ﾀ 縺29135 ﾀ 縺5 [ y 1 x i R 8 x j 1 7,5 2 x , ﾁ7192, (2) ﾁ41299 f 675
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- みりあ みねむら
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1 139ｨ , ﾀ 縺48 縺 ﾀ5 縺 , ﾁ ﾀ 縺1874ｨ ﾁ : , 縺 , 395 ｨ ｨ , 935ｨ ｨ , ｨ 989 ﾁ ﾁ , U ｭ16 9-9SU ｭ ﾁ ｨ ｨ , , 2 ﾁ ｨ ｨｬ ﾀ , ﾁ ｨ ｨ , ｨ ﾁ8, 679 ｨ 縺 ﾁ ﾁ ﾀ , SU ｭ ｨ ﾁ ﾁ ﾁ ｨ ｨ , 51874ｨ XY , ｨ 9, ｨｬ ｨ " ". PACS numbers: 2.2.Nq, Ha, ﾀw, n (627) ﾁ43549 (629) ﾁ ﾁ43549 (63) ｨ (632) (635) XY (637) ｨ (639). ﾀ (64) (643) ｨｬ 2 ﾁ98915, , ｨｬ , 935ｨ ｨ ｨｬ ﾁ71927 [1] ﾀ ｨ ﾁ98919, , (95) (95) polykarp@vxitep.itep.ru; polykarp@vxdesy.desy.de ﾁ ﾁ719252, ﾁ [1] ﾀ [2]. 縺 ﾁ ﾁ , ｨ , 45 ( ) ﾁ ﾁ ﾁ ﾁ , , D , 65355ｨ ﾁ R (798. 1). 629 ｨ ﾁ4129ｨ f ｭR6 9 ｷ3 1 N ｭN X y 1 7 R1 7jx i 1 7x j j ; i;j N ｨｬ , x i ｨｬ , y ｨｬ ﾁ ｨｬ ﾁ7192, 95 f ｭR6 9 /R D f, Df ﾁ719284ｨ R, ｭ16 9 # 3.9. ﾀ
2 ﾀ 縺29135 ﾀ 縺5 [ y 1 x i R 8 x j 1 7,5 2 x , ﾁ7192, (2) ﾁ41299 f R. 縺 , 395 R (34535) ﾁ7192, 9.5. R < L f , 395 R (34535) l f , D f (1) , f ｭR6 9 / R D f, ﾁ ﾁ ｨｬ ｨ , ｨｬ ﾁ71927 ｨｬ 935ｨ [2] ｨ ｨ ; ﾁ7192, , x new ｷ3 sin ｭx old 6 9 6ｦ cos ; y old 1 y new ｷ3 1 7 sin x old 6ｦ cos ｭy old 6 9 : ｭ ｨｬ ｨ ﾁ ﾁ N ("119579"), ｨ " " 929 "39-759" , [3], , ﾁ (798. 2) , "4292ｨ 989"; ｨ , , ｨ ( ). ﾀ ﾁ ( ) ( ). ﾀ , 935ｨ 59 ﾁ719284ｨ ( ); ( ) ｨ , ｨ 9535 ﾁ ( ｨ ), , ﾁ ﾁ ｨ [3] ( ), ﾁ ｨ ﾁ ﾁ ﾁ , (a) 2 49 ﾁ ﾁ ; 154 ﾁ (1) (2) , , "786528ｨ 989" , ｨ ｨ ｨ [3]
