Instabilities and optimization of elastic structures interacting with laminar flows
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(4) _2K2`+B2K2Mib CǶ BK2` Bb /Ƕ #Q`/ `2K2`+B2` H2b K2K#`2b /m Dm`vX J2`+B ¨ . pB/ 6 #`2 2i ¨ 6` MÏQBb : HH B`2 /Ƕ pQB` T`Bb H2 i2KTb /Ƕ2t KBM2` K2b i` p mt- ¨ 1KK Mm2H /2 G M;`2 /Ƕ pQB` /2 THmb ++2Tiû /2 T`ûbB/2` H2 Dm`v ě 2i TQm` H /û/B+ +2 5 CǶ B ûiû i`ĕb ?QMQ`û T ` pQi`2 T`ûb2M+2X J2`+B #2 m+QmT ¨ J ii?2r CmMBT2` 2i ¨ h?QK b qB+F /Ƕ pQB` ++2Tiû H HQm`/2 i+?2 /2 `2HB`2 +2 K Mmb+`Bi 2z2+@ iBp2K2Mi Ŀ T b BM}MBK2Mi /B;2bi2 ŀ U: HH B`2- kyRNVX oQb /2mt b2MbB#BHBiûb +QKTHûK2Mi B`2b QMi D2 +`QBb T2`KBb /2 +Qmp`B` m KB2mt H2b i?ûK iB[m2b #Q`/û2b / Mb +2ii2 i?ĕb2X J2`+B ¨ .2MBb aBTT /Ƕ pQB` ++2Tiû /Ƕ2M bbmK2` H /B`2+iBQM ě 2i /2 KǶ pQB` b mpû T ` H¨ KāK2 /2 #B2M /2b i` + b /KBMBbi` iB7bX m@/2H¨ /2 +2H - H [m HBiû /2 H bQmi2M M+2 /QBi #2 m+QmT ¨ i2b +QKK2Mi B`2b T2`iBM2Mib HQ`b /2 H `ûTûiBiBQM- 2i iQmi2 +2ii2 p2Mim`2 /QBi }M H2K2Mi #2 m+QmT ¨ iQM +Qm`b /2 J bi2` bm` H2 +QMi`ƬH2 /Ƕû+QmH2K2Mi- [mB KǶ p Bi HBiiû` H2K2Mi #Hmzû ¨ HǶûTQ[m2- 2i BMbB iiB`û p2`b HǶPL1_X Zm2 /2 +?2KBM T `+Qm`m /2TmBb +2b T`2KB2`b DQm`b /2 i?ĕb2 Qɍ- T2`TH2t2 /2p Mi mM }+?B2` i2ti2 pB/2- D2 K2 /2K M/ Bb #B2M T ` Qɍ +QKK2M+2` TQm` T `p2MB` ¨ H2 `2KTHB` /2 HB;M2b /2 +Q/2b ¨ H 7QBb bQHB/2b 2i ~mB/2bXXX PHBpB2`- K2`+B BM}MBK2Mi /2 KǶ pQB` T2`KBb /2 K2M2` ¨ #B2M +2 i` p BH / Mb H2b K2BHH2m`2b +QM/BiBQMb TQbbB#H2b- ¨ b pQB` , /2 MQK#`2mt û+? M;2b p2+ H2b mi`2b K2K#`2b /2 iQM T`QD2i 1_* 1_P6G1sR - [m2H[m2b pQv ;2b 2i +QM7û`2M+2b KûKQ` #H2b- 2i #B2M bȿ` 2i p Mi iQmi iQM bmBpB T2`bQMM2HX h + T +Biû ¨ +`2mb2` m 7QM/ /2b T`Q#HĕK2b Dmb[mǶ¨ +2 [mǶ2M D BHHBbb2Mi /2b B/û2b MQmp2HH2b MǶ T b }MB /2 K2 bm`T`2M/`2X 1M THmb /2 i2b MQK#`2mb2b bm;;2biBQMb- H [m HBiû /m i` p BH `û HBbû /QBi mbbB #2 m+QmT ¨ iQM 2tB;2M+2 +QMbi Mi2 /2 `B;m2m` 2i /2 +H `iû- MQi KK2Mi / Mb HǶ2t2`+B+2 /B{+BH2 K Bb 7Q`K i2m` /2 H `û/ +iBQM /Ƕ `iB+H2bX 1M}M- K2`+B TQm` i ;2biBQM /Ƕ1_P6G1s- [m2 im b /B`B;û 2M H Bbb Mi mM2 ;` M/2 HB#2`iû / Mb H2b Q`B2Mi iBQMb /2 `2+?2`+?2 /2 +? +mM- iQmi 2M /QMM Mi /2b BKTmHbBQMb /û+BbBp2b HQ`b[m2 +Ƕûi Bi Mû+2bb B`2X C2 /QBb BMbB #2 m+QmT mt MQK#`2mt û+? M;2b p2+ H2b K2K#`2b /2 H Ŀ i2 K 1_* ŀ , /2b Tbv+?Qi?û` TB2b /2 ;`QmT2 mt T bbBQMM Mi2b /Bb+mbbBQMb b+B2MiB}[m2b- D2 K2 b2` Bb b2MiB #B2M b2mH b Mb pQmbX J `+Q- K2`+B TQm` iQM B/2 2i i2b +QMb2BHb m /û#mi /2 H i?ĕb2- HQ`b [m2 `B2M M2 pQmH Bi 2M+Q`2 +QMp2`;2`- 2i TQm` i2b HmKBĕ`2b bm` H2 +QMi`ƬH2 +iB7 T ` TBûxQûH2+i`B[m2bX LB+QHǁ- K2`+B /Ƕ pQB` T `i ;û p2+ KQB i b+B2M+2 /2b +Qm+?2b HBKBi2b m T`Q}i /2 MQb TH BbB`b pBb+QûH biB[m2b- 2i TQm` H2b /Bb+mbbBQMb T bbBQMM Mi2b [mB bǶ2M bQMi 2MbmBpBX h`Bbi M- K2`+B /Ƕ pQB` i`Qmpû ¨ T2m T`ĕb mM #m; `2iQ`b T ` HB;M2 /2 K2b +Q/2b 2i /2 KǶ pQB` TQbû i Mi /2 [m2biBQMb T2`iBM2Mi2bX GmBb- K2`+B TQm` iQM 2Mi?QmbB bK2 +QKKmMB+ iB7- DǶ2bTĕ`2 [m2 im }MB` b i i?ĕb2 +QKK2 mM TQBbbQM / Mb HǶ2 mX 1M}M- mM2 K2MiBQM bTû+B H2 ¨ CQ? MM- K ŗi`2 ĕb T`û+QM/BiBQMM2m`b 2i + H+mH T ` HHĕH2- p2+ [mB DǶ B T `i ;û i Mi /2 T2`TH2tBiû /2p Mi H K ;B2 MQB`2 6`2262KYY- /2 Mƾm/b m +2`p2 m- K Bb mbbB [m2H[m2b@mMb /2 +2b ` `2b KQK2Mib Qɍ [m2H[m2 +?Qb2 /2 M2i b2K#H2 2M}M b2 /û; ;2` /2 H #`mK2 ûT Bbb2 /2b aSEGA_ c /2 J2m/QM Dmb[mǶ2M GQmBbB M2- 2M T bb Mi T ` H2b HT2b 2i mM +2Mi`2 bT iB HX J2b aBM+ĕ`2b 2i KB+ mt 1M+Qm` ;2K2Mib TQm` H bmBi2 /2b ûpĕM2K2Mib 5 CǶ B mbbB 2m H +? M+2 /2 i` p BHH2` p2+ /2b bi ;B B`2b 2Mi?QmbB bK Mib , K2`+B :2Q`;- K2BM amT2`T` FiBF Mi/Ƕ pQB` /û#`Qmbb BHHû HǶ M Hvb2 /2 `ûbQHp Mi- iQmDQm`b / Mb H #QMM2 ?mK2m` #B2M [mǶQM b2 bQBi }@ M H2K2Mi mM T2m ûHQB;Mû /2b ?ûHB+QTiĕ`2bXXX J2`+B _QK BM GX /Ƕ pQB` i2biû KQM T2iBi KQ/ĕH2 `û/mBi#` pQ ¨ S mHBM2 /Ƕ pQB` +Qm` ;2mb2K2Mi 2bbmvû [m2H[m2b THi`2b MmKû`B[m2bX 1M}M K2`+B J `B2 2i _ûKB- pQmb KǶ p2x 7 Bi `āp2` p2+ pQb HHû2b /2 pQM E`KM b pQMM2mb2b- [m2 DǶ B Tm BKKQ`i HBb2` ;`+2 ¨ * `QHBM2 2i *û/`B+ AX [mB KǶQMi Qmp2`i H2b TQ`i2b /2 +2ii2 7Q`KB/ #H2 `KQB`2 ¨ K iû`B2H T?QiQX. R ?iiTb,ffrjXQM2` X7`f2`+@ 2`Q7H2tf?QK2.
(5) G2b 2t+2HH2Mi2b +QM/BiBQMb /2 i` p BH /QMi DQmBi mM /Q+iQ` Mi ¨ HǶPL1_ /2 J2m/QM /QBp2Mi mbbB #2 m+QmT ¨ HǶ iKQbT?ĕ`2 +? H2m`2mb2 [mB v `ĕ;M2- D2 iB2Mb BMbB ¨ `2K2`+B2` HǶ2Mb2K#H2 /2b +QHHĕ;m2b 2i T2`bQMM2Hb [m2 DǶv B +ƬiQvûX J2`+B ¨ H }M2 û[mBT2 Ŀ PL1_ /`2 K i2 K ŀ TmBb Ŀ j@R ŀ ě #B2MiƬi Ŀ y@9 ŀ \ ě /Ƕ pQB` û; vû H2 [mQiB/B2MX * `HQb- im b ûiû mM +QHHĕ;m2 /2 #m`2 m /2 ;` M/2 p H2m`X LQb /Bb+mbbBQMb +`QBbû2b bm` H2 7ûKBMBbK2- H2 pûHQ 2i H +QMi` BMi2 ûM2`;B2@+HBK i pQMi #B2M K2 K M[m2`X 1/Q- K2`+B /Ƕ pQB` TTQ`iû iQmi H2 bQH2BH /ǶAi HB2 2i /2b ?BbiQB`2b BM+`Qv #H2b ¨ +? +mM2 /2 i2b pBbBi2bX Zm2MiBM- K2`+B /Ƕ pQB` b mpû KQM bûDQm` ¨ * K#`B/;2 ;`+2 ¨ i p2bi22i TQm` i2b +QKTi2b@`2M/mb bm` H2b #Bx ``2`B2b 2tTû`BK2Mi H2bX CQ? MM- K2`+B /Ƕ pQB` ûi #HB mM MQmp2 m bi M/ `/ 2M K iBĕ`2 /2 + H2K#Qm`bX G2b +QM7û`2M+2b QMi mbbB ûiû HǶQ++ bBQM /2 T `iB+BT2` ¨ /2 DQv2mb2b +QHQMB2b /2 p + M+2b PL1_- D2 ; `/2 BMbB mM 2t+2HH2Mi bQmp2MB` /m bûDQm` ¨ aûpBHH22i /m r22F@2M/ T`QHQM;û ¨ aiQ+F?QHK 2M +QKT ;MB2 /2 GûQTQH/- Gm+ b 2i 1/Q `/QX úpB/2KK2Mi- D2 M2 bmBb T b T`āi /ǶQm#HB2` H2 +û`ûKQMB H /2 H T mb2 + 7û- /Ƕ #Q`/ +?2x H2b Ŀ M+B2Mb ŀ- . KB2M- >QHHv- LB+QH b- _Q#BM- a KB` 2i u2@"QMM2 c TmBb miQm` /2 MQi`2 #` p2 K @ +?BM2 2i /m Km` /2 + TbmH2bX 1M THmb /2b K2K#`2b /2b /Bp2`b2b 7 +iBQMb bmb@MQKKû2b- MQi`2 #m`2 m bǶ2bi BMbB i`Qmpû Tû`BQ/B[m2K2Mi 2i bvKT i?B[m2K2Mi 2Mp ?B T ` `M m/- `K M/- * KBHH2- : û@ i M- :mBHH mK2- CmHB2M- _QK BM SX- J ii?B2mXXX G2b +QMp2`b iBQMb /m #m`2 m u@yy@kR v Mi ûiû /ǶmM +QKKmM ++Q`/ +H bbû2b +QM}/2MiB2H /û72Mb2 U/2b #QMM2b Kƾm`bV- ;mĕ`2 / p Mi ;2 MǶ2M b2` /ûpQBHû B+BX J2`+B mbbB ¨ H2t M/`2- Mi?QMv- `MQH/- "2MD KBM U×2V- *QHBM- * i?2`BM2- *û/`B+ lX- .2MBb "X- .BQ;Q- 6` MÏQBb- C ?M pB- Cm M- AHB b- L p`Qb2- aBKQM- hQ#B b- hQMB- M2 b2` Bi@+2 [m2 TQm` KǶ pQB` ii2M/m UQm T bV ¨ H + MiBM2XXX 1M}M- K2`+B ¨ *H B`2- .QKBMB[m2 2i h Mv TQm` KǶ pQB` #B2M B/û TQm` H2b /ûK `+?2b /KBMBbi` iBp2b 2i HǶQ`; MBb iBQM /2 H bQmi2M M+2X C2 M2 T2mt +QM+Hm`2 b Mb T2Mb2` ¨ K2b KBb 2i bQmiB2Mb /2 THmb HQM;m2 / i2- /2 ai` b#Qm`;S `Bb Qm BHH2m`bX J2`+B /Ƕ pQB` ûiû H¨ HQ`b[m2 +Ƕûi Bi Mû+2bb B`2- K2`+B TQm` +2 [m2 HǶQM pû+m 2M@ b2K#H2X J2`+B G¤iBiB /Ƕ pQB` bmTTQ`iû b Mb #`QM+?2` +2ii2 HQM;m2 [māi2 2M i2``2b ?QbiBH2b T2mTHû2b /Ƕû[m iBQMb 5% j$yI%9 jx{#‘Mx#‘V 2i /2 bvK#QH2b #b+QMb- 2i TQm` i #B2Mp2BHH M+2 m [mQiB/B2MX 1M}MK2`+B ¨ K bƾm` 2i ¨ K2b T `2Mib- b Mb [mB `B2M MǶ m` Bi ûiû TQbbB#H2X C2 pQmb /QBb #2 m+QmT TQm` 2M āi`2 ``Bpû Dmb[m2 H¨X.
