l µ l µ l 0 (1, x r, y r, z r ) 1 r (1, x r, y r, z r ) l µ g µν η µν 2ml µ l ν 1 2m r 2mx r 2 2my r 2 2mz r 2 2mx r 2 1 2mx2 2mxy 2mxz 2my r 2mz 2 r

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "l µ l µ l 0 (1, x r, y r, z r ) 1 r (1, x r, y r, z r ) l µ g µν η µν 2ml µ l ν 1 2m r 2mx r 2 2my r 2 2mz r 2 2mx r 2 1 2mx2 2mxy 2mxz 2my r 2mz 2 r"

Transcription

1 2 1 (7a)(7b) λ i( w w ) + [ w + w ] 1 + w w l 2 0 Re(γ) α (7a)(7b) 2 γ 0, ( w) 2 1, w 1 γ (1) l µ, λ j γ l 2 0 Re(γ) α, λ w + w i( w w ) 1 + w w γ γ 1 w 1 r [x2 + y 2 + z 2 ] 1/2 ( w) 2 x2 + y 2 + z 2 w 2 1 γ α + iβ β 0 l 2 0 λ i 1 (7a)(7b) l 2 0 Re(γ) 1 r λ w + w i( w w ) 1 + w w w ( x w, y w, z w ), w ( x w, y w, z w ) λ 1 2 x w yz i( w zy 2 w ) 2 x w x r λ 2 y r λ 3 z r 1

2 l µ l µ l 0 (1, x r, y r, z r ) 1 r (1, x r, y r, z r ) l µ g µν η µν 2ml µ l ν 1 2m r 2mx r 2 2my r 2 2mz r 2 2mx r 2 1 2mx2 2mxy 2mxz 2my r 2mz 2 r 2 2mxy 1 2my2 2myz 2mxz 2myz 1 2mz2 ds 2 (dx 0 ) 2 (dx) 2 2m r (dx0 + xdx + ydy + zdz ) 2 r m γ γ 1 r [(x a 1) 2 + (y a 2 ) 2 + (z a 3 ) 2 ] 1/2 a i const (1) a a γ γ 1 r [x2 + y 2 + (z ia) 2 ] 1/2 γ γ l 2 0 λ i (7a)(7b) w w + iσ [x 2 + y 2 + (z ia) 2 ] 1/2 (r 2 a 2 2iaz) 1/2 (2) r 2 x 2 + y 2 + z 2 σ σ 2

3 ( + iσ) 2 2 σ 2 + 2iσ r 2 a 2 2iaz 2 σ 2 r 2 a 2 σ az 4 2 (r 2 a 2 ) a 2 z r2 a 2 ± (r 2 a 2 ) 2 + 4a 2 z 2 2 r2 a 2 2 ± ( (r2 a 2 ) a 2 z 2 ) 1/2 ± + r a 2 r2 2 + r2 2 r2 r (2) a + iσ (r 2 a 2 2iaz) 1/2 r l0 2 γ γ 1 + iσ iσ ( + iσ)( iσ) 2 + σ 2 iσ 2 + σ 2 l 2 0 Re(γ) 2 + σ a2 z a 2 z 2 3

4 (7a) λ w w (2) w (r 2 a 2 2iaz) 1/2 ( x(r 2 a 2 2iaz) 1/2, y(r 2 a 2 2iaz) 1/2, (z ia)(r 2 a 2 2iaz) 1/2) r iak w w r + iak w r r (x, y, z) k k (0, 0, 1) z (7a) w w r2 + a 2 ww r2 + a 2 w 2, w w ( 2iya w 2, 2ixa w 2, 0) λ w + w i( w w ) 1 + w w w (r iak) + w(r + iak) + 2a(r k) w 2 + r 2 + a 2 ( iσ)(r iak) + ( + iσ)(r + iak) + 2a(r k) w 2 + r 2 + a 2 2[r aσk + a(r k)] w 2 + r 2 + a 2 w w 2 (r 2 a 2 2iaz) 1/2 (r 2 a 2 + 2iaz) 1/2 ((r 2 a 2 ) 2 + 4a 2 z 2 ) 1/2 (( 2 σ 2 ) 2 + 4σ 2 2 ) 1/2 (( 2 + σ 2 ) 2 ) 1/2 2 2 r 2 a 2 + 2a 2 λ λ 2[r aσk + a(r k)] w 2 + r 2 + a 2 [r + ak az + a(r k)] ( 2 + a 2 ) 2 + a 2 [r + a2 z 2 k + a (r k)] λ 4

5 λ 1 λ 2 λ 3 x + ay 2 + a 2 y ax 2 + a a 2 [z + a2 z 2 ] z r a l µ l 0 (1, x + ay y ax 2, + a2 2 + a 2, z ), 3 l a 2 z 2 g µν η µν 2ml µ l ν g m a 2 z 2, g m 3 + ay 4 + a 2 (x z2 2 + a 2 )2 g m 3 ax 4 + a 2 (y z2 2 + a 2 )2, g m a 2 z 2 (z )2 g 01 2m 3 x + ay 4 + a 2 z a 2, g 02 2m 3 y ax 4 + a 2 z a 2 g 03 2m 3 z 4 + a 2 z 2, g 12 2m 3 (x + ay)(y ax) 4 + a 2 z 2 ( 2 + a 2 ) 2 ds 2 g 13 2m 3 z(x + ay) 4 + a 2 z 2 ( 2 + a 2 ), g 23 2m 3 z(y ax) 4 + a 2 z 2 ( 2 + a 2 ) ds 2 (dx 0 ) 2 dx 2 2m3 4 + a 2 z 2 [(dx0 ) 2 x + ay + ( 2 + a 2 )2 dx 2 y ax + ( 2 + a 2 )2 dy 2 + ( z )2 dz 2 + 2(x + ay) 2 + a 2 dx 0 dx + 2(x + ay)(y ax) + ( 2 + a 2 ) 2 dxdy + 2(y ax) 2 + a 2 dx 0 dy + 2z dx0 dz 2z(x + ay) 2z(y ax) ( 2 + a 2 dxdz + ) ( 2 + a 2 ) dydz] 2m 3 /( 4 + a 2 z 2 ) (a + b + c + d) 2 a 2 + b 2 + c 2 + d 2 + 2ab + 2ac + 2ad + 2bc + 2cd + 2bd 5