3 , 2 6] , 縺 縺 , [1, 2] ﾁ , " ﾁ7192" ﾁ ﾀ , ﾁ ｨ [456], 縺 , ｨｬ ｨｬ ｨ. ﾀ79394, , 812ｨ , ｨ (83., , [7]) , ｨ , '9 5 ﾁ [8, 9], ｨ , ｨ , [1] ｨ , , ; ｨ 9 " " , ｨ , ｨ 9 ﾁ71927 [11], D f ﾁ ﾁ ﾁ ｨｬ SU ｭ ｨ ﾁ ｨ ﾁ ﾁ , ｨｬ ﾁ , ﾀ5ｨ 953, , " " , ﾁ , ｨ , ﾁ ﾁ , 11 q m A m ｷ3, ｨ 843, , ﾁ ｨ , , ﾁ XY " " XY ﾀ , ｨ ﾁ ﾁ43549 [12] 2 32ｨ ﾁ ﾁ ﾁ ﾁ43549 ﾀ (T c 2 3ｨ 2) 2 32ｨ ﾁ , ﾁ ﾁ , [12], , ﾁ ﾁ SU ｭ ｨ ｨ ﾁ ﾀ Ns 3N t a 8254ｨ : T ｷ3 1= ｭN t a6 9 (N s ｨｬ , N t ｨｬ ｨ ; , 4745, N s 5 N t a g, , N t, 929 g : 5 ｨ ﾁ =g 2 c 2; 32 [13, 14]. ﾀ ﾀ [15], ｨ ｨ : L / exp ｭ1 7F=T6 9. ﾀ ｨ L ｷ Tr exp4i 1=T ｭ 3 7 dt A 4 ｭx6 9 5 ; L ｭx6 9 ｷ3 1 YNt Tr U x; 4 ; 2 nｷ31 x ｷ3 ｭx; na , 2 ﾁ ﾁ43549, 345 F ｷ3 1, hli ｷ3, ﾁ F < 1 9 hli 6ｷ , L. 縺 hli , L ﾀ ｨ , ﾁ ﾁ4-3549, L, ｨ 555 ｨ , ｨ L, ｨ , E. 5 ｨ , 395 ﾁ ﾁ ｨ 59 ｨ , , ｨ ｨ 9 515ｨ 3748, , , ﾁ ﾁ ﾁ ｨ 989, , E, , ﾁ85 1 ﾀ " " ﾀ
4 ﾀ 縺29135 ﾀ 縺5 [ ｨ a I ｷ3 1; 15 ; a ｷ3 1; 3 ; 3, g 2 ｷ3 1, L. ﾀ , g 2 ｷ L > E ｨ ﾁ ﾁ ﾁ ﾁ43549, ﾁ57327 (1), , 395 D f ｷ3 2; 3 ; , D f , , ﾁ ｨ (1152) , , ｨ , , N l N s, ﾀ ﾁ SU ｭ ｨ , : T ; 95T c D f ｷ3 Nl N s : ｭ ﾁ43549 ﾁ : ﾁ , 11 ｨ , ﾁ ﾁ ﾁ =g 2 ｷ3 2; ﾁ57325 V ｷ3 const A a, 345 a ｷ3 1; 12 ; 5: 629 4=g 2 ｷ3 2; 29 ｭT < T c =g 2 ｷ3 2; 35 ｭT > T c ｨ , 95 2 ｨ V ｷ3 const A 3=2, ｨ , ｨ 9 "7712ｨ " , ﾁ [165 18], ﾁ , 縺1653, a 3 5 E ｷ3,35 5,4 5,45 6ｦ 5,5 1 1 ﾀ25548, a ﾁ V ｷ3 const A 3= D D , 65ｨ , 849-3ｨ ｨ ｨ ﾀ ｨ ﾁ ﾁ43549, , 395 D f ｷ3 2; 5 ; E ｷ3 ; 41 7; 45: , , ｨ 9, 395 a : ﾁ ﾁ [11]. 縺 , ｨ ﾁ (154 ﾁ ﾁ43549), ｨｬ ｨ s [19] ﾀ L [15] ｨｬ ｨ , 45892ｨ ﾀ5ｨ 953 s ｷ3 2 ﾁ ﾁ s 6ｷ3 2 ﾁ ﾁ , 2 ﾁ ﾁ43549 L 6ｷ3, 2 ﾁ ﾁ43549 L ｷ3 : ﾀ , , , ｨ [2522] ｨ ｨ ﾁ ｨｬ ｨ ｨ ｨｬ ｨ
