Centrale Physique 2 PC 2017

S*
9 ?2m`2b

*H+mHi`B+2b miQ`Bbû2b

kyRd

S?vbB[m2 k
AMi2`7û`QKûi`B2 iQKB[m2

G2b QM/2b /2 KiB`2 T2`K2ii2Mi /2 `ûHBb2` /2b 2tTû`B2M+2b /BMi2`7û`QKûi`B2 iQmi 
¨ 7Bi MHQ;m2b ¨ +2HH2b
`2M+QMi`û2b 2M QTiB[m2X PM bBMiû`2bb2 B+B ¨ mM BMi2`7û`QKi`2 /2 J+?@w2?M/2` ¨ 
QM/2b /2 KiB`2 U};m`2 RVX
lM i2H BMi2`7û`QKi`2  ûiû +QMbi`mBi T` /2b +?2`+?2m`b /m G#Q`iQB`2 *QHHBbBQMb- 
;`û;ib- 2i _û+iBpBiû
UG*_V ¨ hQmHQmb2X G bQm`+2 2bi mM D2i bmT2`bQMB[m2 +QHHBKiû /iQK2b /2 HBi?BmK 
d- H2b KB`QB`b 2i HK2b
bûT`i`B+2b bQMi `ûHBbûb ¨ HB/2 /QM/2b HmKBM2mb2b bm` H2b[m2HH2b H2b iQK2b bQMi 
/Bz`+iûb c 2M}M- bm` HmM2
/2b bQ`iB2b /2 HBMi2`7û`QKi`2- mM /ûi2+i2m` K2bm`2 HBMi2MbBiû /m 7Bb+2m iQKB[m2 
`ûbmHiMi /2 HBMi2`7û`2M+2
2Mi`2 H2b QM/2b /2 KiB`2 [mB b2 T`QT;2Mi /Mb H2b /2mt #`b /2 HBMi2`7û`QKi`2X
UJRV

UJkV

UJjV

aQm`+2

.ûi2+i2m`

6B;m`2 R a+?ûK /2 T`BM+BT2 /2 HBMi2`7û`QKi`2 /2 J+?@w2?M/2` ¨ QM/2b /2 KiB`2
UJRV- UJkV 2i UJjV bQMi /2b KB`QB`b THMb c  2i  bQMi H2b 72Mi2b /2 +QHHBKiBQM 
/m D2i bmT2`bQMB[m2 c 
2bi H 72Mi2 /2 /ûi2+iBQM c H /BbiM+2 2Mi`2 /2mt QM/2b biiBQMMB`2b 2bi    NN
G2b +QMbiMi2b T?vbB[m2b miBH2b m T`Q#HK2 BMbB [mmM 7Q`KmHB`2 bQMi /QMMûb 2M }M 
/ûMQM+ûX
G2b p2+i2m`b mMBiB`2b b2HQM - -  bQMi MQiûb  -  -  X

A *`+iû`BbiBQM /2 H bQm`+2 iQKB[m2
G T`Q/m+iBQM /mM2 pT2m` iQKB[m2 b2z2+im2 2M +?mzMi HûHûK2Mi +?BKB[m2 TQm` 
ii2BM/`2 mM2 T`2bbBQM
/2 pT2m` bim`Mi2 bm{bMi2X G2 HBi?BmK vMi mM2 T`2bbBQM /2 pT2m` bim`Mi2 7B#H2 mt 
i2KTû`im`2b
2tTû`BK2MiH2K2Mi ++2bbB#H2b- QM H2 pTQ`Bb2 /Mb mM ;x /`;QM bQmb ?mi2 T`2bbBQM- 
}M /Q#i2MB` mM2
bm`T`2bbBQM THmb BKTQ`iMi2 /Mb H2 7Qm`X G2 KûHM;2 ;x2mt BMbB Q#i2Mm +QMiB2Mi 
KDQ`BiB`2K2Mi /2 H`;QM
2i mM2 7B#H2 T`QTQ`iBQM /2 HBi?BmKX *2 ;x 2bi 2MbmBi2 ++ûHû`û ¨ i`p2`b mM2 
imv`2 /2 HQM;m2m` M2ii2K2Mi
bmTû`B2m`2 ¨ b b2+iBQM U};m`2 kV }M /2 7Q`K2` mM D2i iQKB[m2X PM bQm?Bi2 /Mb 
+2ii2 T`iB2 +`+iû`Bb2` H2
D2i iQKB[m2 BMbB +`ûûX
A(z )
Chambre
a vide

P0 , T 0
Four

z
0

6B;m`2 k a+?ûK /2 H imv`2X PM  `2T`ûb2Miû [m2H[m2b HB;M2b /2 Hû+QmH2K2Mi BMbB 
[m2 H bm`7+2  
T2`T2M/B+mHB`2 mt HB;M2b /2 Hû+QmH2K2MiX

