A Deceptive Parallel (2.60) Gauss ρ ρ f ɛ 0 E D D E D Coulumb D(r) 1 r r 4π r r 3 ρ f (r )dτ (2.65) 2.20: D E A A A E =0 Gauss E = ρ/ɛ 0 D

Chapter 3 Special Techniques). Laplace 3. Laplace s Equation) (3.. Introduction) Lapla

2 25 Chapter 3 Special Techniques). Laplace 3. Laplace s Equation).............................. (3.. Introduction).................................2 Laplace 3..2 Laplace s Equation in One Dimension).......

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

i

009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3

2 Part A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44, 77, 55, 48 (2) 92, 74, 56, 81, 84, 86, 1, 27,

/ (1) (2) (3) ysawano@tmu.ac.jp (4) (0) (10) 11 (10) (a) (b) (c) (5) - - 11160939-11160939- - 1 2 Part 1. 1. 1. A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44,

第5章 偏微分方程式の境界値問題

October 5, 2018 1 / 113 4 ( ) 2 / 113 Poisson 5.1 Poisson ( A.7.1) Poisson Poisson 1 (A.6 ) Γ p p N u D Γ D b 5.1.1: = Γ D Γ N 3 / 113 Poisson 5.1.1 d {2, 3} Lipschitz (A.5 ) Γ D Γ N = \ Γ D Γ p Γ N Γ

211 ‚æ2fiúŒÚ

2.5 (Gauss) (flux) v(r)( ) S n S v n v n (1) v n S = v n S = v S, n S S. n n S v S v Minoru TANAKA (Osaka Univ.) I(2012), Sec p. 1/30

2.5 (Gauss) 2.5.1 (flux) v(r)( ) n v n v n (1) v n = v n = v, n. n n v v I(2012), ec. 2. 5 p. 1/30 i (2) lim v(r i ) i = v(r) d. i 0 i (flux) I(2012), ec. 2. 5 p. 2/30 2.5.2 ( ) ( ) q 1 r 2 E 2 q r 1 E

A B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P

1 1.1 (population) (sample) (event) (trial) Ω () 1 1 Ω 1.2 P 1. A A P (A) 0 1 0 P (A) 1 (1) 2. P 1 P 0 1 6 1 1 6 0 3. A B P (A B) = P (A) + P (B) (2) A B A B A 1 B 2 A B 1 2 1 2 1 1 2 2 3 1.3 A B P (A

II (No.2) 2 4,.. (1) (cm) (2) (cm) , (

II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0,

KENZOU Karman) x

KENZO 8 8 31 8 1 3 4 5 6 Karman) 7 3 8 x 8 1 1.1.............................. 3 1............................................. 5 1.3................................... 5 1.4 /.........................

: 2005 ( ρ t +dv j =0 r m m r = e E( r +e r B( r T 208 T = d E j 207 ρ t = = = e t δ( r r (t e r r δ( r r (t e r ( r δ( r r (t dv j =

72 Maxwell. Maxwell e r ( =,,N Maxwell rot E + B t = 0 rot H D t = j dv D = ρ dv B = 0 D = ɛ 0 E H = μ 0 B ρ( r = j( r = N e δ( r r = N e r δ( r r = : 2005 ( 2006.8.22 73 207 ρ t +dv j =0 r m m r = e E(

t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z

I 1 m 2 l k 2 x = 0 x 1 x 1 2 x 2 g x x 2 x 1 m k m 1-1. L x 1, x 2, ẋ 1, ẋ 2 ẋ 1 x = 0 1-2. 2 Q = x 1 + x 2 2 q = x 2 x 1 l L Q, q, Q, q M = 2m µ = m 2 1-3. Q q 1-4. 2 x 2 = h 1 x 1 t = 0 2 1 t x 1 (t)

N/m f x x L dl U 1 du = T ds pdv + fdl (2.1)

23 2 2.1 10 5 6 N/m 2 2.1.1 f x x L dl U 1 du = T ds pdv + fdl (2.1) 24 2 dv = 0 dl ( ) U f = T L p,t ( ) S L p,t (2.2) 2 ( ) ( ) S f = L T p,t p,l (2.3) ( ) U f = L p,t + T ( ) f T p,l (2.4) 1 f e ( U/