(6) #bi` +i G `;2 bi iB+ M/ /vM KB+ /27Q`K iBQMb `Bb2 r?2M 2H biB+ bQHB/b BMi2` +i rBi? pBb+Qmb ~QrbX h?2v K v ++m` i2Hv #2 + Tim`2/ #v +QMbB/2`BM; bi`QM; MmK2`B+ H +QmTHBM; #2ir22M i?2 G ;` M;B M bQHB/ /vM KB+b M/ i?2 1mH2`B M ~mB/ /vM KB+b- 2bT2+B HHv r?2M H `;2 //2/@K bb 2z2+ib `2 i TH vX "2bB/2b `mMMBM; mMbi2 /v MQM@HBM2 ` bBKmH iBQMb- HBM2 `Bb2/ KQ/ H TT`Q +?2b `2 mb27mH iQ B/2MiB7v ?v/`Q@2H biB+ BMbi #BHBiB2b i i?2 Q`B;BM Q7 i?Qb2 pB#` iBQMbX h?2v + M HbQ #2 mb2/ iQ /2bB;M T bbBp2 +QMi`QH bi` i2;B2b BKBM; i ii2Mm iBM; Q` 2p2M bmTT`2bbBM; i?2 bi`m+im` H pB#` iBQMbX h?2 Q#D2+iBp2b Q7 i?Bb i?2bBb `2 iQ /2p2HQT M/ TTHv K2i?Q/b- }`bi iQ ++m` i2Hv /2b+`B#2 i?2 HBM2 ` /vM KB+b Q7 bi`QM;Hv +QmTH2/ ~mB/@bQHB/ bvbi2Kb- M/ i?2M iQ QTiBKBx2 i?2 b? T2 Q` i?2 2H biB+ T`QT2`iB2b Q7 i?2 bQHB/ bQ b iQ +QMi`QH i?2 HBM2 ` /vM KB+bX h?2 }`bi T `i Q7 i?Bb i?2bBb T`2b2Mib i?2 i?2Q`2iB+ H M/ MmK2`B+ H K2i?Q/b /2p2HQT2/ iQ BM@ p2biB; i2 i?2 HBM2 ` /vM KB+b Q7 ~mB/@bQHB/ T2`im`# iBQMb `QmM/ MQM@HBM2 ` bi2 /v bi i2bX h?2 ~mB/ /vM KB+b Bb ;Qp2`M2/ #v i?2 BM+QKT`2bbB#H2 L pB2`@aiQF2b 2[m iBQMb- r?BH2 i?2 bQHB/ Bb /2@ b+`B#2/ #v ?vT2`2H biB+ KQ/2HbX M `#Bi` `v G ;` M;B M 1mH2`B M +QmTHBM; Bb +?Qb2M- `2bmHiBM; BM +QM7Q`K H /2b+`BTiBQM Q7 i?2 ~mB/@bQHB/ BMi2`7 +2 BM iBK2@BM/2T2M/2Mi `272`2M+2 +QM};m` @ iBQMX M 2t +i HBM2 `Bb iBQM Q7 i?Bb 7Q`KmH iBQM Bb /2`Bp2/- M/ irQ M Hvb2b Q7 i?2 `2bmHiBM; 7mHHv +QmTH2/- HBM2 `Bb2/ ~mB/@bQHB/ QT2` iQ` `2 +QMbB/2`2/X M 2B;2Mp Hm2 M HvbBb HHQrb iQ /2i2`KBM2 b2H7@bmbi BM2/ ~mB/@bQHB/ BMbi #BHBiB2b `2bTQMbB#H2- 7Q` BMbi M+2- 7Q` i?2 pQ`i2t@BM/m+2/ pB#` iBQMb Q7 #Hmz #Q/B2b Q` i?2 ~mii2` Q7 bH2M/2` #Q/B2bX h?2 `2bQHp2Mi M HvbBb- BX2X bBM;mH ` p Hm2 M HvbBb Q7 i?2 ~mB/@bQHB/ QT2` iQ`- HHQrb iQ /2i2`KBM2 i?2 HBM2 ` `2bTQMb2 Q7 i?2 ~mB/@bQHB/ bvbi2K iQ 2ti2`M H 7Q`+BM;b- bm+? b ;mbibX h?2 b2+QM/ T `i Bb /2pQi2/ iQ i?2 M HvbBb M/ +QMi`QH Q7 i?2 pB#` iBQMb Q7 2H biB+ TH i2b i@ i +?2/ #2?BM/ `B;B/ +B`+mH ` +vHBM/2`- M/ BKK2`b2/ BM mMB7Q`K BM+QKBM; ~QrX 6B`bi- +QKTH2t 2B;2MKQ/2b- `2H i2/ iQ pQ`i2t@BM/m+2/ pB#` iBQMb- `2 B/2MiB}2/ #v K2 Mb Q7 i?2 2B;2Mp Hm2 M H@ vbBbX h?2b2 KQ/2b #2+QK2 mMbi #H2 r?2M `2/m+BM; i?2 biBzM2bbX 7m`i?2` /2+`2 b2 Q7 biBzM2bb vB2H/b iQ i?2 /2bi #BHBx iBQM Q7 `2 H 2B;2MKQ/2- +? ` +i2`BbiB+ Q7 bvKK2i`v@#`2 FBM; /Bp2`;2M+2 BMbi #BHBivX LQM@HBM2 ` bi2 /v M/ mMbi2 /v bBKmH iBQMb `2 T2`7Q`K2/ iQ 2Hm+B/ i2 i?2 MQM@HBM2 ` BMi2` +iBQMb #2ir22M i?2 mMbi #H2 KQ/2bX a2+QM/Hv- M /DQBMi@# b2/ b? T2 QTiBKBx iBQM Q7 i?2 `B;B/ #Q/v bmTTQ`iBM; i?2 2H biB+ TH i2 Bb T`QTQb2/ iQ +QMi`QH i?2 mMbi #H2 +QKTH2t KQ/2b- BKBM; 2Bi?2` i /2+`2 bBM; i?2 ;`Qri? ` i2 Q` p `vBM; i?2 7`2[m2M+vX bi #BHBx iBQM Q7 i?2 +QKTH2t KQ/2 Bb +?B2p2/ #v i?BMMBM; Q7 i?2 `B;B/ #Q/vX JQ`2 2tQiB+ b? T2b `2 Q#i BM2/ r?2M +QMbB/2`BM; i?2 p `B iBQM Q7 i?2 7`2[m2M+vX 7`2[m2M+v /2+`2 b2 Bb +?B2p2/ #v dz.@b? T2/Ǵ +vHBM/2`b- r?BH2 7`2[m2M+v BM+`2 b2 Bb Q#i BM2/ rBi? dz*@b? T2/Ǵ +vHBM/2`bX h?2 H bi T `i Q7 i?2 i?2bBb Bb /2/B+ i2/ iQ i?2 /2H v Q7 H KBM `fim`#mH2Mi i` MbBiBQM BM irQ@ /BK2MbBQM H #QmM/ `v@H v2` ~Qrb i? MFb iQ pBb+Q@2H biB+- }MBi2@H2M;i? +Q iBM;bX `2bQHp2Mi M H@ vbBb Q7 i?2 ~mB/@bQHB/ QT2` iQ` Bb mb2/ iQ [m MiB7v i?2 ii2Mm iBQM Q7 HQr@7`2[m2M+v hQHHKB2M@ a+?HB+?iBM; BMbi #BHBiv r p2b r?2M i?2 biBzM2bb Q7 i?2 +Q iBM; Bb `2/m+2/X PM i?2 Qi?2` ? M/- i?2 2B;2Mp Hm2 M HvbBb b?Qrb i? i ?B;?@7`2[m2M+v bQHB/@# b2/ KQ/2b `2 /2bi #BHBx2/ r?2M i?2 bQHB/ pBb+Qmb / KTBM; Bb iQQ HQrX ;` /B2Mi@# b2/ bi` i2;v iQ QTiBKBx2 i?2 biBzM2bb /Bbi`B#miBQM Q7 i?2 +Q iBM; rBi? `2bT2+i iQ i?2 2M2`;v KTHB}+ iBQM Q7 #Qi? BMbi #BHBiB2b Bb 2p2Mim HHv T`QTQb2/X h?2 QTiBKBx2/ +Q iBM;b ? p2 M Qp2` HH bi`m+im`2 Q`; MBx2/ BM H v2`b HB;M2/ rBi? i?2 ~Qr- rBi? Km+? bi`QM;2` MBbQi`QTv BM #Qi? i?2 bi`2 KrBb2 M/ i` Mbp2`b2 /B`2+iBQMb +HQb2 iQ i?2 2/;2b M/ K F2 Bi TQbbB#H2 #Qi? iQ ii2Mm i2 hQHHKB2M@a+?HB+?iBM; r p2b M/ iQ HBKBi i?2 /2p2HQTK2Mi Q7 bQHB/@# b2/ BMbi #BHBiB2bX.
(7)
(8) h #H2 Q7 MQi iBQMb ˆ Ω Ω ˜t Ω. bi`2bb@7`22 `272`2M+2 /QK BM, [m MiBiB2b qˆ(ˆ x, t) bi2 /v /27Q`K2/ `272`2M+2 /QK BM, [m MiBiB2b q(x, t) ˜ (˜ BMbi Mi M2Qmb- iBK2@/2T2M/2Mi /27Q`K2/ /QK BM, [m MiBiB2b q xt , t). i λ = λr + iλi ω Re(·), Im(·) (·). BK ;BM `v MmK#2` +QKTH2t 2B;2Mp Hm2 7Q`+BM; 7`2[m2M+v `2 H- BK ;BM `v T `i +QKTH2t +QMDm; i2. Q(x) q (x, t) q ◦ (x) q † (x) Q† (x). bi2 /v- # b2 }2H/ T2`im`# iBQM }2H/ 2B;2MKQ/2 Q` QTiBK H 7Q`+BM;f`2bTQMb2 /DQBMi T2`im# iBQM }2H/ /DQBMi bi2 /v # b2 }2H/. u p ξ ub ξ2 λ λ2. ~mB/ p2HQ+Biv ~mB/ T`2bbm`2 bQHB/ /BbTH +2K2Mi U+ TBi H H2ii2`, ΞV bQHB/ p2HQ+Biv 2ti2MbBQM /BbTH +2K2Mi BMi2`7 +2 bi`2bb U+ TBi H H2ii2`, ΛV BMi2`7 +2 2ti2MbBQM Tb2m/Q@bi`2bb. ˜ = ∂/∂ x ∇ ˜t ∇ = ∂/∂x ˆ = ∂/∂ x ∇ ˆ ˆ P ˆ - P P ˆ S ˆ - S S ˆ E ˆ - E E ˆ F ˆ Jˆ = det(F). /Bz2`2MiB iBQM QT2` iQ` BM i?2 BMbi Mi M2Qmb /QK BM /Bz2`2MiB iBQM QT2` iQ` BM i?2 bi2 /v /27Q`K2/ `272`2M+2 /QK BM /Bz2`2MiB iBQM QT2` iQ` BM i?2 bi`2bb@7`22 `272`2M+2 /QK BM }`bi SBQH @EB`+??Qz bi`2bb i2MbQ` BM bi`2bb@7`22 +QM};m` iBQM U1[X URXRXeV T ;2 R3V HBM2 `Bb2/ SBQH @EB`+??Qz bi`2bb i2MbQ` U1[X UkXRXeV T ;2 98 M/ 1[X UkXRXReV T ;2 93V b2+QM/ SBQH @EB`+??Qz bi`2bb i2MbQ` BM bi`2bb@7`22 +QM};m` iBQM U1[X URXRXdV T ;2 R3V HBM2 `Bb2/ b2+QM/ SBQH @EB`+??Qz bi`2b i2MbQ` U1[X UkXRXdV T ;2 98 M/ 1[X UkXRXRdV T ;2 93V :`22M@G ;` M;2 bi` BM i2MbQ` BM bi`2bb@7`22 +QM};m` iBQM U1[X URXRX3V T ;2 R3V HBM2 `Bb2/ :`22M@G ;` M;2 bi` BM i2MbQ` U1[X UkXRX3V T ;2 98 M/ 1[X UkXRXR3V T ;2 93V /27Q`K iBQM ;` /B2Mi BM bi`2bb@7`22 +QM};m` iBQM U1[X URXRXNV T ;2 R3V i` Mb7Q`K iBQM C +Q#B M U1[X URXRXkdV T ;2 kkV. ˆ −1 ˆ = Jˆ F Φ ˆ - Φ Φ σ ˜ ˆ Σ. ˆ - Σ Σ ˆ D ˆ - D D. /27Q`K iBQM QT2` iQ` BM bi`2bb@7`22 +QM};m` iBQM U1[X URXRXkdV T ;2 kkV HBM2 `Bb2/ /27Q`K iBQM QT2` iQ` U1[X UkXRXNV T ;2 98 M/ 1[X UkXRXRNV T ;2 93V ~mB/ * m+?v bi`2bb i2MbQ` U1[X URXRXR8V T ;2 RNV ~mB/ bi`2bb i2MbQ` BM i?2 bi`2bb@7`22 `272`2M+2 +QM};m` iBQM U1[X URXRXk3V T ;2 kkV HBM2 `Bb2/ ~mB/ bi`2b i2MbQ` U1[X UkXRXRRV T ;2 98 M/ 1[X UkXRXkRV T ;2 93V p2HQ+Biv ;` /B2Mib i2MbQ` U1[X URXRXkNV T ;2 kkV HBM2 `Bb2/ p2HQ+Biv ;` /B2Mib i2MbQ` U1[X UkXRXRyV T ;2 98 M/ 1[X UkXRXkyV T ;2 93V.
