solutionJIS.dvi
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- せとか さんきち
- 5 years ago
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1 May 0, morimune@econ.kyoto-u.ac.jp /9/005 (7 0/5/ (a) (b) (c) c + c + + c = nc (x 1 x)+(x x)+ +(x n x) =(x 1 + x + + x n ) nx = nx nx =0 c(x 1 x)+c(x x)+ + c(x n x) =c (x i x) =0 y i (x i x) = y i x i y i x = = = y i x i (y 1 x + y x + + y n x) y i x i x(y 1 + y + + y n ) y i x i x(ny) 1
2 x i (y i y) = y i x i x i y = y i x i y(nx) (x i x)(y i y) = y i x i nyx n 1 (x i x)(y i y) = 1 y i x i yx n n 1. (a) x = 1 3 ( ) = 5 3, 5 x 3, y = 1 3 ( ) = 5 3, 5 3 /( )= 1. (b) (a) = 1 3 ( ) = 5 3, (c) x y = 1 3 (1 1+ +( 3) ( 3) + ( 4) ( 4) 4 ( 1) ( 1)) = 6 3, = 1 3 (1 ( 4) + ( 3) ( 1).5) = /( )= y =( 4, 3, 3, 4) -3.5 = 1 3 (1 ( 4) + ( 3) + 3 ( 3) + 4 ( 4) 4 ( 3.5).5) = 0
3 1.3 x : (1,),(,4),(-1,),(-,4) y : (1,),(,4),(1,-),(,-4) (1,),(,4),(-1,-),(-,-4), t = = t t 5% t = = (t 1.089) 16 t t = ( 0.1) ( 0.1) 15 t t y x x xy y = = =6 7 6= = =
4 b = /3 14 (6 6/3) = 9 a = (18/3) 9 (6/3) = 3. y x x xy y b = = 9, a =0 9 0=0..3 b = (t t)y t (t t) t t t = t 1979 t = t 1979 t t =(t 1979) (t 1979) = t t b = b (t t )y t (t t ) = (t t)y t (t t)
5 .4 β = (x t x)(y t y) (x t x), γ = (y t y)(x t x) (y, t y) r = (y t y)(x t x) (y t y) n (x t x) r = β γ.5 r = = β = (x t x)(y t y) (x t x) α = y βx β = (x t x )(yt y n ) n = 100(x t x)10(y t y) (x t x ) n (100(x = 1 t x)) 10 β α = y β x =10y 1 10 β 100x =10 α ŷ i =1+x i 5
6 x ŷ i =10+0x i 10ŷ i = (100x i) =10+0. (100x i ).6 y i = µ + u i µ (y i µ) = = µ (y i µ) (y i µ) µ (y i µ) = =0 (y i µ) (y i µ) =0 ( ) µ y i n µ =0 µ = 1 n y i = y ( ) ŷ i = µ 6
7 ŷ i µ, RSS = = (y i µ) (y i y) TSS ESS = (ŷ i y) =0..7 y i = βx i + u i β (y i βx i ) = β (y i βx i ) = (y i βx i ) β (y i βx i ) = (y i βx i )x i ( ) = { =0 y i x i β x i x i } β = y ix i n. x i y i = βx i y i βx i, ( ) x i 0 7
8 ln(439/479) = R ntt =0.0001(0.11) (0.6)R nikkei % = 0.09 (R ntt 0.005) = (0.034) (0.6)(R nikkei 0.005). t P 0.97t P x t =0, z t =0, x =0, z =0. z tx t =0, y t = n α y t x t = β x t y t z t = γ 3 z t 1 = 6 α =4 β 8
9 9=6 γ. y y c x z ( 1) + 3 ( 1) = (1) + 3 ( 1) = (0) + 3 ( 1) = ( 1) + 3 (1) = (1) (1) = (0) (1) = TSS = = 35 R =1 35 3=9 35. y 7 1 x y x y (3.7) 0 y x 1 z x,y 1 z y β = y t x t (x t ) θ = y t x t (y t ) β θ = ( y t x t ) (x t ) (y t ) =
10 3.3 RES RES t =0 3.4 RES RESi = = RES t x t =0 RES t z t =0 RES i (y i α βx i γz i ) RES i y i α RES i β RES i x i γ RES i z i RES iy i RES i y i = 3.5 Φ (y i α βx i γz i )y i Φ α = y βx γz y i y = β(x i x)+ γ(z i z)+error (x i x) (z i z) (x i x) =δ(z i z)+error 10
