Centrale Informatique MP-PC-PSI 2017

Thme de l'preuve Mars Exploration Rovers: mission d'exploration martienne
Principaux outils utiliss algorithmique, recherche de minimum, listes, SQL
Mots clefs numpy, calcul de distances, minimisation, algorithme gntique, algorithme du plus proche voisin, jointure, robot, Mars

Corrig

 : 👈 gratuite pour tous les corrigs si tu cres un compte
- - - - - - - - - - - - - - - - - - - - - - - - - -

nonc complet

(tlcharger le PDF)

Rapport du jury

(tlcharger le PDF)

nonc obtenu par reconnaissance optique des caractres


JS- S*- SaA- haA
j ?2m`2b

*H+mHi`B+2b miQ`Bb2b

kyRd

AM7Q`KiB[m2
J`b 1tTHQ`iBQM _Qp2`b
JBbbBQM /2tTHQ`iBQM K`iB2MM2

J`b 1tTHQ`iBQM _Qp2`b UJ1_V 2bi mM2 KBbbBQM /2 H La [mB +?2`+?2  im/B2` H2 
`H2 DQm T` H2m /Mb
H?BbiQB`2 /2 H THMi2 J`bX .2mt `Q#Qib ;QHQ;m2b- aTB`Bi 2i PTTQ`imMBiv U};m`2 
RV- b2 bQMi TQbb bm` +2ii2
THMi2- bm` /2mt bBi2b QTTQbb- 2M DMpB2` kyy9X G2m` KBbbBQM 2bi /2 `2+?2`+?2` 
2i /MHvb2` /Bz`2Mib ivT2b /2
`Q+?2b 2i /2 bQHb [mB T2mp2Mi +QMi2MB` /2b BM/B+2b bm` H T`b2M+2 /2mX AHb bQMi 
[mBTb /2 bBt `Qm2b 2i /mM2
bmbT2MbBQM bT+BH2K2Mi +QMm2 TQm` H2m` T2`K2ii`2 /2 b2 /TH+2` [m2HH2 [m2 bQBi 
H Mim`2 /m i2``BM `2M+QMi`X
G2m` +?B2` /2b +?`;2b T`pQvBi mM2 /m`2 /2 pB2 /2 Ny DQm`b K`iB2Mb UH2 DQm` 
K`iB2M 2bi 2MpB`QM 9y KBMmi2b
THmb HQM; [m2 H2 DQm` i2``2bi`2VX aTB`Bi  +2bb /K2ii`2 H2 kk K`b kyRy- bQBi 
kkRy DQm`b K`iB2Mb T`b bQM
``Bp2 bm` H THMi2X .#mi kyRd- PTTQ`imMBiv 2bi iQmDQm`b 2M +iBpBi 2i BH  
T`+Qm`m THmb /2 99 FK bm` J`bX

6B;m`2 R om2 /`iBbi2 /mM `Q#Qi ;QHQ;m2 /2 H KBbbBQM J`b 1tTHQ`iBQM _Qp2`b 
ULafCSG  *H@
i2+?f*Q`M2HHV
*?[m2 `Q#Qi 2bi [mBT /2 THmbB2m`b BMbi`mK2Mib /MHvb2 U+K`- KB+`Qb+QT2- 
bT2+i`QKi`2bV 2i /mM #`b
[mB T2`K2i /K2M2` H2b BMbi`mK2Mib m THmb T`b /2b `Q+?2b 2i bQHb /B;M2b /BMi`iX 
 T`iB` /2 T?QiQ;`T?B2b /2
H bm`7+2 /2 H THMi2- T`Bb2b  THmbB2m`b HQM;m2m`b /QM/2b T` /Bz`2Mib bi2HHBi2b 
2i T` H2 `Q#Qi HmB@KK2- H2b
b+B2MiB}[m2b /2 H La /}MBbb2Mi mM2 HBbi2 /2KTH+2K2Mib UTQBMib /BMi`i Qm SAV Q 
2z2+im2` /2b MHvb2bX
*2ii2 HBbi2 2bi i`MbKBb2 m `Q#Qi [mB /QBi b2 `2M/`2  +?[m2 2KTH+2K2Mi BM/B[m 
2i v 2z2+im2` H2b MHvb2b
T`pm2bX *?[m2 `Q#Qi 2bi +T#H2 /2z2+im2` mM +2`iBM MQK#`2 /2 ivT2b /MHvb2b 
;QHQ;B[m2b +Q``2bTQM/Mi
mt /Bz`2Mib BMbi`mK2Mib /QMi BH /BbTQb2X lM2 7QBb iQmb H2b TQBMib /BMi`ib 
pBbBib 2i H2b `bmHiib /2b MHvb2b