6 [ ds 2 (dx 0 ) 2 dx 2 2m3 4 + a 2 z 2 dx 0 + (dx 0 ) 2 dx 2 2m3 4 + a 2 z 2 x + ay y ax 2 dx + + a2 2 + a 2 dy + z ] 2 dz [ dx 0 (xdx + ydy) a(ydx xdy) a a 2 + z dz ] 2 (3) (Kerr) θ cos θ z φ x + iy ( sin θ) cos φ + i( sin θ) sin φ sin θ(cos φ + i sin φ) ( sin θ)e iφ ia ( ia) sin θe iφ x + iy φ u x 0 + (3) dz 2 dz 2 (cos θd sin θdθ) 2 dx 2 + dy 2 dx 2 + dy 2 d(x + iy) 2 [sin θe iφ d + ( ia) cos θe iφ dθ + i( ia) sin θe iφ dφ] [sin θe iφ d + ( + ia) cos θe iφ dθ i( + ia) sin θe iφ dφ] sin 2 θd cos 2 θdθ 2 + a 2 cos 2 θdθ sin 2 θdφ 2 + a 2 sin 2 θdφ sin θ cos θddθ + 2a sin 2 θddφ (sin θd + cos θdθ + a sin θdφ) 2 + ( sin θdφ a cos θdθ) 2 6

7 xdx + ydy xdx + ydy 1 2 (2xdx + 2ydy) 1 2 d(x2 + y 2 ) 1 d x + iy d[(2 + a 2 ) sin 2 θ] sin 2 θd + ( 2 + a 2 ) sin θ cos θdθ xdy ydx xdy ydx Im[(x + iy)d(x iy)] Im[( ia)e iφ sin θd{( + ia)e iφ sin θ}] Im[( ia)e iφ sin θ{sin θe iφ d + ( + ia)e iφ cos θdθ i( + ia)e iφ sin θdφ}] Im[( ia) sin 2 θd i( 2 + a 2 ) sin 2 θdφ + ( 2 + a 2 ) sin θ cos θdθ] ( 2 + a 2 ) sin 2 θdφ + a sin 2 θd zdz zdz cos θ(cos θd sin θdθ) cos 2 θd 2 cos θ sin θdθ xdy ydx 2m a 2 z 2 2m a 2 2 cos 2 θ 2m 2 + a 2 cos 2 θ dx 0 du d (x ) 7

8 [ ds 2 (dx 0 ) 2 dx 2 2m3 4 + a 2 z 2 dx 0 (xdx + ydy) a(xdy ydx) a a 2 + z ] 2 dz (du 2 + d 2 2dud) [(sin θd + cos θdθ + a sin θdφ) 2 + ( sin θdφ a cos θdθ) 2 + (cos θd sin θdθ) 2 ] [ 2m 2 + a 2 cos 2 du d + ( sin2 θd + ( 2 + a 2 ) sin θ cos θdθ) θ 2 + a 2 + a{(2 + a 2 ) sin 2 θdφ + a sin 2 θd} 2 + a 2 + cos2 θd 2 ] 2 cos θ sin θdθ (du 2 + d 2 2dud) (d dθ 2 + (a ) sin 2 θdφ 2 + 2a sin 2 θddφ + a 2 cos 2 θdθ 2 ) 2m [ du d + d + a sin a 2 cos 2 θdφ ] 2 θ (du 2 2dud) ( 2 dθ 2 + (a ) sin 2 θdφ 2 + 2a sin 2 θddφ + a 2 cos 2 θdθ 2 ) (1 2m 2 + a 2 cos 2 θ [du2 + a 2 sin 4 θdφ 2 + 2a sin 2 θdφdu] 2m 2 + a 2 cos 2 θ )du2 ( 2 + a 2 cos 2 θ)dθ 2 [(a ) sin 2 θ + 2ma2 sin 4 θ 2 + a 2 cos 2 θ ]dφ2 2dud 4ma sin2 θ 2 + a 2 cos 2 θ dφdu 2a sin2 θddφ (4) φ (4) ω ds 2 (c 2 ω 2 r 2 )dt 2 (dr 2 + r 2 dφ 2 + 2ωr 2 dφdt + dz 2 ) dφdt (4) ddφ, dud ds 2 g 00 du 2 + g 22 dθ 2 + g 33 dφ 2 + 2g 03 dudφ + 2g 01 dud + 2g 13 ddφ (5) cˆt u A(), du cdˆt + A d ˆφ φ B(), dφ d ˆφ + B d A B (11) 8