5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0

5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â = Tr Âe βĥ Tr e βĥ = dγ e βh (p,q) A(p, q) dγ e βh (p,q) (5.2) e βĥ A(p, q) p q Â(t) = Tr Â(t)e βĥ Tr e βĥ = dγ() e βĥ(p(),q())

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

46 4 E E E E E 0 0 E E = E E E = ) E =0 2) φ = 3) ρ =0 1) 0 2) E φ E = grad φ E =0 P P φ = E ds 0

4 4.1 conductor E E E 4.1: 45 46 4 E E E E E 0 0 E E = E E E =0 4.1.1 1) E =0 2) φ = 3) ρ =0 1) 0 2) E φ E = grad φ E =0 P P φ = E ds 0 4.1 47 0 0 3) ε 0 div E = ρ E =0 ρ =0 0 0 a Q Q/4πa 2 ) r E r 0 Gauss

18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb

r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)

4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7

elemag.dvi

II 2006 1 24 i 1 3 1.1... 3 1.2... 5 1.3... 6 1.4... 6 1.5 (Gauss)... 7 1.5.1... 8 1.5.2 (Green)... 9 1.6 (Stokes)... 9 2 11 2.1... 11 2.2... 12 2.3... 13 2.4... 14 2.4.1... 15 2.4.2... 15 2.4.3... 16

80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t = 0 i r 0 t(> 0) j r 0 + r < δ(r 0 x i (0))δ(r 0 + r x j (t)) > (4.2) r r 0 G i j (r, t) dr 0

79 4 4.1 4.1.1 x i (t) x j (t) O O r 0 + r r r 0 x i (0) r 0 x i (0) 4.1 L. van. Hove 1954 space-time correlation function V N 4.1 ρ 0 = N/V i t 80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t

TOP URL 1

TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)

1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r

R = Ar l B r l. A, B A, B.. r 2 R r = r2 [lar r l B r l2 ]=larl l B r l.2 r 2 R = [lar l l Br ] r r r = ll Ar l ll B = ll R rl.3 sin θ Θ = ll.4 Θsinθ

.3.2 3.3.2 Spherical Coorinates.5: Laplace 2 V = r 2 r 2 x = r cos φ sin θ, y = r sin φ sin θ, z = r cos θ.93 r 2 sin θ sin θ θ θ r 2 sin 2 θ 2 V =.94 2.94 z V φ Laplace r 2 r 2 r 2 sin θ.96.95 V r 2 R

量刑における消極的責任主義の再構成

ii 3.,. 4. F. (), ,,. 8.,. 1. (75% ) (25% ) =9 7, =9 8 (. ). 1.,, (). 3.,. 1. ( ).,.,.,.,.,. ( ) (1 2 )., ( ), 0. 2., 1., 0,.

23(2011) (1 C104) 5 11 (2 C206) 5 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 ( ). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5.. 6.. 7.,,. 8.,. 1. (75%

t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1

t χ F Q t χ F µ, σ N(µ, σ ) f(x µ, σ ) = ( exp (x ) µ) πσ σ 0, N(0, ) (00 α) z(α) t χ *. t (i)x N(µ, σ ) x µ σ N(0, ) (ii)x,, x N(µ, σ ) x = x+ +x N(µ, σ ) (iii) (i),(ii) z = x µ N(0, ) σ N(0, ) ( 9 97.

広報みはま.indd

2

LLG-R8.Nisus.pdf

d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H

1 1 1.1 *1 1. 1.3.1 n x 11,, x 1n Nµ 1, σ x 1,, x n Nµ, σ H 0 µ 1 = µ = µ H 1 µ 1 µ H 0, H 1 * σ σ 0, σ 1 *1 * H 0 H 0, H 1 H 1 1 H 0 µ, σ 0 H 1 µ 1, µ, σ 1 L 0 µ, σ x L 1 µ 1, µ, σ x x H 0 L 0 µ, σ 0

renshumondai-kaito.dvi

3 1 13 14 1.1 1 44.5 39.5 49.5 2 0.10 2 0.10 54.5 49.5 59.5 5 0.25 7 0.35 64.5 59.5 69.5 8 0.40 15 0.75 74.5 69.5 79.5 3 0.15 18 0.90 84.5 79.5 89.5 2 0.10 20 1.00 20 1.00 2 1.2 1 16.5 20.5 12.5 2 0.10