5 , 2 6] , 縺 縺 A m, , , ｨ 9 1 7p < A m a 4 p (a ｨｬ ) ｨ ﾁ (679 b < b c, 345 b ｷ3 1=e 2, e ｨｬ ) , ｨ 2p=a, ( ｨｬ ﾁ5732 (5)) , ｨ [21, 22] , ｨ S, 閨88: q ｷ3 1 ｭ E ds ｷ3 1 ｭ F mn d 2 s mn : 4p 4p S S , , m ｷ3 1 ｭ E mnab F mn d 2 s ab : ｭ46 9 8p S m ｨ ( ) 2 F mn. ﾀ m, ｨ y ｭ1 7p 4 y < p ﾀ y x; m, ｨ , x ｨ m, : y x; m ｷ3 A m ｭx6 9a, 345 a ｨｬ (ｨ ) ﾁ8, : y p ｷ3 y x; m 6ｦ y x6ｦ^m; n 1 7 y x; n 1 7 y x6ｦ^n; m ｭmod 2p6 9 ｷ3 ｷ3 a 2 F mn ｭx6 9 6ｦ O ｭa ; ^m ｨｬ a, m ﾁ ( ﾀ.1) S ｷ3 b ｭ1 1 7 cos y p 6 9. ﾀ ﾁ5732 (4) 1 ｨ ｨ ( , 395 a 325), ﾁ5732 m ｷ3 1 X y p ; ｭ66 9 4p p ﾁ , ｨ ; ｨ , y x; m (6) 42747: "6ｦ", "1 7", 9 m , y p (5) mod 2p mod 2p m ｷ ｨ ﾁ ｨ ｨ m 6ｷ p ｨ , 395 m ｷ3 ; 1; ｭ 縺 , 9229ｨ , ﾁ57325 (6) ｨ , ( ｨ , " "). 2ｨ , ｨ m (6), j ｷ3 m (83. ﾀ ) , , 9 ｨ 95, , ｨ [23525], ﾁ ｨ ｨ , 412ｨ ﾁ ﾀ ｨ ﾁ [24, 25]. 縺 , , ｨ , ｨｬ ｨ 95 ﾁ D f, (3) b U ｭ ﾁ ( ) b , ﾁ ﾁ43549 ｭb < b c D f (516519, , D f > 1). ﾀ79 b > b c D f ｷ3 1: ﾀ D f ﾁ ﾁ ﾁ85, , , ｨ ｨ ﾁ ﾁ [26], ｨ ﾁ ﾁ ; 5187-
6 ﾀ 縺29135 ﾀ 縺5 [ x 4 x 3 x , , ﾁ ｨ ｨ b ﾁ , , L, ｨ ﾁ41295 f ｭL6 9 ｷ3 A exp ｭ1 7mL6 9 L a 6ｦ C 4 ; ｭ A, a; m 9 C ｨｬ C 2 59 b f ｭx6 9 ｨｬ , hf ｭ6 9 f ｭ6 9f ｭx6 9 f ｭx6 9i, C ﾁ19: 2 ﾁ , b > b c (2 ﾁ , b < b c ), ( ) 42ｨ, 395, , , ﾁ (D f ) ﾁ , D f D f > 429 b < b c 9 D f b > b c. 1 x 1 C 2 1, ｨ : () ﾁ ; (1) ﾁ , ﾁ ｨ , ｨ ( ), 2 ﾁ ｨ , [27, 28] [29, 3] , , ﾁ ,5 2, D f,5 1, b 1, ｨ b ,,5 1, 1,5 2, b ｨ b c b ｨ '9 5 ﾁ9 [31] ﾁ SU ｭN6 9-32ｨ , ﾁ ｨ 3766 U ｭ16 9 N ｨ ｨ ｨ ｨ , ｨｬ