9 ds 2 g 00 du 2 + g 22 dθ 2 + g 33 dφ 2 + 2g 03 dudφ + 2g 01 dud + 2g 13 ddφ g 00 (cdˆt + A d) 2 + g 22 dθ 2 + g 33 (d ˆφ + B d) 2 + 2g 03 (cdˆt + A d)(d ˆφ + B d) + 2g 01 (cdˆt + A d)d + 2g 13 (d ˆφ + B d)d g 00 [(cdˆt) 2 + A 2 d 2 + 2A cdˆtd] + g 22 dθ 2 + g 33 (d ˆφ 2 + B 2 d 2 + 2B d ˆφd) + 2g 03 (cdˆtd ˆφ + A dd ˆφ + A B d 2 + B cdˆtd) + 2g 01 (cdˆt + A d)d + 2g 13 (d ˆφ + B d)d g 00 (cdˆt) 2 + (g 00 A 2 + g 33 B 2 + 2g 03 A B + 2g 01 A + 2g 13 B )d 2 + g 22 dθ 2 + g 33 d ˆφ 2 + 2g 03 cdˆtd ˆφ + 2(g 33 B + g 03 A + g 13 )d ˆφd + 2(g 00 A + g 03 B + g 01 )cdˆtd (6) d ˆφd, cdˆtd 0 A B g 33 B + g 03 A + g 13 0 g 00 A + g 03 B + g 01 0 { A g03b +g 01 g 00 B g 03A +g 13 g 33 B g 13g 00 g 03 g 01 g 2 03 g 00g 33 A g 01g 33 g 03 g 13 g 2 03 g 33g 00 g µν A g 00 g 33 (1 2m 2 + a 2 cos 2 θ )[(a2 + 2 ) sin 2 θ + 2ma2 sin 4 θ 2 + a 2 cos 2 θ ] (a ) sin 2 θ 2ma2 sin 4 θ 2 + a 2 cos 2 θ + (a2 + 2 ) sin 2 2m θ 2 + a 2 cos 2 θ + (2m)2 a 2 sin 4 θ ( 2 + a 2 cos 2 θ) 2 g 2 03 (2ma sin2 θ) 2 ( 2 + a 2 cos 2 θ) 2 9

10 g 2 03 g 00 g 33 (a ) sin 2 θ + 2ma2 sin 4 θ 2 + a 2 cos 2 θ (a2 + 2 ) sin 2 2m θ 2 + a 2 cos 2 θ (2m)2 a 2 sin 4 θ ( 2 + a 2 cos 2 θ) 2 + (2ma sin2 θ) 2 ( 2 + a 2 cos 2 θ) 2 (a2 + 2 )( 2 + a 2 cos 2 θ) sin 2 θ + 2ma 2 sin 4 θ 2m(a ) sin 2 θ 2 + a 2 cos 2 θ A g 33 g 01 [(a ) sin 2 θ + 2ma2 sin 4 θ 2 + a 2 cos 2 θ ] g 03 g 13 a sin 2 θ 2ma sin2 θ 2 + a 2 cos 2 θ g 33 g 01 g 03 g 13 (a2 + 2 )( 2 + a 2 cos 2 θ) sin 2 θ + 2ma 2 sin 4 θ 2ma 2 sin 4 θ 2 + a 2 cos 2 θ (a2 + 2 )( 2 + a 2 cos 2 θ) sin 2 θ 2 + a 2 cos 2 θ A A (a )( 2 + a 2 cos 2 θ) sin 2 θ (a )( 2 + a 2 cos 2 θ) sin 2 θ + 2ma 2 sin 4 θ 2m(a ) sin 2 θ (a )( 2 + a 2 cos 2 θ) (a )( 2 + a 2 cos 2 θ) + 2ma 2 (1 cos 2 θ) 2m(a ) (a )( 2 + a 2 cos 2 θ) ( 2 + a 2 cos 2 θ)[(a ) 2m( 2 + a 2 cos 2 θ)/( 2 + a 2 cos 2 θ)] a a m B g 00 g 13 a sin 2 θ(1 2m 2 + a 2 cos 2 θ ) g 03 g 01 2ma sin2 θ 2 + a 2 cos 2 θ 10

11 g 00 g 13 g 03 g 01 a(2 + a 2 cos 2 θ) sin 2 θ 2 + a 2 cos 2 θ B a( 2 + a 2 cos 2 θ) sin 2 θ (a )( 2 + a 2 cos 2 θ) sin 2 θ + 2ma 2 sin 4 θ 2m(a ) sin 2 θ a( 2 + a 2 cos 2 θ) (a )( 2 + a 2 cos 2 θ) + 2ma 2 (1 cos 2 θ) 2m(a ) a a m (6) d 2 g 00 A 2 + g 33 B 2 + 2g 03 A B + 2g 01 A + 2g 13 B A (g 00 A + g 03 B + g 01 ) + B (g 03 A + g 33 B + g 13 ) + g 01 A + g 13 B d ˆφd, cdˆtd ( ) 0 d 2 g 01 A + g 13 B A B (4) (6) g 01 A a a m, g 13B a 2 sin 2 θ a m a2 a 2 cos 2 θ a m ds 2 g 00 (cdˆt) 2 + (g 01 A + g 13 B )d 2 + g 22 dθ 2 + g 33 d ˆφ 2 + 2g 03 cdˆtd ˆφ (1 2m 2 + a 2 cos 2 θ )(cdˆt) a 2 cos 2 θ a m d2 ( 2 + a 2 cos 2 θ)dθ 2 [(a ) sin 2 θ + 2ma2 sin 4 θ 2 + a 2 cos 2 θ ]d ˆφ2 2 2ma sin2 θ 2 + a 2 cos 2 θ cdˆtd ˆφ (Boyer-Lindquist) a 0 e 0 11

12 dˆtd ˆφ dˆt, d ˆφ dˆtd ˆφ ( ) ds 2 a2 sin 2 θ (cdt) 2 Σ Σ d2 (2 + a 2 ) 2 a 2 sin 2 θ Σ sin 2 θdφ 2 Σdθ 2 2 2ma sin2 θ cdtdφ Σ ( Σ 2 + a 2 cos 2 θ 2 + a 2 2m 12