11 δ {(x i x) δ(z i z)} ( ) δ x i =(x i x) δ(z i z) x i (x i ĉ ζz i ) ( ) ĉ ζ ζ ĉ ĉ = x ζz ( ) ( ) 4 15 (4.8) β K β K β K 4.1 x y y y x x xy sum y =3.6(5.9) + 1.5(5.)x, R =0.96,RSS =1.17,ESS =
12 4. x z y,x,z y x z y 5/ 1/4 3/4 x 1/4 3/ 0 z 3/4 0 53/ y =0.4565( )x ( )z. t b t 5% K= K-1=5 DW=1.8 5% U=1.86 L=1.0 U L U F f = = f = = F 3 1 5% % % log(l) b log(k) c b+c=1+d, b=1+d-c, log Y log L = a + d log L + c{log K log L} + e log H4+error log(y/l)=a + d log L + c log(k/l)+e log H4+error 1
13 log(y/l) log(k/l) log(y/l) = (4.73) log L (7.74) log(k/l) (6.1) log H4, R =0.9119,RSS= , t d d 4.5 y i = a + bx i + error x =(x 1 + x )/ (x 1 x) +(x x) = (x 1 x ) (x 1 x)y 1 +(x x)y = (x 1 x ) y 1 + (x x 1 ) y = (x 1 x ) (y 1 y ) b = (y 1 y ) (x 1 x ) y = c + (y 1 y ) (x 1 x ) x c y 1 = c + (y 1 y ) (x 1 x ) x 1 y = c + (y 1 y ) (x 1 x ) x ĉ = y (y 1 y ) (x 1 x ) x 13
14 4.6 (4.15) (4.5) m (4.5) x mi =1 {y i ( β 1 x 1i + + β K x Ki )} =0 (y i ŷ i )=0 y i = n 4.7 (4.5) ŷ i (y i ŷ i )x mi =0 4.8 ŷ i = β 1 x 1i + + β K x Ki (4.5) (y i ŷ i )ŷ i = β n 1 (y i ŷ i )x 1i + + β n K (y i ŷ i )x Ki =0 14
15 (y i ŷ i )ŷ i = y i ŷ i y i ŷ i = (ŷ i ) =0, (ŷ i ). n(y) y i = ŷi (y i y)(ŷ i y) = (ŷ i y). ± n (ŷ i y) 4.9 {y i ( β 1 x 1i + + β K x Ki )} β 1,, β K x 1i x i k l {y i ( β 1 x 1i + + β K x Ki )},i m,i l + {y m ( β 1 x 1m + β x m + + β K x Km )} + {y l ( β 1 x 1l + β x m + + β K x Kl )} x 1l =1,x m =0, x 1l =0,x m = 1, x 1l =0,x m =0,,i m,i l {y i ( β 3 x 3i + + β K x Ki )} + {y m ( β 1 + β 3 x 3m + + β K x Km )} + {y l ( β + β 3 x 3l + + β K x Kl )} 15
16 β 3 β K β 1 β β 1 = y m ( β 3 x 3m + + β K x Km ) β = y l ( β 3 x 3l + + β K x Kl ) 4.10 b=c d=1 b c = e d 1=f b = c + e d =1+f b d y t = a + ex t + c(x t + z t )+z t + fz t + u t (y t z t )=a + ex t + c(x t + z t )+fz t + u t e =0,f =0 F (y t z t )=a + c(x t + z t )+u t (y t z t )=a + c(x t + z t )+u t F 16
17 4.11 t V (b c) =V (b)+v (c) Cov(b, c) b c V (b)+v (c) Cov(b, c) t = ( ) =0.6 5% Y 1 t n=5 K=5 k=4 5% L=1.04,U=1.77 DW 1.7 L L TSS= r =1 dw = =1 70 TSS f = =0 4,0 F 1%
18 5..1 y x y = y x = x y x (x ) 16 1 (1/4) = 3 1 (1/4) 16 = = = = = (, 3), ( 1, 4) -1/3 (,3) 3=a a=11/3. b = 6 (7 + 3)( )/3 197 (1 + 8 = ) /3 a = y = 3 1 x, RSS =0 3 E(y t )=E(a + bx t + u t ) = a + bx t + E(u t ) = a + bx t =3.604 V (y t )=E{(a + bx t + u t ) E(a + bx t + u t )} = E{(a + bx t + u t ) (a + bx t )} = E(u t ) = V (u t ) t 1, t