7 , 2 6] , 縺 縺 ｨ , , , , [9, 8]: 213 ｨｬ ｨ , ｨ , ｨｬ ｨ ｨ (83., , [32]) ｨ U ｭ , SU ｭ ｨ s U ｭ16 9, U ｭ (65929, , ｨｬ ｨ SU ｭ ), SU ｭ [33] [34] 4 95, , ｨ ｨ ｨ [35] [36, 37], SU ｭ ｨ , ﾁ , 2 ﾁ [24, 25] ｨ 959 ﾁ ﾁ , ｨ , ｨ , SU ｭ ｨ , ( ) , , ﾁ ｨ 2 ﾁ [27, 28] ｨ ﾁ ﾁ [38] : , 395 ｨ ｨ , SU ｭ ｨ ﾁ , 54415, , [24, 25] 縺 , , ﾁ ﾁ [31] ｨ 3766 SU ｭ ｨｬ ｨ ﾁ , ﾁ ﾀ ﾁ ｨｬ ｨ F mn ｭx m 9 n ｨ ﾁ U x; m, ｨｬ U x; mn ( ﾀ.2), ( ﾀ.6) 11 U x; mn ｷ3 O xu x; mn O 6ｦ x : ｭ86 9 ﾀ m 9 n ( , m ｷ3 1; n ｷ3 2) O x, 395 Ux; mn 縺 , O x! exp ｭia x6 9 O exp ｭ1 7ia x 6 9 x ｭ Ux; mn ﾀ5ｨ O ｨ (9). ﾀ79 ｨ ﾁ ｨ U x; m ｨ ｨ : U 11 x; m! U11 x; m exp i ｭa x 1 7 a x6ｦm 6 9 ; U 12 x; m! U12 x; m exp i ｭa x 6ｦ a x6ｦm 6 9 : ｭ y x; m ｨ ｭU 11 ｷ3 exp ｭiy x; m 6 9jU 11 x; mj : y x; m! y x; m 6ｦ a x 1 7 a x6ｦm. ﾀ SU ｭ ｨ ｨ : 1. 閨 ﾁ93729 SU ｭ exp ｭ1 7S6 9, 345 S ｨｬ SU ｭ ﾀ SU ｭ , , U x; ﾁ ｨ y x; m ﾁ57325 (6), , ｨ U x; mn, ﾁ SU ｭ26 9! U ｭ , , ｨ , (8): X ｭx6 9! O x X ｭx6 9O 6ｦ x , ｨ ﾀ L ｭx6 9 ｷ3 YN iｷ31 U x6ｦ ｭi ^m; m ; m ｷ3 4 ; x; m ｷ , , ｨｬ ｨ [24, 25], ｨ : max O x X x; m Tr ｭU x; m s 3U 6ｦ x; m s 36 9 : ｭ Ux; m ｨｬ ( ﾀ.6), , 395 ｨ U x; m , 縺 , (11) (9), 9 ﾁ8 ｭUx; m , ﾁ ｨ ｨ : A ii m! Aii m 6ｦ i q ma, ｨｬ : A m! A m exp ｭ2ia , , 2 6
8 ﾀ 縺29135 ﾀ 縺5 [ ｨ , , SU ｭ ｨ , , y x; m, , U ｭ [39] , 395 SU ｭ U ｭ ｨ a; 2a; , ﾁ57325 (6) , ﾁ ｨ ( ), 45 9 ﾁ a (798. 9), 3a; " " [39] ; 3 3 ; ｨ 9, , 274ｨ ﾁ ｨ [4].,8,6,4,2 C 2 s=l ,4,8 1,2 1,6 T=T c () () 2 SU ｭ ｨ 縺 , ﾁ ｨ s (8925, 45892ｨ ), [39, 27, 28] : ｨｬ ﾁ ｨｬ ; ｨｬ ﾁ ｨｬ [27, 28] 429 SU ｭ ｨ ( ﾁ57325 (7) ) s, [41] , , ｨ T ｷ3 T c [28] , T < T c ( ) ｭD f ｷ T > T c , ﾁ SU ｭ ｨ ｨ [39] [42545] U x; m , , , (U x; m ｷ x 9 m) [46], ｨ [47] , ﾁ ｨ expf1 7Sg, ﾀ ﾁ , A m ｷ3 O 6ｦ q m O [39] ﾁ SU ｭ ｨ ﾁ SU ｭ g 2 1; 78, 8953 ｨ ﾁ , ﾁ ﾁ , , 395 ﾁ , ｨ 縺935993,
