Centrale Physique et Chimie 2 PSI 2017

SaA
9 ?2m`2b

*H+mHi`B+2b miQ`Bbû2b

kyRd

S?vbB[m2@+?BKB2 k
1tTHQbBQM- T`QTmHbBQMb +?BKB[m2
2i ûH2+i`QK;MûiB[m2 U+QBH;mMV

G?v/`xBM2 2bi H2 T`2KB2` T`QT2`;QH ¨ pQB` ûiû miBHBbû TQm` H T`QTmHbBQM 
û`QMmiB[m2- 2M T`iB+mHB2` /Mb H2b
pBQMb 7mbû2b J2bb2`b+?KBii J2 RejX G 7Q`KmH2 /2 H?v/`xBM2 2bi Lk>9X
*2`iBM2b /QMMû2b miBH2b bQMi `bb2K#Hû2b 2M }M /ûMQM+ûX

A G?v/`xBM2
G i#H2m bmBpMi +QKT`2 [m2H[m2b /QMMû2b T?vbB+Q@+?BKB[m2b /2 H?v/`xBM2 ¨ +2HH2b 
/2 H2m- /2 Hûi?MQH 2i
/2 Hûi?M2X
>v/`xBM2
1m
úi?MQH
úi?M2 U*k>eV
h2KTû`im`2 7mbBQM Uê*V

k

y

RRd

R3j

h2KTû`im`2 û#mHHBiBQM Uê*V

RR9

Ryy

dN

3N

JQK2Mi /BTQHB`2 U.V

R-d8

R-38

R-ee

AX 
.QMM2` H bi`m+im`2 /2 G2rBb /2 H KQHû+mH2 /?v/`xBM2X
.QMM2` mM Q`/`2 /2 ;`M/2m` TQm` H2b M;H2b >L>X
*QKTi2 i2Mm /2b /QMMû2b- [m2HH2 bi`m+im`2 i`B/BK2MbBQMM2HH2 T2mi@QM T`QTQb2` 
TQm` H?v/`xBM2 \
AX" 
*QKK2Mi 2tTHB[m2` H pH2m` ûH2pû2 /2b i2KTû`im`2b /2 7mbBQM 2i /û#mHHBiBQM /2 
H?v/`xBM2 \ .T`b
pQmb- H?v/`xBM2 2bi@2HH2 i`b KBb+B#H2 Qm T2m KBb+B#H2 /Mb H2m \ CmbiB}2`X
AX* 
*QKK2 H2m- H?v/`xBM2 2bi mM KT?Qi`2X ú+`B`2 Hû[miBQM #BHM /2 HmiQT`QiQHvb2 /2 
H?v/`xBM2X
G +QMbiMi2 /2 +2i û[mBHB#`2 ¨ kN3 E 2bi    X 6B`2 mM2 +QKT`BbQM p2+ H2mX

AA SBH2 ¨ ?v/`xBM2
G?v/`xBM2  ûiû `2KBb2 m ;Qmi /m DQm` T` H2 +QMbi`m+i2m` miQKQ#BH2 .B?ibm , 2HH2 
`2KTH+2 H?v/`Q;M2
/Mb H2b TBH2b ¨ +QK#mbiB#H2b- bQm`+2b /ûM2`;B2 TQm` H2b KQi2m`bX
lM2 TBH2 ¨ +QK#mbiB#H2 2bi +QMbiBimû2 /2 U};m`2 RV ,
 /2mt ûH2+i`Q/2b KûiHHB[m2b TQ`2mb2b T2`K2iiMi H2 Tbb;2 /m +QK#mbiB#H2 2i /m 
/BQtv;M2 c
 mM ûH2+i`QHvi2 +QMi2MMi /2b BQMb >Y TQm` H TBH2 ¨ ?v/`Q;M2 2i P> TQm` H TBH2 ¨ 
?v/`xBM2X
JQi2m`
.BQtv;M2