19 y x y/σ x/σ x*y* x* y* sum b = / /3 = 1.5 a = a =3 ( 1.5) 16/3 = y t = a + bx t + u t a = b y t = b(1 + x t )+u t b = (1 + x t )y t (1 + x t ) y t + x t yt = 3+ x t + x t a= = =0.4 RSS a = (y t ) a y t b x t y t =41 (11) 9 ( 1.5) 41 = 3.5 RSS 0 = (y t ) b (1 + x t )y t =41 (0.4) (41 + 9) = 1 19
20 f = =6 1,1 F 5% 1 t t d=0 a = b + d y t = d + b(1 + x t )+u t d t y t = α + β 0 x t + β 1 x t 1 + β x t + ε t β 0 = γ 0 β 1 = γ 0 + γ 1 β = γ 0 +γ 1 3β γ 3β β β β 0 β 1 γ 1 = β 1 β 0 γ 1 = β β 1 β β 1 = β 1 β 0 β =β 1 β 0 0
21 P=3 q= y t = α + β 0 x t + β 1 x t 1 + β x t + β 3 x t 3 + ε t β 0 = γ 0 β 1 = γ 0 + γ 1 + γ β = γ 0 +γ 1 +4γ β 3 = γ 0 +3γ 1 +9γ 1 4β 1 3β β 1 β 0 = γ 1 + γ β β 1 = γ 1 +3γ β 3 β = γ 1 +5γ (β β 1 ) (β 1 β 0 )=γ (β 3 β ) (β β 1 )=γ (β 3 β ) (β β 1 )=(β β 1 ) (β 1 β 0 ) 6. y t = α + β 0 x t + β 1 x t 1 + β x t + ε t, β 0 = γ 0 β 1 = γ 0 + γ 1 1
22 β = γ 0 +γ 1 β 1 = γ 0 γ 1 =0 γ 0 = γ 1 β 0 = γ 0 β 1 = γ 0 + γ 1 =β 0 β = γ 0 +γ 1 =3β 0 y t = α + β 0 (x t +x t 1 +3x t )+ε t, SUR
23 W trend tax W g G X 1 C W p X P W C α W p 0 γ γ 0-1 γ 1 X [ 1] (0,1) 1 P ( 1 3 < X< 3 ) 7.1 1/ 1/1 P ( < X< 3 )=P{ 1 1 = P { <Z<1 1 6 } = P { <Z<} 0.05 ( ) < 1 1 (X 1 1 ) < ( )} 1 X (a,b) 3
24 [ ] 8 α=4 P (m <X<m) E(X) = = E(X )= m m = α α 1 m = m m = α α m x αm α x α 1 dx αm α x α dx x αm α x α 1 dx αm α x 1 α dx V (X) = α α α m ( α 1 m) α = (α )(α 1) m. P (m <X<m+ m ) = P (m α α 1 m<x α α 1 m<m + m α α 1 m) = P ( 1 α 1 m<x α α 1 m< α (α 1) m) = P ( n( 1 (α 1) (α ) m) <Z< n α = P ( n α 1 (α ) α m α <Z< n(α ) (α 1) (α ) α ) m = P ( <Z< 4 ) = P ( <Z<) (α 1) (α ) m m ) α 4
25 X,Y 7. X = Y = Z X = Y = P (Z = 1) = 1 81, P (Z = 0.5) = 8 81, P (Z =0)= 4 81, P (Z =0.5) = 3 81, P (Z =1)= n=3 X ( 1 3 )3, 1 3( 1 3 ) ( 3 ), 1 1 3( 1 3 )( 3 ), 1 0 ( 3 )3, E(Z) = ( 1 3 )3 +3( 1 3 ) ( 3 ) 3(1 3 )( 3 ) +( 3 )3 =( 1 3 )3 +3( 1 3 ) ( 3 )+3( 1 3 )( 3 ) +( 3 )3 =(( 1 3 )+( 3 ))3 =( 1 3 )3 5
26 E(Z )=( 1 3 )3 +3( 1 3 ) ( 3 )+3(1 3 )( 3 ) +( 3 )3 =(( 1 3 )+( 3 ))3 = (1) 3 =1 V (Z) =E(Z ) E(Z) =1 ( 1 3 )6 E(Z) =( 1 3 )n 7.3 V (Z) =1 ( 1 3 )n x 1 E(X) = 0 x xdx = 3 E(X )= x xdx =1 0 V (X) =1 ( 3 ) = 1 9 6
27 7.4 P(-1)=1/3,P(1)=/3. {X 1,X,X 3 } s = {(X 1 X) +(X X) +(X 3 X) } = 1 {X 1 + X + X 3 3X } s =0, ( 1 3 ) s = 4 3, 3( 1 3 ) ( 3 ) s = 4 3, 3( 3 ) ( 1 3 ) s =0, ( 3 )3. s s =0, ( 1 3 )3 +( 3 )3 = 9 7 = 1 3. s = 4 3, 3( 3 ) ( 1 3 )+3(1 3 ) ( 3 )= = X s X s 1 (-1,-1) = (-1,1) or (1,-1) = (1,1) 3 3 = X s X = 1 X =0 X =1 s s = s 4 = 0 X X s E(X) =( 1) (1) 4 9 = 1 3 E(s )= () 4 9 = 8 9 E(X s )=0. Cov(X,s )= =