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(10) *QMi2Mib. _2K2`+B2K2Mib. BBB. #bi` +i. p. h #H2 Q7 MQi iBQMb AMi`Q/m+iBQM 6HmB/@bi`m+im`2 BMbi #BHBiB2b X X X X X X X X X X X X X .2b+`BTiBQM Q7 HBM2 ` ~mB/@bi`m+im`2 BMbi #BHBiB2b X X S bbBp2 +QMi`QH Q7 HBM2 ` ~mB/@bi`m+im`2 BMbi #BHBiB2b P`; MBb iBQM Q7 i?2 K Mmb+`BTi X X X X X X X X X X X. pBB X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. R R e N Rk. R LQMHBM2 ` K2i?Q/b 7Q` ~mB/@bi`m+im`2 T`Q#H2Kb RXR 1[m iBQMb 7Q` pBb+Qmb ~mB/ BMi2` +iBM; rBi? M 2H biB+ bi`m+im`2 X RXRXR LQM@/BK2MbBQM H T ` K2i2`b /2b+`B#BM; ~mB/@bQHB/ bvbi2K RXRXk 1[m iBQMb 7Q` M 2H biB+ bQHB/ rBi? H `;2 /27Q`K iBQMb X X X RXRXj L pB2`@aiQF2b 2[m iBQMb BM G1 +QQ`/BM i2b X X X X X X X X X RXRX9 AMi2`7 +2 #QmM/ `v +QM/BiBQMb X X X X X X X X X X X X X X X RXRX8 JQMQHBi?B+ r2 F 7Q`KmH iBQM X X X X X X X X X X X X X X X X X RXRXe amKK `v X X X X X X X X X X X X X X X X X X X X X X X X X X X X RXk AKTHB+Bi b+?2K2 7Q` bQHpBM; i?2 MQM@HBM2 ` G1 2[m iBQMb X X X X X RXkXR *QmTHBM; b+?2K2b 7Q` G1 T`Q#H2Kb X X X X X X X X X X X X X RXkXk hBK2 /Bb+`2iBx iBQM X X X X X X X X X X X X X X X X X X X X X X X RXkXj UZm bBV@L2riQM Bi2` iBQMb bT +2 /Bb+`2iBx iBQM X X X X X X RXkX9 1ti2MbBQM T`Q#H2K 7Q` MQM@HBM2 ` +QKTmi iBQMb X X X X X X X RXj > M/HBM; i?2 H `;2@b+ H2 `2bmHiBM; HBM2 ` bvbi2Kb X X X X X X X X X X RXjXR .B`2+i pbX Bi2` iBp2 K2i?Q/b X X X X X X X X X X X X X X X X X X RXjXk S`2+QM/BiBQMBM; i?2 7mHHv +QmTH2/ ~mB/@bi`m+im`2 T`Q#H2K X RX9 hm`2FǶb #2M+?K `F + b2b X X X X X X X X X X X X X X X X X X X X X X X X RX9XR aQHB/ K2+? MB+b + b2b X X X X X X X X X X X X X X X X X X X X X RX9Xk 6HmB/ K2+? MB+b + b2b X X X X X X X X X X X X X X X X X X X X X RX9Xj 6HmB/@bi`m+im`2 +QmTH2/ + b2b X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X. R8 Re Re Rd RN kk kj k3 kN kN jy jR jk j9 j9 j9 je jd jd j3. X X X X X X X X X X X X. 9R 9k 9k 99 9N 8R 8k 8k 8k 8j 89 89 8d. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. X X X X. k 1B;2Mp Hm2 M HvbBb Q7 ~mB/@bi`m+im`2 bi2 /v@bi i2b kXR 6HmB/@bi`m+im`2 HBM2 ` T2`im`# iBQM 2[m iBQMb X X X X X X X X X X kXRXR ai2 /v@bi i2 bQHmiBQMb X X X X X X X X X X X X X X X X X X X kXRXk G ;` M;B M@# b2/ T2`im`# iBQM 2[m iBQMb X X X X X X X X kXRXj GBMF rBi? ~mii2` /2`Bp iBp2b 2`Q2H biB+Biv X X X X X X kXRX9 GBMF rBi? 1mH2`B M@# b2/ T2`im`# iBQM 2[m iBQMb X X X X kXk LmK2`B+ H 7Q`KmH iBQM 7Q` M 2B;2Mp Hm2 M HvbBb X X X X X X X X kXkXR JQ/ H /2+QKTQbBiBQM Q7 i?2 T2`im`# iBQMb X X X X X X X X kXkXk AKTH2K2Mi iBQM Q7 i?2 2B;2Mp Hm2 bQHp2` X X X X X X X X X kXkXj _2/m+2/ 2B;2Mp Hm2 T`Q#H2K X X X X X X X X X X X X X X X X kXj LmK2`B+ H i2biBM; Q7 i?2 G ;` M;B M@# b2/ TT`Q +? X X X X X X kXjXR h2bi + b2 rBi? pQ`i2t@BM/m+2/@/27Q`K iBQM BMbi #BHBiv kXjXk h2bi + b2 rBi? ~mii2` BMbi #BHBiv X X X X X X X X X X X X. X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X.
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(12) 8Xj. 8X9. 8X8. 8Xe. 8XkX9 *QmTH2/ T`Q#H2K M/ MmK2`B+ H b2iiBM;b X X X 1B;2Mp Hm2 M HvbBb X X X X X X X X X X X X X X X X X X X 8XjXR 6`22 bQHB/ /vM KB+b X X X X X X X X X X X X X X 8XjXk 6HmB/@2H biB+ 2B;2Mp Hm2 M HvbBb X X X X X X X X 1H biB+ `2bTQMb2 iQ QTiBK H ~mB/ T2`im`# iBQMb X X X 8X9XR _2bQHp2Mi M HvbBb BM i?2 `B;B/@r HH + b2 X X X 8X9Xk 6HmB/@2H biB+ `2bTQMb2 iQ M QTiBK H `B;B/@r HH 8X9Xj J2+? MBbK Q7 r p2 ii2Mm iBQMf KTHB}+ iBQM 6HmB/@2H biB+ `2bQHp2Mi M HvbBb X X X X X X X X X X X X 8X8XR 6mHHv +QmTH2/ `2bQHp2Mi M HvbBb X X X X X X X X 8X8Xk _2bmHib X X X X X X X X X X X X X X X X X X X X X *QM+HmbBQM X X X X X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 7Q`+BM; X X X X X X X X X X X X X X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. X X X X X X X X X X X X. R99 R98 R98 R8y R88 R8e R83 ReR Re8 Re8 Re8 Ree. e *QKTHB Mi +Q iBM; bi`m+im`2 QTiBKBx iBQM 7Q` #QmM/ `v@H v2` BMbi #BHBiB2b KBiB@ ; iBQM ReN eXR AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Rdy eXk 6mHHv +QmTH2/ `2bQHp2Mi M HvbBb 7Q` i?2 ~mB/@bi`m+im`2 T`Q#H2K X X X X X X X X X X X RdR eXj :` /B2Mi Q7 i?2 2M2`;v ; BM rBi? `2bT2+i iQ bi`m+im` H T ` K2i2`b X X X X X X X X X X Rdk eXjXR G ;` M;B M 7Q`KmH iBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Rdk eXjXk ai`m+im` H ;` /B2Mib X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Rdj eX9 PTiBKBx iBQM Q7 i?2 biBzM2bb /Bbi`B#miBQM X X X X X X X X X X X X X X X X X X X X X X X X Rd8 eX9XR PTiBKBb iBQM 7Q` hq6 BMbi #BHBiB2b ii2Mm iBQM X X X X X X X X X X X X X X X X Rde eX9Xk *QK#BM2/ QTiBKBx iBQM 7Q` haqfhq6 ii2Mm iBQM X X X X X X X X X X X X X R3y eX8 *QM+HmbBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X R3j d *QM+HmbBQM T2`bT2+iBp2b R38 dXR amKK `v M/ K BM `2bmHib X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X R38 dXk S2`bT2+iBp2b X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X R33 _2bQHp2Mi pb 2B;2Mp Hm2b RNR XR h2KTQ` H- KQ/ H bi #BHBiv M HvbBb X X X X X X X X X X X X X X X X X X X X X X X X X X X RNk Xk 6`2[m2M+v `2bTQMb2 M HvbBb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X RN9 " 6HmB/@bQHB/ #HQ+F QT2` iQ`b 2tT`2bbBQM RNd "XR LQM@HBM2 ` ~mB/@bQHB/ 2[m iBQMb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X RNd "Xk GBM2 `Bb2/ ~mB/@bQHB/ 2[m iBQMb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X RN3 * h2+?MB+ H 7Q`KmH b kyR *XR h` MbTQ`i 7Q`KmH b #2ir22M i?2 /Bz2`2Mi +QM};m` iBQMb X X X X X X X X X X X X X X X kyR *Xk 6`QK G ;` M;B M@# b2/ iQ 1mH2`B M@# b2/ T2`im`# iBQM 2[m iBQMb X X X X X X X X X X kyd *Xj G ;` M;2 B/2MiBiB2b 7Q` /DQBMi G1 2[m iBQMb X X X X X X X X X X X X X X X X X X X X X ky3 . .2`Bp iBQM Q7 i?2 ~mB/@2H biB+ b? T2 ;` /B2Mi kRj .XR G ;` M;B M 7Q`KmH iBQM rBi? *û Ƕb K2i?Q/ X X X X X X X X X X X X X X X X X X X X X X kRj .Xk 1tTHB+Bi 7Q`KmH 7Q` i?2 b? T2 ;` /B2Mi X X X X X X X X X X X X X X X X X X X X X X X X X kkR "B#HBQ;` T?v. kk9.
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(14) AMi`Q/m+iBQM M/ bQHB/ K2+? MB+b `2 i` /BiBQM HHv i`2 i2/ b irQ /Bz2`2Mi bm#D2+ibX h?2B` +QmTHBM;6HmB/ H2 /BM; iQ ~mB/@bi`m+im`2 BMi2` +iBQMb- Bb +QMb2[m2MiHv +? HH2M;BM; Bbbm2X G `;2 #2M2}ib +QmH/. #2 `2i`B2p2/ 7`QK /22T2`- M/ KQ`2 T`2+Bb2 mM/2`bi M/BM; Q7 i?2 Kmim H BMi2` +iBQM Q7 ~mB/b M/ bQHB/bX PM QM2 ? M/- i?Bb + M ?2HT iQ T`2p2Mi i?2 TT2 ` M+2 Q7 mM/2bB` #H2 pB#` iBQMb- 7Q` i?2v Q7i2M +QK2 rBi? M BM+`2 b2/ 2M2`;v /BbbBT iBQM- K i2`B Hb 7 iB;m2 M/ 2p2M 7 BHm`2X h?2 KQbi r2HH@FMQrM 2t KTH2 #2BM; T`Q# #Hv i?2 ~Qr@BM/m+2/ iQ`bBQM H pB#` iBQMb i? i H2 / iQ i?2 /2bi`m+@ iBQM Q7 i?2 h +QK L ``Qrb #`B/;2X PM i?2 Qi?2` ? M/- i?2 H `;2@ KTHBim/2 /27Q`K iBQMb i? i bTQMi M2QmbHv TT2 ` BM ~mB/@2H biB+ bvbi2Kb KB;?i #2 2tTHQBi2/ 7Q` /2bB;MBM; M2r- #BQ@BMbTB`2/ HQ+QKQiBQM KQ/2b U: /2H? 2i HX- kyRyV Q` 2M2`;v@? `p2biBM; /2pB+2b U#/2HF2}- kyReVX h?2 T`2b2Mi rQ`F 7QHHQrb i?Bb T i?- #v HQQFBM; mTQM #Qi? i?2 M HvbBb Q7 ~mB/@bQHB/ BMbi #BHBiB2b M/ i?2B` +QMi`QHX. 6HmB/@bi`m+im`2 BMbi #BHBiB2b h?2 MQiBQM Q7 bi #BHBiv Bb Q7 T ` KQmMi BKTQ`i M+2 BM 2M;BM22`BM; b+B2M+2bX h?2 T`2@bBxBM; Q7 K2+? MB+ H bi`m+im`2b Bb Q7i2M + ``B2/ Qmi mM/2` M bbmKTiBQM Q7 bi2 /v@bi i2 2[mBHB#`BmKBM Q`/2` iQ #2 #H2 iQ [mB+FHv /2i2`KBM2 r?B+? HQ /b TTHv M/ r?B+? K i2`B H T`QT2`iB2b `2 `2[mB`2/X AM K Mv + b2b- i?2 bbmKTiBQM Q7 bi iBQM `Biv mM7Q`imM i2Hv ;Bp2b +QKTH2i2Hv 2``QM2Qmb `2bmHib- #2+ mb2 i?2 ?vTQi?2iB+ H bi iBQM `v bi i2 QM r?B+? i?2v ? p2 `2HB2/ Bb mMbi #H2 rBi? `2bT2+i iQ bK HH /Bbim`# M+2b, Mv bK HH T2`im`# iBQM i`B;;2`b `2+QM};m` iBQM iQr `/b M2r- Q7i2M KQ`2 +QKTH2t 2[mBHB#`BmKX. 6HmB/- bQHB/ M/ +QmTH2/ BMbi #BHBiB2b K DQ` iQTB+ BM ~mB/ K2+? MB+b Bb iQ mM/2`bi M/ ?Qr bi2 /v- dz;2MiH2Ǵ ~Qrb /2;2M2` i2 iQr `/b +QKTH2t- mMbi2 /v- i?`22@/BK2MbBQM H im`#mH2Mi ~Qrb r?2M BMi`BMbB+ UbBx2 Q7 i?2 Q#bi +H2- p2HQ+BivpBb+QbBiv- 2i+XV Q` 2ti2`M H U +QmbiB+ MQBb2- ?2 i bQm`+2- 2i+XV +? ` +i2`BbiB+ T ` K2i2`b `2 p `B2/X h?2 `Qmi2 iQ im`#mH2M+2 Bb MQi bi` B;?i7Q`r `/ i HH iQ 7QHHQr- #mi i?2 2 `Hv bi ;2b `2 Q7i2M +? ` +i2`Bx2/ #v HBM2 ` BMbi #BHBiv K2+? MBbKb i? i K F2 i?2 i` MbBiBQM #2ir22M i?2 bi2 /v ~Qr M/ M mMbi2 /v ~Qr rBi? `2H iBp2Hv bBKTH2 bi`m+im`2X Ai Bb 7Q` BMbi M+2 r2HH@FMQrM i? i i?2 ~mB/ ~Qr #Qmi M Q#bi +H2 bm//2MHv +2 b2b iQ #2 bi @ iBQM `v r?2M i?2 p2HQ+Biv Bb BM+`2 b2/, i?2 b?2 ` H v2`b ;2M2` i2/ #v i?2 T`2b2M+2 Q7 i?2 Q#bi +H2 ;Bp2 #B`i? iQ mMbi2 /v pQ`iB+2b i? i /2i +? T2`BQ/B+ HHv 7`QK i?2 Q#D2+i M/ `2 /p2+i2/ BM i?2 r F2- r?B+? `2bmHib BM Qb+BHH iQ`v HQ /b QM i?2 Q#bi +H2 M/ M BM+`2 b2/ KBtBM; /QrMbi`2 KX 6Q` i?2 ~Qr #Qmi `B;B/ +B`+mH ` +vHBM/2`- #B7m`+ iBQM Q++m`b i _2vMQH/b MmK#2` bHB;?iHv #2@ HQr 50 Uh`BiiQM- RN8Nc aBTT G2#2/2p- kyydVX "2HQr i?Bb i?`2b?QH/- i?2 ~Qr Bb bi2 /vX #Qp2 i?2 +`BiB+ H _2vMQH/b MmK#2`- i?2 bQ@+ HH2/ #B@/BK2MbBQM H- mMbi2 /v pQM E`KM pQ`i2t r F2 Bb Q#b2`p2/- b `2T`2b2Mi2/ BM 6B;X R r?2`2 bQ T@}HK pBbm HBx iBQM Bb b?QrMX h?Bb mMbi2 /v r F2 TT2 `b mM/2` i?2 7Q`K Q7 HQ+ HBx2/ /Bbim`# M+2b i? i bT`2 / mTbi`2 K M/ /QrMbi`2 K- 7QHHQrBM; i?2 K2+? MBbK Q7 M #bQHmi2 BMbi #BHBiv U>m2``2 JQMF2rBix- RNNyVX AM i? i + b2- i?2 +QMp2+iBQM #v i?2 bi2 /v ~Qr Bb MQi bm{+B2Mi iQ T`2p2Mi 7`QK i2KTQ` H KTHB}+ iBQM Q7 i?2 BMbi #BHBivX h?2b2 ivT2 Q7 ~Qrb `2 Q7i2M `272``2/ iQ b Qb+BHH iQ` ~Qrb- 7Q` i?2v `2 bbQ+B i2/ iQ /QKBM Mi 7`2[m2M+v T2 FbX AM+`2 bBM; 7m`i?2` i?2 _2vMQH/b MmK#2` `2bmHib BM b2+QM/ `v BMbi #BHBiB2b H2 /BM; iQ i?`22@/BK2MbBQM H pQ`iB+2b UqBHHB KbQM- RNNeV- i?2M iQ KQ`2 M/ KQ`2 B``2;mH ` bi`m+im`2b M/ 2p2Mim HHv- im`#mH2Mi ~QrX.
