |g oE|px%stzcqx6¢z%s#|z{g
%xrorE|tz%s) e
d z%s6ro o gBux}pv$v| z%s66xcqx¦sYxrv!f¦s§u{gCxczx&#| orvcz#
8| |)x orvx§urorx%stzrvvE| zcqxtz tz6tz oE|6§urorxro
&§ucqivrox}px$xtzrvcz%s6tz%sg#|tqz d tz o xtz tz6tz o)
rrE|66xx zks#| vcz ucqxxuRzx}px s#| xdqrorx%s#|6gue
#
£R !" £ ¡e § &yVe&W¡¦7! 3 § &B
x
z |6}Rz g
r%s| ro o dfrqE|Yxx} x}pxzx}pxwEu o"31}Yxzx}p2wu z ucqrxxuRzx}Yx$vro § &Hz%stzx} g
#
£ ¡ §&V &W¡¢7 9 © §¨&B
vro{xE|6} d z stzrvx}uz{g
vcz ucqrxxu)
#| gux}istzrxrx| ux x urx©|6 z zf} xxu g o"3
#|`xuv |tzx} sxuHwg
%xrowrox} |6}xu%s6s6u
tzx}px x wEuizxWE| zx}pxgzxxf'z{g¤weyA opBl¦IUlxv l D | v| vx§urorxE| stzrvx}uwEuAxczvAvrox}pxurx stzHwYz%s{vcz orxcz uv$z
x
dwfqE|pxx} x}pxRzx}Y2wEuvx o"3 ¥¦wEu$vcz ucqxxuRzx}px E£¤&yV e& ¡¢z stzrvx}uz{gszrv#uf666v gBu ~
d s§uw)xuwoxxb} okspxrvro
%xworrox} |6}uks6 zrx}Worvrvu6
zx§u{v$gBux}pv ¡ z%s6ro d wYzrorcz6}PwEu zczks§cz | u%s w¥xwo }pvroxx orxrvro urx &##tie u§u 8 stzrxw8|snxvpq5PWqI lRI yCze"
d zrx |pv© o| ux ox}q|g}pxro$g
zrxE| ocqxurvrvE|ivcz ocqxtz tz6tz o6E|6§urorxro §ucq{zx}px x orxcqroxtz zks66xcqx¦spxrvifRs§u{g1xczx&| ovcz#
8| ~ z%s6ro £
m x2
... x x1
θ
x zq uq z d " ¥l P q ¥y q z } u o|v zq z zv z } | hz fq|x }x z }x o v
xtcx§c!x} 05oP ¤rp ¨slswstI | frx Eprvo cxtx £xYx rzx 6)Epx} xp!xpp E|
£ z u ¨ p q q l yz " P l qpn ¡ ¡ ¢
q w " l P q y q P ¥ Pl qpto
6 "tx} d #8ee xu 8 ©!poxsv5qaPI RI Ce¦¨¨aX0 " svPs%oP 5¥ rp ¨slq¥ wstx%vUe ¨wt sybds6¥q D
3 £ |q o v o uq zvz }x vz
ox|v x| }x £ & v uqx u wu zv| |x
d! § #| rzrEtiwvxxwuwxo xcRrcxpic"CrvrEY$E6pR ¤ & cz crxErE6} YE| # ~
! #
£ &
& (
eW¡ 8 § B &
$ ©¨ e § yV
vzvvux sz }xu z }x wu x z o | o uq z } g & wu vvux }q|z wu uqx
#| crr#{txp#xpEtz t6tz pr
w6§rurrxo §cRfGrwo !E!r#rEtEz crxu
! !
z } z } v o o | } us | ov
} zvz }x gu f z g u
xpx txpx crzrrxworx} 6x%6eEtrqr§6rcxpBxxk{G ow rrv ~ d z 6} {g §rurrxo 6 | ue | z o )
! ! !
¦
d Et6pRrirzxW}rr#f¥rv{rEYr!cEtE6p{z 6E| z R ©©r#xtz
}q|z x| }x uv ovvu o zx|xv }q|z x| }x vv d ¨ zxu
z } o uqx }q|z wu v o o } | } us | ov
} z }x z
|q z
{g rqx} g z cxu cEtE)crzrrxrowx&6%6 Etrqrx69xp)x ¨z #t){g rzx | pEpx} xpx hz fq|x }
z}x £ | | wu us | wu uqx u z } x zvzs z uq os o }
xpg o v ~ d §wzo ( z xwuP£Eir#%5£E9z crx9xYx trc%6t%s xxc`rzx} | %| rvxpx
h s u dvzx|x ¥ £ } o os uqx u zxzsq | |
wzx | z §" dcrEpv ¦¤prx$g & rzx} | %#| z crxx`c%trrvo pz 6} z g x #E| o u ~ z o g
¡
P l lo vzx |x u gx v | } os uqx s | h o o }x
d p Wq xv #| p D ¨ crEpv {1gr
x§u 6drzx} | %| z crxu 6u rzx 6z rzx rv rvxpg e
zv| } |x
d rE6&pE|
z }x s u qv q lv p v t q ¡ | zs | x | }x
| zv | |x z }x
xpi§w aXxp xv xrmwdsodX ¢e p £%#3 #| © E6Y)tYv z d r6} pE| xpp o wvrEYAEtf} x xpx o|x wu sz z}
| |z } w sz z } o x zs x | }x s oszxv u z } ux x zs
#)v txREu tf} pxpx rv)#| rzc%)rvo E6pirE| §ru%tr#6pxpx r)#| wzckr os rvo cz crxu v uqx
z }x szv } u z g } o s s u z } x | }x zx u zv | |x ovv u
| o ox osx
xpgz trxg{crqx} g o tz x9xpx 6p9r$~ d r6} pE| rzxW}rr6#tz # §rurxbW}%prrvo
s os zxv u v o z s zx | z s uw ox osx s os zvv zvv | | z g z q
§ru%tr#6 rrx)x o tcz #tq {g x §5xwuxb} kprrvo §ru%6p| rcrrE)z 6} {cx§u rvo E6} x|
! £ 7
¡£ ¥ 2 $! 43 © 7 9 © 3 ¡
| } g z } ¡ zv| } |x z }x o o|x | |z szv } u z g |sz z
z 6Rz XtxYx 'rE6&pE| xY) $rvrEp{3 #v tx} © z trx{ ow Ertxt# ue
£ 7
¡£ B " ! $! 3 W&¡
!
o|x}u o |x ov | szv } u z g s ds guss | x } v
Epxxz g rvwp!wzx RRz trx{ ow r
%#| ro o tz B%#69r
r#xwrorirvo #| §r%s x} o
z } u zx o }v o s oszxv u z } zxqz hz zs o o | o } |s zx o
xpx rx rw xprvi§ru%trr6£xYx e rccf v ~ d %6r pw
rEtrqx6#§ rcrqxtz rvo %6 cx%6 zs zq us
o } | } us | ov
} z }x wu ox osx
o } | } us
d %rxrowx&6%6Etrqr§6RxpEg§rurxbW}%prrvo %rxrowx&6%6
s oszxv u z }x zx u u zs uz }x vz
w u zv z }x w u ox o | o } |s
§ru%tr#6pxp9xb cq rx %§cxp c#8| 9rx xpj(§rurcrqxtz Etrqx6#rx ~ %6r zs o £
θ θ θ
1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0
→ x
p(θ|heads,ξ) p(θ|ξ)
t
!
x| }
o | } us z }x ux | z wu ox|xqz h z } ox osx x } o o | v|
E6px %rxrorx} 6%6$xpr66 E!§rurEYcc66z xYx xwuxb} kprrvo cwzxcrq%s iAE6} ¨ tx} g z
u d |v u o s uw p t qv Iqzv Gy q ¥ l o l E e y | ox osx x } o o
wv ~ wx wox peE o| x wxx §b&pyxxe R6x qp D Hs5naPsG xv QgV t ¨X iwvo §rurxbW}%prrvo crzxrq%s
z } x| }x s |v u o s zv q o ox osx x } o o z }x x| }x
|
xpx E6pxu x rox p$ o| x rrxx tz 6 rwuc!rv5§rurxbW}%pwvo cwzxcrq%s xYRE6pp8pv z
!
t
6¥ !