『共形場理論』

『共形場理論』 T (z) SL(2, C) T (z) SU(2) S 1 /Z 2 SU(2) (ŜU(2) k ŜU(2) 1)/ŜU(2) k+1 ŜU(2)/Û(1) G H N =1 N =1 N =1 N =1 N =2 N =2 N =2 N =2 ĉ>1 N =2 N =2 N =4 N =4 1 2 2 z=x 1 +ix 2 z f(z) f(z) 1 1 4 4 N =4 1 = = 1.3

More information

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

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

More information

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e 7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z

More information

Z: Q: R: C: 3. Green Cauchy

Z: Q: R: C: 3. Green Cauchy 7 Z: Q: R: C: 3. Green.............................. 3.............................. 5.3................................. 6.4 Cauchy..................... 6.5 Taylor..........................6...............................

More information

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B 9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A

More information

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3 13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >

More information

48 * *2

48 * *2 374-1- 17 2 1 1 B A C A C 48 *2 49-2- 2 176 176 *2 -3- B A A B B C A B A C 1 B C B C 2 B C 94 2 B C 3 1 6 2 8 1 177 C B C C C A D A A B A 7 B C C A 3 C A 187 187 C B 10 AC 187-4- 10 C C B B B B A B 2 BC

More information

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t 1 1.1 sin 2π [rad] 3 ft 3 sin 2t π 4 3.1 2 1.1: sin θ 2.2 sin θ ft t t [sec] t sin 2t π 4 [rad] sin 3.1 3 sin θ θ t θ 2t π 4 3.2 3.1 3.4 3.4: 2.2: sin θ θ θ [rad] 2.3 0 [rad] 4 sin θ sin 2t π 4 sin 1 1

More information

gr09.dvi

gr09.dvi .1, θ, ϕ d = A, t dt + B, t dtd + C, t d + D, t dθ +in θdϕ.1.1 t { = f1,t t = f,t { D, t = B, t =.1. t A, tdt e φ,t dt, C, td e λ,t d.1.3,t, t d = e φ,t dt + e λ,t d + dθ +in θdϕ.1.4 { = f1,t t = f,t {

More information

body.dvi

body.dvi ..1 f(x) n = 1 b n = 1 f f(x) cos nx dx, n =, 1,,... f(x) sin nx dx, n =1,, 3,... f(x) = + ( n cos nx + b n sin nx) n=1 1 1 5 1.1........................... 5 1.......................... 14 1.3...........................

More information

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t 6 6.1 6.1 (1 Z ( X = e Z, Y = Im Z ( Z = X + iy, i = 1 (2 Z E[ e Z ] < E[ Im Z ] < Z E[Z] = E[e Z] + ie[im Z] 6.2 Z E[Z] E[ Z ] : E[ Z ] < e Z Z, Im Z Z E[Z] α = E[Z], Z = Z Z 1 {Z } E[Z] = α = α [ α ]

More information

研修コーナー

研修コーナー l l l l l l l l l l l α α β l µ l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

More information

1 1 1 1 1 1 2 f z 2 C 1, C 2 f 2 C 1, C 2 f(c 2 ) C 2 f(c 1 ) z C 1 f f(z) xy uv ( u v ) = ( a b c d ) ( x y ) + ( p q ) (p + b, q + d) 1 (p + a, q + c) 1 (p, q) 1 1 (b, d) (a, c) 2 3 2 3 a = d, c = b

More information

( ) 2002 1 1 1 1.1....................................... 1 1.1.1................................. 1 1.1.2................................. 1 1.1.3................... 3 1.1.4......................................

More information

* 1 2014 7 8 *1 iii 1. Newton 1 1.1 Newton........................... 1 1.2............................. 4 1.3................................. 5 2. 9 2.1......................... 9 2.2........................

More information

CKY CKY CKY 4 Kerr CKY

CKY CKY CKY 4 Kerr CKY ( ) 1. (I) Hidden Symmetry and Exact Solutions in Einstein Gravity Houri-Y.Y: Progress Supplement (2011) (II) Generalized Hidden Symmetries and Kerr-Sen Black Hole Houri-Kubiznak-Warnick-Y.Y: JHEP (2010)

More information

untitled

untitled . 96. 99. ( 000 SIC SIC N88 SIC for Windows95 6 6 3 0 . amano No.008 6. 6.. z σ v σ v γ z (6. σ 0 (a (b 6. (b 0 0 0 6. σ σ v σ σ 0 / v σ v γ z σ σ 0 σ v 0γ z σ / σ ν /( ν, ν ( 0 0.5 0.0 0 v sinφ, φ 0 (6.

More information

lim lim lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d

lim lim lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d lim 5. 0 A B 5-5- A B lim 0 A B A 5. 5- 0 5-5- 0 0 lim lim 0 0 0 lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d 0 0 5- 5-3 0 5-3 5-3b 5-3c lim lim d 0 0 5-3b 5-3c lim lim lim d 0 0 0 3 3 3 3 3 3

More information

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1) D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y

More information

PDF

PDF 1 1 1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5 1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV

More information

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C 0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,

More information

量子力学A

量子力学A c 1 1 1.1....................................... 1 1............................................ 4 1.3.............................. 6 10.1.................................. 10......................................

