gr09.dvi

Size: px
Start display at page:

Download "gr09.dvi"

Transcription

1 .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 { D, t =,t B, t =.1.5, t.1.4 d = e φ,t dt + e λ,t d +, t dθ +in θdϕ.1.6, t m = m 8

2 . 9 Γ t tt = φ Γ t = λe λ φ Γ t t =Γ t t = φ Γ t θθ = e φ Γ = λ Γ tt = φ e φ λ Γ t =Γ t = λ Γ θθ = e λ Γ ϕϕ = e λ in θ Γ θ tθ =Γ θ θt = Γ ϕ tϕ =Γ ϕ ϕt = Γ t ϕϕ = e φ in θ Γ θ θ =Γ θ θ = Γ ϕ ϕ =Γ ϕ ϕ = : Γ θ ϕϕ = in θ co θ Γ ϕ θϕ =Γ ϕ ϕθ =cotθ..1.7 R αβ μ Γ μ αβ β Γ μ αμ +Γ μ γμγ γ αβ Γ μ γβγ γ αμ.1.8 : 8πGT t t = G t t = λ + e φ + G α β = R α β 1 δα βr μ μ.1.9 G α β =8πGT α β λ e λ πGT t = G t = e φ φ + λ.1.1 8πGT = G φ = + e λ + φ e φ πGT θ θ = G θ θ = λ + λ φ λ φ + λ + e φ + φ + φ λ φ + φ λ + e λ.1.14 ϕ, ϕ θ, θ. 1 1 pefect fluid ideal fluid

3 . 3 T μν =ρ + pu μ u ν + pg μν T μ ν =ρ + pu μ u ν + pδ μ ν..1 u μ 4 ρ p T μ ν u μ, θ, ϕ 4 u μ = dx μ /dτ u t = dt dτ = e φ u t = g tt u t = e φ, u = u θ = u ϕ = : T tt = ρe φ, T = pe λ, T θθ = p, T ϕϕ = p in θ..3 T t t = ρ, T = T θ θ = T ϕ ϕ = p..4 T μ ν;μ = : T μ ν;μ = 1 gt μ ν 1 g μα g x μ x T μα..5 ν g g μν.1.6 g = e φ+λ in θ t- T μ t;μ = 1 gt μ t 1 g μα g x μ t T μα = 1 gt t t 1 ġtt T tt +ġ T +ġ θθ T θθ +ġ ϕϕ T ϕϕ g t = 1 ρe φ+λ 1 e φ+λ t = ρ ρ φρ λρ + φρ φt t t + λt + T θ + θ T ϕ ϕ λ + p =...7 =

4 T μ ;μ = θ- ϕ- 1 ρe φ+λ 1 φ ρ +λ p +4 e φ+λ t p = p + φ ρ + φ p =...8 T μ θ;μ = 1 p in θ 1 coθ in θ θ in θ p = p =, θ..9 T μ ϕ;μ = p =, ϕ..1 ρ + λ + ρ + p =,..11 φ + 1 ρ + p p = : 8πGρ = λ + e φ + + λ e λ = φ + λ.3. 8πGp = φ + e λ + φe φ πGp = λ + λ φ λ φ φ + + λe +φ + φ λ φ + φ λ + e λ.3.4 φ, λ,, ρ, p 5 4 p ρ p = pρ

5 tt, t 3 dτ e φ dt : u τ = 1 d e φ dt = e φ.3.5 u =e φ = e φ φ }{{} = e φ λ e φ u λ =u u = u..3.7 Γ e λ.3.8 Γ =Γ +Γ Γ = e λ + λ πGρ =1+u + u + λ e λ }{{} = Γ / = [ 1 + u Γ ]..3.1 Γ= 1+u G 4πρ d.3.11 = 4 e λ d d λ Γ=e.3.11 : m, t,t 1 =,=.3.1 4πρ d