kyRd@yk@kk R8,Ry,jy

S;2 Rfd

PM +QMbB/û`2` H2b ?vTQi?b2b bmBpMi2b ,
 /Mb H2 7Qm`- H2 ;x 2bi ¨ H T`2bbBQM  2i H i2KTû`im`2  c
 QM bmTTQb2 [m2 H2 HB#`2 T`+Qm`b KQv2M /Mb H2 7Qm` 2i /Mb H imv`2 2bi i`b 
BM7û`B2m` m /BKi`2 /2
H imv`2X *2ii2 ?vTQi?b2 T2`K2i /2 /û+`B`2 H2 ~mB/2 +QKK2 mM KBHB2m +QMiBMm 2i 
/miBHBb2` H2b HQBb /2 H
/vMKB[m2 /2b ~mB/2b c
 H2b /Bzû`2Mi2b [mMiBiûb T?vbB[m2b [mB /û+`Bp2Mi Hû+QmH2K2Mi UT`2bbBQM   - 
i2KTû`im`2   - Kbb2 pQHm@
KB[m2   - 2Mi?HTB2 KbbB[m2   - pBi2bb2   V QMi KK2 pH2m` 2M iQmi TQBMi /2 H 
bm`7+2   [mQ++mT2
H2 ~mB/2- T2`T2M/B+mHB`2K2Mi mt HB;M2b /2 Hû+QmH2K2Mi U};m`2 kVX .Mb H K2bm`2 Q 
H2 /BKi`2 /2 H
imv`2 p`B2 H2Mi2K2Mi p2+ - QM bbBKBH2 H bm`7+2   m THM    X *2ii2 TT`QtBKiBQM 
2Mi`BM2
[m2 H2b +QKTQbMi2b i`Mbp2`bH2b /2   bQMi T`iQmi Mû;HB;2#H2b /2pMi H +QKTQbMi2 
/2   b2HQM Ht2  c
 Hû+QmH2K2Mi 2bi bmTTQbû mMB/BK2MbBQMM2H H2 HQM; /2 Ht2 - biiBQMMB`2 2i T`7Bi c
 H2 ;x 2bi bmTTQbû T`7Bi- KQMQiQKB[m2- /2 Kbb2 KQHB`2     LHNPM 2i /2 +Q2{+B2Mi 
/B#iB[m2
   bmTTQbû BM/ûT2M/Mi /2 H i2KTû`im`2 c
 H pBi2bb2 KQv2MM2  /2b iQK2b /Mb H2 7Qm` 2bi Mû;HB;û2 /2pMi H pBi2bb2 /2b 
iQK2b /Mb H2 D2iX

PM MQi2`   - Q  2bi H +QMbiMi2 /2b ;x T`7BibX

PM /QMM2 H2b T`Ki`2b /2 H2tTû`B2M+2 bmBpMib ,
 /BKi`2 /2 +QH /2 H imv`2    ËN c
 i2KTû`im`2 /m ;x /Mb H2 7Qm`    , c
 T`2bbBQM /m ;x /Mb H2 7Qm`    NCBSX
AX 

_ûHBbiBQM /mM D2i bmT2`bQMB[m2

AXXRV Zm2 T2mi@QM /B`2 /m /û#Bi KbbB[m2  /2 +2i û+QmH2K2Mi \ *QKK2Mi 
b2tT`BK2@i@BH 2M 7QM+iBQM /2
  -   2i   X
AXXkV ú+`B`2 H `2HiBQM `2HBMi   -   2i   X 1tT`BK2` H p`BiBQM E /2 H2Mi?HTB2 
KbbB[m2 /m ;x
2M 7QM+iBQM /2 -  2i /2 H p`BiBQM E /2 b i2KTû`im`2X
AXXjV G2b i`Mb72`ib i?2`KB[m2b 2Mi`2 H2 ;x 2i H2b T`QBb /2 H imv`2 bQMi 
Mû;HB;2#H2b- /2 bQ`i2 [m2 H2 ;x
bû+QmH2 b2HQM mM2 i`Mb7Q`KiBQM /B#iB[m2 2i `ûp2`bB#H2X 1M /û/mB`2 mM2 `2HiBQM 
2Mi`2   2i   BMbB
[mmM2 `2HiBQM 2Mi`2 E-   2i EX
AXX9V G2b 7Q`+2b /2 T2bMi2m` ûiMi Mû;HB;û2b /2pMi H2b 7Q`+2b T`2bbMi2b 2t2`+û2b 
bm` H2 ~mB/2- `2HB2` H
pBi2bb2   ¨ H2Mi?HTB2 KbbB[m2   ¨ H TQbBiBQM  2i ¨ H2Mi?HTB2 KbbB[m2  /Mb H2 
7Qm`X
AXX8V PM `TT2HH2 [m2 H +ûHû`Biû /m bQM  /Mb mM ;x 2bi `2HBû2 ¨ b Kbb2 pQHmKB[m2 
 2i b +QKT`2bbB#BHBiû

 T`   
X
Bb2Mi`QTB[m2  

.QMM2` H2tT`2bbBQM /2 H +ûHû`Biû /m bQM /Mb H imv`2   ¨ H#b+Bbb2  2M 7QM+iBQM 
/2 -  2i   X
.Mb H bmBi2- QM MQi2`   H2 `TTQ`i /2 H pBi2bb2 /2b iQK2b /m D2i   bm` H 
+ûHû`Biû /m bQM ¨ H#b+Bbb2
- TT2Hû H2 MQK#`2 /2 J+?