More information

untitled

untitled (a) (b) (c) (d) Wunderlich 2.5.1 = = =90 2 1 (hkl) {hkl} [hkl] L tan 2θ = r L nλ = 2dsinθ dhkl ( ) = 1 2 2 2 h k l + + a b c c l=2 l=1 l=0 Polanyi nλ = I sinφ I: B A a 110 B c 110 b b 110 µ a 110

More information

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP 1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

More information

I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co

I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co 16 I ( ) (1) I-1 I-2 I-3 (2) I-1 ( ) (100 ) 2l x x = 0 y t y(x, t) y(±l, t) = 0 m T g y(x, t) l y(x, t) c = 2 y(x, t) c 2 2 y(x, t) = g (A) t 2 x 2 T/m (1) y 0 (x) y 0 (x) = g c 2 (l2 x 2 ) (B) (2) (1)

More information

IV.dvi

IV.dvi IV 1 IV ] shib@mth.hiroshim-u.c.jp [] 1. z 0 ε δ := ε z 0 z

More information

= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds

More information

http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n

http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 1 1 1.1 ɛ-n 1 ɛ-n lim n a n = α n a n α 2 lim a n = 1 n a k n n k=1 1.1.7 ɛ-n 1.1.1 a n α a n n α lim n a n = α ɛ N(ɛ) n > N(ɛ) a n α < ɛ

More information

untitled

untitled 0 ( L CONTENTS 0 . sin(-x-sinx, (-x(x, sin(90-xx,(90-xsinx sin(80-xsinx,(80-x-x ( sin{90-(ωφ}(ωφ. :n :m.0 m.0 n tn. 0 n.0 tn ω m :n.0n tn n.0 tn.0 m c ω sinω c ω c tnω ecω sin ω ω sin c ω c ω tn c tn ω

More information

第86回日本感染症学会総会学術集会後抄録(I)

第86回日本感染症学会総会学術集会後抄録(I) κ κ κ κ κ κ μ μ β β β γ α α β β γ α β α α α γ α β β γ μ β β μ μ α ββ β β β β β β β β β β β β β β β β β β γ β μ μ μ μμ μ μ μ μ β β μ μ μ μ μ μ μ μ μ μ μ μ μ μ β

More information

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-7 O1-8 O1-9 O1-10 O1-11 O1-12 O1-13 O1-14 O1-15 O1-16 O1-17 O1-18 O1-19 O1-20 O1-21 O1-22 O1-23 O1-24 O1-25 O1-26 O1-27 O1-28 O1-29 O1-30 O1-31 O1-32 O1-33 O1-34 O1-35

More information

L1-a.dvi

L1-a.dvi 27 Q C [ ] cosθ sinθ. A θ < 2π sinθ cosθ A. A ϕ A, A cosϕ cosθ sinθ cosθ sinθ A sinθ cosθ sinθ +cosθ A, cosθ sinθ+sinθ+cosθ 2 + 2 cosθ A 2 A,A cosθ sinθ 2 +sinθ +cosθ 2 2 cos 2 θ+sin 2 θ+ 2 sin 2 θ +cos

More information

学習内容と日常生活との関連性の研究-第2部-第6章

学習内容と日常生活との関連性の研究-第2部-第6章 378 379 10% 10%10% 10% 100% 380 381 2000 BSE CJD 5700 18 1996 2001 100 CJD 1 310-7 10-12 10-6 CJD 100 1 10 100 100 1 1 100 1 10-6 1 1 10-6 382 2002 14 5 1014 10 10.4 1014 100 110-6 1 383 384 385 2002 4

More information

CVMに基づくNi-Al合金の

CVMに基づくNi-Al合金の CV N-A (-' by T.Koyama ennard-jones fcc α, β, γ, δ β α γ δ = or α, β. γ, δ α β γ ( αβγ w = = k k k ( αβγ w = ( αβγ ( αβγ w = w = ( αβγ w = ( αβγ w = ( αβγ w = ( αβγ w = ( αβγ w = ( βγδ w = = k k k ( αγδ

More information

17 3 31 1 1 3 2 5 3 9 4 10 5 15 6 21 7 29 8 31 9 35 10 38 11 41 12 43 13 46 14 48 2 15 Radon CT 49 16 50 17 53 A 55 1 (oscillation phenomena) e iθ = cos θ + i sin θ, cos θ = eiθ + e iθ 2, sin θ = eiθ e

More information

1

1 016 017 6 16 1 1 5 1.1............................................... 5 1................................................... 5 1.3................................................ 5 1.4...............................................

More information

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1. 1.1 1. 1.3.1..3.4 3.1 3. 3.3 4.1 4. 4.3 5.1 5. 5.3 6.1 6. 6.3 7.1 7. 7.3 1 1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N

More information

34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2 ガウス 型 関 数 1.2 1 関 数 値 0.8 0.6 0.4 0.2 0 15 10 5 0 5 10

34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2 ガウス 型 関 数 1.2 1 関 数 値 0.8 0.6 0.4 0.2 0 15 10 5 0 5 10 33 2 2.1 2.1.1 x 1 T x T 0 F = ma T ψ) 1 x ψ(x) 2.1.2 1 1 h2 d 2 ψ(x) + V (x)ψ(x) = Eψ(x) (2.1) 2m dx 2 1 34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2

More information

-

- - - v vt t y r y W0W9WwWq c zx t - -4 ud d dr y r y x dx id d d d d x d d r Wq Wq d Uu Xd Xd -5 x dt r o Tx Ii Xd XdXd v c z x d t r o Ii Xd XdXd -6 -7 o y v vt t y W0W9WwWq -8 cc zx t d d v z r d y -9

More information

5 36 5................................................... 36 5................................................... 36 5.3..............................

5 36 5................................................... 36 5................................................... 36 5.3.............................. 9 8 3............................................. 3.......................................... 4.3............................................ 4 5 3 6 3..................................................