6 Γ e λ =1+u Gm, Gm, t u = Γ u = e φ φe φ πGp = φ + e λ + φe φ 1 = φ +1 Γ u ue φ πGp = Γ p ρ + p ue φ Gm φ u e t = Gm/ p 1+u ρ + p Gm 4πGp u ρ + eφ + u eφ ρ + p = t 6 u m p ρ φ= log g [ u 1 t = eφ 1+u Gm p ρ + p + Gm ] +4πGp.3. t = eφ u.3.1 ρ u t = eφ +u ρ + p.3. φ = 1 p.3.3 ρ + p m =4πρ.3.4

7 p = φ e φ dt dt φ Γ t = t e = λ λ t + t e λ = u + u e λ =..4.1 p = Γ d = e φ dt, t + d +, t dθ +in θdϕ.4. Γ p = φ = Γ Γ t =u u t G m t + Gm t = G m t.4.3 Γ m.3.14 : t = Γ 1+ Gm t = d.4.4 Gm +Γ 1 Gm +Γ 1 Gm Γ 1 Γ 1 Γ inh 1 Γ 1 > 1 3/ Gm t t = 9Gm 3/ Γ 1= Gm 1 Γ Gm 1 Γ 1 Γ 1 Γ in 1 Γ 1 < 3/ Gm.4.5 t = t = t > = t <t t t.4.4 Γ 1 Γ 1/3 9Gm t t 9Gm 3/, t t t /3.4.6, t m 1/3 G t t /3 + t 1/3 4Gm t t 1/

8 t / d dl = 1 Γ.3.4, t d 1 t Γ 1/3 4Gm t t 1/3 d, ρ, t = m 4π 1 t t.4.9 t t, t dv p =4π d 1πGm t t td.4.1 Γ Γ t t t / =.4.7 t t dl t t /3, dv p t t, ρ t t , t.1 d = e φ dt + e λ d + dθ + in θdϕ Gm ρ + p p p + Gm +4πGp = = Gρ + pm +4πp3,.5. 1 Gm/ TOV p ρ c c, 4πp 3 m 3p ρ 3c c, Gm m M.5.3

9 . 36 Gm.5. TOV ρ, p, m 3 p = Gρm.5.4 m = 4πx ρdx.5.5 p = pρ.5.5 = m = TOV i : ρ ii :.5. p = = R m mr iii :.3.14 e λ = 1 1 Gm/.5.6 iv tt : φ = 1 p ρ + p = Gm +4πp3 Gm..5.7 e φ =1 [ Gm +4πpx 3 ] φ = x Gmx dx Gm +4πpx 3 eφ =exp x Gmx dx.5.8 > p =.5.8 Gm φ = xx Gm dx = 1 1 =ln x Gm x Gm x x =ln 1 Gm e φ =1 Gm >.5.9

10 . 37 <.5.8 [ e φ Gm ] =exp xx Gm dx Gm +4πpx 3 x Gmx dx = 1 Gm [ ] Gm +4πpx 3 exp x Gmx dx = 1 Gm [ p ] dp exp ρ + p TOV : dp d = Gρ + pm +4πp3 1 Gm/.6.1 ρ =ρ.6. m.6.1 dp d = 4πGρ + pρ 3 /3+p 3 1 8πGρ /3 1 dp 4πG m = 4π 3 ρ p + ρ p + ρ /3 d = 1 8πGρ /3 = 1πG 1 8πGρ 1/κ dp p + ρ p + ρ /3 ρ d = ρ 1/κ +1/κ 1 1/κ..6.4 p + ρ p + ρ /3 κ 8πGρ /3.6.1 = R p = <R p.6.4 p = 3 p + ρ p + ρ /3 =1+ρ 1 3 p + ρ /3 =3 1 κ R <R 1 κ..6.5