kyRd@yj@kd ky,Rj,98

S;2 Rf3

i`MbKBb  H h2``2- H2 `Q#Qi `2QBi mM2 MQmp2HH2 HBbi2 /2 TQBMib /BMi`ib 2i 
/K``2 mM2 MQmp2HH2 2tTHQ`iBQMX
*QKTi2@i2Mm /2b +QMi`BMi2b /2 i`MbKBbbBQM 2Mi`2 H h2``2 2i H2b `Q#Qib UHi2M+2- 
T`BQ/2b /QK#`2- 7B#H2 /#Bi2i+XV BH 2bi T`pm [m2 H2b `Q#Qib i`pBHH2Mi 2M 
miQMQKB2 TQm` THMB}2` H2 T`+Qm`b /2 +?[m2 2tTHQ`iBQMX BMbBmM2 7QBb H HBbi2 /2b 
TQBMib /BMi`i `2m2- H2 `Q#Qi MHvb2 H2 i2``BM }M /2 /i2+i2` /p2Mim2Hb 
Q#bi+H2b 2i
/i2`KBM2 H2 K2BHH2m` +?2KBM HmB T2`K2iiMi /2 pBbBi2` H2Mb2K#H2 /2 +2b TQBMib 
2M /T2MbMi H2 KQBMb /M2`;B2
TQbbB#H2X
T`b bi`2 BMi`2bb  H2M`2;Bbi`2K2Mi /2b 2tTHQ`iBQMb- /2b TQBMib /BMi`ib 
+Q``2bTQM/Mib 2i /2b MHvb2b
 v K2M2`- +2 bmD2i #Q`/2 i`QBb H;Q`Bi?K2b [mB T2mp2Mi i`2 miBHBbb T` H2 `Q#Qi 
TQm` /i2`KBM2` H2 K2BHH2m`
T`+Qm`b HmB T2`K2iiMi /2 pBbBi2` +?[m2 TQBMi /BMi`i mM2 2i mM2 b2mH2 7QBbX 
SQm` +2H MQmb 7BbQMb [m2H[m2b
?vTQi?b2b bBKTHB}+i`B+2bX
 G xQM2 /2tTHQ`iBQM 2bi /TQm`pm2 /Q#bi+H2 , H2 `Q#Qi T2mi `2DQBM/`2 
/B`2+i2K2Mi 2M HB;M2 /`QBi2 MBKTQ`i2
[m2H TQBMi /BMi`iX
 G2 bQH 2bi ?Q`BxQMiH 2i /2 Mim`2 +QMbiMi2 , HM2`;B2 miBHBb TQm` b2 /TH+2` 
2Mi`2 /2mt TQBMib M2 /T2M/
[m2 /2 H2m` /BbiM+2- mi`2K2Mi /Bi H2 K2BHH2m` +?2KBM 2bi H2 THmb +Qm`iX
 G +Qm`#m`2 /2 H THMi2 2bi M;HB;2 +QKTi2 i2Mm /2 H /BK2MbBQM `/mBi2 /2 H 
xQM2 /2tTHQ`iBQM , MQmb
i`pBHH2`QMb 2M ;QKi`B2 2m+HB/B2MM2 2i H2b TQBMib /BMi`ib b2`QMi `2T`b T` 
H2m`b +QQ`/QMM2b +`ibB2MM2b
 HBMi`B2m` /2 H xQM2 /2tTHQ`iBQMX
G2b b2mHb HM;;2b /2 T`Q;`KKiBQM miQ`Bbb /Mb +2ii2 T`2mp2 bQMi Svi?QM 2i aZGX 
hQmi2b H2b [m2biBQMb
bQMi BM/T2M/Mi2bX LMKQBMb- BH 2bi TQbbB#H2 /2 7B`2 TT2H  /2b 7QM+iBQMb Qm 
T`Q+/m`2b +`2b /Mb /mi`2b
[m2biBQMbX .Mb iQmi H2 bmD2i QM bmTTQb2 [m2 H2b #B#HBQi?[m2b Ki?- MmKTv 2i 
`M/QK QMi i BKTQ`i2b ;`+2
mt BMbi`m+iBQMb
BKTQ`i Ki?
BKTQ`i MmKTv b MT
BKTQ`i `M/QK
aB H2b +M/B/ib 7QMi TT2H  /2b 7QM+iBQMb /mi`2b #B#HBQi?[m2b BHb /QBp2Mi 
T`+Bb2` H2b BMbi`m+iBQMb /BKTQ`i@
iBQM +Q``2bTQM/Mi2bX
*2 bmD2i miBHBb2 H bvMit2 /2b MMQiiBQMb TQm` T`+Bb2` H2 ivT2b /2b `;mK2Mib 2i 
/m `bmHii /2b 7QM+iBQMb 
+`B`2X BMbB
/27 K6QM+iBQMUM,BMi- t,7HQi- /,bi`V @= MTXM/``v,
bB;MB}2 [m2 H 7QM+iBQM K6QM+iBQM T`2M/ i`QBb `;mK2Mib- H2 T`2KB2` 2bi mM 
2MiB2`- H2 /2mtBK2 mM MQK#`2 
pB`;mH2 ~QiiMi2 2i H2 i`QBbBK2 mM2 +?BM2 /2 +`+i`2b 2i [m2HH2 `2MpQB2 mM i#H2m 
MmKTvX
lM2 HBbi2 /2 7QM+iBQMb miBH2b 2bi /QMM2  H }M /m bmD2iX

A *`iBQM /mM2 2tTHQ`iBQM 2i ;2biBQM /2b TQBMib /BMi`i
lM2 2tTHQ`iBQM 2bi mM 2Mb2K#H2 /2 TQBMib /BMi`ib  HBMi`B2m` /mM2 xQM2 
;Q;`T?B[m2 HBKBi2- mM2 b`B2
/MHvb2b iMi bbQ+B2  +?[m2 TQBMi /BMi`iX *?[m2 ivT2 /MHvb2 [m2 H2 `Q#Qi T2mi 
2z2+im2` 2bi +Q/B}
2i `7`2M+ T` mM MQK#`2 2MiB2`X lM TQBMi /BMi`i 2bi `2T` T` /2mt 2MiB2`b- 
TQbBiB7b Qm MmHb- +Q``2bTQM/Mi
 b2b +QQ`/QMM2b +`ibB2MM2b 2M KBHHBKi`2b  HBMi`B2m` /2 H xQM2 /2tTHQ`iBQMX 
G2Mb2K#H2 /2b TQBMib
/BMi`ib /mM2 2tTHQ`iBQM [mB 2M +QMiB2Mi  2bi `2T`b2Mi T` mM Q#D2i /2 ivT2 
MmKTvXM/``v-  HK2Mib
2MiB2`b-  k +QHQMM2b 2i  HB;M2b- HHK2Mi /BM/B+2 B-y +Q``2bTQM/Mi  H#b+Bbb2 
/m TQBMi /BMi`i  2i HHK2Mi
/BM/B+2 B-R  bQM Q`/QMM2X

y

j98

ej8

R

Ryde

9R8

k

j3

38N

j

RkR

83k

6B;m`2 k 1t2KTH2 /2tTHQ`iBQM p2+
[mi`2 TQBMib /BMi`i
AX 

:M`iBQM /mM2 2tTHQ`iBQM /2bbB

AXXRV

*?QBt /2 TQBMib m ?b`/

V }M /2 /BbTQb2` /2 /QMM2b TQm` i2bi2` H2b /Bz`2Mib H;Q`Bi?K2b /2 +H+mH /2 
+?2KBM [mB b2`QMi /p2HQTTb
THmb i`/- +`B`2 mM2 7QM+iBQM [mB +QMbi`mBi mM2 2tTHQ`iBQM m ?b`/X *2ii2 
7QM+iBQM /2Mii2
/27 ;M`2`nSAUM,BMi- +Kt,BMiV @= MTXM/``v,
kyRd@yj@kd ky,Rj,98