The Physics of Atmospheres CAPTER :

The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(

( ) LAN LAN tex ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1

( ) LAN LAN tex ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 4 2 17 3 Coulomb 23 4 43 5 49 6 51 7 53 8 58 9 66 10 74 11 Lienard-Wiechert potential 78 12 86 13 89 14 Laplace 114 15 138 16 152 17 162 18 166 19 191

2013 5

12 (SL) (L) (SL) 2013 5 5 29 () 4 ( ) 7 17 20 ( ) 2 14. 4.17 14. 5. 1 14. 5.22 14. 6. 5 14. 4.17 14. 5. 1 14. 5. 8 14. 5.22 14. 4.17 14. 5. 1 14. 5.22 14. 6. 5 4 10 7 7 10 7 31 8 14.4.10 14.7.10 14.7.31

1000

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 SL 1000 1000 1000 1000 1000 1000 1000 1000 1000 ( 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

1 2 2 (Dielecrics) Maxwell ( ) D H

2003.02.13 1 2 2 (Dielecrics) 4 2.1... 4 2.2... 5 2.3... 6 2.4... 6 3 Maxwell ( ) 9 3.1... 9 3.2 D H... 11 3.3... 13 4 14 4.1... 14 4.2... 14 4.3... 17 4.4... 19 5 22 6 THz 24 6.1... 24 6.2... 25 7 26

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1

1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2

Venkatram and Wyngaard, Lectures on Air Pollution Modeling, m km 6.2 Stull, An Introduction to Boundary Layer Meteorology,

65 6 6.1 No.4 1982 1 1981 J. C. Kaimal 1993 1994 Turbulence and Diffusion in the Atmosphere : Lectures in Environmental Sciences, by A. K. Blackadar, Springer, 1998 An Introduction to Boundary Layer Meteorology,

大野川水系中流圏域

-------------------------------------------------------------------- 1 -------------------------------------------------------------------------- 1 -----------------------------------------------------------------------------

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

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

マイクロメカトロニクス 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/077331 このサンプルページの内容は, 初版 1 刷発行当時のものです. 1984.10 1986.7 1995 60 1991 Piezoelectric Actuators and Ultrasonic Motors

( ) ( 40 )+( 60 ) Schrödinger 3. (a) (b) (c) yoshioka/education-09.html pdf 1

2009 1 ( ) ( 40 )+( 60 ) 1 1. 2. Schrödinger 3. (a) (b) (c) http://goofy.phys.nara-wu.ac.jp/ yoshioka/education-09.html pdf 1 1. ( photon) ν λ = c ν (c = 3.0 108 /m : ) ɛ = hν (1) p = hν/c = h/λ (2) h

L L L L C C C C (a) (b) (c) 4.4 (a) (b) (a) RG59/U 6.2mm ( ) 73Ω web page (c) 4 4 dx 4 J V dx dj Ydx Zdx dv Z,Y dv = JZdx, dj = VYdx (4.8) d 2 J dx 2

8 ( ) 2014 11 23 OP h g m r d 4 ( ) 4.2 + (lumped constant circuit) 4.2.1 3 (Poynting ) (strip line) (waveguide) (coaxial cable) GHz 4.4(a) dj dx dv Zdx Ydx ( ) (distributed constatn circuit) *1 4.4(c)

/Volumes/NO NAME/gakujututosho/chap1.tex i

2012 4 10 /Volumes/NO NAME/gakujututosho/chap1.tex i iii 1 7 1.1............................... 7 2 11 2.1........................................... 11 2.2................................... 18 2.3...................................