*QK#mbiB#H2
úH2+i`QHvi2
S`Q/mBi R

S`Q/mBi k
6B;m`2 R

SQm` H TBH2 ¨ ?v/`Q;M2- H2 +QK#mbiB#H2 2bi /m /B?v/`Q;M2 bQmb 7Q`K2 ;x2mb2- H 
`û+iBQM b2 7Bi 2M KBHB2m
i`b +B/2X SQm` H TBH2 ¨ ?v/`xBM2- H2 +QK#mbiB#H2 2bi mM2 bQHmiBQM [m2mb2 ¨ 8W 
2M ?v/`xBM2- H `û+iBQM b2
7Bi 2M KBHB2m #bB[m2X
AAX  PM /QMM2 H2b TQi2MiB2Hb biM/`/
*QmTH2

)  )

Pkf>kP

LkfLk>9

 UoV

y-yy

R-kj

y-jj

AAXXRV SQm` +?+mM2 /2b TBH2b- û+`B`2- TQm` H2b /Bzû`2Mib +QmTH2b bmb+2TiB#H2b 
/BMi2`p2MB`- H2b /2KB@û[miBQMb
`û/QtX

kyRd@yj@yk yN,jN,RR

S;2 Rfd

AAXXkV SQm` +?+mM2 /2b TBH2b- `2T`Q/mB`2 bm++BM+i2K2Mi H };m`2 R 2M BM/B[mMi ,

H2 MQK /2b ûH2+i`Q/2b c
H2 MQK /2b T`Q/mBib R 2i k c
H2 b2Mb /2 +B`+mHiBQM /2b ûH2+i`QMb c
H2 b2Mb /2 +B`+mHiBQM /m +Qm`Mi c
H2 b2Mb /2 /ûTH+2K2Mi /2b BQMb /Mb HûH2+i`QHvi2 c
H2b TH2b /2 H TBH2X

AAXXjV SQm` +?[m2 TBH2- û+`B`2 Hû[miBQM #BHM /2 H `û+iBQM 2i /ûi2`KBM2` H pH2m` 
/2 b +QMbiMi2 /û[mB@
HB#`2X *QKK2Mi2` H2b `ûbmHiib Q#i2MmbX
AAXX9V ú+`B`2 Hû[miBQM /2 +QK#mbiBQM /2 Hûi?M2 T` H2 /BQtv;M2X Zm2H 2bi mM 
pMi;2 /2 H TBH2 ¨
+QK#mbiB#H2 T` `TTQ`i ¨ mM KQi2m` i?2`KB[m2 miBHBbMi H +QK#mbiBQM /2 Hûi?M2 \
AAX" 

*?QBt /2b ûH2+i`Q/2b

AAX"XRV .Mb H TBH2 ¨ ?v/`Q;M2- H2b ûH2+i`Q/2b bQMi 2M THiBM2X .Mb H TBH2 ¨ 
?v/`xBM2- HûH2+i`Q/2 2M +QMi+i
p2+ H?v/`xBM2 2bi 2M MB+F2H- +2HH2 2M +QMi+i p2+ H2 /BQtv;M2 2bi 2M +Q#HiX 
Zm2HH2 /QBi i`2 H T`BM+BTH2
T`QT`Bûiû /2b ûH2+i`Q/2b miBHBbû2b /Mb H2b TBH2b ¨ +QK#mbiB#H2 \
AAX"XkV G2b /B;`KK2b TQi2MiB2H@T> bBKTHB}ûb /m +Q#Hi- /m MB+F2H 2i /m THiBM2 
bQMi /QMMûb };m`2 kX G2b
/B;`KK2b TQi2MiB2H@T> /m +Q#Hi 2i /m MB+F2H T2mp2Mi i`2 +QMbB/û`ûb +QKK2 
B/2MiB[m2bX
*Q#Hi 2i LB+F2H

SHiBM2

*

 UoV

 UoV

*

"

"