S;2 kf3

T`2M/ 2M T`Ki`2b H2 MQK#`2 /2 TQBMib /BMi`ib  ;M`2` 2i H H`;2m` /2 H xQM2 
/2tTHQ`iBQM UbmTTQb2
+``2V 2i `2MpQB2 mM Q#D2i /2 ivT2 MmKTvXM/``v +QMi2MMi H2b +QQ`/QMM2b /2  
TQBMib /2mt  /2mt
/BbiBM+ib +?QBbBb m ?b`/ /Mb H xQM2 /2tTHQ`iBQM U};m`2 kVX
#V Zm2HH2b +QMi`BMi2b /QBp2Mi p`B}2` H2b `;mK2Mib /2 H 7QM+iBQM ;M`2`nSA \
AXXkV *H+mH /2b /BbiM+2b
PM /BbTQb2 /2 H 7QM+iBQM /2Mii2
/27 TQbBiBQMn`Q#QiUV @= imTH2,
[mB `2MpQB2 mM +QmTH2 /QMMMi H2b +QQ`/QMM2b +im2HH2b /m `Q#Qi /Mb H2 bvbiK2 /2 
+QQ`/QMM2b /2 H2tTHQ`iBQM
 THMB}2`X BMbB HBMbi`m+iBQM t- v 4 TQbBiBQMn`Q#QiUV T2`K2i /2 `+mT`2` H2b 
+QQ`/QMM2b +Qm`Mi2b /m
`Q#QiX
}M /2 7+BHBi2` HTTHB+iBQM /2b /Bz`2Mib H;Q`Bi?K2b /2 `2+?2`+?2 /2 +?2KBM- QM 
bQm?Bi2 +QMbi`mB`2 mM i#H2m
/2b /BbiM+2b 2Mi`2 H2b /Bz`2Mib TQBMib /BMi`i /mM2 2tTHQ`iBQM 2i 2Mi`2 
+2mt@+B 2i H TQbBiBQM +Qm`Mi2 /m
`Q#Qi m KQK2Mi /m +H+mHX +`B`2 mM2 7QM+iBQM /2Mii2
/27 +H+mH2`n/BbiM+2bUSA,MTXM/``vV @= MTXM/``v,
[mB T`2M/ 2M T`Ki`2 mM i#H2m /2  TQBMib /BMi`i i2H [m2 /+`Bi T`+/2KK2Mi 2i 
`2MpQB2 mM i#H2m /2
MQK#`2b ~QiiMib- /2 /BK2MbBQM      - i2H [m2 HHK2Mi /BM/B+2 B-D 7Qm`MBi H 
/BbiM+2 2Mi`2 H2b
TQBMib /BMi`i  2i - HBM/B+2 M /bB;MMi H2 TQBMi /2 /T`i /m `Q#QiX
AX" 
h`Bi2K2Mi /BK;2
PM /BbTQb2 /2 T?QiQ;`T?B2b /mM2 xQM2 /2tTHQ`iBQM 2z2+im2b  /Bz`2Mi2b 
HQM;m2m` /QM/2X *?[m2 T?QiQ@
;`T?B2  i KBb2b  H+?2HH2 /2 H xQM2 /2tTHQ`iBQM TmBb biQ+F2 /Mb mM i#H2m 
MmKTv UMTXM/``vV 
/2mt /BK2MbBQMbX G2b /BK2MbBQMb +Q``2bTQM/2Mi mt +QQ`/QMM2b ;Q;`T?B[m2b /m 
TQBMi T?QiQ;`T?B- +?[m2
HK2Mi 2bi mM 2MiB2`- +QKT`Bb 2Mi`2 y 2i k88- /QMMMi HBMi2MbBi /m TQBMi 
+QMbB/` bm` HBK;2X BMbB HHK2Mi
/BM/B+2 t-v +QMiB2Mi mM 2MiB2`- +QKT`Bb 2Mi`2 y 2i k88- +Q``2bTQM/Mi  
HBMi2MbBi bm` H T?QiQ;`T?B2 +QMbB/`2
/m TQBMi /2 +QQ`/QMM2b   X  T`iB` /2 +2b T?QiQ;`T?B2b- H2b ;QHQ;m2b 
/i2`KBM2Mi H2b 2M/`QBib  MHvb2`
2M }Hi`Mi +2mt [mB QMi mM T`Q}H /KBbbBQM +`+i`BbiB[m2 /2 +2`iBM2b `Q+?2b 
BMi`2bbMi2bX
AX"XRV MHvb2 /mM2 BK;2
G 7QM+iBQM 6R +B@/2bbQmb T`2M/ 2M T`Ki`2 mM2 T?QiQ;`T?B2 `2T`b2Mi2 +QKK2 
/+`Bi THmb ?miX 1tTHB[m2`
+2 [m2 7Bi +2ii2 7QM+iBQM 2i /+`B`2 bQM `bmHiiX
R
k
j
9
8
e
d

/27 6RUT?QiQ,MTXM/``vV @= MTXM/``v,
M 4 T?QiQXKBMUV
# 4 T?QiQXKtUV
? 4 MTXx2`QbU# @ M Y R- MTXBMie9V
7Q` T BM T?QiQX7Hi,
?(T @ M) Y4 R
`2im`M ?

AX"XkV

aH2+iBQM /2 TQBMib /BMi`ib

+`B`2 mM2 7QM+iBQM /2Mii2
/27 bH2+iBQMM2`nSAUT?QiQ,MTXM/``v- BKBM,BMi- BKt,BMiV @= MTXM/``v,
Q T?QiQ 2bi mM i#H2m `2T`b2MiMi mM2 T?QiQ;`T?B2X G2 `bmHii /2 H 7QM+iBQM 
bH2+iBQMM2`nSA 2bi mM
i#H2m  /2mt /BK2MbBQMb- /2 bi`m+im`2 bBKBHB`2  +2HmB /+`Bi };m`2 k- +QMi2MMi 
H2b +QQ`/QMM2b /2b TQBMib
/QMi HBMi2MbBi bm` H T?QiQ;`T?B2 2bi +QKT`Bb2 2Mi`2 BKBM 2i BKtX
AX* 
"b2 /2 /QMM2b
}M /bbm`2` bQM miQMQKB2 QT`iBQMM2HH2- H2 `Q#Qi /BbTQb2 HQ+H2K2Mi /2b 
BM7Q`KiBQMb M+2bbB`2b  bQM
7QM+iBQMM2K2Mi [mQiB/B2MX BMbB- BH 2M`2;Bbi`2 H /m`2 /miBHBbiBQM /2 b2b 
/Bz`2Mib BMbi`mK2Mib 2K#`[mbX AH
+QMMBi ;H2K2Mi H2b /Bz`2Mib ivT2b /MHvb2b [mBH T2mi 2z2+im2` 2i- TQm` +?+mM 
/2 +2b ivT2b- H2b BMbi`mK2Mib
 miBHBb2`X AH 2M`2;Bbi`2 H T`Q+?BM2 2tTHQ`iBQM- +2bi@@/B`2 H2b /Bz`2Mib 
TQBMib /BMi`ib [mBH /QBi pBbBi2` 2i
TQm` +?+mM H Qm H2b MHvb2b [mBH /QBi 2z2+im2`X .mi`2 T`i- BH +QMb2`p2 H2b 
`bmHiib /MHvb2b 2z2+im2b
HQ`b /2 b2b 2tTHQ`iBQMb Tbb2bX *2b `bmHiib M2 bQMi 2z+b [mT`b +QM}`KiBQM /2 
H2m` #QMM2 i`MbKBbbBQM
bm` h2``2X
*2b /Bz`2Mi2b BM7Q`KiBQMb bQMi biQ+F2b /Mb mM2 #b2 /2 /QMM2b `2HiBQMM2HH2 
/QMi H2 KQ/H2 T?vbB[m2 2bi
b+?KiBb };m`2 jX
kyRd@yj@kd ky,Rj,98

S;2 jf3

1sSGP

SA

LGu

1snLlJ BMi2;2`

1snLlJ BMi2;2`

1snLlJ BMi2;2`

1sn*>:

`2H

SAnLlJ BMi2;2`

SAnLlJ BMi2;2`

1sn.1"