(15) k. AMi`Q/m+iBQM U V. U#V. 6B;m`2 R Ĝ hrQ ivTB+ H ~mB/ BMbi #BHBiB2bX U V h?2 pQM E`KM pQ`i2t r F2 #2?BM/ }t2/ +B`+mH ` +vHBM/2` i? i `2bmHib 7`QK ~Qr BMbi #BHBivX SB+im`2b i F2M #v i?2 mi?Q`- QM bQ T@}HK ~Qr 2tT2`BK2Mi i PM2` b2i@mT #v _ûKB HH M/`B2m M/ J `B2 *QmHBQmX oBbm HBb iBQM #v r?Bi2@HB;?i BMi2`72`QK2i`v, pBbB#H2 +QHQm`b `2 `2H i2/ iQ i?2 HQ+ H i?B+FM2bb Q7 i?2 }HK- r?B+? Bib2H7 Bb `2H i2/ iQ i?2 HQ+ H ~Qr p2HQ+Biv Uw? M; 2i HX- kyyyVX h?2 K2 M ~Qr Bb 7`QK i?2 H27i iQ i?2 `B;?iX U#V "QmM/ `v@H v2` ~Qr QM M BMHBM2/ TH i2 BM r i2` +? MM2H- TB+im`2 7`QK >X q2`Hû i F2M 7`QK o M .vF2 URN3kV. "QmM/ `v@H v2`b `2 MQi?2` ivTB+ H 2t KTH2 Q7 mMbi #H2 ~QrbX 6Q` i?2 bBKTH2 + b2 Q7 ~ i TH i2 rBi?Qmi Mv /p2`b2 T`2bbm`2 ;` /B2Mi- r?BH2 i?2 ~Qr `2K BMb bi iBQM `v M2 ` i?2 H2 /BM; 2/;2 r?2M i?2 7`22@bi`2 K im`#mH2M+2 H2p2H Bb HQr- mMbi2 /v bi`m+im`2b TT2 ` mM/2` i?2 7Q`K Q7 i?2 bQ@+ HH2/ hQHHKB2M@a+?HB+?iBM; r p2b Ua+?m# m2` aF` Kbi /- RN9dV b QM2 KQp2b r v 7`QK i?2 H2 /BM; 2/;2X h?2 BMbi #BHBiv K2+? MBbK Bb ?Qr2p2` /Bz2`2Mi 7`QK i?2 + b2 Q7 i?2 +vHBM/2`X h?2 /vM KB+b Bb Q7 i?2 KTHB}2` ivT2, BMbi #BHBiB2b TT2 ` BM i?2 ~Qr r?2M Bi Bb bm#D2+i2/ iQ M 2ti2`M H 7Q`+BM; r?B+? HHQrb iQ K BMi BM i?2 TT2 ` M+2 Q7 /Bbim`# M+2bX h?2b2 T2`im`# iBQMb `2 }`bi /p2+i2/ #v i?2 ~Qr rBi?Qmi #2BM; KTHB}2/- mT iQ +`BiB+ H TQBMi r?2`2 M KTHB}+ iBQM b2ib BMX h?2 `2;BQM r?2`2 M KTHB}+ iBQM Q++m`b Bb [m HB}2/ b +QMp2+iBp2Hv mMbi #H2 U>m2``2 JQMF2rBix- RNNyVX h?2b2 KTHB}2/ +QMp2+iBp2 r p2b 2p2Mim HHv i`B;;2` b2+QM/ `v #B7m`+ iBQMb r?2M i?2v `2 +? bm{+B2Mi KTHBim/2 UE +? MQp- RNN9V- i? i i?2M /2;2M2` i2 BMiQ + b+ /2 Q7 #B7m`+ iBQMb M/ im`#mH2Mi ~Qr 7 `i?2` /QrMbi`2 KX pBbm HBx iBQM Q7 #QmM/ `v@H v2` ~Qr BM r i2` +? MM2H Bb `2T`Q/m+2/ BM 6B;X R#- i? i BHHmbi` i2b i?2 bm++2bbBp2 i` MbBiBQM bi2Tb ě hQHHKB2M@ a+?HB+?iBM; r p2b `2 Q#b2`p2/ QM i?2 7Q`K Q7 i?2 bK HH p `B iBQMb Q7 i?2 +QMi` bi QM i?2 H27i- r?BH2 KQ`2 M/ KQ`2 +QKTH2t bi`m+im`2b TT2 ` b QM2 KQp2b iQ i?2 `B;?i- /QrMbi`2 KX PM i?2 +QMi` `v iQ Qb+BHH iQ` ~Qrb- MQBb2@ KTHB}2`b ~Qrb `2 T `iB+mH `Hv b2MbBiBp2 iQ 2ti2`M H T2`im`# iBQMbX LQi2 i? i 7Q` i?2 #QmM/ `v@H v2` ~Qr- BM //BiBQM iQ i?2 i` MbBiBQM i?`Qm;? hQHHKB2M@a+?HB+?iBM; r p2bK Mv Qi?2` H KBM `@im`#mH2Mi i` MbBiBQM b+2M `BQb K v HbQ ? TT2M /2T2M/BM; QM i?2 H2p2H Q7 7`22@bi`2 K im`#mH2M+2 Ua `B+ 2i HX- kyykVX h?2 bim/v Q7 ?v/`Q/vM KB+ BMbi #BHBiB2b i?mb `2T`2b2Mib M +iBp2 /QK BM Q7 `2b2 `+? U.` xBM _2B/- kyy9c *? ``m- kyydc a+?KB/ >2MMBM;bQM- kyRkVX .2bTBi2 +QMbi Mi BMi2`2bi 7Q` i?2b2 [m2biBQMb / iBM; # +F iQ i?2 MBM2i22Mi? +2Mim`v- K Mv [m2biBQMb bi v ?Qr2p2` mM Mbr2`2/- 2bT2@ +B HHv #2+ mb2 Q7 i?2 p2`v H `;2 MmK2`B+ H TQr2` M22/2/ 7Q` +QKTmi iBQM H ~mB/ K2+? MB+b UaHQiMB+F.
(16) j 2i HX- kyR9V M/ i?2 /B{+mHiv 7Q` BMp2biB; iBM; 2tT2`BK2Mi HHv i?2 #2? pBQm` Q7 ~mB/ ~QrbX 1H biB+ bQHB/b `2 HbQ bm#D2+i iQ BMbi #BHBiB2bX 6Q` BMbi M+2- r?2M M 2HQM; i2/ bi`m+im`2 Bb bm#D2+i2/ iQ +QKT`2bbBp2 bi`2bb- bm//2M bB/2r vb /2~2+iBQM Q7 bi`m+im` H K2K#2` K v Q++m`X h?Bb b2H7@/2p2HQTBM; BMbi #BHBiv + M H2 / iQ bi`m+im` H 7 BHm`2X ai `iBM; 2bT2+B HHv rBi? i?2 bim/v Q7 i?2 #m+FHBM; BMbi #BHBiv Q7 +QHmKMb #v G2QM? `/ 1mH2` b 2 `Hv b i?2 v2 ` 1757- i?2 bim/v Q7 i?2 bi #BHBiv Q7 2H biB+ bi`m+im`2b ? b ;`2 iHv ~Qm`Bb?2/ mMiBH iQ/ v- r?2`2 7Q` BMbi M+2 # bB+ HHv 2p2`v +QKTmi2`@ B/2/ /2bB;M bQ7ir `2 ? b HBM2 ` #m+FHBM; T`2@ /B+iBQM KQ/mH2X M BMi`Q/m+iBQM iQ i?2 /QK BM + M #2 7QmM/ BM i?2 +H bbB+ H #QQF #v hBKQb?2MFQ :2`2 URNeRVX *QKT `2/ iQ ~mB/b- bQHB/b HBM2 ` BMbi #BHBiB2b `2 bBKTH2` iQ M Hvb2- 7Q` i?2B` FBM2@ K iB+b `2K BMb Q7i2M KQ`2 2 bBHv i` +i #H2 U#Qi? 2tT2`BK2Mi HHv- MmK2`B+ HHv M/ +QM+2Tim HHvVX 6m`i?2`KQ`2- i?2 +QKTmi iBQM H TQr2` BMpQHp2/ BM MmK2`B+ H bBKmH iBQMb Bb /` K iB+ HHv `2/m+2/X 6Q` i?2b2 `2 bQMb- `2+2Mi /2p2HQTK2Mib `2 2bb2MiB HHv /2pQi2/ iQ MQM@HBM2 ` bQHB/ BMbi #BHBiB2b Um@ /QHv SQK2 m- kyRyVX q?2M +QmTH2/ iQ;2i?2`- ~mB/b M/ bQHB/b T`2b2Mi QM QM2 ? M/ ivTB+ H T`2@2tBbi2Mi ~mB/ M/ bQHB/ BMbi #BHBiB2b- #mi rBi? 72 im`2b KQ/B}2/ #v i?2 BMi2` +iBQM, 7Q` BMbi M+2- i?2 pQ`i2t@b?2//BM; T bi #Hmz@#Q/B2b Bb Hi2`2/ #v bQHB/ pB#` iBQMb i? i KB;?i /2p2HQT BM i?2 bQHB/ UqBHHB KbQM :Qp `/? Mkyy9VX PM i?2 Qi?2` ? M/- M2r +H bb2b Q7 BMbi #BHBiB2b TT2 `- `2bmHiBM; 7`QK M mMbi #H2 +QmTHBM; Q7 i?2 bQHB/ M/ ~mB/ /vM KB+bX 6Q` BMbi M+2- i?2 ~Qr T bi `B;B/ +vHBM/2` #2?BM/ r?B+? ~2tB#H2 }H K2Mi Bb ii +?2/ Bb `2@ TQ`i2/ BM 6B;X k X h?2 T`2@2tBbiBM; BMbi #BHBiv BM i?2 r F2 ;2M2` i2b mMbi2 /v HQ /b QM i?2 bi`m+im`2 i? i `2 KTHB}2/- `2bmHiBM; BM i?2 H `;2@ KTHBim/2 Qb+BHH iBQMb Q7 i?2 }H K2MiX h?2 /2p2HQTK2Mi Q7 i?2 #QmM/ `v@H v2` BMbi #BHBiB2b `2 HbQ z2+i2/ #v i?2 ~2tB#BHBiv Q7 i?2 mM/2`HvBM; bm`7 +2X ai iB+ `2+QM};m` iBQMb b i?Qb2 Q#b2`p2/ BM bQHB/b KB;?i HbQ #2 T`Q/m+2/ #v i?2 HQ /b 2t2`i2/ #v i?2 bm``QmM/BM; ~mB/, M TT `2Mi M2; iBp2 biBzM2bb + M TT2 `- i? i + M mHiBK i2Hv i`B;;2` #m+FHBM; BMbi #BHBiv mbm HHv `272``2/ iQ b i?2 /Bp2`;2M+2 BMbi #BHBiv BM 2`Q2H biB+Biv U"BbTHBM;?Qz 2i HX- RN88VX aim/vBM; i?2 BMi2` +iBQM Q7 #QmM/ `v@H v2` ~Qr rBi? ~2tB#H2 +QKTHB Mi pBb+Q2H b@ iB+ +Q iBM;- : /@1H@> F 2i HX URN39V Q#b2`p2/ [m bB@bi2 /v `BTTH2b /2p2HQTBM; i i?2 bm`7 +2 Q7 i?2 +Q iBM;- b `2TQ`i2/ BM 6B;X k#X h?2 /2p2HQTK2Mi Q7 #QmM/ `v@H v2` BMbi #BHBiB2b Bb i?2M ;`2 iHv z2+i2/ #v i?2 r p2b i` p2HHBM; BM i?2 bQHB/- i? i + M BMi2` +i rBi? i?2 ~Qr M/ ;2M2` i2 M2r ivT2b Q7 BMbi #BHBiB2b U* `T2Mi2` : `` /- RN3e- RN38VX 1p2M B7 i?2 ~Qr #v Bib2H7 M/ i?2 2H biB+ bQHB/ /Q MQi T`2b2Mi BMi`BMbB+ BMbi #BHBiv K2+? MBbKb- i?2B` Kmim H BMi2` +iBQM K v `2bmHi BM mMbi #H2 bBim@ iBQMbX h?2 KQbi +H bbB+ H BMbi #BHBiv Q7 bm+? ivT2 Bb T`Q# #Hv i?2 +QmTH2/@KQ/2 ~mii2` BMbi #BHBiv Q7 rBM; T`Q}H2b- i? i `Bb2b r?2M i?2 ~2tBQM M/ iQ`bBQM KQ/2b Q7 pB#` iBQM Q7 i?2 bQHB/ BMi2` +i 7 pQm` #Hv mM/2` i?2 +iBQM Q7 i?2 ~mB/ U/2 G M;`2- kyykVX. GBM2 ` bi #BHBiv M Hvb2b 1p2M B7 i?2 rQ`H/ Bb /22THv MQM@HBM2 `- BM bQK2 + b2b Bi Bb M2p2`i?2H2bb mb27mH M/ `2H2p Mi iQ 7Q`;2i #Qmi i?Bb BM?2`2Mi +QKTH2tBivX *HQb2 iQ i?2 QMb2i Q7 i?2 BMbi #BHBiv- QM2 + M BM/22/ ?QT2 i? i i?2 T2`im`# iBQM KTHBim/2b `2 bK HH- M/ bK HH i?BM;b mbm HHv ;`Qr 2tTQM2MiB HHv #27Q`2 i?2v #2+QK2 iQQ #B; iQ ;`QrX h?Bb `2 bQMBM; 7Q`Kb i?2 # bBb Q7 i?2 HBM2 ` bi #BHBiv M HvbBb, ?Qr rBHH i?2 dzbK HH i?BM;Ǵ ;`Qr Q` /2+ v U2tTQM2MiB HHv- b bQHmiBQM Q7 HBM2 `Bb2/ T`Q#H2KV BM bT +2 M/ iBK2 \ h?Bb TT`Q +? Bb Q7 ;`2 i T` +iB+ H BMi2`2bi- 7Q` HBM2 ` T`Q#H2Kb `2 +QMbB/2` #Hv 2 bB2` iQ bQHp2 i? M MQM@HBM2 ` T`Q#H2KbX AM i?2 KQbi ;2M2` H + b2- i?2 ~mB/@bi`m+im`2 bvbi2K + M #2 /2b+`B#2/ #v /vM KB+ H bvbi2K Q7 ivT2 ∂q − N7bB (q) = 0 T7bB (q) ∂t r?2`2 q Bb bi i2 p2+iQ` +QMi BMBM; i?2 ~mB/ p2HQ+Biv }2H/- i?2 bQHB/ /BbTH +2K2Mi }2H/- 2i+X .2T2M/BM; QM i?2 KQ/2Hb +?Qb2M 7Q` i?2 ~mB/ M/ i?2 bi`m+im`2- Bib /BK2MbBQM + M ` M;2 7`QK 72r /2;`22b Q7 7`22/QK- HBF2 7Q` i?2 BMi`Q/m+iQ`v bT`BM;@KQmMi2/ ~mii2` KQ/2H 7QmM/ BM 2p2`v ;QQ/ 2`Q2H biB+Biv i2ti#QQF U"BbTHBM;?Qz 2i HX- RN88c /2 G M;`2- kyykc .Qr2HH 2i HX- kyy9V- iQ KQ`2 i? M 108 7Q` MmK2`B+ H i?`22@/BK2MbBQM H KQ/2Hb Q7 MQM@HBM2 ` 2H biB+Biv +QmTH2/ rBi? i?2 L pB2`@aiQF2b 2[m iBQMb U.2T `Bb 2i HX- kyReVX b K2MiBQM2/ #Qp2- ` i?2` i? M i`vBM; iQ bQHp2 i?Bb 2[m iBQM.