¥ £ !£ £
¡¡ ¨
©§
#
£
x } o o u o & ¡ zv | |x o wu ox osx s oszxv u
crzxrq%s rrvE| rvRE£ V e& r6} pE| tz #!©¨ Eg§rurxbW}%Yrrvo §ru%trr6
z } z } x } o o o wu ox osx s os z }x x| }x zzv z ox |
xpx txpx crzxcrq%s )wvP©¨ Eg§rurxbW}%Yrrvo §ru%6pxpR ow E6pgcr){g 6t §rur6 u % us
4
10(& § vx z u h } o ox osx
d 1 § 3( ¥ § #| 25' 4r#txx66z prx$g §rurxbW}%prrvo
4
|xz } | o zs z }x w u ov | }x } o z }x u ox osx
o | } us z
pcf9rv`k6"
xp£E5z ru #6C§r%s xpg§(xwuxb} kprrvo rxrorx} 6%65x} d 1 § 3(§ ¥
10(& § vx z u h } o g ox osx |xz zs o w ov | } w z }
#| ¡ 2)' %rtx§f z prx$§rurxbW}%pwvo pc6} | rvo %6rEu z ru 6CHxYrz)xpx §u
ox osx
o } | } us z d qv qzv lv oI v | g u f u | o ox osx x } o o z }
§rurxbW}%prrvo %rxrowx&6%6Rx} t syxe I ¨xr qp D xdRT| E)ixxSrrvEiwvg§rurxbW}%Yrrvo cwzxcrq%s xpx
z d £ ox s uw o w u zx |xv s zv z } w ox q zs § vx z u h z z } x | }x zx
6 £ tx} w§rurE| § E{rEpAv tx'xpx u §rurcx6@w | %| $#tx§f {xpx E6p{r#u ~
z s u z } | ox osx z }x x| } zzx |s | u | }x szx |zs z } xv
d c%roE| §x6X#tq §rurxbW}%prrvo xpE6px cr#r#6 rx #6ptrt%§6trx !rtx§66z § vx z u h
z ¡ v q q ¨ x| }x
|v u z ox osx x } o o |
x} A d5oP WX¨pz¢#Wpq ¡£ § E6pg8p)rrvE| {g xwuxb} kprrvo cwzxcrq%s | z 6} ¨ crzx} | %| xpx v os z }
z & & vz
ox|v } o } oxq l ¥ z }x
tx} id d #| B & 5d B c"Crvrppcwqxig §rurcx6`w s¥ l & xprvo ¡ %tx} g zsz
! !
!
§
d ¦ § ¥ ¨ !
# ) '
" !£ § ! ¡£ ©§
o o w u o x o s x
o } | } u s z } z §
#} tz #iwv!©¨ Eg§rurxbW}%prrvo %rxrowx&6%6Rxpx tx} g V §
1 2 ¡ ¢ ¡ 2
pv t o t " o q w qv Iq zv v q q | | u o | v zs v os z d v oxs z us x o
sdw&y V pvPt pyxxe R¨xr qp D d5oP aX¨pz¢!z 6} rx EY%#| ©¨ crzx} | %#| x} dcrzr%tf§%6#trzx
u q |s zv v | o zv | q z ox osx x } o o z }x v zv zxw u z s z g u z ox q |s
¨z §cErtz $E6} rxrx tcf} §rurxbW}%prrvo cwzxcrq%s xp$crxXtrEx§u tz {Bx} crqrcE6)ue
s u ox osx
o | } us
| vvzvv u zzs o szv |v u o
d ¨ xHw §rurxbW}%prrvo rxrorx} 6%6 ##{rcrr| x c%uw rv{trx| wzx pE o| x rrxx | tz o 8
|v u o z }x s uw ox ox |xv x o v | zs § § vx u q z }
d rzx p© o| x rrxx xY{§iwqrrvrEpritwzcq &6!R%#| V e ©r6cxpx
x| }x zx u ~ dx |xv uq ox| s u
( & v ox w u s z
E6pr$Pd#prxxc)§rurEt5roE| §x | rvo #| ¡ o 8 cz rE{t6} xRxpiwvo ¨%tx} g z}x § zsz
!
!
t
¨ ¥ £ ¡ £
¡£ § ¦¤ ¢ ¡ ¡ § ¨
|} v uqx u w
z 6Rz g cz crxEu
!
¡ zv| |x
| o u zq zs xzv vzxu u
v z } uv s uw
rE6} p| ##gtz # rrv ~ d cxtktz o ccr#xtz #6} rxpx ( z r{§R ¨
! !
} os z } s ox osx
vcwzx&| k#| xYx tz u §rurxbW}%prrvo | r
wtwqx6ccrgwv©¨ §w §rurxbW}%prrvo xpx #
| o }qzx o s u ox osx z } )
zv |qz x| }x zx zv|q xhz z }x & x | }x
o | } us s u
x tc6} 6ppr#u ~ d Et)§x xpg o ( 'E6p(%wxrorx} 6k6)6)rvo ¡£ ( & %tx} g zsz
¡£ ! #&
( ©¨ ¡£ ¨
©§ ! #!
% ( &
¡£ 8 B
|} | hz fq|x }x z }x ux v u |
z 6z g rzx 6!Epx} YRxp!r$xx##ruE6 ~
dsz | o }x o v ovv q o o z
tf#6wvxY) x§rurrxdrrvo x x | %s
z } u |sx zq z } o | |s z } ox | |s z z v | |v u o | w
xpx x rptcR6Prr$g rzx pv u #r!xpx xwuEt5wortxt#$rrxo #Srzx pE o| x rrxx AEu
¡ f
Q g D Q D X Q` I g D h x d E D x Q X Q S ` T d 3 D XU S E D E Q
" D I T D S T C S a T X ` d Q C X D i D XU I D g
FBS BybFFf©e!yBBwR©y4b©Ry!gC y©6cVBHb¨V#6Y& yBbF
DgQ x D h ) " % " E T D`` T I X D xU S D x Q X XU E
FVQ ©$©($!'§&$#!R3bWR!b6B!b©RT i bWRFV#E y©¨V'Vb6#WB6BbeVbB¨b D U` T x g Q D h S Q E E T I E QU S d hU g S XU g QU g
XU C
o | } us z } o|x } z h s u | } | xq| z g x| } ¨ o zq
u
%rxworx} 6x%6`xpx Epxu xxu g {g wzx | z §1d z 6r
rE66cEp{uE6px ©¦ pcxtz &§cq
|v z }x | } ux s s u zq |s u zx u u oxs |xv zzv | } u | | u
z Y£xY£z 69itz §p o cx#§x§ro rcrzx cq %s w x r%#Yrptcr!z 69rx 6} z 6} x{g
£ $
z g v ox szv } w sz z }x o qp " ¥lp v t Pl q eco | v
{sx§rurE| trxu Eu t6} )xp! r rX5oP ¤fwd5o¨0a`xfd#!E| § crrE#tq {g x} vvzvv| | z v
ox|
o ox osx x } o o z }x z u
d & §rurE6bP#} tz #g§rurxbW}%prrvo cwzxcrq%s Rxpf} x{g
s os s ox|
z §
v ox ox|xv x o v } o g vzv|
§ru%6!6u 6t §rurE6bP } tx} d V § cwqrrvrEpr!trzcq &6Pprx$scrEtq § 0pPtxpx g|v z}
z g zvu x z u h z } q | z } o o x |
o v |
{ur#f66 d § tx§66gEtgprx$g & xwuE6 u#} tz #E$g ¡£ ©§ §rurxbW}%prrvo ¨ ox osx
s x| }x o
6u rvo E6p E| u | xf} | #rxx§ro r
crcrzx c)r
rE| rrxx $%t{{gr#666¨v xwuwxo 6 | e
x u x |s u zx uq o o o zsz g z g zv u o
d cxtz &§cq v trxxpEu §rurcc"d%s rvo § xx}
zq
u szv z }x w oxqz 3z | v
t § !