`2H

SAns

BMi2;2`

hunLlJ BMi2;2`

1sn6AL

`2H

SAnu

BMi2;2`

Ln.h

`2H

1snGh

`2H

SAn__

`2H

Ln.h_

`2H

1snGPL

`2H

SAn.1S

`2H

Ln_1a

#HQ#

ALah_

ALhuS

huL

ALnLlJ

BMi2;2`

hunLlJ BMi2;2`

hunLlJ

BMi2;2`

ALn6*h

`2H

ALnLlJ BMi2;2`

hun.1a p`+?`U3yV

ALn.1_

`2H

Ahn.l_

`2H

ALnLPJ p`+?`U3yV
6B;m`2 j ai`m+im`2 T?vbB[m2 /2 H #b2 /2 /QMM2b /mM `Q#Qi
*2ii2 #b2 +QKTQ`i2 H2b bBt i#H2b bmBpMi2b ,
 H i#H2 1sSGP /2b 2tTHQ`iBQMb- p2+ H2b +QHQMM2b
r 1snLlJ MmK`Q U2MiB2`V /2 H2tTHQ`iBQM U+H27 T`BKB`2V
r 1sn*>: /i2 /2 i`MbKBbbBQM /2b TQBMib /BMi`ib /2 +2ii2 2tTHQ`iBQM
r 1sn.1" /i2 /2 /#mi /2 H2tTHQ`iBQM ULlGG bB H2tTHQ`iBQM M2bi Tb 2M+Q`2 
+QKK2M+2V
r 1sn6AL /i2 /2 }M /2 H2tTHQ`iBQM ULlGG bB H2tTHQ`iBQM M2bi Tb 2M+Q`2 i2`KBM2V
r 1snGh HiBim/2 U2M /2;`b /+BKmtV /m TQBMi /2 +QQ`/QMM2b   /2 H xQM2 
/2tTHQ`iBQM
r 1snGPL HQM;Bim/2 U2M /2;`b /+BKmtV /m TQBMi /2 +QQ`/QMM2b   /2 H xQM2 
/2tTHQ`iBQM
 H i#H2 SA /2b TQBMib /BMi`ib- /2 +H27 T`BKB`2 U1snLlJ- SAnLlJV- p2+ H2b 
+QHQMM2b
r 1snLlJ MmK`Q /2 H2tTHQ`iBQM  H[m2HH2 TT`iB2Mi H2 TQBMi /BMi`i
r SAnLlJ MmK`Q /m TQBMi /BMi`i /Mb H2tTHQ`iBQM Um b2BM /mM2 2tTHQ`iBQM H2b SA 
bQMi MmK`Qib 2M
b[m2M+2 2M +QKK2MMi  y- +2 MmK`Q M Tb /2 `TTQ`i p2+ HQ`/`2 /Mb H2[m2H H2b 
SA bQMi 2tTHQ`b
T` H2 `Q#QiV
r SAns H#b+Bbb2 /m TQBMi /BMi`i /Mb H xQM2 /2tTHQ`iBQM U2MiB2` TQbBiB7 2M 
KBHHBKi`2bV
r SAnu HQ`/QMM2 /m TQBMi /BMi`i /Mb H xQM2 /2tTHQ`iBQM U2MiB2` TQbBiB7 2M 
KBHHBKi`2bV
r SAn__ /i2 /``Bp2 /m `Q#Qi m TQBMi /BMi`i ULlGG bB +2 TQBMi M Tb 2M+Q`2 i 
pBbBiV
r SAn.1S /i2  H[m2HH2 H2 `Q#Qi  [mBii H2 TQBMi /BMi`i ULlGG bB +2 TQBMi M Tb 
2M+Q`2 i 2tTHQ` Qm
bB H pBbBi2 2bi 2M +Qm`bV
 H i#H2 ALah_ /2b BMbi`mK2Mib 2K#`[mb- p2+ H2b +QHQMM2b
r ALnLlJ H2 MmK`Q U2MiB2`V /2 HBMbi`mK2Mi U+H27 T`BKB`2V
r ALn6*h H /m`2 T2M/Mi H2[m2H HBMbi`mK2Mi  /D i miBHBb /2TmBb H``Bp2 bm` 
H THMi2 UMQK#`2
/+BKH , 7`+iBQM /2 DQm` K`iB2MV
r ALn.1_ H /i2 /2 H /2`MB`2 miBHBbiBQM /2 HBMbi`mK2Mi
r ALnLPJ MQK /2 HBMbi`mK2Mi
 H i#H2 huL /2b ivT2b /MHvb2b  2z2+im2`- p2+ H2b +QHQMM2b
r hunLlJ H2 MmK`Q /2 `7`2M+2 U2MiB2`V /m ivT2 /MHvb2 U+H27 T`BKB`2V
r hun.1a H2 MQK /m ivT2 /MHvb2
 H i#H2 ALhuS /2b BMbi`mK2Mib miBHBbb TQm` mM ivT2 /MHvb2- /2 +H27 T`BKB`2 
UhunLlJ- ALnLlJV- p2+ H2b
+QHQMM2b
r hunLlJ H2 MmK`Q /2 `7`2M+2 U2MiB2`V /m ivT2 /MHvb2
r ALnLlJ H2 MmK`Q U2MiB2`V /2 HBMbi`mK2Mi
r Ahn.l_ H /m`2 biM/`/ /miBHBbiBQM /2 HBMbi`mK2Mi /Mb +2 ivT2 /MHvb2 UMQK#`2 
/+BKH , 7`+iBQM
/2 DQm` K`iB2MV
 H i#H2 LGu BM/B[mMi TQm` +?[m2 TQBMi /BMi`i H2b ivT2b /MHvb2b  2z2+im2` Qm 
2z2+im2b- /2 +H27
T`BKB`2 U1snLlJ- SAnLlJ- hunLlJV 2i p2+ H2b +QHQMM2b
r 1snLlJ MmK`Q /2 H2tTHQ`iBQM  H[m2HH2 TT`iB2Mi H2 TQBMi /BMi`i
r SAnLlJ MmK`Q /m TQBMi /BMi`i /Mb H2tTHQ`iBQM
r hunLlJ ivT2 /2 HMHvb2
kyRd@yj@kd ky,Rj,98

S;2 9f3

r Ln.h /i2 /2 HMHvb2 ULlGG bB HMHvb2 M Tb i 2z2+im2V
r Ln.h_ /i2 /2 i`MbKBbbBQM bm` h2``2 /2b `bmHiib /2 HMHvb2 ULlGG bB HMHvb2 M 
Tb i i`MbKBb2V
r Ln_1a `bmHii /2 HMHvb2 U/QMM2 QT[m2 /QMi H bB;MB}+iBQM /T2M/ /m ivT2 
/MHvb2V
hQmi2b H2b /i2b bQMi biQ+F2b bQmb 7Q`K2 /mM MQK#`2 /+BKH +Q``2bTQM/Mi m 
MQK#`2 /2 DQm`b K`iB2Mb
/2TmBb H``Bp2 /m `Q#Qi bm` H THMi2X
AX*XRV +`B`2 mM2 `2[mi2 aZG [mB /QMM2 H2 MmK`Q /2 H2tTHQ`iBQM 2M +Qm`b- bBH v 
2M  mM2X
AX*XkV +`B`2 mM2 `2[mi2 aZG [mB /QMM2- TQm` mM2 2tTHQ`iBQM /QMi QM +QMMBi H2 
MmK`Q- H HBbi2 /2b TQBMib
/BMi`ib /2 +2ii2 2tTHQ`iBQM p2+ H2m`b +QQ`/QMM2bX
AX*XjV +`B`2 mM2 `2[mi2 aZG [mB /QMM2 H bm`7+2- 2M Ki`2b +``b- /2 +?[m2 xQM2 
/D 2tTHQ`2 T` H2
`Q#QiX G xQM2 /2tTHQ`iBQM 2bi /}MB2 +QKK2 H2 THmb T2iBi `2+iM;H2 [mB 2M;HQ#2 
H2Mb2K#H2 /2b TQBMib /BMi`ib
/2 H2tTHQ`iBQM 2i /QMi H2b #Q`/b bQMi T`HHH2b mt t2b /2 `7`2M+2 Ut2b /2b 
#b+Bbb2 2i /2b Q`/QMM2bVX
AX*X9V Zm2HH2 2bi H bm`7+2 KtBKH2 /mM2 xQM2 /2tTHQ`iBQM [m2 T2mi biQ+F2` +2ii2 
#b2 /2 /QMM2b \
AX*X8V +`B`2 mM2 `2[mi2 aZG [mB /QMM2- TQm` H2tTHQ`iBQM 2M +Qm`b- H2 MQK#`2 /2 
7QBb Q +?[m2 BMbi`mK2Mi
/QBi i`2 miBHBb 2i b /m`2 /miBHBbiBQM i?Q`B[m2 U2M DQm`b K`iB2MbV TQm` H 
iQiHBi /2 H2tTHQ`iBQMX