11 . 38 p M 4πρ R 3 /3 1 p + ρ /3= ρ 1 κ 3 R 3 1 κ 1 = ρ 1 κ κ R 1 κ 1 κ p =ρ 1 κ R 3 1 κ R 1 κ = 3M 4πR e λ = 1 1 Gm/ 1 GM /R 3 1 GM /R 3 1 GM /R 1 GM /R 3 [ e φ =exp ] Gm +4πpx 3 x Gmx dx >R p =,ρ = m = m 1 1 R e λ = φ = = 1 1 Gm/ = 1 1 8πGρ /3 = GM /R 3 R 1 x 1 x GM Gm +4πpx 3 x Gmx dx GM x GM x dx + dx = 1 ln R x x GM 4πGx 3 p + ρ /3 x κ x4 dx..6.9 = 1 R ln 1 GM R a 1 κ R, ux 1 κ x..6.1 = R R = ln 4πGx ρ 1 κ x 3 κ x 1 κ x 1 κ x 3 1 κ R 1 κ 1 κ x 3 1 κ R 1 κ x dx x dx = a u du 3a u 3a u a 3a u φ =lna + ln[3a u] lna =ln e φ = GM 1 GM R R 3

12 . 39 <R d = GM 1 GM dt 4 R R GM 1 d + dθ +in θdϕ.6.13 R 3.6. >R p =,ρ =,m = M e λ = 1 1 GM /.6.14 Gm +4πpx 3 φ = x Gmx dx = = 1 ln 1 GM >R GM x GM x dx d = 1 GM dt + 1 GM 1 d + dθ +in θdϕ.6.16 = R Sch : R Sch GM = GM.6.17 c.6.3 <R GM > 1 GM >,.6.18 R 3 R 3 1 GM 1 GM > 3 1 GM 1 >.6.19 R R 3 R

13 R >R Sch = GM c,.6. GM R < 8 9 R > 9 8 R Sch.6.1 R < 9 8 R Sch = 9 8πG 8 3 ρ R 3 R > c 3πGρ.6. M =4πρ 3 /3 d dt = GM = 4πG 3 ρ.6.3 τ dyn 3 τ dyn.6.4 4πGρ.6. R R.6.4 : d = 1 R Sch dt + d 1 R Sch / + dθ +in θdϕ.6.5 4π π +Δ Δl Δ.6.5 Δl = Δ 1 / > Δ..6.6

14 l 1.1: > 1 1 l 1 x / l 1 = 1 d /1 1 / = / dx x 1 x..6.7 dx 1 x x 1 x = x x ln 1+ 1 x x l 1 = [ x + 1 ] /1 1 1 x ln 1+ 1 x / = 1 / 1 1 / 1 + ln = 1 / 1 1 / 1 + ln > / / 1 / / l ln l 1 > 1 1 = l 1 l 1 = 1 / + ln / + /

15 m = 4πx ρxdx in θddθdϕ d 3 p = g g θθ g ϕϕ ddθdϕ = e λ in θddθdϕ dv p = d π dϕ π dθ g g θθ g ϕϕ =4π e λ d.7. d 3 p dv p M p = ρdv p = 4πx ρxe λ 4πx ρx dx = dx Gm/x ρ ρ m ρ I : m = ρ = ρ m + ρ I.7.4 ρ m + ρ I 1 Gm x dv p..7.5 Gm/x 1, ρ I ρ m m = ρ m + ρ I 1 Gm x dv p ρ m + ρ I 1 Gm dv p x Gmρ m ρ m dv p + ρ I dv p dv p..7.6 x }{{}}{{}}{{} =M m =U I =U G M p M m + U I M p >M m >m M p M m M m m M p m 5 M p >m>m m U I

16 d = e φ,t dt + e λ,t d + dθ +in θdϕ , t =.8.1 = = =, =1.1.1 e φ λ = λ = λ e λ 1 =.8.3 φ + 1 e λ 1 =.8.4 φ + φ λ φ + φ λ e λ = λ + φ = λ + φ = C 1 =.8.6 C 1 = λ e λ = d d e λ =1 e λ =1+ C.8.7 C.6. M C = GM.8.7 λ +λ λ e λ = φ = λ

17 : d = 1 GM dt + 1 GM 1 d + dθ +in θdϕ.8.9 Bikhoff.9 :.9.1 d = g μν dx μ dx ν d = g tt t, dt + g t, d + g θθ t, dθ +in θdϕ.9.1 d = dt + at [ W xdx + x dθ +in θdϕ ].9. g tt = 1 d = dt + γ ij dx i dx j : d = e φx,t dt + e λx,t dx + x, t dθ +in θdϕ.9.4 R R = λ + λ φ λ φ + + φ φ + λ φ + λ + λ + e φ φ e λ