T>

.QKBM2 /2 +Q``QbBQM
/m KûiH

.QKBM2 /BKKmMBiû
/m KûiH

T>

.QKBM2 /2 TbbBpBiû
/m KûiH

6B;m`2 k .B;`KK2b TQi2MiB2H@T> /m +Q#Hi- /m MB+F2H 2i /m THiBM2
V ZmTT2HH2@i@QM /QKBM2b /BKKmMBiû- /2 +Q``QbBQM 2i /2 TbbBpBiû \
#V § [mQB +Q``2bTQM/2Mi H2b i`QBb /QKBM2b - " 2i * /ûHBKBiûb T` H2b /2mt 
/`QBi2b 2M TQBMiBHHûb `2HiBp2b mt
+QmTH2b `û/Qt /2 H2m \
AAX"XjV *QKTi2 i2Mm /2b +QM/BiBQMb QTû`iQB`2b TQm` +?+mM2 /2b TBH2b 2i 2M 
2tTHQBiMi H2b /B;`KK2b
TQi2MiB2H@T> /2 H };m`2 k- DmbiB}2` H2 +?QBt /2b ûH2+i`Q/2bX 1bi@BH TQbbB#H2 
/miBHBb2` mM2 ûH2+i`Q/2 2M +Q#Hi
Qm MB+F2H TQm` H TBH2 ¨ ?v/`Q;M2 \ Zm2HH2b T2mp2Mi i`2 H2b `BbQMb [mB QMi 
+QM/mBi m +?QBt /2b ûH2+i`Q/2b 2M
MB+F2H 2i 2M +Q#Hi TQm` H TBH2 ¨ ?v/`xBM2 \
AAX*  _2M/2K2Mi /2 H TBH2 ¨ +QK#mbiB#H2
PM b2 TH+2 ¨    ,X PM /QMM2 ,
*QKTQbMi

Lk>9 UV

   UFCKQHRV

UCKQH E V
R

R

Pk U;V

8R
RkR

ky8

Lk U/BbbQmbV

>kPUV

Ry

k3e

ej

dy

AAX*XRV lM2 pH2m` /2Mi?HTB2 /2 7Q`KiBQM M2bi Tb T`û+Bbû2 /Mb H2 i#H2m 
T`û+û/2MiX SQm`[mQB \
AAX*XkV SQm` mM ++`QBbb2K2Mi ûHûK2MiB`2 E /2 HpM+2K2Mi /2 H `û+iBQM- QM MQi2 
`2bT2+iBp2K2Mi  2i
 H2 i`Mb72`i i?2`KB[m2 2i H2 i`pBH ûH2+i`B[m2 Ui`pBH miBH2V `2Ïmb T` H TBH2X

X CmbiB}2` +2ii2 2tT`2bbBQMX
G2 `2M/2K2Mi i?2`KQ/vMKB[m2 /2 H TBH2 2bi /û}MB T`  
 
kyRd@yj@yk yN,jN,RR

S;2 kfd

AAX*XjV SQm` bBKTHB}2` H2b +H+mHb- QM 7Bi H?vTQi?b2 /mM 7QM+iBQMM2K2Mi 
`ûp2`bB#H2- BbQi?2`K2 2i BbQ#`2X
V SQm` mM ++`QBbb2K2Mi ûHûK2MiB`2 E /2 HpM+2K2Mi /2 H `û+iBQM- /QMM2`- /Mb +2b 
+QM/BiBQMb- H2b 2tT`2b@
bBQMb /2  2i  2M 7QM+iBQM /2 E 2i E- `2bT2+iBp2K2Mi H2b p`BiBQMb /2 H2Mi?HTB2 
2i /2 H2Mi?HTB2 HB#`2
/2 H TBH2X
#V _2HB2` E 2i E ¨ EX
+V 1M /û/mB`2 HQ`b H2tT`2bbBQM /m `2M/2K2Mi 2M 7QM+iBQM /2b ;`M/2m`b biM/`/ /2 
`û+iBQMX 6B`2 HTTHB+iBQM
MmKû`B[m2X
AAX*X9V PM bQm?Bi2 +QKT`2` +2 `ûbmHii ¨ +2HmB Q#i2Mm TQm` mM KQi2m` i?2`KB[m2 
7QM+iBQMMMi b2HQM mM
+v+H2 /2 *`MQiX S`QTQb2` /2b pH2m`b TQm` H2b i2KTû`im`2b /2b bQm`+2b 7`QB/2 2i 
+?m/2 2M +QMi+i p2+ H2
KQi2m`X T`b HpQB` /û}MB- ûpHm2` H2 `2M/2K2Mi i?2`KQ/vMKB[m2 /2 +2 KQi2m` 
i?2`KB[m2X *QKK2Mi2`X