図 : CGC 回転面. 左の図は 正の場合の平行曲面として得られる平均曲率 一定回転面 ダラネーアンデュロイド 上 とノドイド 下, 中の図は その平行正 CGC 回転面 右の図は負 CGC 回転面 ミンディング曲面と呼 ばれる 図 2: 回転面でない位相的な円柱面 螺旋対称性を持つ. ダラネー

shimpei@cc.hirosaki-u.ac.jp (K ) Nick Schmitt (Tübingen ) [6] R 3 K CGC [], R 3 CGC, R 3 CGC CGC CGC CGC 2, [2]. CGC CGC [6] C 3 CGC [4] CGC. 図 : CGC 回転面. 左の図は 正の場合の平行曲面として得られる平均曲率 一定回転面 ダラネーアンデュロイド 上

untitled

( œ ) œ 138,800 17 171,000 60,000 16,000 252,500 405,400 24,000 22 95,800 24 46,000 16,000 16,000 273,000 19,000 10,300 57,800 1,118,408,500 1,118,299,000 109,500 102,821,836 75,895,167 244,622 3,725,214

.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T

NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977

log1-500

平成27年度三菱重工グループ保険　フルガードくん（シニア）

TEL 0120-004-443 TEL 045-200-6560 TEL 042-761-2328 TEL 0120-539-022 TEL 042-762-0535 TEL 052-565-5211 TEL 077-552-9161 TEL 0120-430-372 TEL 0120-45-9898 TEL 0120-63-0051 TEL 0120-252-892 TEL 083-266-8041

/Volumes/NO NAME/gakujututosho/chap1.tex i

2010 4 8 /Volumes/NO NAME/gakujututosho/chap1.tex i iii 1 5 1.1............................... 5 2 9 2.1........................................... 9 2.2................................... 16 2.3...................................

2005 2006.2.22-1 - 1 Fig. 1 2005 2006.2.22-2 - Element-Free Galerkin Method (EFGM) Meshless Local Petrov-Galerkin Method (MLPGM) 2005 2006.2.22-3 - 2 MLS u h (x) 1 p T (x) = [1, x, y]. (1) φ(x) 0.5 φ(x)

取扱説明書

ED-601 ED-501 ED-401 2 3 4 23 14 5 6 18 10 7 1 2 6 3 4 8 9 16 16 16 12 1 2 18 10 2 1 5 12 11 1 2 1 2 12 1 2 13 16 14 3 2 4 1 1 2 16 3 4 18 15 1 2 16 2 3 1 1 2 3 18 17 18 22 19 D A C 20 A B 22 B C D 22

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

01

2 0 0 7 0 3 2 2 i n d e x 0 7. 0 2. 0 3. 0 4. 0 8. 0 9. 1 0. 1 1. 0 5. 1 2. 1 3. 1 4. 1 5. 1 6. 1 7. 1 8. 1 9. 2 0. 2 1. 2 3. 2 4. 2 5. 2 6. O k h o t s k H a m a n a s u B e e f 0 2 http://clione-beef.n43.jp

keisoku01.dvi

2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5 Mon, 2006, 401, SAGA, JAPAN Dept.

FREE

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2

2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6

B 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................

,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising

,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising Model 1 Ising 1 Ising Model N Ising (σ i = ±1) (Free

0406_total.pdf

59 7 7.1 σ-ω σ-ω σ ω σ = σ(r), ω µ = δ µ,0 ω(r) (6-4) (iγ µ µ m U(r) γ 0 V (r))ψ(x) = 0 (7-1) U(r) = g σ σ(r), V (r) = g ω ω(r) σ(r) ω(r) (6-3) ( 2 + m 2 σ)σ(r) = g σ ψψ (7-2) ( 2 + m 2 ω)ω(r) = g ω ψγ

D v D F v/d F v D F η v D (3.2) (a) F=0 (b) v=const. D F v Newtonian fluid σ ė σ = ηė (2.2) ė kl σ ij = D ijkl ė kl D ijkl (2.14) ė ij (3.3) µ η visco

post glacial rebound 3.1 Viscosity and Newtonian fluid f i = kx i σ ij e kl ideal fluid (1.9) irreversible process e ij u k strain rate tensor (3.1) v i u i / t e ij v F 23 D v D F v/d F v D F η v D (3.2)

Untitled

II 14 14-7-8 8/4 II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ 6/ ] Navier Stokes 3 [ ] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I 1 balance law t (ρv i )+ j

s = 1.15 (s = 1.07), R = 0.786, R = 0.679, DW =.03 5 Y = 0.3 (0.095) (.708) X, R = 0.786, R = 0.679, s = 1.07, DW =.03, t û Y = 0.3 (3.163) + 0

