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2011 7 9 28.1 41.4 30.5 35.8 31.9% 32.3 DI 18.2 2.4 8.1 3.5 DI 9.4 32.2 0.0 25.9 2008 1 3 2 3 34.8 65.2 46.753.8 1 2 8.82.9 43.1 10 3 DI 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

31, 21% 24, 17% 8, 5% 23, 16% 24, 16% 91, 62% 19, 13% 39, 27% 33, 23% 73 48 57 51 31 1 9 13.0% 7.4% 5.3% 12.5% 17.1% 13.2% 17.9% 4.5% 36.4% 56.5% 40.7% 36.8% 50.0% 67.1% 56.3% 65.8% 75.0% 26.0% 37.0%

37 27.0% 26 19.0% 74 54.0% 9 6.4% 13 9.2% 28 19.9% 26 18.4% 37 26.2%. 24 17.0% 99 69 75 59 39 1 6 4.5% 1.4% 7.7% 2.9% 25.0% 17.9% 20.8% 50.0% 41.7% 47.0% 51.4% 54.3% 61.5% 57.1% 55.6% 42.4% 50.0% 58.3%

3 DI 29 7 1 5 6 575 11 751, 13 1,1,25 6 1,251,5 2 1,51,75 1,752, 1 2,2,25 2,252,5 2,53, 3,3,5 3,5 5 1 15 2 25 3 5 6 575 12 751, 21 1,1,25 27 1,251,5 9 1,51,75 1,752, 1 2,2,25 2 2,252,5 2,53, 2 3,3,5

2 DI 28 7 1 37 28 4 18 27 11 21 5 2 26 4 5 1 15 2 25 3 35 4 17 7 5 48 76 31 47 17 2 92 12 2 2 4 6 8 1 12 1 2 4 1 12 13 18 19 3 42 57 57 1 2 3 4 5 6 1 1 1 3 4 4 5 5 5.5 1 1.5 2 2.5 3 3.5 4 4.5 5

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

Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, P

Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, PC ( 4 5 )., 5, Milnor Milnor., ( 6 )., (I) Z modulo

τ τ

1 1 1.1 1.1.1 τ τ 2 1 1.1.2 1.1 1.1 µ ν M φ ν end ξ µ ν end ψ ψ = µ + ν end φ ν = 1 2 (µφ + ν end) ξ = ν (µ + ν end ) + 1 1.1 3 6.18 a b 1.2 a b 1.1.3 1.1.3.1 f R{A f } A f 1 B R{AB f 1 } COOH A OH B 1.3

Anderson ( ) Anderson / 14

Anderson 2008 12 ( ) Anderson 2008 12 1 / 14 Anderson ( ) Anderson 2008 12 2 / 14 Anderson P.W.Anderson 1958 ( ) Anderson 2008 12 3 / 14 Anderson tight binding Anderson tight binding Z d u (x) = V i u

20169 3 4 5003 n=3,000 61.8% 38.2% n=3,000 20 7.3% 30 21.3% 40 34.8% 50 36.6% n=3,000 3.0% 2.0% 1.5% 12.1% 14.0% 41.4% 25.9% n=3,000 37.7% % 24.8% 28.8% 1.9% 3.1% 0.2% n=3,000 500 64.0% 500 1,000 31.3%

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21 2 26 i 1 1 1.1............................ 1 1.2............................ 3 2 9 2.1................... 9 2.2.......... 9 2.3................... 11 2.4....................... 12 3 15 3.1..........

SO(3) 7 = = 1 ( r ) + 1 r r r r ( l ) (5.17) l = 1 ( sin θ ) + sin θ θ θ ϕ (5.18) χ(r)ψ(θ, ϕ) l ψ = αψ (5.19) l 1 = i(sin ϕ θ l = i( cos ϕ θ l 3 = i ϕ

SO(3) 71 5.7 5.7.1 1 ħ L k l k l k = iϵ kij x i j (5.117) l k SO(3) l z l ± = l 1 ± il = i(y z z y ) ± (z x x z ) = ( x iy) z ± z( x ± i y ) = X ± z ± z (5.118) l z = i(x y y x ) = 1 [(x + iy)( x i y )

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9118 154 B-1 B-3 B- 5cm 3cm 5cm 3m18m5.4m.5m.66m1.3m 1.13m 1.134m 1.35m.665m 5 , 4 13 7 56 M 1586.1.18 7.77.9 599.5.8 7 1596.9.5 7.57.75 684.11.9 8.5 165..3 7.9 87.8.11 6.57. 166.6.16 7.57.6 856 6.6.5

r

73 29 2008 200 4 416 2008 20 042 0932 10 1977 200 1 2 3 4 5 7 8 9 11 12 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 200r 11 1 1 1 1 700200 200

No. 1261 2003. 4. 9 14 14 14 14 15 30 21 19 150 35 464 37 38 40 20 970 90 80 90 181130 a 151731 48 11 151731 42 44 47 63 12 a 151731 47 10 11 16 2001 11000 11 2002 10 151731 46 5810 2795195261998 151731

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301 21 1 (1),, (3), (4) 2 (1),, (3), (4), (5), (6), 3,?,?,??,?? 4 (1)!?, , 6 5 2 5 6 1205 22 1 (1) 60 (3) (4) (5) 2 (1) (3) (4) 3 (1) (3) (4) (5) (6) 4 (1) 5 (1) 6 331 331 7 A B A B A B A 23 1 2 (1) (3)

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数論 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. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published

構造と連続体の力学基礎

II 37 Wabash Avenue Bridge, Illinois 州 Winnipeg にある歩道橋 Esplanade Riel 橋6 6 斜張橋である必要は多分無いと思われる すぐ横に道路用桁橋有り しかも塔基部のレストランは 8 年には営業していなかった 9 9. 9.. () 97 [3] [5] k 9. m w(t) f (t) = f (t) + mg k w(t) Newton

4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.

A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c

Powered by TCPDF ( Title 第 11 講 : フィッシャー統計学 II Sub Title Author 石川, 史郎 (Ishikawa, Shiro) Publisher Publication year 2018 Jtitle コペンハーゲン解

Powered by TCPDF (www.tcpdf.org) Title 第 11 講 : フィッシャー統計学 II Sub Title Author 石川, 史郎 (Ishikawa, Shiro) Publisher Publication year 018 Jtitle コペンハーゲン解釈 ; 量子哲学 (018. 3),p.381-390 Abstract Notes 慶應義塾大学理工学部大学院講義ノート

QMI_09.dvi

25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 3.1.2 σ τ 2 2 ux, t) = ux, t) 3.1) 2 x2 ux, t) σ τ 2 u/ 2 m p E E = p2 3.2) E ν ω E = hν = hω. 3.3) k p k = p h. 3.4) 26 3 hω = E = p2 = h2 k 2 ψkx ωt) ψ 3.5) h