( & ! ( &
¦ ¡£ 8 B 2 ¡£ 8 B ! ¡£ b£ ¢
o o ox osx x } o o z }x w zq os z
#} tz #iwvg§rurxbW}%Yrrvo crzxcwqks xY2Eu cx#| %#| x} d ¨ §w #tz xp) o su | z}x
t ¨ yX szv w u zs v| o z q os z }x x | } o |v v ox uv o xe z | } zx q z h
o6X do D ©t ¨v txu| %66Etz | rvRcx#| %#| xp{E6Yx Ep$cz cz rirv$d x#6q rcc66z
} szx|zs z } zq os z } sz } o z dv ox szv } gz o z | }q u zxqz h
zxpx trEt%§ xpx cx#| %#| xpx tx§rx} x} 0x§rurE| trxu xtz # #x6grx rcc66z rvo
wu | z}x }q g u } w u uo x | q o vo s u uo x }o s x v | w u z q o s z
©¨ 5#tz xY5x BxREg§rrEtro 5#| rp©¨ §w §rrxbW%prro REgcx#| %#| x}
ovvzvv s u u }x ov xvz v v ox szv } u g o g u
d § x rrcrr| xHw xpcz rzx r!| c##x6$xxwuE| tx!u Cx x $Bwur#w
z } zs s z }xs s | gs uwx } o |sxv ¡ & ovv zv d x |xv u ox | s u
xpx k§u txpk6e¤d #$C§%#xwrprirvo £ B x rrcrrv ~ d#prx§cq §rurEt5roE| xx | rvo %tx} g zsz
!
!
¡ ¢ £ ¨
¡ ! ¡£ ©§
# ¦ £
'§¥ ¤!
v ox| z o gz
| & §rurE6bPwxks %s
z o uv ox szv } u x hz z } s u ¡ & ox osx
o } | } us
8| {g x #u r( e d § #| §rur| trxx)§x xpx §w £ YB §rurxbW}%pwvo %rxrowx&6%6
zxp5x rrczrr| §rurxbW}%prrvo cwzx}crq%s p| rvcrEt)z sE6Yx §8pv rqx} g 6f xwuE6 u§u
}x ovv vv
} ox osx x o o v zvv| |q g x| } v
| } o ¡ ox|
zv| } }x z z s xs | vz |s z z u }x z ov |vx o z z
rE6srvo uxpcz x} drc{g r
%#| xdrqor%#6!cc%roEtxt# xpcz c%u¨wzx puCtrzE| xb£x}
z |q
s | } u z } ux
o
s
d rvt)%#6 ox1&§xRxpx )rxxdq o x §%|
} z |s z z } | u }x z z z o v x o z | w s uw z }x x
prxo$g c5roErtzxt#g6#tq v xpcz vcx} d c5rv)rzx |p)#trzE| x 5#Eu §)xp5 o tz
vvz v z z | o z }x u
o ox osx z }x wu | s osz v u z }x ovvzvv
CrcvrE| #| cqxtz o Atwqxcxp#66} tz #P§rurxb}W%prrvo xp$Evxtz §ru%txr#6 xp9x rrcrE|
v ox | w ov oxq x osx ox z } w x v zvv |zs ox z s |
crzrrcqEs px rxxwucx6`w §ruorxbW}%prrvo z rE| x dq xpx Eu!tz rvcrE| vEt%#|9z E| c%s x o #§
z v xvz ov ox osx
o | us z }x u x vzvv qz }x q o u}x
¨%s xxwuorcx x x§rurxbW}%prvro rxrorx} 6}%69xY¥w£tz vcrrE| xcc% os zxppz cx !v xpcz
zvz s f
} o ox o x |xz | ov zvv s u u }
rcx} d £ t trzb o(!Stz #{rvo §rurxbW}%spwvo pc6}s!x rvcrrE| §wAv xpxcz wEu!cz 66v ~
s
d o s| s u
wx xr#trz{§w
!
s os wzv x } o o z }x z v oxsz us zvz } zz | }v g
§ru%6{x`Yx| crzxcrq%s £xY£f | crzrkt6§%6 rcxpx crv w6p!z ¢v ~ d § ) %tx} g
§ zsz
§ !
f
¡ ! ¡£ ( & B ! ¡£ (
§
£ ovvzs h ov | v| ox szv } u xv
z }x
§rurc%6 z rzx r!E6} §rurE| trx$%s gxp) o ( 8 &
zxzsq zs o v os z }x | zsz g zv |q oqz v z }x vv q
#| rc%twvo k#| 2 crzx} | %#| xprE£ktx} rt©E| ccfpRxpgr
x§u xdrrvo z {d § ©Ei%trcz ¥ wu vszx
|s | z }x o s | w fv | z }x s ov uq z oxqzv o }x e d o
#6£xp)x xrtwzAu 6Epx xpitz rx§cR{g §rurccwvxY)u¢i E| u xpix6&| wz xxf z}x xu } z gu
|v | q s usw h z s w ox s uw o o }x zxx u | }
Epx t6xu %uywzx | xHu §rur| § wvxYtrr#Az 6R8| z ¤¨¦%66cxRpri¦§{Ccx d § ¥ zs xq sxv fs u gxz
ovz
s oxs | u uq z z | ox osx
o | } us | ov
} zx os o
&#| rc#8| #| xdrqr%#6 z v o z cxt56} tq §rurxbW}%Yrrvo %wxrorx} 6k6 twq§6rE| %| rx
o }x x| } gu f z g zvu f o g u z } s ov uq v x s z gu g
x rvxpiE6px BxxS{ur#f66 d rzb ks g x o rur#w xpx tz x§cxqcrz tz {Bx} Bu ~
x u u z z zv o | zs | vs zx |s | z }x s uw vs os zx | u z g o
d £ 8 §%s 8 RcrH rzx} | rE| R%#i%trcz #6Rxp{§{%xwuk6RrE§x¦ §cq tx} srzx rv
oqz vz ox o d ox osx z }x wu vszx |s | z } x u } | vs os s zx |
r
w| ccfpc{rvo x rE| 6rvx} i§rurxbW}%prrvo xpeEAktrcz r6jxpx x6&¥k§ru%6{6u E| 6X#tq
z ox osx
o } | } us | ov
} u | |s d osx zq os u
{g §rurxbW}%prrvo %rxrowx&6%6eEtrqrx#6| ks w rzx pv u rR| tz o 8 e5h%p| cx#| %#| cq #|
uxq |
z oszxq |s | } ox osx s u zx os o d z u ox os
s§rccz #tz | } c%ktrcEr#6cq §rurxbW}%pwvo E| §x¨rE| %| rrxx | w d HzS6} xxcq §rurxbW}%px
o } v os v u ox u q u v o | x u q we d v o o | } us | ov
} zx zs q w ox q u
wvo rvxpx crzx} | %| xxx r#xc£r
x§x EY#§ctdcrzrrxrorx} 6%6"Etrqrx6 rc%trrvo Eu §rurccrzr#cq
z o | xv o ox osx o } v os zxzsq u v o|x uq d s ox osx
wxx
!rx wv5xwuxb} kprrvo wvxYx crzx} | %| rc%twvo w
xx£x EY#§c we q xHuw §rurxbW}%prrvo
o | } us | ov
} zx os o | z o | z &
o
%rxworx} 6x%6©Etrqrx#6RE| %#| rrxx Rx #E| o #tq {g yV e& E| u )tz o 8 drc{g | z
v| } os z u | }x zs o o|x uq v o ux vz |sz z |
Eiwzx&| k#| xxR6p{%§u x x EY#§cx E| u r{cc5wortxt#{rzx pv u r| Eu §rur#x$x} |s w oxu z
£ ¥
¢¤vvwg¤ ¢©# eC¦( q§S¦¤% ¤¨vt ¤¢
¡ ¨ " ¥ ¥ £
szx | } xu u z |z
d tx#6$ f £ t #x%s 8 t%s
u }v v ox osx zvz }x x u | o s |
xxYRx§rurxbW}%pwvo rcxYx6} 9x xrtwzd o rc%tr itz t%s x} 5nWPsrG ¨plxdt y R xpx
zxv zs zx o s | z z d q ¥ l P qv t o " o z } 1
v | ox q u u zss zwzs v ox uv zs | vs os zv z d x } o o z }x w u v oxs z us zv u } u
E5w
cz ccwzr#cq rx %rtY%Rcz rcz R%#Rk§ru%6 rcx} dcrzxcrq%s £xYAERcrzr%tf§%6!r#xpx rx