9 , 2 6] , 縺 縺 ,6 D f 2, D f 1, , , ,6 1, ,4 1,2 1,1 1,2 1,,,2,4,6,8 1, 1 3 1,,,2,4,6,8 1, s s ﾁ ; SU ｭ ｨ , , SU ｭ ｨ , ｨ 9, ｨ 9, , , 2 " " ; 3 3 ; , ( g); , 縺 ( ), , ｨ , [39]. 4 ｨ , ｨ U x;12 ( ﾀ.2). 縺 , ﾁ ｨ 89747, 9 ｨ , ﾀ [48]. 縺 , ｨ (" "), , , , " " ｨｬ , ｨ U 12 x; m , ｨ ﾁ ｨ U 11 x; m. ﾀ 縺935993, 54415, U 11 x; m ( U ｭ ), U 12 x; m (U ｭ ) [4855] , , SU ｭ , ｨ ﾁ5197, , ｨ U 11 x; m 9 U12 x; m [51] [52555]; ﾁ ﾀ ｨ ｨ 9 91ｨ ｨ 59: ｨ , 29445, ｨ ｨｬ ｨ 9, , , , ｨ ｨ ﾁ (83., , [56] ｨ ) , , ﾁ ｨ *
10 ﾀ 縺29135 ﾀ 縺5 [ ﾁ ｨ , ﾁ , ｨ ｨ , ｨ 9 ﾁ ﾁ , ﾁ ﾁ ﾁ A ｷ 縺 (q m A m ｷ3 ) ｨ , ﾁ ｨ : max O x X F ｭx6 9 ; x F ｭx6 9 ｷ3 XD mｷ31 Re Tr ｭO 6ｦ x U x; mo x6ｦ^m 6 9 : ｭ ﾁ ﾁ ｨ , ｨ 555 ｨ , q m A m ｷ (12) , ｨ , F ｭx6 9, 679 ｨ O x 679 ﾁ O y ｭy 6ｷ3 x6 9. ﾀ , , x ﾁ41299 F ｭx , [57], ﾁ ｨ , e 2 ｷ3 1=2, ﾀ5825
11 , 2 6] , 縺 縺 ﾁ ﾁ41299 F ｭx ,95. 縺 % F ｭx6 9 < ; , ﾁ , , [57] ﾁ719284ｨ , ｨ , , 395 D f ｨ ｨｬ ｨ ( ﾁ ｨ ), , F ｭx6 9 (512899, ﾁ ) , ｨｬ , 65ｨ , , , ｨ ｨ z, A str ｷ3 f 1 p ; x 2 6ｦ y , ﾁ A mon ｷ3 f cos y : r sin y 9845, ｨ 9 ﾁ SU ｭ ｨ [56] ﾁ , , c ﾁ d loghn ｭr=a6 9i=d log ｭr=a log ｭr=a , ﾁ SU ｭ ｨ () , D f () ｨ () ﾁ4129ｨ f ｭR ﾁ57325 (1), D f ｷ3 q ln f ｭR6 9 q ln R : ｭ136 9 ﾀ79 R < R max 1; D f 1; 679 1o R D f c , D f , ｨ ｨ ; R max 2,5. 