(17) 9. AMi`Q/m+iBQM U V. U#V. 6B;m`2 k Ĝ 6HmB/@bi`m+im`2 BMbi #BHBiB2bX U V h?2 pQM E`KM pQ`i2t r F2 #2?BM/ }t2/ +B`+mH ` +vHBM/2` Bb bi`QM;Hv KQ/B}2/ r?2M ~2tB#H2 }H K2Mi Bb ii +?2/ #2?BM/ i?2 +vHBM/2`X SB+im`2b i F2M #v i?2 mi?Q`- QM bQ T@}HK ~Qr 2tT2`BK2Mi i PM2` b2i@mT #v _ûKB HH M/`B2m M/ J `B2 *QmHBQm- pBbm HBb iBQM #v r?Bi2@HB;?i BMi2`72`QK2i`vX h?2 K2 M ~Qr Bb 7`QK i?2 H27i iQ i?2 `B;?iX U#V "QmM/ `v@H v2` ~Qr Qp2` pBb+Q2H biB+ T i+? UpB2r 7`QK i?2 iQTV- 7`QK : /@1H@> F 2i HX URN39VX. M/ /2i2`KBM2 i?2 7mHH ?BbiQ`v Q7 q(x, t) b 7mM+iBQM Q7 i?2 iBK2 t M/ i?2 bT +2 +QQ`/BM i2 xQM2 +QmH/ BMbi2 / i`v iQ /2i2`KBM2 QMHv QM2 bi2 /v- MQM HBM2 ` bi i2 M/ i?2M BMp2biB; i2 r?2i?2` M mMbi2 /v T2`im`# iBQM q (x, t) Q7 bi2 /v bi i2 MQM@HBM2 ` bQHmiBQM Q(x) Bb HBF2Hv iQ ;`Qr Q` MQi BM iBK2 M/fQ` bT +2X a2iiBM; q(x, t) = Q(x) + ε q (x, t) rBi? ε 1- HBM2 `Bb2/ 2[m iBQM 7Q` i?2 7mHHv +QmTH2/ ~mB/@bi`m+im`2 T2`im`# iBQM Bb 7QmM/ #v BMD2+iBM; i?2 #Qp2 /2+QKTQbBiBQM BM i?2 MQM@HBM2 ` 2[m iBQM M/ 2tT M/BM; mT iQ i?2 Q`/2` ε, ∂ () T7bB (Q) − N7bB (Q) q = f , ∂t r?2`2 ∂N7bB /∂q|Q Bb i?2 HBM2 `Bb2/ ~mB/@bi`m+im`2 QT2` iQ`X AM i?Bb HBM2 `Bb2/ T`Q#H2K- 7Q`+BM; i2`K f ? b #22M //2/ BM i?2 `B;?i@? M/ bB/2 bQ b iQ KQ/2H bK HH 2ti2`M H T2`im`# iBQMb FBM 7Q` BMbi M+2 iQ 7`22@bi`2 K im`#mH2M+2 Q` ;mbib- pB#` iBQMb BM i?2 bQHB/- 2i+X PM+2 i?2 HBM2 ` T2`im`@ # iBQM T`Q#H2K () Bb /2`Bp2/- i?2`2 Bb biBHH iQ M Hvb2 i?2 #2? pBQm` Q7 i?2 T2`im`# iBQM }2H/ q BM iBK2 M/ bT +2X a2p2` H [m2biBQMb + M #2 ` Bb2/ i i?Bb TQBMi- 7Q` BMbi M+2, r? i Bb i?2 bvKTiQiB+ #2? pBQm` Q7 q b t → ∞ \ >Qr Bb q z2+i2/ B7 bQK2 +QKTQM2Mib Q7 i?2 bvbi2K `2 7Q`+2/ #v i?2 2ti2`M H MQBb2 bB;M H f \ q? i rQmH/ #2 i?2 KQbi /2i`BK2Mi H ivT2 Q7 bB;M H 7Q` i?2 bi #BHBiv Q7 i?2 bvbi2K \ q? i BMBiB H +QM/BiBQM `2bmHib BM i?2 K tBKmK KTHB}+ iBQM Q7 i?2 T2`im`# iBQM 2M2`;v \ q?2M Bb i?Bb K tBK H p Hm2 `2 +?2/ \ q?2`2 Bb i?2 2M2`;v HQ+ i2/ \ .Q2b i?2 2pQHmiBQM Q7 i?2 T2`im`# iBQM ;Bp2 BMi2`2biBM; BM7Q`K iBQM QM i?2 #2? pBQm` Q7 i?2 7mHH MQM@HBM2 ` bvbi2K \ 2i+X .2T2M/BM; QM i?2 M im`2 Q7 i?2 T?vbB+ H T`Q#H2K- /Bz2`2Mi +H bb2b Q7 M Hvb2b `2 TT`QT`B i2 iQ /2b+`B#2 i?2 HBM2 ` `2;BK2 Q7 HH Q7 i?2b2 BMbi #BHBiB2bX b 2t2KTHB}2/ #27Q`2- r?BH2 bQK2 bvbi2Kb i2M/ iQ bTQMi M2QmbHv 2pQHp2 iQr `/b M Qb+BHH iBM; bi i2- bQK2 Qi?2` bvbi2Kb `2 QM i?2 Qi?2` ? M/ ` i?2` FMQrM iQ KTHB7v 2ti2`M H T2`im`# iBQMbX h?Bb /BbiBM+iBQM Bb mbm HHv K /2 BM ~mB/ K2+? MB+b U>m2``2 JQMF2rBix- RNNyV r?2`2 i?2 HQr@_2vMQH/b MmK#2` ~Qr #2?BM/ +vHBM/2` Bb T`Q# #Hv i?2 KQbi 7 KQmb 2t KTH2 Q7 M Qb+BHH iQ` ~Qr- r?BH2 #QmM/ `v H v2` `2T`2b2Mib .
(18) 8 ivTB+ H MQBb2@ KTHB}2` ~QrX Ai Bb i?mb TT`QT`B i2 iQ +QM+2Tim HHv M/ K i?2K iB+ HHv bTHBi i?2 HBM2 ` #2? pBQm` #2ir22M b2H7@bmbi BM2/ T `i M/ b2+QM/ T `i i? i /2T2M/b QM 2ti2`M H 7Q`+BM;bX h?2 2B;2Mp Hm2 M HvbBb Q7 i?2 HBM2 `Bb2/ QT2` iQ` Bb TT`QT`B i2 7Q` +? ` +i2`BxBM; i?2 b2H7@ /2p2HQTBM; /vM KB+b UaBTT 2i HX- kyRyc h?2Q}HBb- kyRRc CmMBT2` 2i HX- kyR9V, i?2 HQM;@i2`K 2pQHmiBQM Q7 i?2 T2`im`# iBQM + M BM/22/ #2 +? ` +i2`Bx2/ #v i?2 2pQHmiBQM Q7 MQ`K H KQ/2b Re{q ◦ (x) exp(λt)}- λ ∈ C- /2i2`KBM2/ #v bQHpBM; i?2 +QKTH2t 2B;2Mp Hm2 T`Q#H2K λ T7bB (Q) − N7bB (Q) q ◦ = 0. q2 i?2M Q#i BM KQ/2b Q7 BMbi #BHBiv- Qb+BHH iBM; i i?2 7`2[m2M+v Im(λ) M/ ;`QrBM; Q` /2+ vBM; 2tTQM2MiB HHv rBi? iBK2 ++Q`/BM; iQ Re(λ)- M/ ? pBM; i?2 bT iB H bi`m+im`2 q ◦ (x)X h?2b2 KQ/2b `2 `2T`2b2Mi iBp2 Q7 i?2 HQM;@i2`K 2pQHmiBQM Q7 i?2 T2`im`# iBQM- bBM+2 i H `;2 iBK2b i?2 H2 bi bi #H2 KQ/2 /QKBM i2b Qp2` i?2 Qi?2` KQ/2b M/ Bb `2T`2b2Mi iBp2 Q7 i?2 T2`im`# iBQM q X AM i?2 +QMi2ti Q7 ~mB/ /vM KB+b- i?2 T`2/B+iBQMb Q7 2B;2Mp Hm2 M HvbBb r2`2 7QmM/ iQ K i+? i?2 2tT2`BK2Mib BM b2p2` H + b2bX 6Q` BMbi M+2- Bi + M T`2/B+i i?2 QMb2i 7Q` _ vH2B;?@"ûM `/ +QMp2+iBQM U"Q/2Mb+? ix 2i HX- kyyyV- Q` i?2 pQM E`KM pQ`i2t bi`22i #2?BM/ +vHBM/2` Uh`BiiQM- RN8Nc aBTT G2#2/2p- kyydV 2pQF2/ #Qp2X h?Bb TT`Q +? Bb ivTB+ HHv / Ti2/ 7Q` Qb+BHH iQ` ~Qrb i? i 2t?B#Bi QM2 bBM;H2 /QKBM Mi BMbi #BHBiv KQ/2X h?2 QMb2i Q7 bQHB/ #m+FHBM; Bb HbQ r2HH +? ` +i2`Bx2/ #v M 2B;2Mp Hm2 M HvbBb Um/QHv SQK2 m- kyRyVX AM i?2 +QMi2ti Q7 ~mB/@bQHB/ BMbi #BHBiB2b- Bi Bb 7Q` BMbi M+2 TT`QT`B i2 iQ /2i2`KBM2 i?2 QMb2i Q7 pQ`i2t@BM/m+2/ pB#` iBQMb UJBii H aBM;?- kyy8V Q` bQK2 ~ ; BMbi #BHBiB2b U/2 G M;`2- kyykc .Qr2HH 2i HX- kyy9c a?Q2H2 JBii H- kyReVX h?2 2B;2Mp Hm2 M HvbBb ?Qr2p2` Qp2`b? /Qrb M BKTQ`i Mi 2z2+i, B7 2B;2Mp Hm2b ;Bp2 i?2 bvKT@ iQiB+ #2? pBQm` r?2M t → ∞- H `;2 KTHB}+ iBQMb Q7 2X;X M BMBiB H +QM/BiBQM- 2ti2`M H MQBb2- 2i+X + M Q++m` i }MBi2 iBK2@?Q`BxQM Uh`272i?2M 2i HX- RNNjc a+?KB/- kyydVX h?Bb i` MbB2Mi ;`Qri? Q7 T2`im`# iBQMb K v i?2M #2 bm{+B2Mi iQ i`B;;2` MQM@HBM2 ` #B7m`+ iBQMb MQi MiB+BT i2/ #v i?2 2B;2Mp Hm2 M HvbBbX h?2 MQM@Q`i?Q;QM H bmT2`TQbBiBQM Q7 i?2 2B;2MKQ/2b `2T`2b2MiBM; i?2 T2`@ im`# iBQM q K v BM/22/ T`Q/m+2- i }MBi2 iBK2@?Q`BxQM- +QMbB/2` #H2 ;`Qri? Q7 i?2 MQ`K ě i? i Bb mbm HHv +?Qb2M bQ b iQ `2T`2b2Mi M 2M2`;v ě Q7 i?2 T2`im`# iBQMX h?Bb + M Q++m` 2p2M r?2M HH 2B;2Mp Hm2b `2 bi #H2 UBX2X rBi? M2; iBp2 `2 H T `iVX AM bQK2 bBim iBQMb- i?2 bT2+i`mK i?mb +QKTH2i2Hv 7 BHb iQ 2tTH BM i?2 2tT2`BK2MibX 6Q` BMbi M+2- SQBb2mBHH2 ~Qr Bb 7QmM/ iQ #2 mMbi #H2 2tT2`BK2Mi HHv 7Q` _2vMQH/b MmK#2`b #Qp2 #Qmi 1000 U* `HbQM 2i HX- RN3kV- r?BH2 M 2B;2Mp Hm2 M HvbBb UP`bx ;- RNdRV T`2/B+ib +`BiB+ H _2vMQH/b MmK#2` Q7 5772 5 J i?2K iB+ HHvi?2 MQM@MQ`K HBHiv Q7 i?2 HBM2 `Bb2/ L pB2`@aiQF2b 2[m iBQMb H2 /b +im HHv BM bQK2 + b2b iQ H `;2 i` MbB2Mi ;`Qri? Q7 2M2`;v- b `2TQ`i2/ BM i?2 H M/K `F T T2` #v h`272i?2M 2i HX URNNjVX h?2 +Q``2bTQM/BM; QT2` iQ` Bb BM/22/ 7 ` 7`QK ? pBM; Q`i?Q;QM H 2B;2MKQ/2bX S?vbB+ HHv- i?Bb Bb #2@ + mb2 Q7 /p2+iBQM i? i HHQrb 7Q` i?2 T2`im`# iBQMb iQ #2 i` MbTQ`i2/- bi`2i+?2/ M/ bT iB HHv KTHB}2/X 6Q` +QKT`2?2MbBp2 Qp2`pB2r Q7 MQM@MQ`K HBiv 2z2+ib BM ~mB/ /vM KB+b- i?2 `2 /2` Bb `272``2/ iQ i?2 `2pB2r #v a+?KB/ UkyydV M/ i?2 #QQF #v a+?KB/ >2MMBM;bQM UkyRkVX AM i?2 +QMi2ti Q7 +QmTH2/ ~mB/@bi`m+im`2 T`Q#H2Kb- BM //BiBQM iQ i?2 BMi`BMbB+ MQM@MQ`K HBiv Q7 i?2 bQHB/ Q` i?2 ~mB/ HQM2- 2ti` + mb2b Q7 MQM@MQ`K HBiv K v `Bb2 #2+ mb2 Q7 MQM@MQ`K H +QmTHBM;bX AM T `iB+mH `- Bi ? b #22M b?QrM i? i H `;2 i` MbB2Mi ;`Qri? K v Q++m` #2HQr i?2 QMb2i U b T`2/B+i2/ #v 2B;2Mp Hm2bV 7Q` +QmTH2/@KQ/2 ~mii2` Ua+?KB/ /2 G M;`2- kyykV- #mi HbQ i? i MQM@HBM2 ` i` MbBiBQMb +QmH/ #2 i`B;;2`2/ #v i?2 KTHB}+ iBQM Q7 i?2 2M2`;v Q7 ;mbib Ua+?r `ix 2i HX- kyyNc K M/QH2b2 2i HX- kyRjVX _ i?2` i? M i?2 2B;2Mp Hm2b- Bi Bb i?mb KQ`2 TT`QT`B i2 iQ /2i2`KBM2 r?B+? 7Q`+BM;b `2bmHi BM i?2 H `;2bi 2M2`;v KTHB}+ iBQMX bbmKBM; M ? `KQMB+ 7Q`+BM; i i?2 7`2[m2M+v ω- i?2 `2bQHp2Mi M HvbBb +QMbBbib BM /2i2`KBMBM; i?2 QTiBK H 7Q`+BM; f ◦ i? i T`Q/m+2b i?2 H `;2bi `2bTQMb2 q ◦ - bQHmiBQM iQ i?2 QTiBKBx iBQM T`Q#H2K −1 ◦ ◦ q bm+? i? i q = iω T (Q) − N (Q) f ◦. max 7bB 7bB ◦ f =1. .2T2M/BM; QM i?2 T?vbB+ H K2+? MBbKb i TH v- QM2 b?QmH/ i?2`27Q`2 7 pQm` QM2 Q` i?2 Qi?2` TT`Q +?X 6Q` i?2 `2 /2` MQi 7 KBHB ` rBi? i?2b2 +QM+2Tib- KQ`2 /2i BH2/- T` +iB+ H BMi`Q/m+iBQM Bb `2TQ`i2/ BM TT2M/Bt - QM M 2t KTH2 Q7 p2`v bBKTHB}2/ ~mB/@bi`m+im`2 bvbi2K `2T`2b2Mi2/ #v irQ +QmTH2/ Qb+BHH iQ`bX G2i mb MQr BMi`Q/m+2 KQ`2 bT2+B}+ HHv ?Qr ~mB/@bi`m+im`2 BMbi #BHBiB2b K v #2 /2b+`B#2/X.