AXXeV § T`iB` /2 H2Mb2K#H2 /2b `2HiBQMb T`û+û/2Mi2b- ûi#HB` H `2HiBQM bmBpMi2- 
+QMMm2 bQmb H2 MQK /2
`2HiBQM /2 >m;QMBQi ,
E

E       

AXXdV Gû+QmH2K2Mi 2bi TT2Hû bm#bQMB[m2- Qm bmT2`bQMB[m2- b2HQM [m2    - Qm    X 
.û/mB`2 /2 H
`2HiBQM /2 >m;QMBQi [m2- TQm` Tbb2` /mM û+QmH2K2Mi bm#bQMB[m2 ¨ mM û+QmH2K2Mi 
bmT2`bQMB[m2- H b2+iBQM /2
H imv`2 /QBi Mû+2bbB`2K2Mi +QKTQ`i2` mM KBMBKmKX Zm2 pmi H2 MQK#`2 /2 J+? ¨ +2i 
2M/`QBi \
AX" 

1biBKiBQM /2b ;`M/2m`b i?2`KQ/vMKB[m2b ¨ HBbbm2 /2 H2tTMbBQM

AX"XRV 1tT`BK2` H i2KTû`im`2   /m ;x 2M 7QM+iBQM /2  -  2i /m MQK#`2 /2 J+?   X 
*QKK2Mi H
i2KTû`im`2 ûpQHm2@i@2HH2 /Mb H /B`2+iBQM  /m D2i \
AX"XkV 1tT`BK2` H /2MbBiû iQKB[m2 /m D2i   2M 7QM+iBQM /2  -  2i /m MQK#`2 /2 
J+?   X SQm`[mQB
T2mi@QM +QMbB/û`2` [m¨ HBbbm2 /2 H T?b2 /2tTMbBQM- HQ`b[m2  2bi bm{bKK2Mi ;`M/- 
H i2KTû`im`2 2i H
pBi2bb2 /2b iQK2b /m D2i MûpQHm2Mi THmbX G2 MQK#`2 /2 J+? ii2BMi ¨ HBbbm2 /2 H 
T?b2 /2tTMbBQM b2` MQiû
T` H bmBi2  X
AX"XjV 1tT`BK2` /2 KK2 H pBi2bb2 /m D2i   2M 7QM+iBQM /2  - -  2i /m MQK#`2 /2 
J+?   X 1M
bmTTQbMi [m2  2bi ;`M/ /2pMi mM2 [mMiBiû [m2 HQM T`û+Bb2`- KQMi`2` [m2 H 
pBi2bb2 ii2BMi2 2M bQ`iB2 /2
H imv`2  M2 /ûT2M/ Tb /2  2i /QMM2` bQM 2tT`2bbBQM 2M 7QM+iBQM /2  -  2i X 
GûpHm2` MmKû`B[m2K2MiX
kyRd@yk@kk R8,Ry,jy

S;2 kfd

AX"X9V PM /QMM2 bm` H };m`2 j H2b `ûbmHiib /2 K2bm`2b /m MQK#`2 /2 J+? i2`KBMH  
Q#i2Mmb T` mM2
2tTû`B2M+2 bBKBHB`2- KBb TQm` /2b T`Ki`2b 2tTû`BK2Mimt /Bzû`2MibX 1M /û/mB`2 
mM2 2biBKiBQM /2 H pH2m`
/2  TQm` H2b T`Ki`2b /2 H2tTû`B2M+2 ûim/Bû2- TmBb /2 H pH2m` /2 H i2KTû`im`2  
ii2BMi2 ¨ HBbbm2
/2 H2tTMbBQMX G?vTQi?b2 7Bi2 ¨ H [m2biBQM T`û+û/2Mi2 2bi@2HH2 pû`B}û2 \
jy

ky

Ry

6B;m`2 j

UN  1B  , V

LQK#`2 /2 J+? ii2BMi ¨ HBbbm2 /2 H2tTMbBQM 2M 7QM+iBQM /2b T`Ki`2b /2 H bQm`+2

AA .Bz`+iBQM /m D2i iQKB[m2 T` mM2 QM/2 biiBQMMB`2
§ HB/2 /mM Hb2` /2 HQM;m2m` /QM/2    ON- QM +`û2 mM2 QM/2 THM2 2i T`Q;`2bbBp2- 
TQH`Bbû2 `2+iBHB;M2@
K2Mi b2HQM  - /2 p2+i2m` /QM/2   2i /2 TmHbiBQM  - [mB b2 T`QT;2 /Mb H 
/B`2+iBQM  X G2 +?KT ûH2+i`B[m2
/2 +2ii2 QM/2 bû+`Bi ,
           DPT     

AAX  PM/2 biiBQMMB`2
GQM/2 Hb2` b2 `û~û+?Bi 2M BM+B/2M+2 MQ`KH2 bm` mM KB`QB` THM bbBKBHû ¨ mM 
KB`QB` KûiHHB[m2 T`7Bi2K2Mi
+QM/m+i2m`- bBimû /Mb H2 THM    X
       TJO      X
JQMi`2` [m2 H2 +?KT ûH2+i`B[m2 /2 HQM/2 biiBQMMB`2 `ûbmHiMi2 bû+`Bi 
S`û+Bb2` H2tT`2bbBQM /2   2M 7QM+iBQM /2  -  - 2i  X
AAX"  LQiBQM /2 TQi2MiB2H HmKBM2mt
PM bBMiû`2bb2 /#Q`/ ¨ HBMi2`+iBQM /2 +2ii2 QM/2 biiBQMMB`2 p2+ H2b iQK2b /2 
HBi?BmKX GQ`b[mBHb TûMi`2Mi
 H2b iQK2b b2 TQH`Bb2MiX GQ`b[m2 H TmHbiBQM  2bi i`b ûHQB;Mû2 /2b
/Mb H xQM2 Q `;M2 H2 +?KT `ûbQMM+2b iQKB[m2b- H2b /BTH2b BM/mBib Qb+BHH2Mi ¨ H 
TmHbiBQM  /m Hb2` 2t+Bii2m` 2i 2M T?b2 p2+ HmB ,
 Q  2bi H TQH`Bb#BHBiû /2 HiQK2 /2 HBi?BmKX .Mb H2b
H2 /BTH2 iQKB[m2 BM/mBi bû+`Bi HQ`b     
Q       $N 2bi mM2
+QM/BiBQMb /2 H2tTû`B2M+2 UHb2` ?Q`b /2 `ûbQMM+2V- QM    
 