AAA S`QTmHbBQM +?BKB[m2 /m T`QD2+iBH2
G2b KmMBiBQMb ¨ TQm/`2 miBHBb2Mi mM 2tTHQbB7 `TB/2 T`BKB`2 TQm` KQ`+2` H 
/û~;`iBQM /2 H TQm/`2 [mB
T`QTmHb2 HQ`b H2 T`QD2+iBH2X LQmb HHQMb +QMbB/û`2` mM +HB#`2 N KK /QMi H2 
T`QD2+iBH2 2bi /2 Kbb2     H
2i /2 /BKi`2     NNX G +?`;2 T`QTmHbBp2 2bi mM2 TQm/`2 /Bi2  bMb 7mKû2  
+QMbiBimû2 /mM KûHM;2
/2 MBi`Q+2HHmHQb2 2i /2 MBi`Q;Hv+û`BM2X lM2 Kbb2     H /2 +2ii2 KiB`2 2bi 
biQ+Fû2 bQmb 7Q`K2 ;ûHB}û2
/Mb H /QmBHH2 2i v Q++mT2 mM pQHmK2 +vHBM/`B[m2 /2 HQM;m2m`     NN 2i /2 /BKi`2 
X
G2Mi?HTB2 KbbB[m2 /2 `û+iBQM /2 H /û+QKTQbBiBQM /2 H TQm/`2 2M /2 MQK#`2mt ;x 
/BiQKB[m2b 2bi
   n  L+H X PM bmTTQb2 [m2 H2b ;x T`Q/mBib bQMi T`7Bib 2i [m2 H2 `TTQ`i /2 H2m` 
+T+Biû +HQ@
`B}[m2 ¨ T`2bbBQM +QMbiMi2 ¨ +2HH2 ¨ pQHmK2 +QMbiMi 2bi    X S` bQm+B /2 
bBKTHB}+iBQM /m T`Kûi`;2MQmb HHQMb +QMbB/û`2` [m2 H2 7`QMi /2 `û+iBQM /2 H 
TQm/`2 b2 bBim2 /m +iû /m T`QD2+iBH2 2i [mBH 2bi bBimû
¨ H /BbiM+2  /m 7QM/ /2 H /QmBHH2X G2 T`QD2+iBH2  mM2 TQbBiBQM  2i mM2 pBi2bb2 
- i2HH2b [m2 `2T`ûb2Miû2b
bm` H };m`2 jX PM +QMbB/`2` mM2 `K2 /2 TQBM; /QMi H HQM;m2m` /m +MQM 2bi    DN 
2i /2 b2+iBQM 
+Q``2bTQM/Mi m +HB#`2X G };m`2 9 T`ûb2Mi2 /2b BM7Q`KiBQMb bm` H2 iB` p2+ +2ii2 
`K2X

pMi H2 iB`

T`b H KBb2 ¨ 72m

6B;m`2 j

 , TQbBiBQM /2 H #b2 /m T`QD2+iBH2 UKV

h2KTb UKbV

6B;m`2 9 .T`b HQmp`;2 h`+2b /`K2b ¨ 72m /2 HBM :HHmbb2`- 2tT2`i 2M b+B2M+2b 
+`BKBM2HH2b
AAAX  1biBK2` H 7`+iBQM /ûM2`;B2 +?BKB[m2 +QMp2`iB2 2M ûM2`;B2 +BMûiB[m2 /m 
T`QD2+iBH2X

kyRd@yj@yk yN,jN,RR

S;2 jfd

 UKV

S`2bbBQM U#`V

oBi2bb2 UKbRV

S`2bbBQM U#`V

AAAX"  1M +QMbB/û`Mi H2Mb2K#H2 &TQm/`2YT`QD2+iBH2'- KQMi`2` [mm +Qm`b /2 H 
/û~;`iBQM- H +QMb2`piBQM
/2 HûM2`;B2 +QM/mBi ¨ Hû[miBQM /2 #HBbiB[m2 BMiû`B2m`2 bmBpMi2 ,