s ov v o o | } us o s | s uw v oxs z us x o u q s z x | }x vs os zx | u u
#| wo cwzwxrorx} 6k6 x xr#trz §{crzr%tf§%6 trzxtz xcAteBu E6p$k§ru%6jE§x¦ §cq x o §fpv
zss uq x o hz zsz }x v ox osx suo s u q o v ox os x
¨%rxc`wvxktxpx§rurxbW}%pwvo §w x6 #| | | 8 E| xxxho scx $x§rurxbW}%prrvo
|
us v | | su zvv q | } z g zvu }x u s ov vz o }qz
z 6#| %uw crzx pv u #s §" d rrxdrrvo z 6p{r#xYrx | ro rgcx 5x6ccrx
ov ox osx o } usw | | o vs zx |s | zv z }x x u vw z } s zx
x x§rurxbW}%prrvo rvxpx %u$rzx pv u #rs | tz %trcz #6jcxpAxf} | Yrzwocf6u rE|
| z vszx |s | gu f } o ox osx
o | } us | ov
} | }q
&6 #tq {g %tcz r#65 Bxxb6 prx$g xwuxb} kprrvo %rxrorx} 6%6 twq§695x¨v tz o 8
A 5P ¤p ¥ lz | zxw o ox osx
o } | } us
o " ¥ l y D t C| rzwtq trHu rvg§rurxbW}%prrvo %rxrowx&6%6
| ov
} u g| vzv|q wu zv| |x
Etrqrx6| %s w 0rs crtRE)rE6} YE| ~ i§rurxbW}%prrvo xYjEpcx#| %| #tz xpx
d ox osx z }x wu zq os | | z }
z u g vszx |s | z } zv| o }x d ox osx s u d z }
ox osx
f} x{#%trcz #6 xYx Etq rvxpPue ixwuxb} kprrvo E| §x9| w d z68| §rurxbW}%prrvo
o | } u | ov
} z } v u ox uq os uqx z } e vszx |s | v| v o o } | } us
%rxworx} 6x%s6eEtrqr§6 xpx xxx r§c{rvo rzx} | %#| z cxu xYx HwGd %trcz #6 Ecrzrrxrowx&6%6
Etrqrx6 rczxpx ritwY%Rcz rxcz £{g cktx} e #§rurxbW}%prrvo xpg o %wxrorx} 6k6AEtrqr§6
| ov
} zv } ux s z zs v o uv z o zs z | ox osx z }x
o | } us | ov
}
} | ux u vzss u szx |s | | v| ox osx
o | } us | ov
} z }x z } zxzsq
cqEtz )x o x6pc%§cq$tcz r#6 E6} §rurxbW}%pwvo %wxrorx} 6k6AEtrqr§6£xY9txYx rc%trrvo
o os uqx u z } d pz ov ¥ l " x zv z o
|
z os zx q |s | } q z } | q | o
wvpzrx} | %#| z crx9xYx£we rRdx0osCz l 1wEu crprrxx #} c5%trcE#6pf#t(r
rEtrqx %x
ox osx
o } | } us | o
} | x| g| zs vzv | zv | |x } o
§rurxbW}%prrvo %rxorwx&6%6 Etrqrvx6 rvox} d u #rs Eids %#| crtq r6} pE| rqx} g %uw us
v u ox u s xzsq s | ox osx
o | } us | ov
} | z o o |
xxx r§cq §u zc%trrvo rzx} | o%#| )stz u xwuxb} kprrvo %rxworx} 6x%6REtrqrx#6x #E| g#tq
z |s z d uqx zxz q } } os zs ov u u | z s |w
{g rtzxt# ue dvcz crxu rckstrrvo prxo$g wzx&| k#| | %tz rx§cq r
x§pz 6} {g #u5u
z } ux z o
d z 6SRc5rv
rzx p$twz| x xYx #| #¨¡ fqrx
|v x o z z} i z } u £ ¢7
¡ zvvzvv| z g zs o s ox osx
9 © rcrrE{G ow ¡ %6xwX o xHuw §rurxbW}%prrvo
t
d r
crE#6trv
zx|s| z
szx |s| }q|z zx |q z zx u
trcz #6cEt)rE| 6#t){g rcrzx cq rvo rE6} p| xpx z o %6 tx} i} %6r o zv| |x z } us z d zs o
gu }v v x z o zs | vszx |s | z }x wu | x| } s z gu zv u
BxpiE| tz t6tz !%#%trcz #6 xpAErEE6px tz {Bx} r#f66 d #x#6c)rrvEArr$g z|}q u | o
x u } vw zo z } s x u | vw zo z } s u z x | & w v z q z s s q q z z z
¦ £ ¤ | £ ¤ x6&| Yrwcf6u x6} )Ywrcfq6x)rE| 6 #gu ccxt%r6dcxu cv {g
v | hz s u zs
z }x gu }v v| x z zs vszx |s | z }x z g xqzss u x u
E| rzx 6{§1d %6"xp) o Bxp$E!#tz tftz %#| %tcz r#6!xpgtx} cc%§cq xjrvo
} q | us | o } zx | xs uw zx |s | zv s zx |s | } q | z s | ux v z o } q zx os z
cE§%66#!rvxpx w
cE666%§i d r
crr#6tritrcz r#6 cEtPr#trz)r!cxb%x6ccr)rzx} | %#| ¨x§u
s u ox zx zs o
6u r
x6#| rx x rx $rvo rxo | k6rX o Bxp$crzx pv u #2E)xwuccwzr#cixpx tz o 8 gu}v v | |s wu oxq uq z }
d zs o
b| %6r o ixY$ER%66cxRpr!¦xu Ccx&#| rct| )x rx
gu }v v | zs xq sxv fs gxz ovz
| ov
v | |s zvz }x } o zx oq uvv v oxszvv| zq z o | o uq z } x zvzs z
cwzx pv u r`rcxYprx$g r| cxrr| x§rurktrrEcxtz tfWz uE6§rurrxo §c)xpx #tc%6t%s
| o } |s | zv| o o
r
rEtrqx6#rxp#tq z d rtq P& #| ¦ £ ¤ £ ¤ tz ¡ o ¢ u ccxt%r6dcxtxpu xp$Eu w vzq zss qq u sz }x z }x w
x z o | o u zs zv| ¢
tz t6tz r
rE6§rurrxo §cq %#| Etq o #| tz # #tz tftz 5r
rE6§rurrxo §c!%#| ¡ o x z o | o uq zs
o & w u vzq zss qq z } x z zv u s zx |s | } o g |v u o } zs z |w
p2Rccxt%r6dcxu xpx r
r#txbrx§¥Rd ¦ £ ¤ trcz r#6pprx$urzx pAE o| x xX| %#| rrvEurvo
& zs z }
| o v zv | q zv u } x w u v uo x s z v } u z }
3%txig #¥w ScEt!r#xpp o ¢ Ex§rr| trxx£xYx ¡ #| £ ¤ tcz r#6ppr$wx pv s z x | s | } xo g z |
u o } zs | z sx & zsz
| vzv|q zvu }
E o| x x¢| %#ix¦pArvo gktx} g #©w okcEt$r#xYx o ¢ Eu x§rurE| trx$xYx trcz r#6 w v ox szv } u z } szx |s|
} o g | u o } | zs | & wu v ox szv } z } v |v u o } zzs } xv x| w £
prx$¢rzx Yv o| x xq%#)YE{x§rur| trxxu xpx d ' cwzx peE o| x x¢c%6px r#u E2Eu 6
o zv| } |x z }x x| }x v oxszvv | o } zs sz }xs zq| v x o u z } wu vszx |s |
z | rvArE6&pE| xpE6p{crzrox o §rur%trrAwvxYx %§u txY%6evd cE6p #% xYx E%trcz r#6
z } vx o|sxv u u zs | zsz } zs
xpx §u r# Eprx§cq xR%#R%txYx %tz d ¢ H%66cx¦p!¦§{CcxRxpx ks w wzx pv u rs | & z s x q s x v f s u g x z z } u | |
o os u g s u s zv| |x
wvo E| u rzx} | %#| {1x 6{xHuw rE6} p| | 6p$%trE£{sr#f666v rzx 6{txp#x#v ~ x | }x xszvv| z g zv u | hz sz }x u |