+QMbiMi2 +`+iû`BbMi H2 /BTH2 /2 HiQK2 /2 HBi?BmK 2i Q      2bi Hû+`i 2Mi`2 H 
TmHbiBQM Hb2` 
2i H TmHbiBQM  /2 H i`MbBiBQM iQKB[m2 H THmb T`Q+?2X G2 +?KT HmKBM2mt BMi2`;Bi 
p2+ H2 /BTH2 iQKB[m2
 
 [mBH BM/mBi pB mM2 ûM2`;B2 TQi2MiB2HH2      TT2Hû2 TQi2MiB2H HmKBM2mtX

AAX"XRV JQMi`2` [m2 H KQv2MM2 i2KTQ`2HH2 /2 +2 TQi2MiB2H HmKBM2mt bû+`Bi bQmb H 
7Q`K2
        DPT    

AAX"XkV 1tT`BK2`  2i  2M 7QM+iBQM /2b T`Ki`2b /m T`Q#HK2X
AAX*  ú[miBQM /2 T`QT;iBQM /2 HQM/2 /2 KiB`2
lM D2i bmT2`bQMB[m2 /2 HBi?BmK b2 T`QT;2 /Mb H2 THM  ¨ mM2 pBi2bb2    NT 2i 
i`p2`b2 HQM/2
HmKBM2mb2 biiBQMMB`2 ;ûMû`û2 T` mM KB`QB` UJV U};m`2 9VX lM iQK2 /2 HBi?BmK 2bi 
bbBKBHû ¨ mM T[m2i /QM/2b
/2 KiB`2 /û+`Bi T` b 7QM+iBQM /QM/2     /QMi H2 KQ/mH2 m +``û /QMM2 H /2MbBiû 
/2 T`Q
T`ûb2M+2 /2 HiQK2 /Mb H2bT+2 ¨ i`QBb /BK2MbBQMbX PM bBMiû`2bb2 B+B 
2t+HmbBp2K2Mi m T`Q+2bbmb ûHbiB[m2 /2
/BzmbBQM /2b iQK2b T` HQM/2 HmKBM2mb2 biiBQMMB`2- /2 bQ`i2 [m2 HûM2`;B2 /2 
HiQK2 T2mi i`2 +QMbB/û`û2
+QKK2 }tû2 2i û;H2 ¨ bQM ûM2`;B2 +BMûiB[m2 BM+B/2Mi2  X G T`iB2 bTiBH2    /2 b 
7QM+iBQM /QM/2 Q#ûBi
HQ`b ¨ Hû[miBQM /2 a+?`/BM;2`

kyRd@yk@kk R8,Ry,jy

S;2 jfd

¨ HBMiû`B2m` /2 HQM/2 biiBQMMB`2 U    V
¨ H2tiû`B2m` /2 HQM/2 biiBQMMB`2 U   Qm   V

Q       LH 2bi H Kbb2 /2 HiQK2 /2 HBi?BmK d 2i  bQM ûM2`;B2 iQiH2- û;H2 ¨ bQM 
ûM2`;B2 +BMûiB[m2
BM+B/2Mi2X
AAX*XRV _TT2H2` H2tT`2bbBQM /2 H HQM;m2m` /QM/2 /2 /2 "`Q;HB2  /2 HiQK2 
BM+B/2Mi 2i HûpHm2` MmKû@
`B[m2K2Mi /Mb H2 +b T`ûb2MiX
AAX*XkV PM bbBKBH2 H2 T[m2i /QM/2 iQKB[m2 BM+B/2Mi ¨ mM2 QM/2 THM2 /2 p2+i2m` 
/QM/2   X _2HB2`   ¨ H
[mMiBiû /2 KQmp2K2Mi /2 HiQK2   2i 2M /û/mB`2 H2tT`2bbBQM /2 bQM ûM2`;B2  X 
GûpHm2` MmKû`B[m2K2MiX
PM bmTTQb2` /Mb H bmBi2 [m2 H T`Q7QM/2m`  /m TQi2MiB2H HmKBM2mt 2bi #2m+QmT 
THmb 7B#H2 [m2 HûM2`;B2
 /2 HiQK2X
AAX*XjV ú+`B`2 Hû[miBQM /2 T`QT;iBQM- /Mb mM KBHB2m /BM/B+2   - /mM2 QM/2 
HmKBM2mb2      /2
p2+i2m` /QM/2 /Mb H2 pB/2  2i /2 TmHbiBQM X

AAX*X9V 1M /û/mB`2 [m2 H T`QT;iBQM /2 HQM/2 /2 KiB`2 ¨ HBMiû`B2m` /2 HQM/2 
biiBQMMB`2 2bi `û;B2 T` mM2
û[miBQM bBKBHB`2 ¨ +2HH2 /mM2 QM/2 HmKBM2mb2 /Mb mM KBHB2m /BM/B+2   KQ/mHû 
Tû`BQ/B[m2K2MiX Zm2H 2bi
H2 Tb  /2 +2 `ûb2m /BM/B+2 \ GûpHm2` MmKû`B[m2K2MiX .QMM2` H2tT`2bbBQM /2 
HKTHBim/2  /2 KQ/mHiBQM
/2 HBM/B+2 2M 7QM+iBQM /2  2i  X
AAX*X8V PM û+`Bi Hû[miBQM /2 T`QT;iBQM /2 HQM/2 /2 KiB`2 ¨ HBMiû`B2m` /2 HQM/2 
biiBQMMB`2 bQmb H
7Q`K2 bmBpMi2