S`û+Bb2` H2b TT`QtBKiBQMb 7Bi2b 2i H2b DmbiB}2` ¨ T`iB` /2 H };m`2 9X
AAAX*  .Mb H2 +/`2 T`û+û/2Mi- [m2HH2 2bi H 7`+iBQM /2 TQm/`2 #`Hû2 HQ`b[m2 H2 
T`QD2+iBH2 2bi 2tTmHbû /m
+MQM \
AAAX.  G +BMûiB[m2 /2 +QK#mbiBQM /2 H TQm/`2 /ûT2M/ /2 H 7Q`K2 /2 b2b ;`BMb 2i 
2bi /QMMû2 TQm` /2b
E
;`BMb +vHBM/`B[m2b T` H HQB /2 +QK#mbiBQM
 - Q  2bi mM2 +QMbiMi2 TQbBiBp2 2i  H T`2bbBQM bm#B2
E
T` H TQm/`2X 1biBK2` H pH2m` /2 H +QMbiMi2  2M KKbR#`RX
AAAX1  S`QTQb2` KBMi2MMi H2 D2m +QKTH2i /û[miBQMb [mB T2`K2ii`Bi- T` mM2 
`ûbQHmiBQM MmKû`B[m2- /2
/ûi2`KBM2` H HQB   /m T`QD2+iBH2X

Ao "HBbiB[m2
hQmi 2M 7QM+iBQMMMi bm` H2 KK2 T`BM+BT2 [m2 H`K2 /2 TQBM; [mB pB2Mi /i`2 
ûim/Bû2- H2b +MQMb T`QTmHb2Mi
/2b T`QD2+iBH2b #2m+QmT THmb HQm`/b UDmb[m¨ [m2H[m2b +2MiBM2b /2 FBHQ;`KK2bV ¨ 
/2b TQ`iû2b i`b bmTû`B2m`2b
U[m2H[m2b /BxBM2b /2 FBHQKi`2bVX LûMKQBMb TQm` /2b T`QD2+iBH2b 2M+Q`2 THmb 
HQm`/b 2i /2b TQ`iû2b 2M+Q`2 THmb
HQM;m2b- H T`QTmHbBQM T` mM2 +?`;2 2tTHQbBp2 2bi BM/Tiû2 +` 2HH2 Mû+2bbBi2`Bi 
/2b +?`;2b i`QT BKTQ`iMi2bX
PM 2MpBb;2 HQ`b /miBHBb2` H T`QTmHbBQM ûH2+i`QK;MûiB[m2- +QM/mBbMi BMbB ¨ mM 
+MQM ûH2+i`QK;MûiB[m2 Qm
 +QBH;mM X .2b 2bbBb QMi T2`KBb /2z2+im2` mM iB` /mM T`QD2+iBH2 /2 Kbb2    LH ¨ 
98ê T` `TTQ`i ¨
H?Q`BxQMiH2- T2`K2iiMi /ii2BM/`2 mM2 TQ`iû2    LNX
AoX  1M Mû;HB;2Mi iQmi 2z2i /2 7`Qii2K2Mi /2 HB` UbBimiBQM /m pB/2V- ûpHm2` H 
pBi2bb2 2i HûM2`;B2
+BMûiB[m2 /2 /ûT`i /m T`QD2+iBH2X
AoX"  G2 T`QD2+iBH2 2bi mM +vHBM/`2 /+B2` /2 /BKi`2     DNX
PM T`2M/` , pBb+QbBiû /2 HB`       1BT c Kbb2 pQHmKB[m2 /2 HB`     LHN X
AoX"XRV G+iBQM /2 7`2BM;2 /2 HB` `ûbmHi2 /2 H +QK#BMBbQM /mM 2z2i / ¨ H [mMiBiû 
/2 KQmp2K2Mi /m
T`QD2+iBH2 2i /mM 2z2i / ¨ H pBb+QbBiû /m ~mB/2 /Mb H2[m2H 2bi THQM;û +2 
T`QD2+iBH2X G2[m2H /2 +2b /2mt 2z2ib
2bi T`ûTQM/û`Mi \
AoX"XkV 1M bmTTQbMi [m2 b2mH H2z2i / ¨ H [mMiBiû /2 KQmp2K2Mi BMi2`pB2Mi 2i 2M 
b2 THÏMi /Mb H2
`û7û`2MiB2H /m T`QD2+iBH2- KQMi`2` [m2 H 7Q`+2 /2 7`2BM;2 2bi T`QTQ`iBQMM2HH2 ¨ 
 2i ûpHm2` mM Q`/`2 /2 ;`M/2m`
/m +Q2{+B2Mi /2 T`QTQ`iBQMMHBiûX
AoX"XjV G2b T`QD2+iBH2b /`K2b /2 TQBM; QMi mM2 TQ`iû2 `û2HH2 +Q``2bTQM/Mi ¨ 
2MpB`QM RyW /2 H TQ`iû2 /Mb
H2 pB/2- iM/Bb [m2 H2b ;`Qb T`QD2+iBH2b- i2Hb +2mt /mM +MQM /2 jy8 KK- QMi mM2 
TQ`iû2 pQBbBM2 /2 dyW /2 +2HH2
/Mb H2 pB/2X 1tTHB[m2` [mHBiiBp2K2Mi +2 7Bi 2M miBHBbMi H2b `ûbmHiib /2 H 
[m2biBQM AoX"XkX