18 φx, t, λx, t =lnat+ 1 ln W x x, t =atx ȧ R =6ä a [ W a a xw + x 1 1 ] W.9.7 W xw K K.9.8 x W W x W x = 1 1 Kx.9.9 Robeton Walke [ ] d = dt + at dx 1 Kx + x dθ +in θdϕ, T μν T μν =ρ + pu μ u ν + pg μν.9.11 φx, t, λx, t =lnat 1 ln1 Kx x, t =atx [6.6] 8πGρa x +Λa x = 3ȧ x 3Kx.9.13 =ȧ a a ȧ πGpa x +Λa x = Kx aäx ȧ x πGp +Λa x = aäx ȧ x Kx.9.16

19 . 46 : G α β +Λδ α β =8πG T α β Λ : ȧ = 8πG a 3 ρ K a + Λ 3,.9.18 ä a = 4πG 3 ρ +3p+Λ ä = G 4π ρ +3p Λ a a 3 4πG }{{} a ρ Λ = Λ 8πG, p Λ = Λ 8πG.9.1 ρ ρ + ρ Λ p p + p Λ Λ.9.18 ä a = 4πG ρ ȧ 3 a +ρ + Λ ρ = 3ȧ ρ + p..9.3 a i matte: p ρ ii adiation: p = ρ/3 iii comological contant: p = ρ iv dak enegy: p = wρ

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

* 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

『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

B

B B YES NO 5 7 6 1 4 3 2 BB BB BB AA AA BB 510J B B A 510J B A A A A A A 510J B A 510J B A A A A A 510J M = σ Z Z = M σ AAA π T T = a ZP ZP = a AAA π B M + M 2 +T 2 M T Me = = 1 + 1 + 2 2 M σ Te = M 2 +T

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

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

現代物理化学 1-1(4)16.ppt

現代物理化学 1-1(4)16.ppt (pdf) pdf pdf http://www1.doshisha.ac.jp/~bukka/lecture/index.html http://www.doshisha.ac.jp/ Duet -1-1-1 2-a. 1-1-2 EU E = K E + P E + U ΔE K E = 0P E ΔE = ΔU U U = εn ΔU ΔU = Q + W, du = d 'Q + d 'W

More information

10:30 12:00 P.G. vs vs vs 2

10:30 12:00 P.G. vs vs vs 2 1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B

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

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 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

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

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

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

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

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

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

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

(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

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

「産業上利用することができる発明」の審査の運用指針(案)

「産業上利用することができる発明」の審査の運用指針(案) 1 1.... 2 1.1... 2 2.... 4 2.1... 4 3.... 6 4.... 6 1 1 29 1 29 1 1 1. 2 1 1.1 (1) (2) (3) 1 (4) 2 4 1 2 2 3 4 31 12 5 7 2.2 (5) ( a ) ( b ) 1 3 2 ( c ) (6) 2. 2.1 2.1 (1) 4 ( i ) ( ii ) ( iii ) ( iv)

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

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2)

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2) (1) I 44 II 45 III 47 IV 52 44 4 I (1) ( ) 1945 8 9 (10 15 ) ( 17 ) ( 3 1 ) (2) 45 II 1 (3) 511 ( 451 1 ) ( ) 365 1 2 512 1 2 365 1 2 363 2 ( ) 3 ( ) ( 451 2 ( 314 1 ) ( 339 1 4 ) 337 2 3 ) 363 (4) 46

More information

i ii i iii iv 1 3 3 10 14 17 17 18 22 23 28 29 31 36 37 39 40 43 48 59 70 75 75 77 90 95 102 107 109 110 118 125 128 130 132 134 48 43 43 51 52 61 61 64 62 124 70 58 3 10 17 29 78 82 85 102 95 109 iii