szx |s | } o g |v u o | zs wu v ox szv } u z }
d ¤ trcz r69prx$¢rzx Y©E o| x wxx Rk#| ¢ E$xxwuE| txRxpx |
szx |s | } o g |v u o | zs | & wu v ox szv } u z } v |v u o u g
trcz #6pprx$swzx pE o| x rrxx £k#p2Ex§rurE| trx!xpx crzx pE o| x wxx {Cx £
ux zvu uq z } | zv| |x z }x x| }x oxszvv z }x ux x o z o oxszvv | o }
r o #6 ccz f#tq ¡ rE6} p| xpE6pd§rur%trr| xp9£trzE| xb!wvd§rur%trr£rvxpx
x| }x gu }v ux x u o e z sx o & zsz g x z z } } o zx oq uvv
o | } us | ov
}
E6pBxpirArxxdq o #xArvx Ud xRprv!5%tx} v#tz {xpx prx$g rE| c§rE| %wxrorx} 6k6"Etrqr§6
z } ¦¤ ¤ h s w zsz u u |
xpx wvo ¥ yrzx | z §Huyktx} g §)rv #e¦¦ ¤ ¢¤ ¥ # ErYrx§cq ¦¤ ¤ vx o|sxv u
zq z
cxtz tftz o xpp%rvrEpv cE6pv # #%Exp$Eu %trcz #6 xpx E6pp§rurktrrE)xpRrvo 1 #5&
z }x
w ox | z q | x o u z }x w vs zx |s | z } x | }x oxs zvv | z }x ¢ |
zz gxz } qs | u o o |x uq zs xq sxv fs u gxz z } usw |
tc{Cc6S%9x`x x Ep§c!%66cx¦p)¦§{Ccx xpx %u!rzx Yv u #r)!wvo E6Y)x x8pv |s | ¡ x| }x o
|
tx} ! ixwuEp#x | #prv 6u %uw x %#6tz %#R{g 6¦tz xpx x x o 6px #$`'i§u
z d ox |x u s |x s us oxs | zs | z s | }s u z } ov x | } zx u ~ d
u z ¢ | z s & z s z g x z z } x w
o } | } u s | o v
} z } ¦¤ z s z
rv #| rrvE| w rvo #x¦px wvo c%tx} tz ixpeEu %rxrowx&6%6eEtrqrx#6 xYx rvo %tx} g Eu w
z q | v x o u z } x s v o o } | } u s | o v
} d v s z x | s | z } z x u ¦ ¤ ¤ ¦¤ ¤
cE6pi Fxp¥§Huw crzrrxrowx&6%6Etrqr§6 d z xoqktrcz r6£xpx r#xtz ©¦ #| ¨¦ § ¥
xz ¢ | & v os
s | o u gx w u ox ov uq
cd £ #'crzx} | %#| %6 x} {1E5x rrrvrx§c E| u xpx tz rxxcq wzx | P#| v ~ o z } s ov u hz
|s | x| }x
|v ov z
di¨¥ %s w rzx Yv u r)Rrvo ¡ E6Y)tY9r
x r!{g § ¥ o z cxt£f} #tq 6pg§rurxbW}%px
§ u | uq z z | x | }x ox os
o | } us | ov
} zx os o
wvo rxrorx} 6%6{Etrqrx#6)rE| %#| rrxx | %u!rzx pv u #r)| rvo ¡ rE6} p| | tx} usw | |s zv| |x z
dv os v u ox u o|x u
dcrzx} | %#| xxx r§cq Ep§cq
z s z
8| 2%tx} Et)xp)rxdrrvo B#t t#rcz ' ##| trcz #| xB#t x r6 pE|
g zv|q z }x vv q sz o 8 | szfq z ox d |x
o v o|xu zsz } us zs z } s ov u q z ox q e ov " ¥ y
x vrrvo x Ep§cq ¡ %tx} g rzx%6!wxxdq o %xu xpx tz rx§cR{g 6 §rurccz kd xd5oP ¤¨X
| }x
|v
wvo ¡ xE6Y)tYz g cwzx&| k#| xp6WP¨m)§rurE| trxu xpAEirrrvrx§cq § rt)cEtz wvo E6px
o v } os z }x P l wu ox szv } z }x wu vx ov u zv|q }q| x|}
|x
¨p| ov u v o|x u
x rwvo x!x Ep§cq £ V ¡D ¡ E6} pE| d z dHorzx Yv u #s xpx %tx} g
zv| |x | | z } zsz
©
£ # ¨
£ ¡ ! $ § ¥ ¡¡
#
6 §©
¥ $ § £ '¥ $ !£
Epx{g
o|x}u z G
| ( 8 & } o
crqx} g
zv| |x o vzv|q wu sz z }x
o ¡ E6} pE| $crEtE{tf} xRxpirvo
© z dx |xv u ox| s u
§ ow tx} d#prx§cq §rurEt5roE| §x | rvo zsz
%tx} g
¡
¢! £ $ § ¥ ¡ #© ¨
#
¥ $ !©£
§
£ ox osx x } o o | v|
§rurxbW}%prrvo crzxcwqks E6} © z z o } | z x | } x v v v x
¨!xcrv!rx} | %s#| qt$E6pz ¨rE| x'cz
d cE6p$ #%Fxp2u crzrrxo
zq| v x o u z }x w v o
o | } us | ov
} z }x | z szx
rx} 6k6©Etrqrx#6RxprE!x o trcz § ¨¥ }prxo$g§ruorcqx6¦ §cq o
x u " ¨
vszx |s | z }x x| }x zx
%trcz r#6Rxp{E6pir#u ~
© ¨ ! © !
! &
¨
§
© ! ©
¨ &
§
x o | e o (
crz §rurrxo 6 ) d G tz 8 &
w
o | } us | ov
} z } zx u x wu vzx|xv w sz z } z § ¥ ¡
Eu %rxworx} 6x%6 Etrqrx6 xpx r#xtz © cz Sd G Ecrpr$Eu t6} x xpx 6} § £ ¨¦¤£¢
x os wu vzx |x w sz z }x z x zs xq sxv fs u gxz o }x
cwz #| & rzx} | %#| ERcrprv Eu t6} )xp)f} £ crz %66cxRprg¦§{Ccx rvxpPtz o 8 ¤¨¥ d§
zs xq sxv fs u gxz ovz
usw | |s | zv| |x | x| } ovz }xu
%66cxRpr5¦§{Ccx(#| rc#8| | %uprzx Yv u #r5`rvo ¡ rE6} YE| 96px rvrcxp#f }
s oxszvv z } zx u xz d ox|xu u zz z ovv q z } zx uq
§u§rur%trE| xpx r#xtz § ¥ c i§rurEp#x z rv cx {g xwurxdrrvo xYx rcrzx c9u
d vs zx |s | x z | } s uw u }x vv q oxq e do t t " t
0%trcz #6R#tz tftz x ro #6$xH{v xpcz xdrrvo z g 6 §rurccz G06X do D do $o D sq
z ov o ¥ l z os | | sz | z o
zq usx o ox vv | o }x |q
0xdsCz l " ##t tc¦rx%6 e #ptrrxE6} c#crzx } cx %p §rurx 6r`rvxprEtpz
dx z o zs | vszx |s | | x| } vv| | }v z oxqzv o }x wu s o zs z }x
dtz t6tz Rk#jktrcz r62rEE6px z 6rEArE6YR{g §rurccrrvxpAEitz E| %£xpg e
zq z
d 8xtz t6tz o trcz r6 Eu xwux 6rE| z 6 |
szx |s | w ox vv
} o g u } zs xq sxv fs gxz ovz
sz }x u } zs xq sx z } us |
zxpx x $Bxpv %66cxRprp¦xu Ccx&#| rct| txp#x ~ x d ¢ & %66cxRprv xpx %uw wzx pv
| | o zv| |x z } x| }x oxszvv| z }x } zx oq uvv| v oq z o | o u
u rs 9rv)rE6} YE| xpx E6pxwu%trrEpxpYwxo g E| c§rE`8wzcxtz tftz E6§rurrxo §cq
o gu}v o
x $BxpA ¢ & E| u rzx} | %| &%#6 x1B{C$§k66cx¦priR§{1cx&| c#8| t %6r
os
s | o } u gx | s uw zs x q sxv fs u gx z ov z
~ | zs o £
(b) (a)
M M
case 2 y x case 2 y x
case 1 y x case 1 y x
θ y|x θ y|x θx θ y|x θ y|x θx
£
© ! © © # ! "
§
§ !©
db ¡ §
¡ ¡£ § ¥ ¢ ¡
§
© § © § §
© §
! !