1tT`BK2`  2M 7QM+iBQM /2  2i  X

     DPT    

UAAXRV

UJV

6B;m`2 9 _ûb2m HmKBM2mt /2 Tb  2i /ûTBbb2m` 

AAX.  _ûbQHmiBQM /2 Hû[miBQM /2 T`QT;iBQM
G2 7Bb+2m HmKBM2mt [mB +`û2 HQM/2 biiBQMMB`2 2bi HBKBiû i`Mbp2`bH2K2Mi T` mM 
/BT?`;K2 /2 `vQM
   NNX G2 `ûb2m HmKBM2mt bm` H2[m2H pQMi b2 /Bz`+i2` H2b QM/2b iQKB[m2b  /QM+ 
mM2 ûTBbb2m`   
U};m`2 9VX .2mt 72Mi2b i`b }M2b- /2 H`;2m`   ËN- bQMi TH+û2b H2 HQM; /m D2i 
bmT2`bQMB[m2- /2 KMB`2 ¨
bûH2+iBQMM2` i`b T`û+BbûK2Mi HM;H2 /BM+B/2M+2  /2b iQK2b bm` H2 `ûb2m HmKBM2mt 
UHQ`B2MiiBQM /2 HM;H2
 2bi T`û+Bbû2 bm` H };m`2 9VX .Mb +2b +QM/BiBQMb- QM KQMi`2 [m2 b2mH2b /2mt 
QM/2b THM2b b2 T`QT;2Mi
bBKmHiMûK2Mi /Mb H2 `ûb2m HmKBM2mt , HQM/2 BM+B/2Mi2    /KTHBim/2   2i /2 
p2+i2m` /QM/2   - 2i
HQM/2 /Bz`+iû2    /KTHBim/2   2i /2 p2+i2m` /QM/2        Q    2i Q     
+`+iû`Bb2 H Tû`BQ/B+Biû /m `ûb2m HmKBM2mt 2i 2bi +?QBbB B+B /2 KK2 b2Mb [m2 H2 
p2+i2m` /QM/2   /2 HQM/2
Hb2` BM+B/2Mi2 bm` H2 KB`QB` UJVX PM +QMbB/`2 /Mb H bmBi2 H2 +b   X
AAX.XRV JQMi`2` [m2 H +QMb2`piBQM /2 HûM2`;B2 +BMûiB[m2 /2 HiQK2- 2Mi`2 bQM 
2Mi`û2 /Mb H2 `ûb2m 2i
b bQ`iB2 /Mb HQ`/`2    /2 /Bz`+iBQM- BKTHB[m2 mM2 +2`iBM2 `2HiBQM [m2 HQM 
2tTHB+Bi2` 2Mi`2 HM;H2
/BM+B/2M+2  - H2 Tb  /m `ûb2m 2i H HQM;m2m` /QM/2 /2 /2 "`Q;HB2  /2 HiQK2X
AAX.XkV úpHm2` MmKû`B[m2K2Mi HM;H2 /BM+B/2M+2- MQiû  - [mB biBb7Bi +2ii2 
`2HiBQMX
AAX.XjV Zm2H M;H2 7Bi H2 7Bb+2m /Bz`+iû p2+ Ht2  /Mb +2b +QM/BiBQMb \ 6B`2 mM 
b+?ûK BHHmbi`Mi H
/BbTQbBiBQM `2HiBp2 /2b i`Bib /m `ûb2m 2i /2b p2+i2m`b /QM/2   -   2i   X
AAX.X9V PM +?2`+?2 H2b bQHmiBQMb /2 Hû[miBQM /2 T`QT;iBQM UAAXRV bQmb H 7Q`K2
  F 

  F 

V Zm2 `2T`ûb2Mi2 T?vbB[m2K2Mi +?+mM /2b i2`K2b /2 +2ii2 bQHmiBQM \

kyRd@yk@kk R8,Ry,jy

S;2 9fd

#V 1M miBHBbMi +2ii2 2tT`2bbBQM- B/2MiB}2` /Mb Hû[miBQM /2 T`QT;iBQM H2b i2`K2b 
[mB b2 T`QT;2Mi p2+ H2b
p2+i2m`b /QM/2   2i   X PM T2Mb2` TQm` +2H ¨ /ûp2HQTT2` H2 i2`K2 2M DPT     
bQmb H 7Q`K2 /2 /2mt
QM/2b THM2b /2 p2+i2m`b /QM/2   2i   X 1M /û/mB`2 [m2 H2b KTHBim/2b   2i   
biBb7QMi mt /2mt
û[miBQMb /Bzû`2MiB2HH2b +QmTHû2b bmBpMi2b- Q       ,