o S`QTmHbBQM ûH2+i`QK;MûiB[m2 , mM T`QiQivT2 /2 H#Q`iQB`2
}M /ûim/B2` H2 7QM+iBQMM2K2Mi /m +QBH;mM 2i H2b T`Ki`2b BM~m2Mib- mM T`QiQivT2 
¨ T2iBi2 û+?2HH2 U};m`2 8V 
ûiû KQMiû ¨ HAlh /2 K2bm`2b T?vbB[m2b /2 *H2`KQMi@62``M/X lM T`QD2+iBH2 2M +B2` 
>aa- +vHBM/`B[m2- /2 Kbb2
    H- /2 HQM;m2m`    NN- /2 `vQM     NN 2bi TH+û ¨ H2Mi`û2 /mM2 #Q#BM2 ¨ mM2 
/BbiM+2
 p`B#H2X AH 2bi ++ûHû`û T` +2ii2 #Q#BM2 U`vQM BMiû`B2m`    NN- HQM;m2m`    DN-  
  iQm`b
/mM }H /2 +mBp`2 /2 /BKi`2     NNV [mB 2bi HBK2Miû2 T` mM 2Mb2K#H2 /2 
+QM/2Mbi2m`b +?BKB[m2bX G2b
+QM/2Mbi2m`b bQMi T`ûH#H2K2Mi +?`;ûb T` mM ;ûMû`i2m` +QMiBMm +T#H2 /2 /ûHBp`2` 
/2b i2MbBQMb Dmb[m¨
kyy oX lM i?v`BbiQ` T2`K2i H /û+?`;2 /2b +QM/2Mbi2m`b /Mb H #Q#BM2- H2 KQMi;2 
ûH2+i`B[m2 û[mBpH2Mi m
KQK2Mi /m iB` 2bi bbBKBHû ¨ mM +B`+mBi _G* bû`B2 2M `û;BK2 HB#`2X

6B;m`2 8
kyRd@yj@yk yN,jN,RR

S;2 9fd

oX  SQm`[mQB H2 +QMi+i2m` [mB T2`K2i /2 +QMM2+i2` H2b +QM/2Mbi2m`b ¨ H #Q#BM2 
M2 T2mi@BH i`2 mM bBKTH2
BMi2``mTi2m` \
oX"  Zm2HH2 bbQ+BiBQM /2 +QM/2Mbi2m`b 7mi@BH +?QBbB` TQm` m;K2Mi2` H +T+Biû /2 
HbbQ+BiBQM , bû`B2
Qm T`HHH2 \ AH 2bi /2KM/û mM2 DmbiB}+iBQM T` mM +H+mH 2z2+imû bm` /2mt 
+QM/2Mbi2m`bX
oX*  G2 T`QD2+iBH2 2bi ;mB/û T` mM im#2 i`MbT`2Mi /2 HQM;m2m`    DN 2M bQ`iB2 
/2 #Q#BM2X .2mt
T?QiQ/BQ/2b U"Sqj9V û+HB`û2b T` mM 7Bb+2m Bbbm /mM Hb2` >2@L2 T2`K2ii2Mi /2 
/ûi2+i2` H2 Tbb;2 /m
T`QD2+iBH2 2M bQ`iB2 /2 #Q#BM2 2i 2M bQ`iB2 /2 im#2X G };m`2 e T`ûb2Mi2 mM 
2ti`Bi /2 H MQiB+2 i2+?MB[m2 /m
+QKTQbMi miBHBbûX