More information

24.15章.微分方程式

24.15章.微分方程式 m d y dt = F m d y = mg dt V y = dy dt d y dt = d dy dt dt = dv y dt dv y dt = g dv y dt = g dt dt dv y = g dt V y ( t) = gt + C V y ( ) = V y ( ) = C = V y t ( ) = gt V y ( t) = dy dt = gt dy = g t dt

More information

内科96巻3号★/NAI3‐1(第22回試験問題)

内科96巻3号★/NAI3‐1(第22回試験問題) µ µ α µ µ µ µ µ µ β β α γ µ Enterococcus faecalis Escherichia coli Legionella pneumophila Pseudomonas aeruginosa Streptococcus viridans α β 正解表正解記号問題 No. 正解記号問題 No. e(4.5) 26 e 1 a(1.2) 27 a 2

More information

kawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2

kawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2 Hanbury-Brown Twiss (ver. 1.) 24 2 1 1 1 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 3 3 Hanbury-Brown Twiss ( ) 4 3.1............................................

More information

nsg02-13/ky045059301600033210

nsg02-13/ky045059301600033210 φ φ φ φ κ κ α α μ μ α α μ χ et al Neurosci. Res. Trpv J Physiol μ μ α α α β in vivo β β β β β β β β in vitro β γ μ δ μδ δ δ α θ α θ α In Biomechanics at Micro- and Nanoscale Levels, Volume I W W v W

More information

populatio sample II, B II? [1] I. [2] 1 [3] David J. Had [4] 2 [5] 3 2

populatio sample II, B II?  [1] I. [2] 1 [3] David J. Had [4] 2 [5] 3 2 (2015 ) 1 NHK 2012 5 28 2013 7 3 2014 9 17 2015 4 8!? New York Times 2009 8 5 For Today s Graduate, Just Oe Word: Statistics Google Hal Varia I keep sayig that the sexy job i the ext 10 years will be statisticias.

More information

z z x = y = /x lim y = + x + lim y = x (x a ) a (x a+) lim z z f(z) = A, lim z z g(z) = B () lim z z {f(z) ± g(z)} = A ± B (2) lim {f(z) g(z)} = AB z

z z x = y = /x lim y = + x + lim y = x (x a ) a (x a+) lim z z f(z) = A, lim z z g(z) = B () lim z z {f(z) ± g(z)} = A ± B (2) lim {f(z) g(z)} = AB z Tips KENZOU 28 6 29 sin 2 x + cos 2 x = cos 2 z + sin 2 z = OK... z < z z < R w = f(z) z z w w f(z) w lim z z f(z) = w x x 2 2 f(x) x = a lim f(x) = lim f(x) x a+ x a z z x = y = /x lim y = + x + lim y

More information

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................ 5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)

More information

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9 1-1. 1, 2, 3, 4, 5, 6, 7,, 100,, 1000, n, m m m n n 0 n, m m n 1-2. 0 m n m n 0 2 = 1.41421356 π = 3.141516 1-3. 1 0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c),

More information

2 p T, Q

2 p T, Q 270 C, 6000 C, 2 p T, Q p: : p = N/ m 2 N/ m 2 Pa : pdv p S F Q 1 g 1 1 g 1 14.5 C 15.5 1 1 cal = 4.1855 J du = Q pdv U ( ) Q pdv 2 : z = f(x, y). z = f(x, y) (x 0, y 0 ) y y = y 0 z = f(x, y 0 ) x x =

More information

I.2 z x, y i z = x + iy. x, y z (real part), (imaginary part), x = Re(z), y = Im(z). () i. (2) 2 z = x + iy, z 2 = x 2 + iy 2,, z ± z 2 = (x ± x 2 ) +

I.2 z x, y i z = x + iy. x, y z (real part), (imaginary part), x = Re(z), y = Im(z). () i. (2) 2 z = x + iy, z 2 = x 2 + iy 2,, z ± z 2 = (x ± x 2 ) + I..... z 2 x, y z = x + iy (i ). 2 (x, y). 2.,,.,,. (), ( 2 ),,. II ( ).. z, w = f(z). z f(z), w. z = x + iy, f(z) 2 x, y. f(z) u(x, y), v(x, y), w = f(x + iy) = u(x, y) + iv(x, y).,. 2. z z, w w. D, D.

More information

140 120 100 80 60 40 20 0 115 107 102 99 95 97 95 97 98 100 64 72 37 60 50 53 50 36 32 18 H18 H19 H20 H21 H22 H23 H24 H25 H26 H27 1 100 () 80 60 40 20 0 1 19 16 10 11 6 8 9 5 10 35 76 83 73 68 46 44 H11

More information

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3 π 9 3 7 4. π 3................................................. 3.3........................ 3.4 π.................... 4.5..................... 4 7...................... 7..................... 9 3 3. p

More information

-

- - - v vt t y r y W0W9WwWq czx t - -4 u d d dr y r y x dx dd dd d d Wt Wq Wq f d x dt r o rd Wt XdXd Xd tx d Uu Xd Xd -5 v czx d t r o XdXd Xd -6 -7 o t t v vt t y y W0 W9WwWq -8 cc zx t d d y r Xd v iz

More information

96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A

96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A 7 Lorentz 7.1 Ampère I 1 I 2 I 2 I 1 L I 1 I 2 21 12 L r 21 = 12 = µ 0 2π I 1 I 2 r L. (7.1) 7.1 µ 0 =4π 10 7 N A 2 (7.2) magnetic permiability I 1 I 2 I 1 I 2 12 21 12 21 7.1: 1m 95 96 7 1m =2 10 7 N

More information

p.2/76

p.2/76 kino@info.kanagawa-u.ac.jp p.1/76 p.2/76 ( ) (2001). (2006). (2002). p.3/76 N n, n {1, 2,...N} 0 K k, k {1, 2,...,K} M M, m {1, 2,...,M} p.4/76 R =(r ij ), r ij = i j ( ): k s r(k, s) r(k, 1),r(k, 2),...,r(k,

More information

nsg04-28/ky208684356100043077

nsg04-28/ky208684356100043077 δ!!! μ μ μ γ UBE3A Ube3a Ube3a δ !!!! α α α α α α α α α α μ μ α β α β β !!!!!!!! μ! Suncus murinus μ Ω! π μ Ω in vivo! μ μ μ!!! ! in situ! in vivo δ δ !!!!!!!!!! ! in vivo Orexin-Arch Orexin-Arch !!

