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1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1

I, A 25 8 24 1 1.1 ( 3 ) 3 9 10 3 9 : (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4), (3,3,3) 10 : (1,3,6), (1,4,5), (2,2,6), (2,3,5), (2,4,4), (3,3,4) 6 3 9 10 3 9 : 6 3 + 3 2 + 1 = 25 25 10 : 6 3 + 3 3

7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±

7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α

直交座標系の回転

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24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x

24 I 1.1.. ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 1 (t), x 2 (t),, x n (t)) ( ) ( ), γ : (i) x 1 (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 ]

(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1)

1. 1.1...,. 1.1.1 V, V x, y, x y x + y x + y V,, V x α, αx αx V,, (i) (viii) : x, y, z V, α, β C, (i) x + y = y + x. (ii) (x + y) + z = x + (y + z). 1 (iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y

A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6

1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67

References: 3 June 21, 2002 K. Hukushima and H. Kawamura, Phys.Rev.E, 61, R1008 (2000). M. Matsumoto, K. Hukushima,

References: 3 mailto:hukusima@issp.u-tokyo.ac.jp June 21, 2002 K. Hukushima and H. Kawamura, Phys.Rev.E, 61, R1008 (2000). M. Matsumoto, K. Hukushima, and H. Takayama, cond-mat/0204225. Typeset by FoilTEX

u = u(t, x 1,..., x d ) : R R d C λ i = 1 := x 2 1 x 2 d d Euclid Laplace Schrödinger N := {1, 2, 3,... } Z := {..., 3, 2, 1,, 1, 2, 3

2 2 1 5 5 Schrödinger i u t + u = λ u 2 u. u = u(t, x 1,..., x d ) : R R d C λ i = 1 := 2 + + 2 x 2 1 x 2 d d Euclid Laplace Schrödinger 3 1 1.1 N := {1, 2, 3,... } Z := {..., 3, 2, 1,, 1, 2, 3,... } Q

N N 1,, N 2 N N N N N 1,, N 2 N N N N N 1,, N 2 N N N 8 1 6 3 5 7 4 9 2 1 12 13 8 15 6 3 10 4 9 16 5 14 7 2 11 7 11 23 5 19 3 20 9 12 21 14 22 1 18 10 16 8 15 24 2 25 4 17 6 13 8 1 6 3 5 7 4 9 2 1 12 13

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2 : n =1, 2,, 10000 0.5125 0.51 0.5075 0.505 0.5025 0.5 0.4975 0.495 0 2000 4000 6000 8000 10000 2 weak law of large numbers 1. X 1,X 2,,X n 2. µ = E(X i ),i=1, 2,,n 3. σi 2 = V (X i ) σ 2,i=1, 2,,n ɛ>0

1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =

1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i

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Chapter 5 1 2 CHAPTER 5. 5.1 8 (x ) 2 +(y + ) 2 1=j 2 R9 x + y = x + y = p 2 x + y = p 2 ff(x; y; ) =j 2 Rg ( f(x; y; ) = @ @ f(x; y; ) = (5:1) f 3 (x; y) = f 3 (x; y) ==)9 : f(x; y; ) = @f @x @f @y 1

iii 1 1 1 1................................ 1 2.......................... 3 3.............................. 5 4................................ 7 5................................ 9 6............................

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1

67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10

1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2,

1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2,θ n ) = exp(i n i=1 θ i F i ) (A.1) F i 2 0 θ 2π 1

1 2 3 4 5 1 1:30 NPO 16 1 19 16 2 17-6 - 10 2008 2010 120 150 IT( ) 60 21 40-7 - - 8-10 ( ) NPO 2 10 16:40-9 - 10 ii NPO NPO ( ) ( ) 11 12 13 14 15 22 26 27 28 29 30 31 32 33 34 m3 m3

13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x

欧州特許庁米国特許商標庁との共通特許分類 CPC (Cooperative Patent Classification) 日本パテントデータサービス ( 株 ) 国際部 2019 年 1 月 17 日 CPC 版のプレ リリースが公開されました 原文及び詳細はCPCホームページの C

欧州特許庁米国特許商標庁との共通特許分類 CPC (Cooperative Patent Classification) 日本パテントデータサービス ( 株 ) 国際部 2019 年 1 月 17 日 CPC 2019.02 版のプレ リリースが公開されました 原文及び詳細はCPCホームページの CPC Revisions(CPCの改訂 ) 内のPre-releaseをご覧ください http://www.cooperativepatentclassification.org/cpcrevisions/prereleases.html

加速度センサを用いた図形入力

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SUSY DWs

@ 2013 1 25 Supersymmetric Domain Walls Eric A. Bergshoeff, Axel Kleinschmidt, and Fabio Riccioni Phys. Rev. D86 (2012) 085043 (arxiv:1206.5697) ( ) Contents 1 2 SUSY Domain Walls Wess-Zumino Embedding

,., 5., ,. 2.2,., x z. y,.,,,. du dt + α p x = 0 dw dt + α p z + g = 0 α dp dt + pγ dα dt = 0 α V dα dt = 0 (2.2.1), γ = c p /c

29 2 1 2.1 2.1.1.,., 5.,. 2.1.1,. 2.2,., x z. y,.,,,. du dt + α p x = 0 dw dt + α p z + g = 0 α dp dt + pγ dα dt = 0 α V dα dt = 0 (2.2.1), γ = c p /c v., V = (u, w), = ( / x, / z). 30 2.1.1: 31., U p(z),