28 7.6 A= A= B B= B= A A= A= B B= B= A A= A= B B= B= A A= A= B B= B= A A= A= B B= B= A
29 7.7 Z=XY Z Z P = Z 0 1 P V=0 ( )3.. V=1 3( ) ( 4 15 ). 3. V= 3( )( 4 15 ). 4. V=3 ( 4 15 )3. X s X s 1 (-1,-1,-1) (-1,-1,1) 3 7 = (-1,1,1) = (1,1,1) X s X = 1 X = 1 3 X = 1 3 X =1 s s = s = X X s 9
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黒住英司 [ 著 ] サピエンティア 計量経済学 訂正および練習問題解答 (206/2/2 版 ) 訂正 練習問題解答 3 .69, 3.8 4 (X i X)U i i i (X i μ x )U i ( X μx ) U i. i E [ ] (X i μ x )U i i E[(X i μ x )]E[U i ]0. i V [ ] (X i μ x )U i i 2 i j E [(X i
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y = x x R = 0. 9, R = σ $ = y x w = x y x x w = x y α ε = + β + x x x y α ε = + β + γ x + x x x x' = / x y' = y/ x y' =
y x = α + β + ε =,, ε V( ε) = E( ε ) = σ α $ $ β w ( 0) σ = w σ σ y α x ε = + β + w w w w ε / w ( w y x α β ) = α$ $ W = yw βwxw $β = W ( W) ( W)( W) w x x w x x y y = = x W y W x y x y xw = y W = w w
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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
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(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
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20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d
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No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2
No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j
x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x
[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),
.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(
06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,
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) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4
![) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4](/thumbs/92/107866707.jpg ") ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4")
1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev
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y π π O π x 9 s94.5 y dy dx. y = x + 3 y = x logx + 9 s9.6 z z x, z y. z = xy + y 3 z = sinx y 9 s x dx π x cos xdx 9 s93.8 a, fx = e x ax,. a =
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18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
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IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................