More information

vol.31_H1-H4.ai

vol.31_H1-H4.ai http://www.jmdp.or.jp/ http://www.donorsnet.jp/ CONTENTS 29 8,715 Vol. 31 2 3 ac ad bc bd ab cd 4 Point! Point! Point! 5 Point! Point! 6 7 314 611 122 4 125 2 72 2 102 3 2 260 312 0 3 14 3 14 18 14 60

More information

O E ( ) A a A A(a) O ( ) (1) O O () 467

O E ( ) A a A A(a) O ( ) (1) O O () 467 1 1.0 16 1 ( 1 1 ) 1 466 1.1 1.1.1 4 O E ( ) A a A A(a) O ( ) (1) O O () 467 ( ) A(a) O A 0 a x ( ) A(3), B( ), C 1, D( 5) DB C A x 5 4 3 1 0 1 3 4 5 16 A(1), B( 3) A(a) B(b) d ( ) A(a) B(b) d AB d = d(a,

More information

( V V dv = ˆx + x y ŷ + V ) z ẑ (dxˆx + dyŷ + dzẑ) (gradient) ( V V V = ˆx + x y ŷ + V ) z ẑ (infinitesimal displacement) dl = (dxˆx + dyŷ + dzẑ) θ dv

( V V dv = ˆx + x y ŷ + V ) z ẑ (dxˆx + dyŷ + dzẑ) (gradient) ( V V V = ˆx + x y ŷ + V ) z ẑ (infinitesimal displacement) dl = (dxˆx + dyŷ + dzẑ) θ dv ,2 () Needham WIKI WEB... C = A B A, B θ C C = (A B) (A B) C 2 = A 2 + B 2 2AB cos θ..2 f(x) df dx = lim f(x) x x df = (Oridinary Derivatives) ( ) df dx dx 3 V (x, y, z) ( ) ( V V dv = dx + x y ) dy +

More information

Γ Ec Γ V BIAS THBV3_0401JA THBV3_0402JAa THBV3_0402JAb 1000 800 600 400 50 % 25 % 200 100 80 60 40 20 10 8 6 4 10 % 2.5 % 0.5 % 0.25 % 2 1.0 0.8 0.6 0.4 0.2 0.1 200 300 400 500 600 700 800 1000 1200 14001600

More information

2 σ γ l σ ο 4..5 cos 5 D c D u U b { } l + b σ l r l + r { r m+ m } b + l + + l l + 4..0 D b0 + r l r m + m + r 4..7 4..0 998 ble4.. ble4.. 8 0Z Fig.4.. 0Z 0Z Fig.4.. ble4.. 00Z 4 00 0Z Fig.4.. MO S 999

More information

q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ

q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ H k r,t= η 5 Stokes X k, k, ε, ε σ π X Stokes 5.1 5.1.1 Maxwell H = A A *10 A = 1 c A t 5.1 A kη r,t=ε η e ik r ωt 5. k ω ε η k η = σ, π ε σ, ε π σ π A k r,t= q η A kη r,t+qηa kηr,t 5.3 η q η E = 1 c A

More information

I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si

I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si I 8 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No. : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin.

More information

2142B/152142B

2142B/152142B ! EFGH FIJG EFGH O m A kg A lm knm Q m B kg B m B m A A B gms x y z P Q R S T U y xz S T U D F G y F I G J z F I G J D J H G U A I y z x u O d α B P Q R S T F D E A um O ωrads u m A l kω! m A l kω m A

More information

04年度LS民法Ⅰ教材改訂版.PDF

04年度LS民法Ⅰ教材改訂版.PDF ?? A AB A B C AB A B A B A B A A B A 98 A B A B A B A B B A A B AB AB A B A BB A B A B A B A B A B A AB A B B A B AB A A C AB A C A A B A B B A B A B B A B A B B A B A B A B A B A B A B A B

More information

PSCHG000.PS

PSCHG000.PS a b c a ac bc ab bc a b c a c a b bc a b c a ac bc ab bc a b c a ac bc ab bc a b c a ac bc ab bc de df d d d d df d d d d d d d a a b c a b b a b c a b c b a a a a b a b a

More information

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y No1 1 (1) 2 f(x) =1+x + x 2 + + x n, g(x) = 1 (n +1)xn + nx n+1 (1 x) 2 x 6= 1 f 0 (x) =g(x) y = f(x)g(x) y 0 = f 0 (x)g(x)+f(x)g 0 (x) 3 (1) y = x2 x +1 x (2) y = 1 g(x) y0 = g0 (x) {g(x)} 2 (2) y = µ

More information

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

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 675 139ィ 48 1995 3. 753 165, 2 6 86 タ7 9 998917619 4381 縺48 縺55 317832645 タ5 縺4273 971927, 95652539358195 45 チ5197 9 4527259495 2 7545953471 129175253471 9557991 3.9. タ52917652 縺1874ィ 989 95652539358195 45

More information

1

1 1 2 3 4 5 6 7 8 9 10 A I A I d d d+a 11 12 57 c 1 NIHONN 2 i 3 c 13 14 < 15 16 < 17 18 NS-TB2N NS-TBR1D 19 -21BR -70-21 -70-22 20 21 22 23 24 d+ a 25 26 w qa e a a 27 28 -21 29 w w q q q w 30 r w q!5 y

More information

213 2 katurada AT meiji.ac.jp http://nalab.mind.meiji.ac.jp/~mk/pde/ 213 9, 216 11 3 6.1....................................... 6.2............................. 8.3................................... 9.4.....................................