7 DW 7.1 DW u 1, u,, u (DW ) u u 1 = u 1, u,, u + + + - - - - + + - - - + + u 1, u,, u + - + - + - + - + u 1, u,, u u 1, u,, u u +1 = u 1, u,, u Y = α + βx + u, u = ρu 1 + ɛ, H 0 : ρ = 0, H 1 : ρ 0 ɛ 1,

II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re

II 29 7 29-7-27 ( ) (7/31) II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I Euler Navier

平成１２年度

1 1-1 (1) 150[ml] 500[ml/] Cerebral Ventricle Brain 1-1 2 ( ) 1-1 1-2 0.20.5[mm] 13 14[mm] 1-2 3 ( ) (2) 4 2-1 (cerebral ventricle) (peritoneum) R O p O Cerebral Ventricle Valve Brain R o R i P i Peritoneum

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >

表紙_02

野岩鉄道の旅

29th 5:13 5:34 5:56 6:00 6:12 6:20 6:21 6:25 6:29 6:31 6:34 6:38 6:40 6:45 6:52 6:56 7:01 7:07 7:11 7:32 7:34 7:50 7:58 8:03 8:17 8:36 8:44 5:50 5:54 6:15 6:38 6:39 6:51 6:59 6:59 7:03 7:08 7:08 7:11 7:15

高知工科大学電子 光システム工学科

卒業研究報告 題 目 量子力学に基づいた水素分子の分子軌道法的取り扱いと Hamiltonian 近似法 指導教員 山本哲也 報告者 山中昭徳 平成 14 年 月 5 日 高知工科大学電子 光システム工学科. 3. 4.1 4. 4.3 4.5 6.6 8.7 10.8 11.9 1.10 1 3. 13 3.113 3. 13 3.3 13 3.4 14 3.5 15 3.6 15 3.7 17

( š ) š 13,448 1,243,000 1,249,050 1,243,000 1,243,000 1,249,050 1,249, , , ,885

( š ) 7,000,000 191 191 6,697,131 5,845,828 653,450 197,853 4,787,707 577,127 4,000,000 146,580 146,580 64,000 100,000 500,000 120,000 60,000 60,000 60,000 60,000 60,000 200,000 150,000 60,000 60,000 100,000

総研大恒星進化概要.dvi

The Structure and Evolution of Stars I. Basic Equations. M r r =4πr2 ρ () P r = GM rρ. r 2 (2) r: M r : P and ρ: G: M r Lagrange r = M r 4πr 2 rho ( ) P = GM r M r 4πr. 4 (2 ) s(ρ, P ) s(ρ, P ) r L r T

液晶の物理１：連続体理論（弾性，粘性）

The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers

1 G K C 1.1. G K V ρ : G GL(V ) (ρ, V ) G V 1.2. G 2 (ρ, V ), (τ, W ) 2 V, W T : V W τ g T = T ρ g ( g G) V ρ g T W τ g V T W 1.3. G (ρ, V ) V W ρ g W

Naoya Enomoto 2002.9. paper 1 2 2 3 3 6 1 1 G K C 1.1. G K V ρ : G GL(V ) (ρ, V ) G V 1.2. G 2 (ρ, V ), (τ, W ) 2 V, W T : V W τ g T = T ρ g ( g G) V ρ g T W τ g V T W 1.3. G (ρ, V ) V W ρ g W W G- G W

Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE

21 2 27 Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE ) Bethe-Bloch 1 0.1..............................