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( ) δ x V A A V V + x x δ A + x x δ x A V Q AV A+ δx V + δx V A A V AV + A δx+ V δx+ δx V A A δx+ V δx V A A + V ( ) ( AV ) AV Constant Q 1 Text 7.1 ( ) P1 7 7.P8 5 D v g z x + x 1 v ( v+ x ) g + x z z
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
A 2 3. m S m = {x R m+1 x = 1} U + k = {x S m x k > 0}, U k = {x S m x k < 0}, ϕ ± k (x) = (x 0,..., ˆx k,... x m ) 1. {(U ± k, ϕ± k ) 0 k m} S m 1.2.
A A 1 A 5 A 6 1 2 3 4 5 6 7 1 1.1 1.1 (). Hausdorff M R m M M {U α } U α R m E α ϕ α : U α E α U α U β = ϕ α (ϕ β ϕβ (U α U β )) 1 : ϕ β (U α U β ) ϕ α (U α U β ) C M a m dim M a U α ϕ α {x i, 1 i m} {U,
201711grade1ouyou.pdf
2017 11 26 1 2 52 3 12 13 22 23 32 33 42 3 5 3 4 90 5 6 A 1 2 Web Web 3 4 1 2... 5 6 7 7 44 8 9 1 2 3 1 p p >2 2 A 1 2 0.6 0.4 0.52... (a) 0.6 0.4...... B 1 2 0.8-0.2 0.52..... (b) 0.6 0.52.... 1 A B 2
n (1.6) i j=1 1 n a ij x j = b i (1.7) (1.7) (1.4) (1.5) (1.4) (1.7) u, v, w ε x, ε y, ε x, γ yz, γ zx, γ xy (1.8) ε x = u x ε y = v y ε z = w z γ yz
1 2 (a 1, a 2, a n ) (b 1, b 2, b n ) A (1.1) A = a 1 b 1 + a 2 b 2 + + a n b n (1.1) n A = a i b i (1.2) i=1 n i 1 n i=1 a i b i n i=1 A = a i b i (1.3) (1.3) (1.3) (1.1) (ummation convention) a 11 x
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ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
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73 74 ( u w + bw) d = Ɣ t tw dɣ u = N u + N u + N 3 u 3 + N 4 u 4 + [K ] {u = {F 75 u δu L σ (L) σ dx σ + dσ x δu b δu + d(δu) ALW W = L b δu dv + Aσ (L)δu(L) δu = (= ) W = A L b δu dx + Aσ (L)δu(L) Aσ
2012 IA 8 I p.3, 2 p.19, 3 p.19, 4 p.22, 5 p.27, 6 p.27, 7 p
2012 IA 8 I 1 10 10 29 1. [0, 1] n x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 2. 1 x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 1 0 f(x)dx 3. < b < c [, c] b [, c] 4. [, b] f(x) 1 f(x) 1 f(x) [, b] 5.
II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
![II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R](/thumbs/95/125540821.jpg "II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R")
II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
() Remrk I = [0, ] [x i, x i ]. (x : ) f(x) = 0 (x : ) ξ i, (f) = f(ξ i )(x i x i ) = (x i x i ) = ξ i, (f) = f(ξ i )(x i x i ) = 0 (f) 0.
![() Remrk I = [0, ] [x i, x i ]. (x : ) f(x) = 0 (x : ) ξ i, (f) = f(ξ i )(x i x i ) = (x i x i ) = ξ i, (f) = f(ξ i )(x i x i ) = 0 (f) 0.](/thumbs/89/98384840.jpg "() Remrk I = [0, ] [x i, x i ]. (x : ) f(x) = 0 (x : ) ξ i, (f) = f(ξ i )(x i x i ) = (x i x i ) = ξ i, (f) = f(ξ i )(x i x i ) = 0 (f) 0.")
() 6 f(x) [, b] 6. Riemnn [, b] f(x) S f(x) [, b] (Riemnn) = x 0 < x < x < < x n = b. I = [, b] = {x,, x n } mx(x i x i ) =. i [x i, x i ] ξ i n (f) = f(ξ i )(x i x i ) i=. (ξ i ) (f) 0( ), ξ i, S, ε >
『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
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11