縺 , 65ｨ 953, R ( ), D f ｨｬ D f, ﾁ57325 (13) , 395 D f R R 1 1, R ｨ 45989, 9, 1534 R ｭR 5 R 1 6 9, D f ｨｬ R 1, D f , , r r , R R max. ﾀ SU ｭN6 9! U ｭ16 97 N1 71 [31, 24, 25], , ｨ , (11) , ｨ , ﾁ57325 (13), , 395 D f , , , [56] ﾁ93729 SU ｭ g 2 ｷ3 1 (g ｨｬ ) , ﾁ (12) SU ｭ ｨ ﾀ ﾁ , 縺 , , , [56], ﾁ ﾁ ﾁ43549, , , ｭD f 1,3 679 T 4 T c ), ﾁ D f T 5 T c XY , , ｨｬ ; , ｨ ﾁ5197, a
12 ﾀ 縺29135 ﾀ 縺5 [ ｨ 595 " " [58] ｨ , , , ｨ ﾀ ( ) U ｭ , , ｨ ﾁ ﾁ ｨ 2 ｨ 95 ﾁ85, ｨ ｨ , (ｨ ﾁ ﾁ ). ﾀ ﾁ , ｨ ｨ U ｭ , " ｨ 989" ｨ , 935ｨ , " ｨ 989" ｨ , , ｨ 縺 ﾁ51952 ｨｬ ｨ D k, ｨ ﾁ519, , 724 D 1 7 k [59, 6]. 5 XY , ﾀ , ｨｬ ｨ j i, i, k ｷ3. ﾀ5ｨ 953, ﾀ , ﾁ519 j ( ﾀ.13) ｨ 429 D ｷ3 2, D ｷ D ｷ ｨ k ｷ3 1, D ｷ ﾁ519 ｨｬ ｨｬ , ﾁ [61, 62] XY D ｷ3 3 9 D ｷ3 4, , ﾁ XY ｨｬ ｨ F U ｭ ﾀ l ｭjFj F , 679 l! jfj j ｭF ｷ3 jf j exp ｭij j ( ﾀ.12) XY ﾁ ｨ j; ( ﾀ.12), , ｨ 15 2p ﾁ41295, 915, 395 f ｭx ! x! const x 2 : ﾀ , ｭa! S ｭ b ｭHj6 9 2 d D x : , ｨ k; k ｷ3, , , , k ｷ3 1, 429 " " h mn ｭx6 9 ｷ3 1 7h nm ｭx6 9, , k ｷ j 4 j ﾀ f i U ｭ16 9- c ｨ 9 " " [58], ｨ ﾁ XY , ﾀ , F ｨ ﾁ8 2p [58] ｨ ( ), ﾁ519 j 6ｷ3 ( ﾀ.13), j ｨｬ ﾁ F. 991, ﾁ XY ｨｬ ｨ , ﾁ XY ｨｬ ｨ , , l [63, 64]. 65 ﾁ , , ﾁ ﾁ ﾀ ｨ XY D ｷ ( ﾀ.12) ﾁ b c ; 4542 [65, 66] 9 b c ; D ｷ3 4 [6]. 629 D ｷ D ｷ3 4 ﾁ ｨ , ｨ ( ) ｨ ( ) ﾁ ｭb < b c ｨｬ D f > 2, D f > 1; 429 b > b c ｨ , 9 D f ｷ ｭ4DXY6 9 9 D f ｷ ｭ3DXY6 9 [67, 6]. ﾀ ﾁ XY ｨ : 679 b < b c , D ｷ ｨ D ｷ3 4, ﾀ79 b > b c ｨ ｨ. 閨7 ﾁ ﾁ ﾁ b C 59 b [67, 6], ｨ ﾁ , ﾁ , j 3 j 2