AA SHMB}+iBQM /mM2 2tTHQ`iBQM , T`2KB`2 TT`Q+?2
pMi /2 /K``2` mM2 MQmp2HH2 2tTHQ`iBQM- H2 `Q#Qi /QBi /i2`KBM2` mM +?2KBM [mB 
HmB T2`K2i /2 Tbb2` T`
iQmb H2b TQBMib /BMi`ib mM2 2i mM2 b2mH2 7QBbX G2MD2m /2 HQT`iBQM 2bi /2 
i`Qmp2` H2 +?2KBM H2 THmb +Qm`i
TQbbB#H2 }M /2 HBKBi2` H /T2Mb2 /M2`;B2 2i /2 HBKBi2` Hmbm`2 /m `Q#QiX
*?[m2 TQBMi /BMi`i b2` `2T` T` mM 2MiB2` TQbBiB7 Qm MmH +Q``2bTQM/Mi  bQM 
BM/B+2 /Mb H2 i#H2m /2b
TQBMib /BMi`iX lM +?2KBM /2tTHQ`iBQM b2` `2T`b2Mi T` mM Q#D2i /2 ivT2 HBbi 
/QMMMi H2b BM/B+2b /2b
TQBMib /BMi`i /Mb HQ`/`2 /2 H2m` T`+Qm`bX
AAX 

Zm2H[m2b 7QM+iBQMb miBHBiB`2b

AAXXRV GQM;m2m` /mM +?2KBM
+`B`2 mM2 7QM+iBQM /2Mii2
/27 HQM;m2m`n+?2KBMU+?2KBM,HBbi- /,MTXM/``vV @= 7HQi,
[mB T`2M/ 2M T`Ki`2 mM +?2KBM  T`+Qm`B` 2i H Ki`B+2 /2b /BbiM+2b 2Mi`2 TQBMib 
/BMi`i Ui2HH2 [m2
`2MpQv2 T` H 7QM+iBQM +H+mH2`n/BbiM+2bV 2i `2MpQB2 H /BbiM+2 [m2 /QBi 2z2+im2` 
H2 `Q#Qi TQm` bmBp`2
+2 +?2KBM 2M T`iMi /2 b TQbBiBQM +Qm`Mi2 U+Q``2bTQM/Mi  H /2`MB`2 
HB;M2f+QHQMM2 /m i#H2m /V 2i 2M
pBbBiMi iQmb H2b TQBMib /BMi`i /Mb HQ`/`2 BM/B[mX
AAXXkV LQ`KHBbiBQM /mM +?2KBM
+`B`2 mM2 7QM+iBQM /2Mii2
/27 MQ`KHBb2`n+?2KBMU+?2KBM,HBbi- M,BMiV @= HBbi,
[mB T`2M/ 2M T`Ki`2 mM2 HBbi2 /2MiB2`b 2i `2MpQB2 mM2 HBbi2 +Q``2bTQM/Mi  mM 
+?2KBM pHB/2- +2bi@@/B`2
+QMi2MMi mM2 b2mH2 7QBb iQmb H2b 2MiB2`b 2Mi`2 y 2i M U2t+HmVX SQm` +2H +2ii2 
7QM+iBQM +QKK2M+2 T` bmTT`BK2`
H2b p2Mim2Hb /Qm#HQMb U2M M2 +QMb2`pMi [m2 H T`2KB`2 Q++m``2M+2V 2i H2b pH2m`b 
bmT`B2m`2b Qm ;H2b  MbMb KQ/B}2` HQ`/`2 `2HiB7 /2b HK2Mib +QMb2`pb- TmBb 
DQmi2  H }M H2b p2Mim2Hb HK2Mib KM[mMib 2M
Q`/`2 +`QBbbMi /2 MmK`QbX
AAX"  6Q`+2 #`mi2
SQm` `2+?2`+?2` H2 THmb +Qm`i +?2KBM- QM T2mi BK;BM2` /2 +QMbB/`2` iQmb H2b 
+?2KBMb TQbbB#H2b 2i /2 +H+mH2`
H2m` HQM;m2m`X PM Q#iB2M/` BMbB  +QmT b` H2 +?2KBM H2 THmb +Qm`iX
AAX"XRV .i2`KBM2` 2M 7QM+iBQM /2 - MQK#`2 /2 TQBMib  pBbBi2`- H2 MQK#`2 /2 
+?2KBMb TQbbB#H2b TbbMi
2t+i2K2Mi mM2 7QBb T` +?+mM /2b TQBMibX
AAX"XkV *2i H;Q`Bi?K2 2bi@BH miBHBb#H2 TQm` mM2 xQM2 /2tTHQ`iBQM +QMi2MMi ky 
TQBMib /BMi`ib \ CmbiB}2`X
AAX*  H;Q`Bi?K2 /m THmb T`Q+?2 pQBbBM
lM2 B/2 bBKTH2 TQm` Q#i2MB` mM H;Q`Bi?K2 miBHBb#H2 2bi /2 +QMbi`mB`2 mM +?2KBM 
2M +?QBbBbbMi bvbiKiB[m2@
K2Mi H2 TQBMi- MQM 2M+Q`2 pBbBi- H2 THmb T`Q+?2 /2 H TQbBiBQM +Qm`Mi2X
AAX*XRV +`B`2 mM2 7QM+iBQM /2Mii2
/27 THmbnT`Q+?2npQBbBMU/,MTXM/``vV @= HBbi,
[mB T`2M/ 2M T`Ki`2 H2 i#H2m /2b /BbiM+2b `bmHii /2 H 7QM+iBQM 
+H+mH2`n/BbiM+2b U[m2biBQM AXXkV
2i 7Qm`MBi mM +?2KBM /2tTHQ`iBQM 2M TTHB[mMi HH;Q`Bi?K2 /m THmb T`Q+?2 pQBbBMX
kyRd@yj@kd ky,Rj,98