(19) e. AMi`Q/m+iBQM. .2b+`BTiBQM Q7 HBM2 ` ~mB/@bi`m+im`2 BMbi #BHBiB2b *H bbB+ H TT`Q +?2b 7Q` bim/vBM; ~mB/@bQHB/ pB#` iBQMb Q7i2M `2/m+2 i?2 T`Q#H2K iQ bQHB/ K2+? M@ B+b M HvbBb- r?2`2 pB#` iBQM KQ/2b Q7 i?2 bi`m+im`2 `2 +QmTH2/ i?`Qm;? KQ/2Hb 7Q` 2`Q/vM KB+ 7Q`+2b U"BbTHBM;?Qz 2i HX- RN88c .Qr2HH 2i HX- kyy9VX 6Q` BMbi M+2- i?2 bT MrBb2 /27Q`K iBQM Q7 i?2 rBM; Bb Q7i2M KQ/2HH2/ #v bT`BM;@KQmMi2/ irQ@/BK2MbBQM H B`7QBH b2+iBQM- M/ i?2 bQ@+ HH2/ ;2M@ 2` HBx2/ 2`Q/vM KB+ 7Q`+2b `2 T`QTQ`iBQM H iQ i?2 /BbTH +2K2Mi M/fQ` i?2 p2HQ+Biv Q7 i?2 bQHB/X h?Bb TT`Q +? Bb r2HH / Ti2/ 7Q` bim/vBM; +H bbB+ H 2`Q2H biB+ T?2MQK2MQMb, i?2 +? ` +i2`BbiB+ iBK2@b+ H2 7Q` i?2 ~Qr Ui` MbBi iBK2 Q7 i?2 ~mB/ T `iB+H2b Qp2` i?2 rBM;V Bb mbm HHv Km+? bK HH2` i? M i?2 +? ` +i2`BbiB+ iBK2@b+ H2 7Q` i?2 bQHB/ UrBM; pB#` iBQM T2`BQ/V- M/ i?2 BMi`BMbB+ /vM KB+ BM i?2 ~Qr Uim`#mH2Mi r F2- pQ`i2t b?2//BM;V ? b MQ BM~m2M+2X h?2 2`Q/vM KB+ 7Q`+2b i?2M QMHv /2T2M/ QM i?2 bi iB+ TQbBiBQM Q7 i?2 rBM; M/ i?2 2`Q HbiB+ M HvbBb `2/m+2b iQ i?2 +QKTmi iBQM Q7 i?2 bi2 /v 2`Q/vM KB+ 7Q`+2b i /Bz2`2Mi M;H2b Q7 ii +F U/2 G M;`2- kyykVX h?2 +QKTH2tBiv /` K iB+ HHv BM+`2 b2b r?2M Bi Bb MQ HQM;2` TQbbB#H2 iQ b2T ` i2 i?2 bQHB/ 7`QK i?2 ~mB/ /vM KB+bX AM i? i + b2- i?2 /vM KB+ H `2 +iBQM Q7 i?2 ~Qr iQ ;2QK2i`v +? M;2b Bb Q7 Km+? KQ`2 +QKTHB+ i2/ M im`2- M/ K v /2T2M/ QM i?2 ivT2 Q7 ~Qr b r2HH b QM i?2 ivT2 Q7 ;2QK2i`vX h?2b2 + b2b `2 `272``2/ iQ b #2BM; bi`QM;Hv +QmTH2/X JQ`2 2pQHp2/ KQ/2Hb 7Q` i?2 2`Q@ /vM KB+ 7Q`+2b + M BM bQK2 2ti2Mi BMi2;` i2 mMbi2 /v 2z2+ib r?2M i?2 ~Qr Bb bbmK2/ TQi2MiB H Uh?2Q/Q`b2M- RN9NV- r?BH2 b2KB@2KTB`B+ H KQ/2Hb rBi? T ` K2i2`b 2biBK i2/ 7`QK 2tT2`BK2Mib Q` iBK2@K `+?BM; MmK2`B+ H bBKmH iBQMb `2 mb2/ r?2`2 i?2 ~Qr 72 im`2b `2 KQ`2 +QKTH2t UE `T2HRN3kVX AM bQK2 + b2b- i?2 ~Qr Bib2H7 ? b Bib QrM ě TQbbB#Hv mMbi #H2 ě /vM KB+b- b Bb 7Q` BMbi M+2 i?2 + b2 7Q` i?2 pQ`i2t b?2//BM; T bi #Hmz #Q/B2b UqBHHB KbQM :Qp `/? M- kyy9VX AM i?Bb + b2MQ ;2M2` H TT`Q +?2b `2 p BH #H2X A7 T?2MQK2MQHQ;B+ H KQ/2Hb `2 p BH #H2 U6 ++?BM2iiB 2i HXkyy9V- i?2v Q7i2M H +F Q7 ;2M2` HBivX h? MFb iQ `2+2Mi T`Q;`2bb BM ~mB/ K2+? MB+b- M2r /2p2HQTK2Mib + M #2 ?Qr2p2` +QMbB/2`2/ iQ/ vX PM2 Q7 i?2 ;Q Hb Q7 i?2 T`2b2Mi i?2bBb Bb iQ 2H #Q` i2 bm+? M2r K2i?Q/bX "2+ mb2 Q7 i?2 bT2+B H M im`2 Q7 ~mB/@bQHB/ BMi2` +iBQMb- i?2`2 `2 T`BK `BHv i?`22 t2b ++Q`/BM; iQ r?B+? r2 + M T`Q;`2bb, i?2 bQHB/ KQ/2HHBM;- i?2 ~mB/ KQ/2HHBM;- M/ i?2 ~mB/@bQHB/ +QmTHBM;X h?2b2 t2b `2 MQi bi`B+iHv Q`i?Q;QM H- bBM+2 i?2 +QmTHBM; #2ir22M KQ/2Hb /2T2M/b HbQ QM i?2B` +QMi2Mi ě 7Q` BMbi M+2- i?2 +QmTHBM; #2ir22M TQi2MiB H ~Qr iQ Mv 2H biB+Biv KQ/2H rQmH/ M2p2` 2t?B#Bi i?2 +QKTHB+ i2/ iBK2@/2H v 2z2+ib #2ir22M i?2 ~mB/ M/ i?2 bQHB/ /vM KB+b- bBM+2 i?2v `2 T`QpQF2/ #v i?2 KQK2MimK /BzmbBQM #v i?2 pBb+QbBiv Q7 i?2 ~QrX PM i?2 Qi?2` ? M/- p2`v }M2 KQ/2Hb + M HbQ BMi2` +i r2 FHv- b rQmH/ #2 i?2 + b2 BM bBKmH iBQM Q7 i?2 7mHHv im`#mH2Mi ~Qr #Qmi MQM@ HBM2 `- MBbQi`QTB+ 2H biB+ rBM; BM bi M/ `/ ~B;?i +QM/BiBQMbX :2M2` HHv bT2 FBM;- b i?2 KQ/2Hb `2 `2}M2/- Bi Bb TQbbB#H2 U#mi MQi M2+2bb `vV iQ i F2 BMiQ ++QmMi Q7 KQ`2 M/ KQ`2 722/# +F HQQTb #2ir22M i?2 bQHB/ M/ i?2 ~mB/X .2p2HQTK2Mib HQM; i?2 irQ }`bi t2b `2 BHHmbi` i2/ BM 6B;X jX b 2pQF2/ #27Q`2- i?2 +H bbB+ rBM; ~mii2` M HvbBb U V + M #2 + ``B2/ Qmi QM bT`BM;@/ KT2` KQ/2H r?2`2 i?2 irQ Qb+BHH iQ`b `2 +QmTH2/ #v K2 Mb Q7 2`Q/vM KB+ 7Q`+2b T`QTQ`iBQM H iQ i?2 i` MbH iBQMf`Qi iBQM p `B #H2bX S M2H ~mii2` U#V + M #2 bim/B2/ mbBM; bBKTH2 2`Q/vM KB+ KQ/2Hb M/ TH i2 2[m iBQMb 7Q` i?2 bQHB/X h?2 ~ TTBM; /vM KB+b Q7 `B;B/ rBM; Bb r2HH `2T`Q/m+2/ rBi? pQ`i2t K2i?Q/b- r?BH2 i?2 ~ ; ~mii2` BMbi #BHBiv ? b #22M +? ` +i2`Bx2/ rBi? TQBMi pQ`iB+2b BMi2` +iBM; rBi? pB#` iBM; bi`BM; KQ/2HX 2`Q2H biB+ M Hvb2b U2-;V `2 iQ/ v +QKKQMHv + ``B2/ Qmi mbBM; M 1mH2` ~Qr M/ #2 K 2H2K2Mib Q` }MBi2@2H2K2Mi 2H biB+Biv bi`m+im` H KQ/2HX h?2 H KBM ` pQ`i2t@BM/m+2/ pB#` iBQMb U7V Q7 +B`+mH ` +vHBM/2` `2 `2T`Q/m+2/ mbBM; bT`BM;@KQmMi2/ `B;B/ Q#D2+i BMi2` +iBM; rBi? L pB2`@aiQF2b ~QrX 2`Q2H biB+ +QKTmi iBQMb Q7 rBM/ im`#BM2 U?V + M #2 + ``B2/ Qmi #v +QK#BMBM; #2 K@2H2K2Mib 7Q` i?2 #H /2b M/ im`#mH2Mi ~QrX 6BM HHv- i?2 H `;2 2H biB+ /27Q`K iBQMb T`QpQF2/ #v i?2 #HQQ/ ~Qr i?`Qm;? `i2`B2b Bb bBKmH i2/ #v +QmTHBM; i?2 L pB2`@aiQF2b 2[m iBQMb iQ MQM@HBM2 ` 2H biB+Biv KQ/2HX LQi2 i? i i?2b2 2t KTH2b b?Qr ?Qr T?2MQK2MQM `2 +m``2MiHv KQ/2HH2/ ` i?2` i? M ?Qr +QKTHB+ i2/ i?2 `2 H +QM};m` iBQM Bb, i?2 b+ H2 Q7 M B`TH M2 K F2 Bi K M/ iQ`v iQ `2bQ`i iQ bBKTHB}2/ ~Qr KQ/2H- r?BH2 i?2 L pB2`@aiQF2b 2[m iBQMb + M iQ/ v #2 mb2/ 7Q` KQ/2HHBM; bK HH TQ`iBQM Q7 /27Q`K #H2 `i2`vX q?2M Bi +QK2b iQ i?2 i?B`/ tBb Q7 KQ/2HBx iBQM- `2+2Mi /2p2HQTK2Mib /2 HBM; rBi? bi`m+im`2b mM/2`;QBM; TQbbB#H2 i` MbBiBQMb iQr `/b H `;2@ KTHBim/2 Qb+BHH iBQMb BM pBb+Qmb ~Qr ? p2 2KT? @.