¨¤
©§ ! © § © §
#© § #© § © § © § # ) # )
§ ¡ § ©
! § © § § ©§
§ ©§ § § ¢
©
¤ ¦ ! § © § © § © § © § © § © ¡ § § © §
! § © § § ©§ § © § § ¢
© ! ! "
¤ ©
©§ #© ©
¡ ¥! #© § §
¡ § ¡ ¡£ § ¥ ¢ ¡ £
¡ ¡ § ¥
! § #© § © § © § £¡ § ¢
¡ tz # § ©Eu
o ¥ w £
o | } us s oszxv u z } o|x } u z v zx uq
%rxworx} 6x%6{§ru%trr#fjxYx Epxx${g x} d rcrzx c{rvo ¡ rE6&pE| xpAE6Yx §rurx 6rExpx zv| } |x z }x x| } ox vv| z }
s ox | ov ox | o } w ov | } x } os z } szx }q|z zx| z |q
tz 6 6t §rur6 uqx rxu§rur6 z wvxYx u z ru #6 #§r%$xpx §u tr!cEt$E6WE| !t$z
!
§
#
#
£
§ ¥ e § v ¡
§ £
$ § ¥¡ ¡
£
|} xq us z } u u dx |xv uq ox | s u |
z 6Rz g rzx¦s cx %6£xYx %s w rrv ~ d#px§c)§rurt%roE| §x rvo %tx} g zsz
t £ £
§ ¥ ¡ ¡ ¡£ § ¥ Y ¡ ¡ § ¥
z 6j{g ) k§cxpx
| } z zs uz }
v z
c#8| u zs xq sxv fs u gxz ovz
z } u |
%s d § ¥ %6¨cx¦prpR§{1cx| c#8| xYx %s w rzx pv u #`)rvo ¡ rE6&pE| |s | zv| } |x
z }x x| }x ovz }x u
o|xszq gu z } zx u x oxqzv v zs z } o
xp)E6Y`rvrcxY#66#} Epktcx6 x xpx rxtz § ¥ crz §rurcc`xxwuo %6xYx )v ~
d o z}
i E| u xpx
w zs xq sxv z }x x u | s | z o u e dvzv|q zzv z g v| v o o } | } us zvz }x zx |
Eu k66cx¦prixp$xx6} )rtwzi{g x #u rv dcrEticr{tERcrzrrxrowx&6%6rcxprE| 6#tq
z zs sz }xs
{g k§u txpk6ed v o v z } x u
z } o v v u } q | u
§ ¥ rrcxp#f } rxWrr#f`cEtz x ¡£ § ¥
%rwrx} 6x%6§r%6 `x x§rrrE9}
xoo | } u s s uo s | o o v v |
x o |xszq o } vvzs h | vx z wu xzv
} g z }x v uq z x| } zs xq sxv z }
Ep%tcx6rvxpx rc%66z #tq z g rtz eEAc£#| Ywxo iv ~ d xp{cz cxtAE6px %66cx¦p$xpx
x u | o|xszq u | x v o o | } us z } x u | o|xszq x u zs | z g zv u g
xf} p Ep%tcx6rrvERxb} cwzwxrorx} 6k6 xYx xf} p Ep%tcx6 w
xxu #xRk#£{ur6666v u ~
v o o | } us zvz }x v uq z x| } zs xq sx fs u gxz z }x x u | o|xszq x v o o | } us |
ddcrzrrxrorx} 6%6RrcxY$cz cxt{E6Yx %6¨cx¦prv ¦§{Ccxxp$xf} ) Ep%tc{xb} crzrrxworx} 6x%6©Etrqo
v
} z }x x u | o|xszq zs z g zsz g ox| o z } zs ov uq z oxqzv v zs z }
Cx#6xpxf} ) Ep%tcx6%| {%tx} §rurE66rxrv xpx %tz rx§c${g §rurccr{xruo k6 xpx ue
£
¢¤vvwg£ ¤¨vt ¤¢
© ! © ! ©
d § )
§ #| #© § ) ¨%tx} g
§ zsz
§ §
© ! ! "
§ © § (©
t
£
Y $ ¡
¡ 6 £
©
© § §
§ ¥
§
zv | |x z } s zxw | z z z } ux zv | x h z z }
¡ E6} pE| xpx tr89tcrv 6urrtq xxRxpx £
& } q | z x | }
o | } us z }x zx u |q z |v u o
6 £ o G #| ( %cEt{E6px rxrorx} 6%6xpirxb cq #ti{g rzx peE o| x rrxx
}q| u ¡ ox| o zs sz }xs dx |xv uq ox| s u sz }x u u
cEtz rx Q §rurE6bPx xr
x6#| %§u txY%6eP0##Yrx§cg§rurEt5roE| xx$txp#z rv rvo %tx} g zsz
t
E D S# Q XU SU i X e g Q S D E E TU X D a T ` T X d T I C SU EU e g Q E D C D I E D` T fU d 3 D XU X D C S Q
a D x d X X T Q D` h T E Q X T D g E d XU S
Br4bbeBR& #1Vb6yV1RB©R6b& ©WeBR& ©& ©bVRby4Yb6#6yC 2#6BdBS b¨V#VByFbbU
C d Q C S` T i S T C D d g T u h ) ( q ` T S D E T x g D e I D u 0 i T x g ' E ` g T % i Dq E QU S T S D g
g D S EU ` T X d T I T D f T
R©R©6bR#6S #VFR00 0 )!rRYHRFFeB$ V( 0 !( ¨FD (#VT BRD &b¨ yr'Rb6BFBBW¦VB#V5dR©C
X I g T D g D & S XU D X e g Q S D E TU X D a T # Q X E QU SU E " D g D E Q g S i X X D` D C S D E Q D I E D E D
D EU ` T E QU SU E Q # Q X E QU
FVF©C ©Bby" !BR& #E Rb6R$'#Vb6b¨#Fy©RF6BX BbF#6©RY!e©#¨©WV#Vb6b©RI 4!©Rb6S
T S E D X D g
D g X T a`
xU X X D g d S I d g S e g Q S D E E TU X D a T S D g
g D S EU D
BBFFyHbdb6!F6#B6BX BR& #rRb6VFBBWf& ¨byVFfbR©¤©bVRby4D b6©6yyY$ D U f Q g
X ` Q C D I E D` T fU d 3 XU X D C S Q
a
uo x q o x v vo } s } z xw u z
x z s } w u z | z } s u } u } x | v z s
d §rrcx rrro rxpx 6WxtrE{g %wo %6EiEf pv xpx §Hw §xxprEsc%66x
q sxv fs u gxz w u vzvv q zq o o s | s u u }x v zxzs szx o z } | xq u }
¨x¦pRR§{1cx©E{crE| cRcxtrzE| xbz x xr#trzxHw v xpcz | rck6rtr i6Xw
rE6¨cE| xxpv
zs xq sxv fs gxz o s | s u u }x s zs xq sxv fs u gxz ov | | }x sz }x|
%66cxRprp¦xu Ccxx xr#trz §w v xpcz 6u #| %66cx¦pp¦§{Ccx wzx p#6p!txYErs
vzs xq sxv wu vv q zq o z } o g ovz }x u
}q|z zx oq uvv u }
c%6¨cx¦prE{rE| cRcxtrzE| xb!#| prx$twvcxp#66} cEt$r| cxrr| xxpv z g %%t6§k6 rvxpeEu
xsz us o }x w
x } e o t P l q e co qpo y "n | q
xs z us o } |s z z e
o | } us |v z }x |
#§rro uvA ¨X 05o¨dW`QYp r¢¡v bVx¡ rzrEtArvo kt6§%6Arvxpx Ertxt#! d %rxworx} 6x%6$z p{xp{z 6}
o x o z zs & v zs x q sx fs gx z z }
wr$g #| trzE| xb!%#| & ¢ | ¢ Hc%6¨cx¦prv ¦xu Ccx xpx ¢ & E| u rzx} | %| o os