 E 
 E 
 E 

 E 

E
  F  
E
E
J    F  
E

J

AAX.X8V PM BKTQb2 H2b +QM/BiBQMb mt HBKBi2b       2i      X 1M T`û+Bb2` H 
bB;MB}+iBQM
T?vbB[m2X Zm2 `2T`ûb2Mi2  \
AAX.XeV PM bmTTQb2 [m2 H2b KTHBim/2b /2b /2mt QM/2b bQMi H2Mi2K2Mi p`B#H2b ¨ 
Hû+?2HH2 /2  X CmbiB}2`
[m2 +2H T2`K2i /2 Mû;HB;2` H2b /û`Bpû2b b2+QM/2b /Mb H2 bvbiK2 /û[miBQMb 
+QmTHû2b +B@/2bbmbX
E 
    X
AAX.XdV 1M /û/mB`2 [m2 HKTHBim/2   biBb7Bi ¨ mM2 û[miBQM /Bzû`2MiB2HH2 /2 H 
7Q`K2
E 
1tTHB+Bi2` H +QMbiMi2 TQbBiBp2  2M 7QM+iBQM /2  2i DPT  X
AAX.X3V _ûbQm/`2 +2ii2 û[miBQM /Bzû`2MiB2HH2 2M miBHBbMi H2b +QM/BiBQMb mt 
HBKBi2b T`û+Bbû2b 2M AAX.X8VX

AAX.XNV 1M /û/mB`2 H2tT`2bbBQM /2   2i +2HH2b /2b QM/2b THM2b    2i    2M 
bQ`iB2 /QM/2 biiBQMMB`2+2bi@¨@/B`2 TQm`   X *QKK2Mi2` +2b bQHmiBQMbX 
GTT`QtBKiBQM /2b KTHBim/2b H2Mi2K2Mi p`B#H2b pQmb
b2K#H2@i@2HH2 DmbiB}û2 B+B \
AAX.XRyV PM BMi`Q/mBi H2b +Q2{+B2Mib /2 i`MbKBbbBQM     2i /2 /Bz`+iBQM ¨ 
HQ`/`2   -     i2Hb [m2 H2b QM/2b    2i    bû+`Bp2Mi /Mb H xQM2   
       F 

       F 

2i

JQMi`2` [m2
   DPT 

2i

   J TJO  F 

Q 
 /ûbB;M2 H TQbBiBQM /m KB`QB` UJVX
AAX.XRRV 1M /û/mB`2 H2tT`2bbBQM /2 H2{++Biû /2 /Bz`+iBQM X Zm2HH2 pH2m` KtBKH2 
T2mi@2HH2 ii2BM/`2 2M
i?ûQ`B2 \
AAX.XRkV SmBbbM+2 Hb2`
V _TT2H2` H2tT`2bbBQM /2 Hû+HB`2K2Mi U~mt /m p2+i2m` /2 SQvMiBM; ¨ i`p2`b mM2 
bm`7+2 mMBiûV bbQ+Bû ¨
mM2 QM/2 HmKBM2mb2 /QMi H2 +?KT ûH2+i`B[m2 bû+`Bi  DPT       X

#V 1M /û/mB`2 H2tT`2bbBQM /2 H pH2m` H THmb 7B#H2 /2 H TmBbbM+2  /m Hb2` [mB 
T2`K2i /ii2BM/`2 H2{++Biû
/2 /Bz`+iBQM KtBKH2 /Mb HQ`/`2   X úpHm2` +2ii2 TmBbbM+2 MmKû`B[m2K2Mi TQm` mM 
Hb2` /û+Hû 2M
7`û[m2M+2 T` `TTQ`i ¨ H `B2 iQKB[m2 H THmb T`Q+?2 /2 H [mMiBiû     ()[X 
G?vTQi?b2   
pQmb b2K#H2@i@2HH2 pH#H2 \
+V Zm2HH2 2bi H TmBbbM+2 Hb2` KBMBKmK Mû+2bbB`2 TQm` ii2BM/`2 mM2 2{++Biû /2 
/Bz`+iBQM /2 8yW \
AAX.XRjV am` [m2HUbV mi`2UbV T`Ki`2UbV T2mi@QM DQm2` 2M T`iB[m2 TQm` ii2BM/`2 
H2{++Biû /2 /Bz`+iBQM
KtBKH2 \

6B;m`2 8 _ûb2m HmKBM2mt /Mb H2[m2H   
PM KQMi`2`Bi /2 H KK2 7ÏQM [m2- /Mb H bBimiBQM bvKûi`B[m2 /û+`Bi2 T` H };m`2 8 
U/Mb H[m2HH2 H
+QKTQbMi2 /2   b2HQM  2bi Mû;iBp2 ,         TJO  V- H2b QM/2b i`MbKBb2  
U+Q``2bTQM/Mi ¨   V
2i /Bz`+iû2  U+Q``2bTQM/Mi HQ`b ¨   V bû+`Bp2Mi /Mb H xQM2   
       F 

2i

p2+    J TJO  F 
X

kyRd@yk@kk R8,Ry,jy

S;2 8fd

       F 

AAA AMi2`7û`QKi`2 /2 J+?@w2?M/2`
PM `ûHBb2 mM BMi2`7û`QKi`2 /2 J+?@w2?M/2` ¨ QM/2b /2 KiB`2 2M miBHBbMi i`QBb 
QM/2b biiBQMMB`2b /BbiMi2b
2Mi`2 2HH2b /2 H /BbiM+2  U};m`2 RVX *2b i`QBb QM/2b biiBQMMB`2b bQMi +`ûû2b ¨ 
T`iB` /2 H KK2 bQm`+2 Hb2` /2
HQM;m2m` /QM/2    ONX PM  Dmbiû H2b T`Ki`2b /2 H2tTû`B2M+2 /2 bQ`i2 [m2 H2b 
T`2KB`2 2i i`QBbBK2
QM/2b biiBQMMB`2b QMi- +?+mM2- mM2 2{++Biû /2 /Bz`+iBQM /2 8yW- iM/Bb [m2 H 
/2mtBK2 QM/2 biiBQMMB`2
/Bz`+i2 p2+ mM2 2{++Biû /2 RyyWX G2 D2i KQMQ+BMûiB[m2  TQm` p2+i2m` /QM/2   X 
PM MQi2 
 - 
 2i 