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

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

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

untitled

untitled V. 8 9 9 8.. SI 5 6 7 8 9. - - SI 6 6 6 6 6 6 6 SI -- l -- 6 -- -- 6 6 u 6cod5 6 h5 -oo ch 79 79 85 875 99 79 58 886 9 89 9 959 966 - - NM /6 Nucl Ml SI NM/6/685 85co /./ /h / /6/.6 / /.6 /h o NM o.85

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

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

* ἅ ὅς 03 05(06) 0 ἄβιος,-ον, ἄβροτον ἄβροτος ἄβροτος,-ον, 08 17(01)-03 0 ἄβυσσος,-ου (ἡ), 08 17(01)-03 0 ἀβύσσου ἄβυ

* ἅ ὅς 03 05(06) 0 ἄβιος,-ον, ἄβροτον ἄβροτος ἄβροτος,-ον, 08 17(01)-03 0 ἄβυσσος,-ου (ἡ), 08 17(01)-03 0 ἀβύσσου ἄβυ Complete Ancient Greek 2010 (2003 ) October 15, 2013 * 25 04-23 0 ἅ ὅς 03 05(06) 0 ἄβιος,-ον, 15 99-02 0 ἄβροτον ἄβροτος 15 99-02 0 ἄβροτος,-ον, 08 17(01)-03 0 ἄβυσσος,-ου (ἡ), 08 17(01)-03 0 ἀβύσσου ἄβυσσος

More information

2

2 16 1050026 1050042 1 2 1 1.1 3 1.2 3 1.3 3 2 2.1 4 2.2 4 2.2.1 5 2.2.2 5 2.3 7 2.3.1 1Basic 7 2.3.2 2 8 2.3.3 3 9 2.3.4 4window size 10 2.3.5 5 11 3 3.1 12 3.2 CCF 1 13 3.3 14 3.4 2 15 3.5 3 17 20 20 20

More information

2 2 MATHEMATICS.PDF 200-2-0 3 2 (p n ), ( ) 7 3 4 6 5 20 6 GL 2 (Z) SL 2 (Z) 27 7 29 8 SL 2 (Z) 35 9 2 40 0 2 46 48 2 2 5 3 2 2 58 4 2 6 5 2 65 6 2 67 7 2 69 2 , a 0 + a + a 2 +... b b 2 b 3 () + b n a

More information

1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0

1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0 A c 2008 by Kuniaki Nakamitsu 1 1.1 t 2 sin t, cos t t ft t t vt t xt t + t xt + t xt + t xt t vt = xt + t xt t t t vt xt + t xt vt = lim t 0 t lim t 0 t 0 vt = dxt ft dft dft ft + t ft = lim t 0 t 1.1

More information

i

i 14 i ii iii iv v vi 14 13 86 13 12 28 14 16 14 15 31 (1) 13 12 28 20 (2) (3) 2 (4) (5) 14 14 50 48 3 11 11 22 14 15 10 14 20 21 20 (1) 14 (2) 14 4 (3) (4) (5) 12 12 (6) 14 15 5 6 7 8 9 10 7

More information

- - - - - - - - - - - - - - - - - - - - - - - - - -1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2...2...3...4...4...4...5...6...7...8...

- - - - - - - - - - - - - - - - - - - - - - - - - -1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2...2...3...4...4...4...5...6...7...8... 取 扱 説 明 書 - - - - - - - - - - - - - - - - - - - - - - - - - -1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2...2...3...4...4...4...5...6...7...8...9...11 - - - - - - - - - - - - - - - - -

More information

Big Bang Planck Big Bang 1 43 Planck Planck quantum gravity Planck Grand Unified Theories: GUTs X X W X 1 15 ev 197 Glashow Georgi 1 14 GeV 1 2

Big Bang Planck Big Bang 1 43 Planck Planck quantum gravity Planck Grand Unified Theories: GUTs X X W X 1 15 ev 197 Glashow Georgi 1 14 GeV 1 2 12 Big Bang 12.1 Big Bang Big Bang 12.1 1-5 1 32 K 1 19 GeV 1-4 time after the Big Bang [ s ] 1-3 1-2 1-1 1 1 1 1 2 inflationary epoch gravity strong electromagnetic weak 1 27 K 1 14 GeV 1 15 K 1 2 GeV