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(23) Ry. AMi`Q/m+iBQM. T`QT2`iB2b Q7 i?2 Q#D2+i i? i BMi2` +ib rBi? i?2 ~QrX h?2b2 B/2 b `2 2t2+mi2/ i?`Qm;? irQ +QK@ TH2K2Mi `v TT`Q +?2b- TTHB2/ iQ i?2 +QMi`QH Q7 i?2 irQ K BM K2+? MBbKb Q7 HBM2 ` BMbi #BHBiB2b BMi`Q/m+2/ T`2pBQmbHvX. a? T2 QTiBKBx iBQM 7Q` +QMi`QHHBM; b2H7@/2p2HQTBM; BMbi #BHBiB2b q?Bi? i?2B` ?B;? QT2` iBM; +Qbib- b2p2`2 2MpB`QMK2Mib M/ ?B;? b2MbBiBpBiv iQ bK HH ;2QK2i`v +? M;2b- 2`QM miB+ TTHB+ iBQMb T`QpB/2 Q#pBQmb TTHB+ iBQMb iQ b? T2 QTiBKBx iBQMX b 2 `Hv b BM i?2 +QMi2ti Q7 i?2 irQ@/BK2MbBQM H TQi2MiB H ~Qr i?2Q`v- M 2zQ`i r b Tmi QM bQHpBM; i?2 BMp2`b2 T`Q#H2K Q7 }M/BM; rBM; T`Q}H2 i? i +Q``2bTQM/b iQ bT2+B}2/ T`2bbm`2 /Bbi`B#miBQM UGB;?i?BHHRN98VX aQK2 /2+ /2b 7i2`- B/2 b 7`QK i?2 +QMi`QH i?2Q`v UGBQMb- RNdRV r2`2 TTHB2/ 7Q` KBMBKBxBM; i?2 /` ; Q7 T`Q}H2 BM aiQF2b ~Qr #v SB`QMM2 m URNdjV mbBM; M /DQBMi@# b2/ TT`Q +?- M/ 2ti2M/2/ 72r v2 `b H i2` iQ i?2 pBb+Qmb- H KBM ` + b2 #v :HQrBMbFB SB`QMM2 m URNdeVX h?2 /DQBMi TT`Q +? 7Q` i?2 b? T2 QTiBKBx iBQM Q7 rBM; BM ~Qr KQ/2HH2/ #v i?2 +QKT`2bbB#H2 1mH2` 2[m iBQMb r b }`bi //`2bb2/ #v C K2bQM URN33VX Ai ? b bBM+2 i?2M HbQ #22M 2ti2M/2/ iQ i?2 /2bB;M Q7 +QKTH2i2 B`+` 7i U_2mi?2` 2i HX- RNNeVX h?2 pBb+Qmb + b2 ? b HbQ #22M +QMbB/2`2/ UC K2bQM 2i HX- RNN3V- b r2HH b i?2 im`#mH2Mi + b2 UM/2`bQM "QM? mb- RNNNc L2K2+ 2i HX- kyy9VX AM i?2 #`Q /2` +QMi2ti Q7 ?v/`Q/vM KB+ ~Qr QTiBKBx iBQM- i?2b2 K2i?Q/b ? p2 MQr `2 +?2/ K im`Biv, KQ/mH2b 7Q` T2`7Q`KBM; /DQBMi@# b2/ ;2QK2i`B+ b? T2 QTiBKBx iBQM M/ b2MbBiBpBiv M Hvb2b `2 MQr p BH #H2 BM 2M;BM22`BM; *6. bQ7ir `2b- M/ `2 T`QKQi2/ b pB #H2 Hi2`M iBp2b iQ T ` K2i`B+ QTiBKBx iBQM ULaua- kyReVX HH Q7 i?2 #Qp2 TT`Q +?2b ?Qr2p2` `2H v QM i?2 bbmKTiBQM Q7 bi2 /v `2;BK2 M/ `B;B/ bi`m+im`2X q?2M i?2 ~Qr 72 im`2b `2 bBKTH2 UivTB+ HHv 7Q` +`mBb2 `2;BK2bV- 2`Q2H biB+ 2z2+ib + M +im HHv #2 //2/ BM `2H iBp2Hv bBKTH2 r v #v +QMbB/2`BM; [m bB@bi iB+ TT`Q +? U.Qr2HH 2i HX- kyy9VX AM i? i + b2- i?2 b? T2 QTiBKBx iBQM T`Q#H2K `2/m+2b iQ bi`m+im` H QTiBKBx iBQM T`Q#H2K rBi? 2ti2`M H HQ /b i? i KQ/2H i?2 BM~m2M+2 Q7 i?2 ~Qr U> 7iF - RNddVX q?2M i?2 ~Qr 72 im`2b `2 KQ`2 +QKTH2t- i?Bb TT`Q +? Bb mM7Q`imM i2Hv MQ HQM;2` ++m` i2X JQ`2 `2+2MiHvbi`QM;Hv +QmTH2/ TT`Q +?2b ? p2 i?2`27Q`2 #22M HbQ /`2bb2/- #mi HBKBi2/ iQ + b2b r?2`2 QMHv 72r /2bB;M T ` K2i2`b `2 mb2/ iQ `2T`2b2Mi i?2 b? T2 iQ #2 QTiBKBx2/X 6Q` BMbi M+2 >m` 2i HX Ukyy9V +QKTmi2/ /2bB;M b2MbBiBpBiB2b Q7 DQBM2/@rBM; B`+` 7i `2T`2b2Mi2/ #v #2 K KQ/2H- #v i FBM; BMiQ ++QmMi i?2 722/# +F Q7 B`HQ /b iQ i?2 bi`m+im`2- r?BH2 GmM/ 2i HX UkyyjV +QKTmi2/ i?2 KBMBK H /` ; b? T2b Q7 ~2tB#H2 Q#D2+i T ` K2i`Bx2/ #v Ll_"a +m`p2b BM bi2 /v pBb+Qmb ~Qr mbBM; 7mHHv +QmTH2/ TT`Q +?X h?2 b K2 TT`Q +? r b 7QHHQr2/ KQ`2 `2+2MiHv #v ;? D `B a+? 72` UkyR8VX 6Q` HH i?2b2 + b2b- i?2 ;` /B2Mi Bb +QKTmi2/ mbBM; }MBi2@/Bz2`2M+2bX q?2M i?2 MmK#2` Q7 b? T2 T ` K2i2`b BM+`2 b2b- i?2 /DQBMi@# b2/ TT`Q +? #2+QK2b KQ`2 2{+B2MiX h?2 F2v TQBMi Bb i?2M iQ Q#i BM i?2 /DQBMi ~mB/@bQHB/ T`Q#H2K i i?2 +QMiBMmQmb H2p2H- 7Q` Bi HHQrb iQ Q#i BM M 2tTHB+Bi 7Q`KmH 7Q` i?2 b? T2 ;` /B2Mi UHH B`2 a+?Q2M m2`- kyydVX h?Bb Bb T `iB+mH `Hv i2/BQmb i bF BM i?2 ~mB/@2H biB+ +QMi2ti- r?B+? Tmb?2/ 7Q` +QMbB/2`BM; TT`QtBK i2 TT`Q +?2b r?2`2 i?2 ;2QK2i`B+ H +QmTHBM;b `2 M2;H2+i2/ U6 BH2` 2i HX- kyRec 62TTQM 2i HX- kyR3VX hQ Qm` FMQrH2/;2- i?2 }`bi ii2KTi 7Q` /2`BpBM; i?2M bQHpBM; 7mHHv +QmTH2/ ~mB/@bi`m+im`2 /DQBMi T`Q#H2K BM M 1mH2`B M@# b2/ TT`Q +? r b /QM2 #v J MxQMB SQMiB UkyReV- r?Q /2`Bp2/ +QMiBMmQmb /DQBMi ~mB/@bi`m+im`2 T`Q#H2K 7Q` M mMbi2 /v aiQF2b ~Qr BMi2` +iBM; rBi? QM2@ /BK2MbBQM H EQBi2` bQHB/ KQ/2HX h?2B` /2`Bp iBQM `2bmHi2/ BM M mMbi2 /v aiQF2b T`Q#H2K # +Fr `/ BM iBK2 M/ 2tT`2bb2/ BM i?2 /27Q`K2/ +QM};m` iBQM- +QmTH2/ rBi? i?2 bQHB/ KQ/2H i?`Qm;? ` i?2` +QKTHB+ i2/ 7Q`+BM; i2`KX h?Bb i2`K r b 7QmM/ iQ /2T2M/ QM i?2 /DQBMi ~Qr }2H/ M/ QM i?2 ;2QK2i`B+ T`QT2`iB2b Q7 i?2 BMi2`7 +2 U7Q` BMbi M+2- i?2 2tT`2bbBQM BMpQHp2b i?2 i M;2MiB H ;` /B2Mi Q7 i?2 MQ`K HbVX h?2 mi?Q`b mb2/ i?2M i?2 /DQBMi 2[m iBQMb iQ bQHp2 b? T2 QTiBKBx iBQM T`Q#H2K BMbTB`2/ #v ? 2KQ/vM KB+b +QM+2`MbX AM i?2 T`2b2Mi rQ`F- r2 `2Hv QM i?2 G ;` M;B M@# b2/ 7Q`K HBbK 7Q` /2`BpBM; b? T2 ;` /B2Mi 7Q`KmH BM i?2 7mHHv +QmTH2/ + b2X hm`MBM; MQr QM i?2 mMbi2 /v 2z2+ib BM +QmTH2/ ~Qr@bi`m+im`2 QTiBKBx iBQM- i?2v ? p2 7Q` BMbi M+2 #22M +QMbB/2`2/ #v L / ` D ? C K2bQM UkyydV- r?Q mb2/ M /DQBMi@# b2/ K2i?Q/ +QmTH2/ rBi? M 1mH2` bQHp2` iQ QTiBKBx2 i?2 b? T2 Q7 `B;B/ B`7QBH mM/2`;QBM; T`2b+`B#2/ Qb+BH@ H iBQM- BM Q`/2` iQ KBMBKBx2 Bib iBK2@ p2` ;2 +Q2{+B2Mi Q7 /` ;X .` ; `2/m+iBQMb b ?B;? b 46 % ? p2 #22M Q#i BM2/ r?BH2 K BMi BMBM; i?2 iBK2@ p2` ;2/ HB7i +Q2{+B2MiX AM i?2 +QMi2ti Q7 KB+`Q@ B`.
(24) RR p2?B+H2 /2bB;M- ai2r `i 2i HX UkyReV mb2/ pQ`i2t@H iiB+2 2`Q/vM KB+ KQ/2H +QmTH2/ rBi? TH i2 }MBi2@2H2K2Mi KQ/2H iQ +QKTmi2 QTiBK H 7Q`+2/ ~ TTBM; rBM; /2bB;MX hQ Qm` FMQrH2/;2- QMHv 72r ii2KTib 7Q` i FBM; BMiQ ++QmMi b2H7@/2p2HQTTBM; mMbi2 /BM2bb BM i?2 ~Qr #Qmi bi`m+im`2 iQ #2 QTiBKBx2/ r2`2 /QM2X AM i?2 +QMi2ti Q7 Tm`2 ?v/`Q/vM KB+b- QM2 + M K2MiBQM i?2 rQ`F #v >2mp2@ HBM2 ai` mĽ UkyyNV r2`2 i?2 ;2QK2i`v Bb T ` K2i`Bx2/ #v 72r TQBMib- M/ i? i #v L F x r x2; KB UkyReV r?Q mb2/ M /DQBMi@# b2/ TT`Q +? rBi?Qmi M @T`BQ`B T ` K2i`Bx iBQM Q7 i?2 b? T2X 6Q` #Qi? + b2- 2zQ`ib `2 Tmi QM i?2 bi #BHBx iBQM Q7 M mMbi #H2 KQ/2 /2p2HQTBM; QM i?2 bi2 /v pBb+Qmb L pB2`@aiQF2b bQHmiBQM- BM i?2 + b2 Q7 `B;B/ ;2QK2i`vX a? T2 QTiBKBx iBQM Bb +QMbB/2`2/ ?2`2 b r v 7Q` +QMi`QHHBM; b2H7@/2p2HQTBM; ~mB/@ 2H biB+ BMbi #BHBiB2b QM bi2 /v 2[mBHB#`BmKX q2 b?Qr- iQ Qm` FMQrH2/;2 7Q` i?2 }`bi iBK2 BM i?2 +QMi2ti Q7 mMbi2 /v- bi`QM;Hv +QmTH2/ ~mB/@bi`m+im`2 BMbi #BHBiB2b- i? i M TT`QT`B i2 KQ/B}@ + iBQM Q7 i?2 ;2QK2i`v + M +?B2p2 +QMi`QH Q7 i?2b2 BMbi #BHBiB2bX h?2b2 QTiBK H ;2QK2i`B2b `2 +QKTmi2/ mbBM; ;` /B2Mi@# b2/ TT`Q +? r?2`2 M M HviB+ 7Q`KmH Bb /2`Bp2/ 7Q` i?2 b2MbBiBpBiv rBi? `2bT2+i iQ KQ/B}+ iBQM Q7 i?2 ;2QK2i`vX. ai`m+im` H QTiBKBx iBQM 7Q` +QMi`QHHBM; MQBb2@/`Bp2M BMbi #BHBiB2b MQi?2` r v Q7 +QMi`QHHBM; ~mB/@bQHB/ BMbi #BHBiB2b Bb iQ +i- ` i?2` i? M QM i?2 b? T2- i i?2 H2p2H Q7 i?2 K i2`B H T`QT2`iB2b i?2Kb2Hp2b UHQ+ H biBzM2bb- /2MbBiv- 2i+XVX h?Bb TT`Q +? Bb T `iB+mH `Hv / Ti2/ 7Q` i?2 TTHB+ iBQM + b2 Q7 i?2 i` MbBiBQM /2H v #v i?2 mb2 Q7 +QKTHB Mi +Q iBM;bX 6QHHQrBM; i?2 2 `Hv ii2KTib #v E` K2` URNeyV- K Mv 2tT2`BK2Mi H TT`Q +?2b ? p2 BM/22/ i`B2/ iQ `2/m+2 i?2 /` ; rBi? +QKTHB Mi bm`7 +2b rBi? /Bz2`2Mi K i2`B H T`QT2`iB2b- #Qi? BM i?2 +QMi2ti Q7 im`#mH2Mi U*?QB 2i HX- RNNdc " M/vQT /?v v 2i HX- kyy8V M/ H KBM ` U: bi2`- RN33c : /@1H@> F 2i HX- RN39V #QmM/ `v@H v2` ~QrbX h?2b2b bim/B2b ?B;?HB;?i2/ i?2 M22/ 7Q` ?B;?Hv +QKTHB