T g T 0 T 0 fragile * ) 1 9) η T g T g /T *1. τ τ η = Gτ. G τ

615-851 ryoichi@chemekyoto-uacjp 66-852 onuki@scphyskyoto-uacjp 1 T g T T fragile *2 1 11) 1 9) η T g T g /T *1 τ 198 τ η = Gτ G τ T c η τ 12) strong fragile T c strong η η exp(e/k B T ) 1 2/3 E SiO 2

1: 3.3 1/8000 1/ m m/s v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt kg (

1905 1 1.1 0.05 mm 1 µm 2 1 1 2004 21 2004 7 21 2005 web 2 [1, 2] 1 1: 3.3 1/8000 1/30 3 10 10 m 3 500 m/s 4 1 10 19 5 6 7 1.2 3 4 v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt 6 6 10

３

3 S - (sootg) j = j +, = + () = j E ( ) = µ ( ) = = = ( )( µ ) = E µ [ ] E () = E ( ) µ = = (3) = E ( µ ) = = = = = (4) T, At t = + ( ) C ( t) t T T µ C ( t) C( t) = E j, = j (5) (6) (3)(5) T (5) T τ =

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

統計学のポイント整理

.. September 17, 2012 1 / 55 n! = n (n 1) (n 2) 1 0! = 1 10! = 10 9 8 1 = 3628800 n k np k np k = n! (n k)! (1) 5 3 5 P 3 = 5! = 5 4 3 = 60 (5 3)! n k n C k nc k = npk k! = n! k!(n k)! (2) 5 3 5C 3 = 5!

Note.tex 2008/09/19( )

1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................

untitled

( œ ) œ 2,000,000 20. 4. 1 25. 3.27 44,886,350 39,933,174 4,953,176 9,393,543 4,953,012 153,012 4,800,000 164 164 4,001,324 2,899,583 254,074 847,667 5,392,219 584,884 7,335 4,800,000 153,012 4,800,000

1 Slodowy 005 3 9 3 1 ADE ADE (0) ADE (1) SL(, C), R 3 (), (3) ADE, II 1 (4) SL(, Z)- (5) F 4, B, M McKay E 6, E 7, E 8 4 A n 5 5 5... 5 5 5 D n 5 5 5... 5 5 5 E 6 5 5 5 5 5 5 E 7 5 5 5 5 5 5 5 E 8 5

1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2

filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin

. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n

003...............................3 Debye................. 3.4................ 3 3 3 3. Larmor Cyclotron... 3 3................ 4 3.3.......... 4 3.3............ 4 3.3...... 4 3.3.3............ 5 3.4.........

QMI13a.dvi

I (2013 (MAEDA, Atsutaka) 25 10 15 [ I I [] ( ) 0. (a) (b) Plank Compton de Broglie Bohr 1. (a) Einstein- de Broglie (b) (c) 1 (d) 2. Schrödinger (a) Schrödinger (b) Schrödinger (c) (d) 3. (a) (b) (c)

Quz Quz

http://www.ppl.app.keo.ac.jp/denjk III (1969). (1977). ( ) (1999). (1981). (199). Harry Lass Vector and Tensor Analyss, McGraw-Hll, (195).. Quz Quz II E B / t = Maxwell ρ e E = (1.1) ε E= (1.) B = (1.3)

C: PC H19 A5 2.BUN Ohm s law

C: PC H19 A5 2.BUN 19 8 6 3 19 3.1........................... 19 3.2 Ohm s law.................... 21 3.3.......................... 24 4 26 4.1................................. 26 4.2.................................

2 G(k) e ikx = (ik) n x n n! n=0 (k ) ( ) X n = ( i) n n k n G(k) k=0 F (k) ln G(k) = ln e ikx n κ n F (k) = F (k) (ik) n n= n! κ n κ n = ( i) n n k n

. X {x, x 2, x 3,... x n } X X {, 2, 3, 4, 5, 6} X x i P i. 0 P i 2. n P i = 3. P (i ω) = i ω P i P 3 {x, x 2, x 3,... x n } ω P i = 6 X f(x) f(x) X n n f(x i )P i n x n i P i X n 2 G(k) e ikx = (ik) n

平成26年度 化学物質分析法開発報告書

2,2-2,2 -Iminodiethanol Diethanol amine CAS 111-42-2 C 4 H 11 NO 2 105.1356-105.0790-28 C 1) 1.0881 g/cm 3 1)

TOP URL 1

TOP URL http://amonphys.web.fc2.com/ 1 6 3 6.1................................ 3 6.2.............................. 4 6.3................................ 5 6.4.......................... 6 6.5......................

医系の統計入門第 2 版 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. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.

医系の統計入門第 2 版 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/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987