More information

第1部 一般的コメント

第1部 一般的コメント (( 2000 11 24 2003 12 31 3122 94 2332 508 26 a () () i ii iii iv (i) (ii) (i) (ii) (iii) (iv) (a) (b)(c)(d) a) / (i) (ii) (iii) (iv) 1996 7 1996 12

More information

表1票4.qx4

表1票4.qx4 iii iv v 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 22 23 10 11 24 25 26 27 10 56 28 11 29 30 12 13 14 15 16 17 18 19 2010 2111 22 23 2412 2513 14 31 17 32 18 33 19 34 20 35 21 36 24 37 25 38 2614

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

第1章 国民年金における無年金

第1章 国民年金における無年金 1 2 3 4 ILO ILO 5 i ii 6 7 8 9 10 ( ) 3 2 ( ) 3 2 2 2 11 20 60 12 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 14 15 8 16 2003 1 17 18 iii 19 iv 20 21 22 23 24 25 ,,, 26 27 28 29 30 (1) (2) (3) 31 1 20

More information

(I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 Typeset by Akio Namba usig Powerdot. 2 / 47

(I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 Typeset by Akio Namba usig Powerdot. 2 / 47 4 Typeset by Akio Namba usig Powerdot. / 47 (I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 Typeset by Akio Namba usig Powerdot. 2 / 47 (I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 (radom variable):

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 -

- 2 - - 2 - - 3 - (1) (2) (3) (1) - 4 - ~ - 5 - (2) - 6 - (1) (1) - 7 - - 8 - (i) (ii) (iii) (ii) (iii) (ii) 10 - 9 - (3) - 10 - (3) - 11 - - 12 - (1) - 13 - - 14 - (2) - 15 - - 16 - (3) - 17 - - 18 - (4) -

More information

2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1

2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1 1 1979 6 24 3 4 4 4 4 3 4 4 2 3 4 4 6 0 0 6 2 4 4 4 3 0 0 3 3 3 4 3 2 4 3? 4 3 4 3 4 4 4 4 3 3 4 4 4 4 2 1 1 2 15 4 4 15 0 1 2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4

More information

1 (1) (2)

1 (1) (2) 1 2 (1) (2) (3) 3-78 - 1 (1) (2) - 79 - i) ii) iii) (3) (4) (5) (6) - 80 - (7) (8) (9) (10) 2 (1) (2) (3) (4) i) - 81 - ii) (a) (b) 3 (1) (2) - 82 - - 83 - - 84 - - 85 - - 86 - (1) (2) (3) (4) (5) (6)

More information

ÿþ

ÿþ I O 01 II O III IV 02 II O 03 II O III IV III IV 04 II O III IV III IV 05 II O III IV 06 III O 07 III O 08 III 09 O III O 10 IV O 11 IV O 12 V O 13 V O 14 V O 15 O ( - ) ( - ) 16 本 校 志 望 の 理 由 入 学 後 の

More information

PRML pdf PRML (http://critter.sakura.ne.jp) N x t y(x, w) = w 0 + w 1 x + w 2 x w M x m = M w j x j (1.1) j=0 E(w) = 1 {y(x n, w) t n } 2

PRML pdf PRML (http://critter.sakura.ne.jp) N x t y(x, w) = w 0 + w 1 x + w 2 x w M x m = M w j x j (1.1) j=0 E(w) = 1 {y(x n, w) t n } 2 critter twitter ( PRML) PRML PRML PRML PRML 1. 2. 3. PRML PRML 110 PRML 700 1 PRML pdf PRML (http://critter.sakura.ne.jp) 1 1.1 N x t y(x, w) = w 0 + w 1 x + w 2 x 2 + + w M x m = M w j x j (1.1) j=0 E(w)

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

kogi dvi

kogi dvi 10 4 23 ( ) email: tanikawa.ky@nao.ac.jp I. ( ) II. : III. ( ) 1 I. : ( ) :, : :, :? : = : =, ( ). 2 1.... ( ).. (,,,, ),,, ( ) ( ). ( )... ( ).?. 3 1: ( T)... 19 F.R. Stephenson 1990 ΔT 4 II. : (i) (ii))