S;2 8f3

AAX*XkV Zm2HH2 2bi H +QKTH2tBi i2KTQ`2HH2 /2 HH;Q`Bi?K2 /m THmb T`Q+?2 pQBbBM 
2M +QMbB/`Mi [m2 +2i
H;Q`Bi?K2 2bi +QMbiBim /2b /2mt 7QM+iBQMb +H+mH2`n/BbiM+2b 2i 
THmbnT`Q+?2npQBbBM \
AAX*XjV 1M +QMbB/`Mi H2b i`QBb TQBMib /2 +QQ`/QMM2b   -   -   2i 2M 
+?QBbBbbMi mM TQBMi /2
/T`i /[mi TQm` H2 `Q#Qi- KQMi`2` [m2 HH;Q`Bi?K2 /m THmb T`Q+?2 pQBbBM M2 
7Qm`MBi Tb M+2bbB`2K2Mi H2
THmb +Qm`i +?2KBMX
.Mb H T`iB[m2- QM +QMbii2 [m2- /b [m2 H2 MQK#`2 /2 TQBMib /BMi`i /2pB2Mi 
BKTQ`iMi- HH;Q`Bi?K2 /m
THmb T`Q+?2 pQBbBM 7Qm`MBi mM +?2KBM [mB T2mi i`2 8yW THmb HQM; [m2 H2 THmb 
+Qm`i +?2KBMX

AAA .2mtBK2 TT`Q+?2 , H;Q`Bi?K2 ;MiB[m2
G2b H;Q`Bi?K2b ;MiB[m2b bBMbTB`2Mi /2 H i?Q`B2 /2 HpQHmiBQM 2M bBKmHMi 
HpQHmiBQM /mM2 TQTmHiBQMX AHb
7QMi BMi2`p2MB` +BM[ i`Bi2K2MibX
RX AMBiBHBbiBQM
AH b;Bi /2 +`2` mM2 TQTmHiBQM /Q`B;BM2 +QKTQb2 /2  BM/BpB/mb UB+B /2b +?2KBMb 
TQm` H2tTHQ`iBQM 
THMB}2`VX :M`H2K2Mi H TQTmHiBQM /2 /T`i 2bi T`Q/mBi2 HiQB`2K2MiX
kX pHmiBQM
*2ii2 iT2 +QMbBbi2  ii`B#m2`  +?[m2 BM/BpB/m /2 H TQTmHiBQM +Qm`Mi2 mM2 MQi2 
+Q``2bTQM/Mi  b
+T+Bi  `TQM/`2 m T`Q#HK2 TQbX A+B H MQi2 b2` bBKTH2K2Mi H HQM;m2m` /m 
+?2KBMX
jX aH2+iBQM
lM2 7QBb iQmb H2b BM/BpB/mb pHmb- HH;Q`Bi?K2 M2 +QMb2`p2 [m2 H2b  K2BHH2m`b  
BM/BpB/mbX SHmbB2m`b K@
i?Q/2b /2 bH2+iBQM bQMi TQbbB#H2b , +?QBt HiQB`2- +2mt [mB QMi Q#i2Mm H 
K2BHH2m`2 MQi2- HBKBMiBQM T`
iQm`MQB- 2i+X
9X *`QBb2K2Mi
G2b BM/BpB/mb bH2+iBQMMb bQMi +`QBbb /2mt  /2mt TQm` T`Q/mB`2 /2 MQmp2mt 
BM/BpB/mb 2i /QM+ mM2 MQmp2HH2
TQTmHiBQMX G 7QM+iBQM /2 +`QBb2K2Mi UQm `2T`Q/m+iBQMV /T2M/ /2 H Mim`2 /2b 
BM/BpB/mbX
8X JmiiBQM
lM2 T`QTQ`iBQM /BM/BpB/mb 2bi +?QBbB2 U;M`H2K2Mi HiQB`2K2MiV TQm` bm#B` mM2 
KmiiBQM- +2bi@@/B`2
mM2 i`Mb7Q`KiBQM HiQB`2X *2ii2 iT2 T2`K2i /pBi2`  HH;Q`Bi?K2 /2 `2bi2` 
#HQ[m bm` mM QTiBKmK
HQ+HX
1M `TiMi H2b iT2b /2 bH2+iBQM- +`QBb2K2Mi 2i KmiiBQM- HH;Q`Bi?K2 7Bi BMbB 
pQHm2` H TQTmHiBQM- Dmb@
[m i`Qmp2` mM BM/BpB/m [mB `TQM/2 m T`Q#HK2 BMBiBHX *2T2M/Mi /Mb H2b +b 
T`iB[m2b /miBHBbiBQM /2b
H;Q`Bi?K2b ;MiB[m2b- BH M2bi Tb TQbbB#H2 /2 bpQB` bBKTH2K2Mi bB H2 T`Q#HK2 
2bi `bQHm UH2 THmb +Qm`i +?2@
KBM };m`2@i@BH /Mb K TQTmHiBQM \VX PM miBHBb2 /QM+ /2b +QM/BiBQMb /``i 
?2m`BbiB[m2b #b2b bm` mM +`Bi`2
`#Bi`B`2X
G2 #mi /2 +2ii2 T`iB2 2bi /2 +QMbi`mB`2 mM H;Q`Bi?K2 ;MiB[m2 TQm` `2+?2`+?2` 
mM K2BHH2m` +?2KBM /2tTHQ`iBQM
[m2 +2HmB Q#i2Mm T` HH;Q`Bi?K2 /m THmb T`Q+?2 pQBbBMX
AAAX  AMBiBHBbiBQM 2i pHmiBQM
lM2 TQTmHiBQM 2bi `2T`b2Mi2 T` mM2 HBbi2 /BM/BpB/mb- +?[m2 BM/BpB/m iMi 
`2T`b2Mi T` mM +QmTH2 UHQM@
;m2m`- +?2KBMV /Mb H2[m2H
 +?2KBM /bB;M2 mM +?2KBM `2T`b2Mi +QKK2 T`+/2KK2Mi T` mM2 HBbi2 /2MiB2`b 
+Q``2bTQM/Mi mt BM/B+2b
/2b TQBMib /BMi`i /Mb H2 i#H2m /2b /BbiM+2b T`Q/mBi T` H 7QM+iBQM 
+H+mH2`n/BbiM+2b c
 HQM;m2m` 2bi mM 2MiB2` +Q``2bTQM/Mi  H HQM;m2m` /m +?2KBM- 2M i2MMi +QKTi2 /2 
H TQbBiBQM /2 /T`i /m
`Q#QiX
+`B`2 mM2 7QM+iBQM /2Mii2
/27 +`2`nTQTmHiBQMUK,BMi- /,MTXM/``vV @= HBbi,
[mB +`2 mM2 TQTmHiBQM /2  BM/BpB/mb HiQB`2bX *2ii2 7QM+iBQM T`2M/ 2M T`Ki`2 
H2 MQK#`2 /BM/BpB/mb 
2M;2M/`2` 2i H2 i#H2m /2b /BbiM+2b 2Mi`2 TQBMib /BMi`i U2i H TQbBiBQM +Qm`Mi2 
/m `Q#QiV i2H [m2 T`Q/mBi T`
H 7QM+iBQM +H+mH2`n/BbiM+2bX 1HH2 `2MpQB2 mM2 HBbi2 /BM/BpB/mb- +2bi@@/B`2 /2 
+QmTH2b UHQM;m2m`- +?2KBMVX
AAAX"  aH2+iBQM
+`B`2 mM2 7QM+iBQM /2Mii2
/27 `/mB`2UT,HBbiV @= LQM2,
[mB `/mBi mM2 TQTmHiBQM /2 KQBiB 2M M2 +QMb2`pMi [m2 H2b BM/BpB/mb 
+Q``2bTQM/Mi mt +?2KBMb H2b THmb
+Qm`ibX PM `TT2HH2 [m2 T 2bi mM2 HBbi2 /2 +QmTH2b UHQM;m2m`- +?2KBMVX G 
7QM+iBQM `/mB`2 M2 `2MpQB2 Tb /2
`bmHii KBb KQ/B}2 H HBbi2 Tbb2 2M T`Ki`2X