Mi +Q iBM;b- Q7i2M K /2 T` +iB+ HHv b +QK#BM iBQM Q7 TQHvK2`B+ K i2`B HbX b 2 `Hv b BM i?2 rQ`F #v "2MD KBM URNeyV- bm;;2biBQMb ? p2 #22M K /2 bQ b iQ /2bB;M TT`QT`B i2 +Q iBM;b 7Q` /2H vBM; i?2 #QmM/ `v@H v2` i` MbBiBQMX " b2/ QM MmK2`B+ H +QKTmi iBQMb* `T2Mi2` URNNjV 2biBK i2/ i?2 TQi2MiB H #2M2}ib- BM i2`Kb Q7 i` MbBiBQM H _2vMQH/b MmK#2`- i? i +QmH/ #2 `2i`B2p2/ 7`QK i?2 mb2 Q7 bQ7i r HHbX >Bb #2bi@T2`7Q`KBM; +QKTHB Mi T M2H ; p2 M BM+`2 b2 Q7 i?2 i` MbBiBQM H _2vMQH/b MmK#2` #v 7 +iQ` 4.6X *QMbB/2`BM; irQ T M2Hb KQmMi2/ BM b2`B2b- i?2 ; BM `2 +?2/ 7 +iQ` 6X " b2/ QM i?Bb Q#b2`p iBQM- ?2 bm;;2bi2/ i? i mbBM; KmHiB@T M2H r HH- 2 +? i BHQ`2/ 7Q` bT2+B}+ ` M;2 Q7 _2vMQH/b MmK#2`b- rQmH/ T`Q# #Hv T`Q/m+2 i?2 H `;2bi i` MbBiBQM /2H vX * `T2Mi2` JQ``Bb URNNyV BMp2biB; i2/ i?2 2z2+i Q7 K i2`B H MBbQi`QTv- #v //BM; i2`K i? i #`2 Fb i?2 BbQi`QTv Q7 i?2 TH i2 `2bTQMb2 rBi? `2bT2+i iQ ~Qr `2p2`b HX h?Bb TT`Q +? r b BMi2M/2/ 7Q` KBKB+FBM; }#`2@+QKTQbBi2 MBbQi`QTB+ +QKTHB Mi r HHX h?2v Q#b2`p2/ M HKQbi i2M@7QH/ `Bb2 BM i` MbBiBQM H _2vMQH/b MmK#2`X h?2`2 ? p2 HbQ #22M 72r TT`Q +?2b +QMbB/2`BM; k/ KQ/2H U#mi ?QKQ;2M2Qmb BM i?2 bi`2 KrBb2 /B`2+iBQMV 7Q` i?2 +Q iBM;- 7Q` BMbi M+2 #v .mM+ M URN33V- r?Q b?Qr2/ i? i biBz mTT2` H v2` /2H vb i?2 TT2 ` M+2 Q7 i?2 BMbi #BHBiB2b- Q` #v .BtQM 2i HX URNN9V- r?Q Q#b2`p2/ M BM+`2 b2 Q7 i?2 i` MbBiBQM _2vMQH/b MmK#2` #v 7 +iQ` 2.5 7Q` bBM;H2@H v2` +Q iBM; M/ #v 7 +iQ` 5 7Q` irQ@H v2` +Q iBM;X h?2 QTiBKBx iBQM TT`Q +?2b T2`7Q`K2/ BM i?2 7Q`2K2MiBQM2/ T T2`b HH `2HB2/ QM M bbmKT@ iBQM Q7 ?QKQ;2M2Biv BM i H2 bi QM2 /B`2+iBQM, ?QKQ;2M2Biv BM i?2 i` Mbp2`b2 /B`2+iBQM 7Q` R/ +Q iBM;b KQ/2Hb- Q` ?QKQ;2M2Biv BM i?2 bi`2 KrBb2 /B`2+iBQM 7Q` KQ/2Hb mbBM; i?2 L pB2` 2H biB+@ Biv 2[m iBQMX 6Q` #Qi? + b2b- H v2`BM; UBM bi`2 KrBb2 Q` i` Mbp2`b2 /B`2+iBQMV b?Qr2/ M BM+`2 b2 BM i?2 i` MbBiBQM _2vMQH/b MmK#2`X 6`QK i?2b2 Q#b2`p iBQMb- QM2 + M 2tT2+i i? i 7mHHv MQM@ ?QKQ;2M2Qmb QTiBKBx2/ +Q iBM; rQmH/ b?Qr 2p2M ;`2 i2` i` MbBiBQM@/2H vBM; T`QT2`iB2bX h?2 7` K2rQ`F /2p2HQT2/ /m`BM; i?2 i?2bBb HHQrb iQ +QKTmi2 M/ /2b+`B#2 i?2 bi`m+im` H ;` /B2Mib i? i BM/B+ i2 ?Qr iQ KQ/B7v i?2 bQHB/ T`QT2`iB2b bQ b iQ HQr2` i?2 T2`im`@ # iBQM KTHB}+ iBQM ; BMb Q7 MQBb2@BM/m+2/ ~mB/@bQHB/ BMbi #BHBiv- M/ i?2M iQ + ``v Qmi M /DQBMi@# b2/ ;` /B2Mi QTiBKBx iBQMX h?Bb TT`Q +? Bb TTHB2/ iQ i?2 #QmM/ `v@H v2` ~Qr- M/ rBHH ?QT27mHHv QT2M M2r T2`bT2+iBp2b BM i?2 H`2 /v HQM; biQ`v Q7 i` MbBiBQM@/2H vBM; K i2`B HbX.
(25) Rk. AMi`Q/m+iBQM. P`; MBb iBQM Q7 i?2 K Mmb+`BTi h?2 `2bi Q7 i?2 /Bbb2`i iBQM Bb /BpB/2/ BM i?`22 T `ib- 2 +? +QMbBbiBM; Q7 irQ +? Ti2`bX }`bi T `i Bb /2pQi2/ iQ i?2 ;2M2` H K2i?Q/QHQ;v r?BH2 i?2 M2ti T `ib `2 /2pQi2/ iQ TTHB+ iBQMbX RX h?2 }`bi T `i Bb /2pQi2/ iQ ;2M2` H Qp2`pB2r Q7 i?2 MmK2`B+ H K2i?Q/b /2p2HQT2/ 7Q` MQM@ HBM2 ` M/ HBM2 ` ~mB/@bi`m+im`2 bBKmH iBQMbX Ç h?2 *? Ti2` R }`bi BMi`Q/m+2b i?2 ;2M2` H ~mB/@bi`m+im`2 7` K2rQ`F i? i rBHH #2 mb2/ i?`Qm;?Qmi i?2 bm#b2[m2Mi +? Ti2`bX h?2 `#Bi` `v G ;` M;B M 1mH2`B M 7Q`KmH iBQM Bb BMi`Q/m+2/- 7Q`KmH iBQM i? i HHQrb iQ K M ;2 i?2 +QmTHBM; #2ir22M i?2 bQHB/ M/ i?2 ~mB/ BM +QMbBbi2Mi 7 b?BQMX h?2M- 7mHHv +QmTH2/ 7Q`KmH iBQM Q7 i?2 MQM@HBM2 ` ~mB/@bi`m+im`2 T`Q#H2K Bb /2`Bp2/X AM b2+QM/ T `i- r2 T`2b2Mi M/ p HB/ i2 i?2 MmK2`@ B+ H K2i?Q/b /2p2HQT2/ iQ +QKTmi2 MQM@HBM2 ` bi2 /v bQHmiBQMb BM i?2 7Q`2K2MiBQM2/ T`Q#H2KX 7mHHv BKTHB+Bi TT`Q +? mbBM; L2riQM K2i?Q/ iQ i`2 i i?2 MQM@HBM2 `BiB2b Bb mb2/- M/ BKTH2K2Mi2/ T` +iB+ HHv mbBM; }MBi2@2H2K2Mib rBi?BM i?2 T`Q;` KKBM; H M@ ;m ;2 6`2262KYYX T `i 7`QK i?2 MmK2`B+ H BKTH2K2Mi iBQM- i?Bb BMi`Q/m+iQ`v +? T@ i2` /Q2b MQi +QK2 rBi? Q`B;BM H- M2r `2bmHibX Ç h?2 bi #BHBiv M HvbBb Q7 2H biB+ bi`m+im`2b bi`QM;Hv +QmTH2/ iQ BM+QKT`2bbB#H2 pBb+Qmb ~Qrb Bb BMp2biB; i2/ BM i?2 *? Ti2` k- # b2/ QM G ;` M;B M@# b2/ 2t +i HBM2 `Bb iBQM Q7 i?2 ;Qp2`MBM; 2[m iBQMb BMi`Q/m+2/ T`2pBQmbHvX h?2 H2 /BM; 2B;2Mp Hm2bf2B;2MKQ/2b `2 +QKTmi2/ 7Q` i?`22 +QM};m` iBQMb `2T`2b2Mi iBp2 Q7 +H bbB+ H ~mB/@bi`m+im`2 BMi2` +@ iBQM BMbi #BHBiB2b- M/ 7m`i?2` M Hvb2/X AM b2+QM/ bi2T- i?2 G ;` M;B M@# b2/ TT`Q +? Bb +QKT `2/ iQ i?2 1mH2`B M@# b2/ TT`Q +? QM irQ `2T`2b2Mi iBp2 #2M+?K `F + b2bX kX h?2 b2+QM/ T `i Bb /2/B+ i2/ iQ i?2 T?vbB+ H M HvbBb M/ b? T2 QTiBKBx iBQM Q7 KQ/2H T`Q#@ H2K 2t?B#BiBM; b2H7@/2p2HQTBM; ~mB/@bi`m+im`2 BMbi #BHBiB2b, M 2H biB+ bTHBii2` TH i2 +H KT2/ #2?BM/ `B;B/ +vHBM/2` BM H KBM ` ~QrX Ç h?2 HBM2 ` M/ MQM@HBM2 ` /vM KB+b Q7 i?2 7Q`2K2MiBQM2/ bvbi2K Bb M Hvb2/ BM *? T@ i2` j- #v T2`7Q`KBM; HBM2 `- KQ/ H bi #BHBiv M Hvb2b M/ mMbi2 /v MQM@HBM2 ` bBKm@ H iBQMbX o `vBM; i?2 2H biB+Biv Q7 i?2 TH i2- /Bz2`2Mi `2;BK2b Q7 ~mB/@2H biB+ +QmTH2/ /vM KB+b `2 Q#b2`p2/ BM i?2 MQM@HBM2 ` bBKmH iBQMbX h?2b2 `2bmHib `2 }`bi /2b+`B#2/ M/ i?2M M Hvb2/ BM i?2 HB;?i Q7 i?2 HBM2 ` bi #BHBiv M HvbBbX Ç q2 //`2bb BM i?2 *? Ti2` 9 i?2 T`Q#H2K Q7 i?2 T bbBp2 +QMi`QH Q7 i?2b2 BMbi #BHBiB2b mbBM; b? T2 QTiBKBx iBQMX M /DQBMi@# b2/ K2i?Q/ 7Q` Q#i BMBM; M 2tTHB+Bi 7Q`KmH 7Q` i?2 b? T2 ;` /B2Mi Q7 +Qbi@7mM+iBQM # b2/ QM i?2 +QmTH2/ ~mB/@bi`m+im`2 2B;2Mp Hm2 Bb }`bi T`2b2Mi2/X h?2b2 `2bmHib `2 TTHB2/ QM irQ ivT2b Q7 KQ/2b 7QmM/ BM i?2 +vHBM/2` bTHBii2`@TH i2 + b2 T`2pBQmbHv bim/B2/X .27Q`KBM; i?2 +vHBM/2`Ƕb bm`7 +2 ++Q`/BM; iQ r? i Bb T`2b+`B#2/ #v i?2 b? T2 QTiBKBx iBQM H;Q`Bi?K- r2 b?Qr iQ r? i 2ti2Mi Bi Bb TQbbB#H2 iQ +QMi`QH i?2 KQ/2b #v i?Bb K2 MbX jX h?2 H bi T `i Bb /2/B+ i2/ iQ i?2 T?vbB+ H M HvbBb M/ bi`m+im` H QTiBKBx iBQM Q7 ivTB+ H MQBb2@ KTHB}2` ~Qr, #QmM/ `v@H v2` /2p2HQTBM; Qp2` ~2tB#H2 +Q iBM;X Ç AM i?2 *? Ti2` 8- r2 M Hvb2 i?2 x2`Q /p2`b2 T`2bbm`2 ;` /B2Mi- H KBM ` #QmM/ `v@ H v2` ~Qr Qp2` ~ i TH i2 BM r?B+? pBb+Q2H biB+- }MBi2@H2M;i? +QKTHB Mi +Q iBM; Bb 2K#2//2/X lbBM; `2bQHp2Mi M HvbBb- r2 BMp2biB; i2 ?Qr i?2 ~2tB#BHBiv Q7 i?2 +Q iBM; ?2HTb BM `2/m+BM; i?2 ;`Qri? Q7 HQr@7`2[m2M+v hQHHKB2M@a+?HB+?iBM; r p2b- #mi HbQ i`B;@ ;2`b ?B;?2`@7`2[m2M+v- bQHB/@# b2/ BMbi #BHBiB2bX h?2b2 H ii2` r p2b `2 ;HQ# HHv mMbi #H2 7Q` Tm`2Hv 2H biB+ +Q iBM;b M/ `2 bi #BHBx2/ #v pBb+Q2H biB+ / KTBM;- #mi K v biBHH `2bmHi BM H `;2 2M2`;v KTHB}+ iBQMb- r?B+? `2 M Hvb2/X Ç M /DQBMi@# b2/ TT`Q +? 7Q` bi`m+im` H QTiBKBx iBQM Bb T`2b2Mi2/ M/ TTHB2/ BM i?2 b?Q`i2` M/ H bi *? Ti2` e bQ b iQ /2bB;M +QKTHB Mi K i2`B H i? i / KTb i?2 hQHHKB2M@a+?HB+?iBM; r p2b- M/ BM i?2 b K2 iBK2 KBiB; i2b i?2 /2p2HQTK2Mi Q7 i` p2HHBM;@ ~mii2` r p2bX.
(26) *QMi2Mib. Rj. h?2 }M H *QM+HmbBQM bmKK `Bx2b i?2 rQ`F M/ i?2 Q#i BM2/ `2bmHib- i?2M T`2b2Mib T2`bT2+iBp2b QM 7m`i?2` /2p2HQTK2MibX aQK2 i2+?MB+ H `2bmHib- 7Q`KmH b M/ bF2i+?2b 7Q` T`QQ7b `2 `2TQ`i2/ BM i?2 TT2M/B+2b- b r2HH b b?Q`i BMi`Q/m+iBQM iQ i?2 2B;2Mp Hm2 M/ `2bQHp2Mi M Hvb2bX.
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