R-3
R-9

wQM2 T?QiQb2MbB#H2
k-e8 KK  k-e8 KK

*`+iû`BbiB[m2b
 T`iB+mHB`2K2Mi /Tiû TQm` /2b TTHB+@
iBQMb /2 9yy MK ¨ RRyy MK
 +QKKmiiBQM `TB/2 UivTB[m2K2Mi ky MbV
 #QBiB2` THbiB[m2 .AG +QKT+i
 Kbb2 TT`QtBKiBp2 , y-R ;
 "Sq j9 afU1Ny3dV , /Tiû ¨ H bQm/m`2
2M T?b2 pT2m` Qm T` `27mbBQM ¨ BM7`@
`Qm;2 UC1.1* H2p2H 9V

6B;m`2 e
oX*XRV G2 +?QBt /m Hb2` 2bi@BH +QMp2M#H2 \
oX*XkV G2 bB;MH /ûHBp`û T` H T?QiQ/BQ/2 m Tbb;2 /m T`QD2+iBH2 ¨ mM2 pBi2bb2 
+QMbiMi2 /2 HQ`/`2 /2
ky KbR 2bi /QMMû };m`2 dX

h2KTb UbV

6B;m`2 d
V AMi2`T`ûi2` [mHBiiBp2K2Mi H 7Q`K2 /m bB;MHX .Bb+mi2` H/û[miBQM /2b 
+`+iû`BbiB[m2b /2 H T?QiQ/BQ/2
"Sqj9 ¨ H /ûi2+iBQM /m Tbb;2 /m T`QD2+iBH2X
#V 1M /û/mB`2 H pH2m` /2 H pBi2bb2 /m T`QD2+iBH2X
oX.  G };m`2 3 T`QTQb2 /2b 2M`2;Bbi`2K2Mib- m +Qm`b /mM T`2KB2` iB` /2bbB- /2 H 
i2MbBQM mt #Q`M2b
/m +QM/2Mbi2m`- /m +Qm`Mi /Mb H2 KQMi;2 2i /m bB;MH mt #Q`M2b /2 H T?QiQ/BQ/2X
oX.XRV A/2MiB}2` +?+mM2 /2b +Qm`#2b c /QMM2` H i2MbBQM /2 +?`;2 /m +QM/2Mbi2m`- 
BMbB [m2 H2 +Qm`Mi
KtBKH /Mb H2 KQMi;2X
oX.XkV 1M 2tTHQBiMi H };m`2 3- /ûi2`KBM2` H pBi2bb2 /m T`QD2+iBH2X
oX.XjV 1M bmTTQbMi mM2 ++ûHû`iBQM mMB7Q`K2 bm` j +K /2 /BbiM+2- 2M /û/mB`2 mM 
Q`/`2 /2 ;`M/2m` /2 H
7Q`+2 KQv2MM2 bm#B2 T` H2 T`QD2+iBH2X
oX.X9V G pH2m` /2 H +T+Biû iQiH2 /2b +QM/2Mbi2m`b miBHBbûb 2bi /2 Rk-8 K6X Zm2H 
2bi H2 `2M/2K2Mi /m
/BbTQbBiB7 \
oX.X8V G2 iB` 2bi 2z2+imû /Mb mM2 TH[m2 /2 TQHvbiv`M2 2ti`m/û /QMi H `ûbBbiM+2 
¨ H +QKT`2bbBQM b2
+?Bz`2 T` mM2 T`2bbBQM KtBKH2 /KBbbB#H2    L1BX S` mM `BbQMM2K2Mi bBKTH2 [m2 
HQM 2tT`BK2`/ûi2`KBM2` mM Q`/`2 /2 ;`M/2m` /2 HûTBbb2m` /2 TQHvbiv`M2 ¨ T`ûpQB` 
TQm` ``i2` H2 T`QD2+iBH2X