kyRd@yj@kd ky,Rj,98

S;2 ef3

AAAX*  JmiiBQM
AAAX*XRV +`B`2 mM2 7QM+iBQM /2Mii2
/27 Kmi2`n+?2KBMU+,HBbiV @= LQM2,
[mB T`2M/ 2M T`Ki`2 mM +?2KBM 2i H2 i`Mb7Q`K2 2M BMp2`bMi HiQB`2K2Mi /2mt /2 
b2b HK2MibX
AAAX*XkV +`B`2 mM2 7QM+iBQM /2Mii2
/27 Kmi2`nTQTmHiBQMUT,HBbi- T`Q#,7HQi- /,MTXM/``vV @= LQM2,
[mB T`2M/ 2M T`Ki`2 mM2 TQTmHiBQM /QMi 2HH2 7Bi Kmi2` mM +2`iBM MQK#`2 
/BM/BpB/mbX G2 T`Ki`2 T`Q#
U+QKT`Bb 2Mi`2 y 2i RV /bB;M2 H T`Q
/ 2bi H Ki`B+2 /2b
/BbiM+2b 2Mi`2 TQBMib /BMi`iX
AAAX.  *`QBb2K2Mi
AAAX.XRV +`B`2 mM2 7QM+iBQM /2Mii2
/27 +`QBb2`U+R,HBbi- +k,HBbiV @= HBbi,
[mB +`2 mM MQmp2m +?2KBM  T`iB` /2 /2mt +?2KBMb Tbbb 2M T`Ki`2X *2 MQmp2m 
+?2KBM b2` T`Q/mBi 2M
T`2MMi H T`2KB`2 KQBiB /m T`2KB2` +?2KBM bmBpB /2 H /2mtBK2 KQBiB /m /2mtBK2 
TmBb 2M  MQ`KHBbMi 
H2 +?2KBM BMbB Q#i2MmX
AAAX.XkV +`B`2 mM2 7QM+iBQM /2Mii2
/27 MQmp2HH2n;M`iBQMUT,HBbi- /,MTXM/``vV @= LQM2,
[mB 7Bi ;`QbbB` mM2 TQTmHiBQM 2M +`QBbMi b2b K2K#`2b TQm` 2M /Qm#H2` H2z2+iB7X 
SQm` +2H- H 7QM+iBQM 7Bi b2
`2T`Q/mB`2 iQmb H2b +QmTH2b /BM/BpB/mb [mB b2 bmBp2Mi /Mb H TQTmHiBQM UT(B)- 
T(BYR)V 2i UT(K@R)- T(y)V
/2 7QM  T`Q/mB`2  MQmp2mt BM/BpB/mb [mB bDQmi2Mi mt  BM/BpB/mb /2 H TQTmHiBQM 
/2 /T`iX
AAAX1  H;Q`Bi?K2 +QKTH2i
AAAX1XRV +`B`2 mM2 7QM+iBQM /2Mii2
/27 H;Qn;MiB[m2USA,MTXM/``v- K,BMi- T`Q#,7HQi- ;,BMiV @= 7HQi- HBbi,
[mB T`2M/ 2M T`Ki`2 mM i#H2m /2 TQBMib /BMi`ib U};m`2 kV- H iBHH2 K /2 H 
TQTmHiBQM- H T`Q
/2 KmiiBQM T`Q# 2i H2 MQK#`2 /2 ;M`iBQMb ;X *2ii2 7QM+iBQM BKTHMi2 mM 
H;Q`Bi?K2 ;MiB[m2  HB/2
/2b /Bz`2Mi2b 7QM+iBQMb +`Bi2b Dmb[m T`b2Mi 2i `2MpQB2 H HQM;m2m` /m THmb 
+Qm`i +?2KBM /2tTHQ`iBQM 2i H2
+?2KBM HmB@KK2 Q#i2Mmb m #Qmi /2 ; ;M`iBQMbX
AAAX1XkV 1bi@BH TQbbB#H2 p2+ HBKTHMiiBQM `HBb2- [mmM2 Bi`iBQM /2 HH;Q`Bi?K2 
/;`/2 H2 `bmHii , H2
K2BHH2m` +?2KBM Q#i2Mm  H ;M`iBQM   2bi THmb HQM; [m2 +2HmB /2 H ;M`iBQM  \
.Mb H{`KiBp2- +QKK2Mi KQ/B}2` H2 T`Q;`KK2 TQm` [m2 +2ii2 bBimiBQM M2 TmBbb2 
THmb ``Bp2` \
AAAX1XjV Zm2HH2b mi`2b +QM/BiBQMb /``i T2mi@QM BK;BM2` \ i#HB` mM +QKT`iB7 
T`b2MiMi H2b pMi;2b
2i BM+QMpMB2Mib /2 +?[m2 +QM/BiBQM /``i 2MpBb;2X