H2b TQbBiBQMb /2b i`QBb KB`QB`b T2`K2iiMi /2 +`û2` H2b QM/2b biiBQMMB`2bX G2b 
i`QBb KB`QB`b bQMi `B;Qm`2mb2K2Mi
T`HHH2b 2Mi`2 2mt- 2i T2`T2M/B+mHB`2b ¨ H /B`2+iBQM  X PM MQi2 /QM+   H2 
p2+i2m` /QM/2 +QKKmM mt
i`QBb `ûb2mt HmKBM2mt- 2M /û}MBbbMi bQM b2Mb /Q`B2MiiBQM b2HQM H /B`2+iBQM /2 
T`QT;iBQM /2b QM/2b Hb2`
BM+B/2Mi2b UpQB` [m2biBQM AAX.VX 1M}M QM MQi2   H2b +Q2{+B2Mib /2 i`MbKBbbBQM 
2i /2 /Bz`+iBQM /2 HQM/2
iQKB[m2 BM+B/2Mi2 ¨ HQ`/`2     T` HQM/2 biiBQMMB`2 X lM2 72Mi2 /2 /ûi2+iBQM- 
i`b }M2- 2bi bBimû2 2M
X 1HH2 T2`K2i- 2M bQ`iB2 /BMi2`7û`QKi`2- /2 bûH2+iBQMM2` H pQB2 /2 bQ`iB2 bm` 
H[m2HH2 QM K2bm`2 HBMi2`7û`2M+2
2Mi`2 H2b QM/2b /2 KiB`2  2i  [mB QMi T`+Qm`m `2bT2+iBp2K2Mi H2 #`b /m ?mi 
Ui`D2i  V 2i +2HmB /m
#b Ui`D2i  VX G 72Mi2- Q`B2Miû2 b2HQM  -  mM2 H`;2m` /2 8y K b2HQM  2i mM2 
?mi2m`     NN
b2HQM  X
PM MQi2` 
 - 
  - w- H2b TQbBiBQMb /2b TQBMib -  - w
AAAX  aB;MH /2 bQ`iB2 /2 HBMi2`7û`QKi`2
AAAXXRV § [m2Hb +QKTQbMib QTiB[m2b H2b i`QBb QM/2b biiBQMMB`2b bQMi@2HH2b 
û[mBpH2Mi2b- /m TQBMi /2 pm2 /2
H2m` +iBQM bm` H2b QM/2b /2 KiB`2 +QMbB/û`û2b /Mb +2 T`Q#HK2 \ CmbiB}2` pQi`2 
`ûTQMb2X
AAAXXkV 1tT`BK2`  2i  +QKK2 /2b T`Q/mBib /KTHBim/2b   - /2  UKTHBim/2 /2 HQM/2 
THM2 BM+B/2Mi2
2M 2Mi`û2 /BMi2`7û`QKi`2V 2i /2 7+i2m`b /2 T?b2 [mQM 2tT`BK2` 2M 7QM+iBQM /2   
-   2i /2b TQbBiBQMb /2b
TQBMib -  -  -  2i X
PM TQm`` MQi2`    F 2i    F Q  2i  bQMi H2b KTHBim/2b `û2HH2b 2i  2i  H2b T?b2b 
/2b
/2mt 7QM+iBQMb /QM/2X
AAAXXjV 1M /û/mB`2 [m2 H2 MQK#`2 /iQK2b /ûi2+iûb ¨ i`p2`b H 72Mi2 /2 /ûi2+iBQM 
bû+`Bi bQmb H 7Q`K2

DPT  

Q QM 2tTHB+Bi2`  2M 7QM+iBQM /2   - 
 - 
 2i 
 X
AAAXX9V 1tTHB[m2` T`û+BbûK2Mi +2 [mQM Q#b2`p2 bm` H2 /ûi2+i2m` HQ`b[mQM /ûTH+2 
H2 KB`QB` UJjV H2 HQM; /2
Ht2  \
AAAXX8V P#b2`p2@i@QM 2t+i2K2Mi H KK2 +?Qb2 bB +2bi H2 KB`QB` UJkV [m2 HQM 
/ûTH+2 H2 HQM; /2 Ht2  \
1tTHB[m2` pQi`2 `ûTQMb2X
AAAX"  TTHB+iBQM ¨ H K2bm`2 /mM2 pBi2bb2 /2 `QiiBQM
PM T`2M/ /ûbQ`KBb 2M +QKTi2 H `QiiBQM /2 H h2``2 bm` 2HH2@KK2X GBMi2`7û`QKi`2- 
bBimû ¨ hQmHQmb2 UHiBim/2
9j-eêV- 2bi ?Q`BxQMiH /2 bQ`i2 [m2 H p2`iB+H2 b+2M/Mi2 HQ+H2 2bi Q`B2Miû2 b2HQM 
 X PM MQi2  H2 `û7û`2MiB2H
}t2 U/QMi H2b t2b M2 iQm`M2Mi Tb p2+ H h2``2V [mB +QM+B/2 p2+ +2HmB /m 
H#Q`iQB`2 U};m`2 RV ¨ HBMbiMi
 Q HiQK2 2Mi`2 /Mb HBMi2`7û`QKi`2- m TQBMi X G2b KB`QB`b bQMi }t2b /Mb H2 
`û7û`2MiB2H /m H#Q`iQB`2BHb bQMi /QM+ 2M KQmp2K2Mi /Mb  X PM T2mi Mû;HB;2` H2m` 
`QiiBQM T2M/Mi H2 i2KTb /2 Tbb;2 /mM iQK2
/Mb HBMi2`7û`QKi`2- /2 bQ`i2 [mQM /K2i [m2 H2 /ûTH+2K2Mi /2b KB`QB`b /Mb H2 
`û7û`2MiB2H  b2 HBKBi2 ¨ mM2
i`MbHiBQMX PM MQi2   H TQbBiBQM /m KB`QB`  U  \  ^V /Mb H2 `û7û`2MiB2H  b2HQM 
Ht2  ¨ HBMbiMi 
2i   H +QKTQbMi2 /2 b pBi2bb2 b2HQM +2 KK2 t2X PM bmTTQb2 iQmDQm`b [m2 H2b 
i`QBb QM/2b biiBQMMB`2b
bQMi `B;Qm`2mb2K2Mi T`HHH2bX
AAAX"XRV 1tT`BK2` H T?b2  2M 7QM+iBQM /2b #b+Bbb2b  /2b KB`QB`b mt /Bzû`2Mib 
BMbiMib  -  -  Q
HiQK2 i`p2`b2 H2b QM/2b biiBQMMB`2bX
AAAX"XkV PM MQi2`   - Q    NT 2bi H pBi2bb2 /m D2i 2i    NN 2bi H /BbiM+2 2Mi`2 
H2b
QM/2b biiBQMMB`2bX
JQMi`2` T` mM /ûp2HQTT2K2Mi HBKBiû m T`2KB2` Q`/`2 2M  [m2