kyRd@yj@yk yN,jN,RR

S;2 8fd

jy of/Bp
Ryy f/Bp
R of/Bp
R of/Bp

h2KTb UKbV

6B;m`2 3
98y b
jy of/Bp
8y f/Bp
R of/Bp

h2KTb

R Kbf/Bp

6B;m`2 N
oX1 

G };m`2 N T`QTQb2 mM xQQK /2 H2M`2;Bbi`2K2Mi 7Qm`MB };m`2 3X

oX1XRV am` [m2HH2 +Qm`#2 2i /Mb [m2HH2 T`iB2 H2z2i BM/m+iB7 2bi@BH 
T`iB+mHB`2K2Mi pBbB#H2 \
oX1XkV
V .Mb [m2H ivT2 /2 `û;BK2 HB#`2 b2 i`Qmp2 H2 KQMi;2 _G* bû`B2 \
#V .QMM2`- bMb /ûKQMbi`iBQM- H2tT`2bbBQM /2 H +QMbiMi2 /2 i2KTb  /mM +B`+mBi _* 
bû`B2X JK2 [m2biBQM
TQm` H +QMbiMi2 /2 i2KTb  /mM +B`+mBi _G bû`B2X
+V .ûi2`KBM2` H bQHmiBQM /m `û;BK2 HB#`2 /m +B`+mBi _G* /Mb H2 +b +QMbB/û`ûX 
JQMi`2` [m2HH2 2bi +QK#BMBbQM
/2 /2mt i2`K2b [mB i2M/2Mi `2bT2+iBp2K2Mi p2`b H `ûTQMb2 /mM +B`+mBi _G 2i 
+2HH2 /mM +B`+mBi _* ¨ H HBKBi2
Q H2b +QMbiMi2b /2 i2KTb bbQ+Bû2b ¨ +2b /2mt +B`+mBib bQMi i`b /Bzû`2Mi2bX
/V .û/mB`2 /2 H [m2biBQM T`û+û/2Mi2 mM2 BMi2`T`ûiiBQM /2 HHHm`2 /2 H +Qm`#2 /m 
+Qm`MiX
2V § T`iB` /2 H };m`2 N- /ûi2`KBM2` H2b +QMbiMi2b /2 i2KTb +`+iû`BbiB[m2b /m 
bvbiK2X 1M /û/mB`2 H2b pH2m`b
/2  2i /2 X
7V Zm2HH2 2bi H HQM;m2m` /m }H /2 +mBp`2 Mû+2bbB`2 TQm` `ûHBb2` H #Q#BM2 \ 1M 
/û/mB`2 H pH2m` /2 b `ûbBbiM+2X
*QKK2Mi2`X
;V úpHm2` HQ`/`2 /2 ;`M/2m` /2 HBM/m+iM+2 T`QT`2 /mM bQHûMQ/2 /2 HQM;m2m` - 
+QMbiBimû /2  bTB`2b
DQBMiBp2b- 2M Mû;HB;2Mi H2b 2z2ib /2 #Q`/X 1M /û/mB`2 HBM/m+iM+2 T`QT`2 /2 H 
#Q#BM2X *QKK2Mi2` H2 `ûbmHii
Q#i2Mm 2M H2 +QKT`Mi ¨ +2HmB Q#i2Mm ¨ H [m2biBQM 2VX

kyRd@yj@yk yN,jN,RR

S;2 efd

.QMMû2b
++ûHû`iBQM /2 H T2bMi2m`     NT X
am7 K2MiBQM +QMi`B`2- H2b pH2m`b BM/B[mû2b bQMi /QMMû2b ¨ kN3 EX
S`Q/mBi BQMB[m2 /2 H2m ,    X

MO     7X
*QMbiMi2 /2 L2`Mbi ,

S2`Kû#BHBiû K;MûiB[m2 /m pB/2 ,      )N X
*QM/m+iBpBiû /m +mBp`2      4N X
1ti`Bi /m i#H2m Tû`BQ/B[m2 /2b ûHûK2Mib
LmKû`Q iQKB[m2

R

avK#QH2
Jbb2 KQHB`2 iQKB[m2 U;KQHRV

d

3

>

*

L

P

R-yR

Rk-y

R9-y

Re-y

r r r 6AL r r r

kyRd@yj@yk yN,jN,RR

e

S;2 dfd