PT`iBQMb 2i 7QM+iBQMb Svi?QM /BbTQMB#H2b
6QM+iBQMb
 `M;2UMV `2MpQB2 H b[m2M+2 /2b M T`2KB2`b 2MiB2`b U    V
 HBbiU`M;2UMVV `2MpQB2 mM2 HBbi2 +QMi2MMi H2b M T`2KB2`b 2MiB2`b /Mb HQ`/`2 
+`QBbbMi ,
HBbiU`M;2U8VV  (y- R- k- j- 9)
 `M/QKX`M/`M;2U- #V `2MpQB2 mM 2MiB2` HiQB`2 +QKT`Bb 2Mi`2  2i #@R BM+Hmb U 2i 
# 2MiB2`bV
 `M/QKX`M/QKUV `2MpQB2 mM MQK#`2 ~QiiMi iB` HiQB`2K2Mi /Mb < < bmBpMi mM2 /Bbi`B#miBQM mMB7Q`K2 `M/QKXb?m77H2UmV T2`Kmi2 HiQB`2K2Mi H2b HK2Mib /2 H HBbi2 m UKQ/B}2 mV `M/QKXbKTH2Um- MV `2MpQB2 mM2 HBbi2 /2 M HK2Mib /BbiBM+ib /2 H HBbi2 m +?QBbBb HiQB`2K2Mi- bB M = H2MUmV- /+H2M+?2 H2t+2TiBQM oHm21``Q` Ki?Xb[`iUtV +H+mH2 H `+BM2 +``2 /m MQK#`2 Ki?X+2BHUtV `2MpQB2 H2 THmb T2iBi 2MiB2` bmT`B2m` Qm ;H  t kyRd@yj@kd ky,Rj,98 S;2 df3 Ki?X7HQQ`UtV `2MpQB2 H2 THmb ;`M/ 2MiB2` BM7`B2m` Qm ;H  t bQ`i2/UmV `2MpQB2 mM2 MQmp2HH2 HBbi2 +QMi2MMi H2b HK2Mib /2 H HBbi2 m i`Bb /Mb HQ`/`2  Mim`2H  /2 b2b HK2Mib UbB H2b HK2Mib /2 m bQMi /2b HBbi2b Qm /2b imTH2b- HQ`/`2 miBHBb 2bi HQ`/`2 H2tB+Q;`T?B[m2V PT`iBQMb bm` H2b HBbi2b H2MUmV /QMM2 H2 MQK#`2 /HK2Mib /2 H HBbi2 m , H2MU(R- k- j)V  j c H2MU((R-k)- (j-9))V  k m Y p +QMbi`mBi mM2 HBbi2 +QMbiBim2 /2 H +QM+iMiBQM /2b HBbi2b m 2i p , (R- k) Y (j- 9- 8)  (R- k- j- 9- 8) M m +QMbi`mBi mM2 HBbi2 +QMbiBim /2 H HBbi2 m +QM+iM2 M 7QBb p2+ 2HH2@KK2 , j (R- k)  (R- k- R- k- R- k) 2 BM m 2i 2 MQi BM m /i2`KBM2Mi bB HQ#D2i 2 };m`2 /Mb H HBbi2 m- +2ii2 QT`iBQM  mM2 +QKTH2tBi i2KTQ`2HH2 2M k BM (R- k- j)  h`m2 c k MQi BM (R- k- j)  6Hb2 mXTT2M/U2V DQmi2 HHK2Mi 2  H }M /2 H HBbi2 m UbBKBHB`2  m 4 m Y (2)V /2H m(B) bmTT`BK2 /2 H HBbi2 m bQM HK2Mi /BM/B+2 B /2H m(B,D) bmTT`BK2 /2 H HBbi2 m iQmb b2b HK2Mib /QMi H2b BM/B+2b bQMi +QKT`Bb /Mb HBMi2`pHH2 < < mX`2KQp2U2V bmTT`BK2 /2 H HBbi2 m H2 T`2KB2` HK2Mi [mB  TQm` pH2m` 2- /+H2M+?2 H2t+2TiBQM oHm21``Q` bB 2 M2 };m`2 Tb /Mb m- +2ii2 QT`iBQM  mM2 +QKTH2tBi i2KTQ`2HH2 2M mXBMb2`iUB- 2V BMb`2 HHK2Mi 2  H TQbBiBQM /BM/B+2 B /Mb H HBbi2 m U2M /+HMi H2b HK2Mib bmBpMibV c bB B =4 H2MUmV- 2 2bi DQmi 2M }M /2 HBbi2 m(B)- m(D) 4 m(D)- m(B) T2`Kmi2 H2b HK2Mib /BM/B+2 B 2i D /Mb H HBbi2 m mXbQ`iUV i`B2 H HBbi2 m 2M TH+2- /Mb HQ`/`2  Mim`2H  /2 b2b HK2Mib UbB H2b HK2Mib /2 m bQMi /2b HBbi2b Qm /2b imTH2b- HQ`/`2 miBHBb 2bi HQ`/`2 H2tB+Q;`T?B[m2V PT`iBQMb bm` H2b i#H2mt UMTXM/``vV MTX``vUmV +`2 mM MQmp2m i#H2m +QMi2MMi H2b HK2Mib /2 H HBbi2 mX G iBHH2 2i H2 ivT2 /2b HK2Mib /2 +2 i#H2m bQMi //mBib /m +QMi2Mm /2 m MTX2KTivUM- /ivT2V- MTX2KTivUUM- KV- /ivT2V +`2 `2bT2+iBp2K2Mi mM p2+i2m`  M HK2Mib Qm mM2 K@ i`B+2  M HB;M2b 2i K +QHQMM2b /QMi H2b HK2Mib- /2 pH2m`b BM/i2`KBM2b- bQMi /2 ivT2 /ivT2 [mB T2mi i`2 mM ivT2 biM/`/ U#QQH- BMi- 7HQi- wV Qm mM ivT2 bT+B}[m2 MmKTv UMTXBMiRe- MTX7HQijk- wVX aB H2 T`Ki`2b /ivT2 M2bi Tb T`+Bb- BH T`2M/ H pH2m` 7HQi T` /7mi MTXx2`QbUM- /ivT2V- MTXx2`QbUUM- KV- /ivT2V 7QM+iBQMM2 +QKK2 MTX2KTiv 2M BMBiBHBbMi +?[m2 H@ K2Mi  H pH2m` x`Q TQm` H2b ivT2b MmK`B[m2b Qm 6Hb2 TQm` H2b ivT2b #QQH2Mb XM/BK MQK#`2 /2 /BK2MbBQMb /m i#H2m  UR TQm` mM p2+i2m`- k TQm` mM2 Ki`B+2- 2i+XV Xb?T2 imTH2 /QMMMi H iBHH2 /m i#H2m  TQm` +?+mM2 /2 b2b /BK2MbBQMb H2MUV iBHH2 /m i#H2m  /Mb b T`2KB`2 /BK2MbBQM UMQK#`2 /HK2Mib /mM p2+i2m`- MQK#`2 /2 HB;M2b /mM2 Ki`B+2- 2i+XV [mBpH2Mi  Xb?T2(y) XbBx2 MQK#`2 iQiH /HK2Mib /m i#H2m X7Hi Bi`i2m` bm` iQmb H2b HK2Mib /m i#H2m XKBMUV- XKtUV `2MpQB2 H pH2m` /m THmb T2iBi U`2bT2+iBp2K2Mi THmb ;`M/V HK2Mi /m i#H2m  c +2b QT`iBQMb QMi mM2 +QKTH2tBi i2KTQ`2HH2 2M # BM  /i2`KBM2 bB # 2bi mM HK2Mi /m i#H2m  c bB # 2bi mM b+HB`2- p`B}2 bB # 2bi mM HK2Mi /2  c bB # 2bi mM p2+i2m` Qm mM2 HBbi2 2i  mM2 Ki`B+2- /i2`KBM2 bB # 2bi mM2 HB;M2 /2 MTX+QM+i2Mi2UUR- kVV +QMbi`mBi mM MQmp2m i#H2m 2M +QM+iMMi /2mt i#H2mt c R 2i k /QBp2Mi pQB` H2 KK2 MQK#`2 /2 /BK2MbBQMb 2i H KK2 iBHH2  H2t+2TiBQM /2 H2m` iBHH2 /Mb H T`2KB`2 /BK2MbBQM U/2mt Ki`B+2b /QBp2Mi pQB` H2 KK2 MQK#`2 /2 +QHQMM2b TQm` TQmpQB` i`2 +QM+iM2bV r r r 6AL r r r kyRd@yj@kd ky,Rj,98 S;2 3f3