UAAAXRV

Q QM 2tTHB+Bi2` H [mMiBiû   X Zm2 `2T`ûb2Mi2 T?vbB[m2K2Mi H2 T`2KB2` i2`K2 /2 
+2 /ûp2HQTT2K2Mi \ PM
bmTTQb2` /Mb H bmBi2 [m2    X
AAAX"XjV 1tT`BK2` H bûT`iBQM   
   2Mi`2 H2b /2mt #`b /2 HBMi2`7û`QKi`2- m MBp2m /2 H /2mtBK2
QM/2 biiBQMMB`2- 2M 7QM+iBQM /2  2i  - 2i 2M /û/mB`2 HB`2  /2 HBMi2`7û`QKi`2X 
úpHm2` MmKû`B[m2K2Mi +2b
/2mt [mMiBiûbX

kyRd@yk@kk R8,Ry,jy

S;2 efd

AAAX"X9V JQMi`2` [m2  b2tT`BK2 bQmb H 7Q`K2

Q  2bi H pBi2bb2 /2 `QiiBQM /m `û7û`2MiB2H /m H#Q`iQB`2 miQm` /2 Ht2 X *2ii2 
b2MbB#BHBiû ¨ H pBi2bb2 /2
`QiiBQM /m `û7û`2MiB2H 2bi +2 [mQM TT2HH2 H2z2i a;M+X
AAAX"X8V 1M THmb /2 H `QiiBQM /2 H h2``2- H THi2@7Q`K2 bm` H[m2HH2 bQMi 
++`Q+?ûb H2b KB`QB`b T2mi iQm`M2`T` 2t2KTH2 ¨ +mb2 /2 pB#`iBQMb 2M `QiiBQMX G2 
bB;MH /2 HBMi2`7û`QKi`2 2bi b2MbB#H2 ¨ +2b ~m+imiBQMb /2 H
pBi2bb2 /2 `QiiBQMX PM TQbBiBQMM2 H2 KB`QB` UJjV /2 bQ`i2 [m2 +2b ~m+imiBQMb 
BM/mBb2Mi mM2 p`BiBQM KtBKH2

  DPT  2M bQ`iB2 /2 HBMi2`7û`QKi`2X
/m bB;MH MQ`KHBbû  

E
1tT`BK2` H b2MbB#BHBiû 
 /2 HBMi2`7û`QKi`2 /Mb +2b +QM/BiBQMb 2i HûpHm2` MmKû`B[m2K2MiX
E
AAAX"XeV úpHm2` MmKû`B[m2K2Mi  ¨ H HiBim/2 /2 hQmHQmb2X aB QM bmTTQb2 [m2 H2 
/ûi2+i2m` 2bi +T#H2 /2
K2bm`2` mM2 p`BiBQM /2 RW /m bB;MH MQ`KHBbû- H2 /BbTQbBiB7 ûim/Bû T2`K2i@BH /2 
K2bm`2` H pBi2bb2 /2 `QiiBQM
/2 H h2``2 \
AAAX"XdV Zm2H b2`Bi HBMiû`i /2 `H2MiB` H2b iQK2b /m D2i \

.QMMû2b
     )N

S2`Kû#BHBiû K;MûiB[m2 /m pB/2

      'N

S2`KBiiBpBiû /m pB/2

      $

*?`;2 ûHûK2MiB`2

      NPM

*QMbiMi2 /pQ;/`Q

      +,

*QMbiMi2 /2 "QHixKMM

       +, NPM

*QMbiMi2 /2b ;x T`7Bib

      +T

      NT

*QMbiMi2 /2 SHM+F
*QMbiMi2 /2 SHM+F `û/mBi2
oBi2bb2 /2 H HmKB`2 /Mb H2 pB/2

6Q`KmHB`2
DPT 

DPT    DPT

DPT   DPT    TJO

TJO

DPT

r r r 6AL r r r

kyRd@yk@kk R8,Ry,jy

S;2 dfd