E_2+?, hQQH 7Q` _2+?#BHBiv BM S2i`B L2ib
9yd
h?2 T`Q+2/m`2 `2pQHp2b `QmM/ :2M2`HBx2/ oaa U:oaaV- M 2ti2MbBQM Q7
oaaX :oaa G Bb b2[m2M+2 (C 1 , .., C n )- Q7 oaab MMQii2/ rBi? K2i/iKQbi MQi#Hv +QMbi`BMib QM i?2B` 2Mi`v M/ 2tBi +QM};m`iBQMbX h?2 2tBi bii2
Q7 C i Bb /DQBM2/ iQ i?2 2Mi`v bii2 Q7 C i+1 #v i`MbBiBQMX _2+?#BHBiv BM
Qm` Q`B;BMH oaa V Bb BKTHB2/ #v `2+?#BHBiv BM M BM/m+2/ :oaa G(V )-
bBM;H2iQM b2[m2M+2 r?2`2 r2 +QMbi`BM i?2 2Mi`v M/ 2tBi +QM};m`iBQMb b #2BM;
2[mH iQ Qm` BMBiBH m 0 M/ i`;2i mX 6B;m`2 R ;Bp2b M 2tKTH2X
AM QmiHBM2- EQb`DmǶb H;Q`Bi?K QT2`i2b b 7QHHQrbX i 2+? bi2T- ;Bp2M
bi`QM;Hv@+QMM2+i2/ :oaa G,
Ĝ 2Bi?2` G 7mH}Hb θc
Ĝ Q` G pBQHi2b θ- BM r?B+? +b2 r2 +M `2}M2 G BMiQ }MBi2 UTQbbB#Hv 2KTivV
b2i Q7 KQ/B}2/ :oaabX
h?Bb T`Q/m+2b }MBi2Hv@#`M+?BM; i`22 Q7 :oaab BM r?B+? 2p2`v #`M+?
7Q`Kb bi`B+iHv /2b+2M/BM; +?BM rBi? `2bT2+i iQ r2HH@[mbB@Q`/2`BM; (kR)X h?2
H;Q`Bi?K i?2`27Q`2 Hrvb i2`KBMi2b- M/ m Bb `2+?#H2 7`QK m 0 BM i?2 `QQi
:oaa G B7 M/ QMHv B7 bQK2 :oaa BM i?2 i`22 biBb}2b θX
h?2 θ *QM/BiBQM EQb`DmǶb KBM T`2/B+i2 +QKT`Bb2b irQ T`ibX θ 1 Bb ;HQ#H
T`QT2`iv Q7 i?2 bvbi2K- r?BH2 θ 2 Kmbi ?QH/ 7Q` 2+? +QKTQM2MiX
θ 1 , h?2`2 2tBbi Tb2m/Q@`mMb i?`Qm;? i?2 :oaa r?B+? mb2 2p2`v 2/;2 BM 2p2`v
+QKTQM2Mi mM#QmM/2/Hv KMv iBK2b- M/ iiBM mM#QmM/2/Hv H`;2 pHm2b 7Q`
2p2`v mM+QMbi`BM2/ +QQ`/BMi2 U?2`2 Tb2m/Q@`mM Bb `mM Qp2` Z
d `i?2` i?M
Qp2` N
d VX h?Bb +QM/BiBQM +M #2 7Q`KmHi2/ b M BMi2;2` HBM2` T`Q;`KKBM;
T`Q#H2KX 6`QK i?Bb r2 Q#iBM b2KBHBM2` b2i Q7 p2+iQ`b Q7 p`B#H2b `2T`2b2MiBM;
+QmMib Q7 i`MbBiBQM Q++m``2M+2b M/ pHm2b Q7 mM+QMbi`BM2/ +QQ`/BMi2bX A7 i?2`2
Bb MQ #QmM/2/ p`B#H2 i?2M θ 1 ?QH/bX Pi?2`rBb2- QM2 bm+? #QmM/2/ p`B#H2 Bb
dz`2}M2/Ǵ #v 2Bi?2` +QMbi`BMBM; i?2 bbQ+Bi2/ +QQ`/BMi2Ƕb pHm2 Q` #v mM7QH/BM;
i?2 bbQ+Bi2/ i`MbBiBQMX 6Q` 2tKTH2- r2 Kv /2/m+2 i?i i?2 MmK#2` Q7 }`BM;b
Q7 t 0 M2p2` 2t+22/b 1 BM Qm` 2tKTH2 :oaa G ex c r2 ;2M2`i2 i?2 `2}M2K2Mib
b BM 6B;m`2 kX
q
1, 0
r
0, 0
[0, −1]
UV _2}M2K2Mi r?2M t0 Bb +iBpi2/ 0 iBK2bX
q
1, 0
q
r
0, 0
[−1, 1]
[0, −1]
U#V _2}M2K2Mi r?2M t0 Bb +iBpi2/ 1 iBK2X
6B;X k, _2}M2K2Mi Q7 G ex #v `2KQpBM; #QmM/2/ i`MbBiBQM t 0 X
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