u gx z }x | h z s u
o } | } us s os zxv u | s os | z }x | } xv v zs x q sx
{1!xpd o rzx 6i§"sd %rxrowx&6%6 §ru%tr#6 #xwuk6z pv xYRz 6Rrx c%66cxRprv
fs gx z x o z u g x z zv u d | ox z } xv v zs x q sxv fs u gx z x o z u g
¦xu Ccx trzE| xbR{Cx w
#txbrx§{$xEtrqrtz o firx c%66cxRprR§{1cxtwz| x {Cx
} o zx oq uvv| vzvz }xu
} z }x x| } g u zs xq sx fs u gxz z }
prx$g r| cxrr¥ccxp#66jxp{E6Yx v rur#w wxo § ¥ %66cx¦Yrv ¦§{Ccxjxpx o z cxt6X#tq uqz z} |
w z q | v x o u z } x s uw v zo xoo | } u s | qo v
} z } x x | } x uo x s z v v z } x v
Eu cE6Y# #%Expi§!crrrrrx} 6%6{Etrr§6 xpE6pd§rr%trr| xYRro § ¥ E6pptz o 8 x| }x
zs xq sxv fs u gxz o ux x o z zs | x | }x vzs xq sx
d %66cx¦Yr!¦§{Ccx)tz #!| r#trzE| x %¥6p$c%66cxRprv
fs gxz ovz
| o
ox s u } os u | x o z zx |zs v | osz f o }
¦xu Ccx&#| rct| rEx xHw rtz o §Hw prx%§#rE)#trzcq ¨P#| rt%tq E6} ##t x %tErqx$
zq o z zs xq sxv fs u gxz w u ox | os zxq |s | } o } o
cxtrzE| xb%66cx¦YruBR§{1cx )§rurEt5%tcEr#6cq rvxpx x rv d ¢ #p& tc{Cc6k#| xxb} | zz gxz } qs u x
u u u
1¢ rx ¡ %s w #| ¢ rx & ks w %#)#iwvi%txp{E6Yx x6v ¢ & Swzx6¨x %tz §u #| rv$CxRdUYxp
u qs | | o zs z }x x | } } q ¡ zs s o oz ev X ezv
3 2` s | s vzs xq sxv |v z } | v oxqz qs | os u o zs xq sx
~ d ##8¤ %#tz #| | tz ¥ uc%66cx¦pu z pxpx Rx§rurcc% os %#)x %§x§r%66cxRprv
|v z }x | }
z }x o o x o z zs | vzs xq sx fs gxz u g |sz z
z Y9xpgz 6cxpRw r
x§u | w 9trzE| xb)%#)c%66cx¦pv ¦xu Ccx{Cx Etxt# e
d x o z zs uwzs z }x zs v ox osx ovv u | v ox osx
dtrzE| xb%§Y%txp%| | x§rurxbW}%prrvo rzxW}rr#f©rE| r
cz 6 $x§rurxbW}%prrvo
o | } us x o u |v z }x x zvzs zs o o | s uw v zs x q sxv fs u gx z zx u
%rxworx} 6x%6 # #% z p)xp!trc%6t%5 E| u tz #g!§c%6¨cx¦prpR§{1cx)rcrzx cq w ~
d v os z } x w os s u ovv u } q | s uw zs x q sx fs gx z z £ v zs x q s x fs u gx z zx
dcrzx} | %#| xY©Eu x %tz x£rzxW}rr6)cEtz §Hik66cx¦prv ¦xu CcxRx§u c%66cx¦Yrv ¦§{Ccx£rcrzx
u © v | v os ¨ o o|x uq o zq z
cq ¨ 6} crzx} | %#| ©x x EY#§cP E| u ~ d txtz tftz o 6§rurrxo §c$ERx§rurktrrE| x | o uq wu v oxszvv u
v u q z o x | }x v z z ov u v | } x | }x z u o oz ev X ezv p { y wv o t ov " ¥ yX
cz cxtrxo wv6pc# gx rrvo xRE6E6p!x§RrvCxRdUYxX¦z Px0wXxd5oP ¤¨T| rzx |
hz sz}xu| dx o zs | vzs xq sx fs u gxz zvz } x z zv u
&txp#xRv ~ dtrzE| xbz %#Rc%6¨cx¦prv ¦§{Ccx rcxpx w
#txbrx§{ d ¢ Eu tz t6tz o w x z
| o uq zs | zsz g v ox osx z }x vx zvzs zs ¡
r
rE6§rurrxo §c!%9¡ #| & ktx} x§rurxbW}%Yrrvo xprtrc%6t%)¨¤ ¢ §& #| ¦ ¢ ¥& ¤ ¡ ¤
¡ & v z s x q s x f s u g x z z } x w u } q | ¡
£ ¢ 2c%6¨cx¦prv ¦§{Ccx xpE!cEtz ¦¢ ¢ & E| u rzx} | %#| c%6pixpx §Huw rzx 6z o os zzs }x z } s | h
s u s | s v t l q eco zs | vzs xq sxv u gx z }x x | }
| dv ox osx
§"ud ##8G %#tz #| | tz ¥ w0%oP dW`QYu%jc%6¨cx¦pr!{CRxp$6px 8pv z $0x§rurxbW}%prrvo
o | } us w u vxz |v z }x xq | h x zvzs z vzs xq sxv fs u gxz ovz
u gx x | } z
%rxworx} 6x%6 £crv z p)xp5r
rcE6z #tc%6t%s c%66cx¦Yrp¦§{Ccx&#| rc#8| {C!E6px t6
| } |q z d }q| us o }x x u
A#t!rxo x icE§k66#| wvxYRxf} | z | 6} r!r# #f£#p%x6 o c%6px %| %tx} z ux vx o u x |xs u zzs } zs zsz
#
£ $ ¡¡ § ¥ £ § ¥ ¡
¡ 6 £ % £
$ ¡
¡ 6 £
Epx{g
o|x}u z s ov | h
wzxR9§rurx#66z
} u zv| |x | zzv | } z g sz w szv } u z ux zv| x hz z }
zxpx %s d rE6} YE| gtcr9z 69{stHx8| z trxx`f} rgrEtq xx`xpx u ox osx
s§w §rurxbW}%prrvo
o | } us z } zx uq
%rxworx} 6x%6 xpx xb c98| z g 6t xwuE6 u #| crzrrxrorx} 6%6 §ru%trr6
ox| v o o | } us s oszxv u zvz }x o
rcxY9x rv
t
X D d S I d g X e g Q S D E S E D` T fU d 3 D Q S D S T EU xU g I XU Q S
` D S Q E E T D X T h T S T
Fg¨6#B6SBBR& ©fFbRVb¨yd& 5By©WdbBBbeBHW©C #1VI By©RBy
T W5#VbU6yVFDB©R5#6S2y©6XeVB%BbC & 0% C6% @968¤6% 3§" 1) 0©) '4Q Vb6#
#6BvR& #V¨B1bR©RBFg
EU X E Q S T f g X h Q D C S T C S a T X C IU D B A & 7 5 4 2 " & % ( & # E QU S x d X X T g D e T D T S
Q T Q S D` h T E Q X T D
u u z o | x | }
| x o s z g u } | v s z q s | v z s | s z v v z z } x z ~
s
x#r r#x rv!gtz z$E6Yx`rrEptz %tf hz Bxpvz 6}i%tx}k#tzrc%©rtz rv rcrcxpcx§u td %§u
z } o s gv x oxv o d zvz } u
zs q x fs u gxz w u sz
¨xpxg $tz{¦x| urRrxxdq o rvo9xwurczx grvx} 0vcrcxpx#f }R%66xcx¦sYrvuBR§{1cx $tf} xw| v
xv o z £ ¡ zx o hus | |q z sz xz