13 , 2 6] , 縺 縺 ( ) ﾀ79 b ｨ , , / , 935ｨ ( ), ﾁ577 ( ﾁ5739). ﾀ ﾁ ,1 % 縺 ｨ ( , 9577) 412ｨ 4ｨ ｨ , ﾀ b ﾁ b 6ｷ3 b c 8254ｨ ｨ , , b ｷ3, ｨ ｨ % , ,1. ﾀ79 b > b c , b g c N E ｷ g ; : N E ｷ3 n p 1 7 n l 6ｦ n s ; ｭ146 9 ｭ n p ｨｬ , n l ｨｬ n s ｨｬ , 5178ｨ ｨ , [6], " " b : P i hgi ｷ3 g i S i V P i S ; ｭ166 9 i , ﾁ j, b, g i ｨｬ , S i ｨｬ ｭV ｷ3 L ｨ , , ; ; b ﾁ ｨ , " ﾁ85" ｭb < b c ｨ ｨ ｨ ｨｬ ｨｬ hgi ｨ 89747, b < b c ,2,15,1,5 hgi , ﾁ D- 9 4DXY , ﾁ ｭb < b c , ｨ , ﾁ ｨ 35495,2,4,6,8 b , ﾁ51952, 9812ｨ , ｨｬ ﾁ ﾁ ﾀ ﾁ , ( ). 縺 , ﾁ1952 ｨｬ ｨ 95 95, ｨ "32892ｨ 9" ﾁ , ﾁ , , C (7) 4ｨ / 1=b 4975 ﾁ / exp ｭ1 7cb ﾁ ﾁ ﾁ , ﾁ ( , ) [68, 69, 2, 7, 59, 71, 6] , ﾁ519, , ｨ , [72]. ﾀ ｨ : f ｭx6 9 ｷ3 f ｭx6 9 exp ia ｭx6 97. 縺 , 35745
14 ﾀ 縺29135 ﾀ 縺5 [ ｨ : ｭ f c ｭx6 9 ｷ3 f ｭx6 9 exp i B k ｭx 1 7 y6 9A k ｭy6 9 dy : ｭ B k ｨｬ ﾁ41299 閨794: q k B k ｷ3 d ｭx6 9, A m ｨｬ , ｨ : A m ｭx6 9 ｷ3 ｷ3 A m ｭx6 9 6ｦ q m a ｭx6 9. 縺 , 395 f c ｭx6 9 ｨｬ , ｨ , ﾁ [68, 69], ｨ , ﾀ , ｨ 6971 (17), ｨ 95579ｨ, ｨｬ ｨ [71] 縺 , , ﾀ ｨ W C, C. 縺 W C , ; ｨ, ｨ ｨ 6971 (17), , [71], 縺 C ｨ ｨ, [7], ｨ ﾁ , ﾁ SU ｭ ｨ SU ｭ ｨ ｨ , , SU ｭ , , , , SU ｭ26 9! U ｭ16 9, , ﾁ5197 ( ) [48] ｨｬ ; , , , ｧ.- ﾀ. ﾀ ﾁ ﾁ99, 3.5. ﾀ , , 6 閨 h mn ｷ3 1 7h nm ｨｬ ｨ , h mn! h mn 6ｦ q m w n 1 7 q n w m, w m ｨｬ , 閨72845, , , ﾁ ﾁ ﾁ54453 (3749 MJM), ﾁ (3749 JSPS) ﾁ54453 ﾁ ( ) ｨ ﾁ ﾀ ﾀ , , , , , , ｨ , , [73] [74], , , ｨ 95 ﾀ , 縺 ｨｬ ｨ ﾁ ｨ ( D ) ｨ D (95351), 75157, (ｨ ), ｨ ,..., ｨ D , L D, L DL D ( D 75157); D ｭD =27L D , D ｭD ｭD 1 7 d 6ｦ 16 9=d!7L D ｨ d ( ), ｨ , , 75173, (9 837 ｨ ) ｨｬ , s, ｨ , j x (x ｨｬ ) U x; m , x ｨｬ , m ｨｬ , , ｨ ｨ : y x; mn ｨ , , a ｨ 7, ｨ ﾀ ｨｬ ｨ , ｨｬ , , , a ｷ3 1, 5829 ｨ , , a 2 ﾁ57321.