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

provider_020524_2.PDF

provider_020524_2.PDF 1 1 1 2 2 3 (1) 3 (2) 4 (3) 6 7 7 (1) 8 (2) 21 26 27 27 27 28 31 32 32 36 1 1 2 2 (1) 3 3 4 45 (2) 6 7 5 (3) 6 7 8 (1) ii iii iv 8 * 9 10 11 9 12 10 13 14 15 11 16 17 12 13 18 19 20 (2) 14 21 22 23 24

More information

(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law

(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law I (Radom Walks ad Percolatios) 3 4 7 ( -2 ) (Preface),.,,,...,,.,,,,.,.,,.,,. (,.) (Basic of Proability Theory). (Probability Spacees ad Radom Variables...............2, (Expectatios, Meas).............................

More information

7) ẋt) =iaω expiωt) ibω exp iωt) 9) ẋ0) = iωa b) = 0 0) a = b a = b = A/ xt) = A expiωt) + exp iωt)) = A cosωt) ) ) vt) = Aω sinωt) ) ) 9) ) 9) E = mv

7) ẋt) =iaω expiωt) ibω exp iωt) 9) ẋ0) = iωa b) = 0 0) a = b a = b = A/ xt) = A expiωt) + exp iωt)) = A cosωt) ) ) vt) = Aω sinωt) ) ) 9) ) 9) E = mv - - m k F = kx ) kxt) =m d xt) dt ) ω = k/m ) ) d dt + ω xt) = 0 3) ) ) d d dt iω dt + iω xt) = 0 4) ω d/dt iω) d/dt + iω) 4) ) d dt iω xt) = 0 5) ) d dt + iω xt) = 0 6) 5) 6) a expiωt) b exp iωt) ) )

More information

1 180m g 10m/s 2 2 6 1 3 v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) 1.3 2 3 3 r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v =

1 180m g 10m/s 2 2 6 1 3 v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) 1.3 2 3 3 r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v = 1. 2. 3 3. 4. 5. 6. 7. 8. 9. I http://risu.lowtem.hokudai.ac.jp/ hidekazu/class.html 1 1.1 1 a = g, (1) v = g t + v 0, (2) z = 1 2 g t2 + v 0 t + z 0. (3) 1.2 v-t. z-t. z 1 z 0 = dz = v, t1 dv v(t), v

More information

16 16 16 1 16 2 16 3 24 4 24 5 25 6 33 7 33 33 1 33 2 34 3 34 34 34 34 34 34 4 34-1 - 5 34 34 34 1 34 34 35 36 36 2 38 38 41 46 47 48 1 48 48 48-2 - 49 50 51 2 52 52 53 53 1 54 2 54 54 54 56 57 57 58 59

More information

i ii iii iv v vi vii ( ー ー ) ( ) ( ) ( ) ( ) ー ( ) ( ) ー ー ( ) ( ) ( ) ( ) ( ) 13 202 24122783 3622316 (1) (2) (3) (4) 2483 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 11 11 2483 13

More information

http://know-star.com/ 3 1 7 1.1................................. 7 1.2................................ 8 1.3 x n.................................. 8 1.4 e x.................................. 10 1.5 sin

More information

[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization)

[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization) . D............................................... : E = κ ............................................ 3.................................................

More information

10 : 3010 : 54 1F Annex 1! 1 15:3015 : 58 1F Annex 1

10 : 3010 : 54 1F Annex 1! 1 15:3015 : 58 1F Annex 1 4 16 1 10:0010 : 24 1F Annex 1! 2 15:0015 : 24 1F Annex 1!! 10 : 3010 : 54 1F Annex 1! 1 15:3015 : 58 1F Annex 1 ! 2 10:0010 : 28 1F Annex 1 3 15:0015 : 28 1F Annex 1 4 10:3010 : 58 1F Annex 1 1 15:3015

More information

202

202 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 DS =+α log (Spread )+ β DSRate +γlend +δ DEx DS t Spread t 1 DSRate t Lend t DEx DS DEx Spread DS

More information