|Rrx¦ Ix rvxirc{g ¡ 6 £ rE| xB%66#5#t!{gtx}Ycx} grvo zx6rrvR#p%x6 r#u x} v o x |xs u o xv z
% ¨ # ! © ¨ ¥£
$" ¤§ ¦¤¢
d v z v o zv z }x w } q | s ov u q z g uw x | } v ox q zv } v z }
dcx6rrvrcxpEu cEtz tz x§c{g BruwH{6px xxwuccrxb6xpx ue
vszx |s | oz } | vzs xq sxv fs u gxz
z } ux v o o | } us s os ovv| x o
%trcz #6 s cxpx #c%66cx¦p!¦§{Ccx9#| xpx rRcrzrrxrorx} 6%6i§ru%69xwrE`r
rtrzcq ¨z
z g |q gu o
{s#tBx} §rurrxo 6 | e z Wcx {{g xxxpAcrcxY#66#} cwqxig rewe ¡ 6$xpx o crcxp#f }
q o z u }v vzvz }xu
} o } uv v z } vzvz }xu
zvz }x w oxq |sw v | u o o |xzs
zx |s qq £ ¡
rcxpiEu xwucErurE| gr
x§Px x EYc%} r
crEr6dcE| ¡ 6 £ rE| xB%66#| {#$ zx o hus z g |
usw v x zs | vx o |sxv uq | ox |
d # §rurE6bP icrcxp#f } xp©rE| tz )x o 6v %u$x¢#tz %6p#tq # ErYrx§ceE6xwuEpx
ox| o vzvz }xu
z }x s u
u s oxs | e zs ov uq z } xv x | }x vz v o |s zv zs | zs z } vzs xq sxv fs u gxz
&b cq #| xdrqr%#6gutd %tz rx§c6rx E6picx6rrv1Ertz rk#jktxpx c%66cx¦Yr!¦§{Ccx
zvz }x wu | xv | q hz xu | szv z } z x z zv u d o ox z u h | } zs
rcxpE"rEA#u Ez cx#x6#tq trx'xpx tx} g r
rtx x§{v¨ "| #tx§f z #6Yx k§u
o v os ¨ o o|x uq o | s vzs xq sxv fs u gxz wu sz z } vv z }xz
wv!crzx} | %#| ©x x EY#§cd | u xHuw c%66cx¦p)¦§{Ccx Etf} xYx rcrzcxpcx§u ~
zv| |x u v s | x| } |s us szx uq ux o ox|q oqz v o }x v o u
d r6} pE| | ks w xr#trz{E6px rx#%6itrxb c!| r# g§rurEt"
ccfp$rvxpcrzrx cq
z } zxv
v z zs o o gu }v x| } ux s o sz | o v fs u gxz ovz
ov
txpx rrxr!x} d %6r ) BxpiE6px ri#| ro rv tx6#| p i¦§{Ccx9#| rc#8| x rx
ovv u w u x z | s uw vs os o v z o q z s zv |
} zs z
wvcz u rzxW}rr6 Eicrv $§i%§ru%6Rrvx} c"
cc6pv trxX`d%tx} g rrxr%#$CErv | x§rrcz zxv
v zs | gxw u z ov
v| z ox h s u d |x ov v os v u ox u s v ox| |s
E6} xB#t x r6 i rzx | z §" bpE| x rrvo | crzx} | %#| xx r§cq §Huw x§rurEt5roErtz
z oz }x s v ox| zv x z zv } vszx |s | oz } | vzs xq sx
&t# s cxpi§u #5 #| b xxwuE6 uSrx r
rtxbrxb6v #| %trcz #6!s cxYx #Rc%66cxRprv
fs gx z ovv u z }x s uw vs os z }x vv zvv | x q z | z ovv u zs | v zs x q sx fs u gx z
¦xu Ccx)rzx} r#6 xpi§i%§ru%6 xpcrrEr
rcck os #tq x} rzx} r#6 %£c%66cxRprv ¦§{Ccx
ox | s z | gz | u x | }x v z } s zv z } z z oxq |s e zs xq sxv fs u gxz o s |
z rE6trrxEw 9r
x§$6pRcz rzroc6gtrxxpx tx} g cwqcEr6putd %66cx¦Yr!¦§{Ccx9x xr#trz
ux o zsz }x | ox zvvz oxqzv o } zvv q | } z g }q | us | z } oq os
rrv%txprE`r
rE| rtrrciwvo §rurccrrvxpx o rxdrrvo z 6R{X§%66#!xpx rzx cx %69 e
d ox | |sz z o }x z vs x u z s z gu
i§rurt%roEtxt#$rvxpRx¨%6b #x u {g tz {Bx}
sz | o } dvzs xq sxv fs u gxz wu vo
tf#6`rvxpx ue 0c%66cx¦p5¦§{Ccx E0rp | o z cxtz f} #tq §rurxbW}%prrvo %rxrowx&6%6 uq z | ox osx
o } | } us
| ov
} z }x x | } vv ox vv o }x h zs |q z zs xq sxv fs u gxz s oxs |
Etrqrx69xpRE6Yx x o 6rE| §rurx 6r| rvxp| ck#t)Ppd %66cx¦p9R§{1cx #| xdwq%#6
z usw v u zq | v x o u z }x w u ox osx
o | } us | ov
} z }x x | } v oxs zvv | u
x§u %ucz cq cE6pR #%Exp$EP§rurxbW}%prrvo rxrorx} 6%6{Etrqrx#6 xYRE6px x§rur%trE9rx
u vzss u vzvz }x u
ux v zvs z | } z ox| o o g
x o x6pc%§cq ccxp#66} ricz cr%6u rrxo roz 6£{g 6# §rurE6bPx wxks o r
rE6 | o
d usz zs v| w z } o g vzvz }x u
w s u z }
wktc¢%66Etz Eu 6Grr$gcrcxp#f } u #| %tz xpx
zq z v o ov u } | zs x q sx fs u gx z o
| s uw vs zx |s | u vs os
cxtx} #| crzrrxrxtz z 6fSz 6} k66cx¦prv ¦§{Ccxtz #R§%tcz r#6P§!%§ru%6
z }x x| }x vv }q| us | o }x vv z }xz u ~ d s u vzs xq sx fs u gxz x o
xpiE6p!z 6E| z g cE§k66#Rrvxpp o cwzcxYcx§$si#| %tz ic%66cx¦Yrv ¦§{Ccx #trzE| xbz
u zvz }x } zx o q uvv | v zv z }x u
} z } zs uwzs z
&§xprcxpYwxo g rE| cxrrE)crcxp66#pxpx %§Y%tx} d £ ¤ ¤ %rxwo6 gxpx xHkwvEpv
| z z }x o
w ox |
vszx |s | uq z | zs xq sx fs u gxz
x
%trcz r#6)z cxtP#tq %6¨cx¦prv ¦§{Ccxd%x z xpx | ¢ Hc%6¨cx¦prg¦§{Ccx p6} z} & v z s x q s x v f s u g x z }xu
o os u g s u |hz su ov q hz | x x u zs | vzvz }x u
} zvz }
E| u rzx} | %#| B{1x 6g o rzx 6!§" d z rxWc§r
rE66x #x9%#)crcxp66#prcxpx
|zs e ov q hz | x zs vzvv q zq o ovz }x u
} z }x x| }
%rxroEt% d z rxWcxr
rE66x %#| crrE| cpcxtrzE| xbz rvrcxp66#9xp!E6Yx z 6rE)z 6} vv| |
z ox| o o x| } o }q | us o }x x u x o u x |xs u
{g 6# §rurE6bP x rrx%s g o E6Yx rvp§%66#| rvxp!xf} | #6!##Y%§6 o xccrv x} uqz z