More information

ms.dvi

ms.dvi ( ) 2010 11 21 1 review Onsager [1] 2 2 1 1 PPM 2010-09 図 1: 実験装置の図 写真中央にある円筒形の容器が超電導コイルで囲まれた真空 容器で この中に電子を閉じ込める 左側の四角い箱の中には光学系が設置されて おり 電子の像を箱左端の CCD カメラへ導く役割を担う このようにして超電導マ グネットから CCD カメラを遠ざけないと 強磁場の影響を受け正しい撮像が行え

More information

橡博論表紙.PDF

橡博論表紙.PDF Study on Retaining Wall Design For Circular Deep Shaft Undergoing Lateral Pressure During Construction 2003 3 Study on Retaining Wall Design For Circular Deep Shaft Undergoing Lateral Pressure During Construction

More information

3/4/8:9 { } { } β β β α β α β β

3/4/8:9 { } { } β β β α β α β β α β : α β β α β α, [ ] [ ] V, [ ] α α β [ ] β 3/4/8:9 3/4/8:9 { } { } β β β α β α β β [] β [] β β β β α ( ( ( ( ( ( [ ] [ ] [ β ] [ α β β ] [ α ( β β ] [ α] [ ( β β ] [] α [ β β ] ( / α α [ β β ] [ ] 3

More information

( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED)

( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED) rational number p, p, (q ) q ratio 3.14 = 3 + 1 10 + 4 100 ( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED) ( a) ( b) a > b > 0 a < nb n A A B B A A, B B A =

More information

I 1 V ( x) = V (x), V ( x) = V ( x ) SO(3) x = R x: R SO(3) Lorentz R t JR = J: J = diag(1, 1, 1, 1) x = x + a Poincarré ( ) 2

I 1 V ( x) = V (x), V ( x) = V ( x ) SO(3) x = R x: R SO(3) Lorentz R t JR = J: J = diag(1, 1, 1, 1) x = x + a Poincarré ( ) 2 III 1 2005 Jan 30th, 2006 I : II : I : [ I ] 12 13 9 (Landau and Lifshitz, Quantum Mechanics chapter 12, 13, 9: Pergamon Pr.) [ ] ( ) (H. Georgi, Lie algebra in particle physics, Perseus Books) [ ] II

More information

2 FIG. 1: : n FIG. 2: : n (Ch h ) N T B Ch h n(z) = (sin ϵ cos ω(z), sin ϵ sin ω(z), cos ϵ), (1) 1968 Meyer [5] 50 N T B Ch h [4] N T B 10 nm Ch h 1 µ

2 FIG. 1: : n FIG. 2: : n (Ch h ) N T B Ch h n(z) = (sin ϵ cos ω(z), sin ϵ sin ω(z), cos ϵ), (1) 1968 Meyer [5] 50 N T B Ch h [4] N T B 10 nm Ch h 1 µ : (Dated: February 5, 2016), (Ch), (Oblique Helicoidal) (Ch H ), Twist-bend (N T B ) I. (chiral: ) (achiral) (n) (Ch) (N ) 1996 [1] [2] 2013 (N T B ) [3] 2014 [4] (oblique helicoid) 2016 1 29 Electronic

More information

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1 1 1.1......... 1............. 1.3... 1.4......... 1.5.............. 1.6................ Bownian Motion.1.......... Einstein.............. 3.3 Einstein........ 3.4..... 3.5 Langevin Eq.... 3.6................

More information

86 6 r (6) y y d y = y 3 (64) y r y r y r ϕ(x, y, y,, y r ) n dy = f(x, y) (6) 6 Lipschitz 6 dy = y x c R y(x) y(x) = c exp(x) x x = x y(x ) = y (init

86 6 r (6) y y d y = y 3 (64) y r y r y r ϕ(x, y, y,, y r ) n dy = f(x, y) (6) 6 Lipschitz 6 dy = y x c R y(x) y(x) = c exp(x) x x = x y(x ) = y (init 8 6 ( ) ( ) 6 ( ϕ x, y, dy ), d y,, dr y r = (x R, y R n ) (6) n r y(x) (explicit) d r ( y r = ϕ x, y, dy ), d y,, dr y r y y y r (6) dy = f (x, y) (63) = y dy/ d r y/ r 86 6 r (6) y y d y = y 3 (64) y

More information

‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í

‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í Markov 2009 10 2 Markov 2009 10 2 1 / 25 1 (GA) 2 GA 3 4 Markov 2009 10 2 2 / 25 (GA) (GA) L ( 1) I := {0, 1} L f : I (0, ) M( 2) S := I M GA (GA) f (i) i I Markov 2009 10 2 3 / 25 (GA) ρ(i, j), i, j I

More information

untitled

untitled .. 3. 3 3. 3 4 3. 5 6 3 7 3.3 9 4. 9 0 6 3 7 0705 φ c d φ d., φ cd, φd. ) O x s + b l cos s s c l / q taφ / q taφ / c l / X + X E + C l w q B s E q q ul q q ul w w q q E E + E E + ul X X + (a) (b) (c)

More information