, , 3.5. 縺1846 [ ｨ , ｨ , ,
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Chap10.dvi
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x (x, ) x y (, y) iy x y z = x + iy (x, y) (r, θ) r = x + y, θ = tan ( y ), π < θ π x r = z, θ = arg z z = x + iy = r cos θ + ir sin θ = r(cos θ + i s
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1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2
1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
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40 4 4.3 I (1) I f (x) C [x 0 x 1 ] f (x) f 1 (x) (3.18) f (x) ; f 1 (x) = 1! f 00 ((x))(x ; x 0 )(x ; x 1 ) (x 0 (x) x 1 ) (4.8) (3.18) x (x) x 0 x 1 Z x1 f (x) dx ; Z x1 f 1 (x) dx = Z x1 = 1 1 Z x1
( ) 2.1. C. (1) x 4 dx = 1 5 x5 + C 1 (2) x dx = x 2 dx = x 1 + C = 1 2 x + C xdx (3) = x dx = 3 x C (4) (x + 1) 3 dx = (x 3 + 3x 2 + 3x +
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0 = m 2p 1 p = 1/2 p y = 1 m = 1 2 d ( + 1)2 d ( + 1) 2 = d d ( + 1)2 = = 2( + 1) 2 g() 2 f() f() = [g()] 2 = g()g() f f () = [g()g()]
![0 = m 2p 1 p = 1/2 p y = 1 m = 1 2 d ( + 1)2 d ( + 1) 2 = d d ( + 1)2 = = 2( + 1) 2 g() 2 f() f() = [g()] 2 = g()g() f f () = [g()g()]](/thumbs/92/110082312.jpg "0 = m 2p 1 p = 1/2 p y = 1 m = 1 2 d ( + 1)2 d ( + 1) 2 = d d ( + 1)2 = = 2( + 1) 2 g() 2 f() f() = [g()] 2 = g()g() f f () = [g()g()]")
8. 2 1 2 1 2 ma,y u(, y) s.t. p + p y y = m u y y p p y y m u(, y) = y p + p y y = m y ( ) 1 y = (m p ) p y = m p y p p y 2 0 m/p U U() = m p y p p y 2 2 du() d = m p y 2p p y 1 0 = m 2p 1 p = 1/2 p y
A A = a 41 a 42 a 43 a 44 A (7) 1 (3) A = M 12 = = a 41 (8) a 41 a 43 a 44 (3) n n A, B a i AB = A B ii aa
1 2 21 2 2 [ ] a 11 a 12 A = a 21 a 22 (1) A = a 11 a 22 a 12 a 21 (2) 3 3 n n A A = n ( 1) i+j a ij M ij i =1 n (3) j=1 M ij A i j (n 1) (n 1) 2-1 3 3 A A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33
e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,
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chap1.dvi
1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f
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dynamics-solution2.dvi
1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj
I y = f(x) a I a x I x = a + x 1 f(x) f(a) x a = f(a + x) f(a) x (11.1) x a x 0 f(x) f(a) f(a + x) f(a) lim = lim x a x a x 0 x (11.2) f(x) x
11 11.1 I y = a I a x I x = a + 1 f(a) x a = f(a +) f(a) (11.1) x a 0 f(a) f(a +) f(a) = x a x a 0 (11.) x = a a f (a) d df f(a) (a) I dx dx I I I f (x) d df dx dx (x) [a, b] x a ( 0) x a (a, b) () [a,
120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2
9 E B 9.1 9.1.1 Ampère Ampère Ampère s law B S µ 0 B ds = µ 0 j ds (9.1) S rot B = µ 0 j (9.2) S Ampère Biot-Savart oulomb Gauss Ampère rot B 0 Ampère µ 0 9.1 (a) (b) I B ds = µ 0 I. I 1 I 2 B ds = µ 0
z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy
f f x, y, u, v, r, θ r > = x + iy, f = u + iv C γ D f f D f f, Rm,. = x + iy = re iθ = r cos θ + i sin θ = x iy = re iθ = r cos θ i sin θ x = + = Re, y = = Im i r = = = x + y θ = arg = arctan y x e i =
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II(c) 1 October. 21, 2009 1 CS53 yamamoto@cs.kobe-u.ac.jp 3 1 7 1.1 : : : : : : : : : : : : : : : : : : : : : : 7 1.2 : : : : : : : : : : : : : : : : 8 1.2.1 : : : : : : : : : : : : : : : : : : : 8 1.2.2
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構造と連続体の力学基礎
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数学Ⅱ演習（足助・09夏）
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