untitled

Size: px
Start display at page:

Download "untitled"

Transcription

1 Sb-lattice -l [I.nsara, N.Dpin, H..kas, and.sndan, J.lloys and Coponds, 7(997, 0-0] by T.Koyaa

2 φ φ i i φ φ φ i= SER ref id ex x H (98.5K = + + ref id ex φ φ φ SER = x { H (98.5K} i= = RT x x φ φ φ φ, i i i φ φ φ i i i= = x x n φ ν φ φ φ ν, =, ( ν = 0 x x = + T + ν φ ν φ ν φ,,, fcc- -l φ φ SER i i i= x H = + + ref φ id φ ex φ (98.5K φ φ SER φ φ φ φ φ xi { i Hi (98.5K} xx, RT xi xi i= i= = + + = x ( H + x ( H + x x + RT( x x + x x SER SER l l l l l, l l = + ( x x + ( x x + ( x x 0 l, l, l, l l, l l, l [fcc-] 0 fcc l, fcc l, fcc l, fcc l, = T = T = T = T ' ( ( ( ( ( ( y y y y = + + ord ref ord id ord ex ord

3 ref ord ( ( ord = yi yj i : j i= j= id ord = RT y y + y y ( ( ( ( i i i i i= i= ex ord ( ( ( ord ( ( ( ord = yi yj yk i,: j k + yi yj yk k:, i j i= j> i k i= j> i k + i= j> i k= l> k y y y y ( ( ( ( i j k l ord i,:, j k l n ord ν ord ( ( ν i,: j k= i,: j k( i j ν = 0 y y n ord ν ord ( ( ν ki :, j = ki :, j( i j ν = 0 y y x = y + y ( ( i i i ( ( x = y = y i i i -l = + + ord ref ord id ord ex ord ( ( ord ( ( ( ord ( ( ( ord = yi yj i : j + yi yj yk i, j: k + yi yj yk k: i, j i= j= i= j> i k i= j> i k + y y y y + RT y i= j> i k= l> k ( ( ( ( ord ( ( ( ( i j k l i,:, j k l i yi + yi yi i= i= = y y + y y + y y + y y ( ( ( ( ( ( ( ( l l l: l l l: l : l : ( + y y y + y + y y y ( + y ( ( ( ( ( ( ( ( l l l, : l l, : l l l: l, : l, + y y y y ( ( ( ( l l l, : l, + RT y y + y y + y y + y y ( ( ( ( ( ( ( ( ( l l ( l l = + ( y y ord 0 ord ord ( ( l, : l l, : l l, : l l = + ( y y ord 0 ord ord ( ( l, : l, : l, : l = + ( y y ord 0 ord ord ( ( l: l, l: l, l: l, l = + ord 0 ord ord ( ( : l, : l, : l, l = ord 0 ord l, : l, l, : l, ( y y []

4 l, l, fcc fcc : l l l, fcc fcc l: l l, 0 0 l, : l l, : l, 0 0 l: l, = T = T = = = = 6 = = : l, l, : l l, = l, : l, = l: l, l, = : l, l, = 0 ( ( ( ( ( ( ( ( ( ( ( ( y y y y y y y y = + + ord ref ord id ord ex ord ref ord ( ( ( ( ord = yi yj yk yl i ::: j k l i= j= k= l= id ord = RT y y + y y + y y + y y ( ( ( ( ( ( ( ( i i i i i i i i i= i= i= i= ex ord ( ( ( ( ( ord ( ( ( ( ( ord = yi yj yk yl y i,::: j k l + yi yj yk yl y k:, i jl :: i= j> i k, l, i= j> i k, l, ( ( ( ( ( ord ( ( ( ( ( ord + yi yj yk yl y kli ::, j : + yi yj yk yl y kli :: :, j i= j> i k,, l i= j> i k,, l + + ( ( ( ( ( ( ord yi yj yk yl yp yq i,:,:: j k l p q i= j> i k= l> k p, q ( ( ( ( ( ( ( ord + yi yj yk yl yp yq yr i,:,: j k l p,: q r + i= j> i k= l> k p= q> p r + i= j> i k= l> k p= q> p r= s> r y y y y y y y ( ( ( ( ( ( ( ( i j k l p q r s y ord i,:,: j k l p,:, q r s dis ord ( ( ord = ( i + ( i, i ( i x y y x

5 ' d ( ( ( ( = ( l + ( + ( l + ( yl y yl y = y y + y y + y y + y y ord ( ( ( ( ( ( ( ( l l l: l l l: l : l : (, :, : ( :, :, + y y y + y + y y y + y ( ( ( ( ( ( ( ( l l l l l l l l l l ( ( ( ( ( ( ( ( ( ( ( ( ( ( + yl y yl y l, : l, + RT yl yl + y y + yl yl + y y = y y + y y + y y + y y ( ( ( ( ( ( ( ( l l l: l l l: l : l : ( ( (0 (0 ( ( (0 (0 + y ly ( yl ll, : + y l, : + yl y ( yl ll :, + y l :, + y y y y ( ( ( ( 0 l l l, : l, ( + y y ( y y ( y + y + y y ( y y y + y ( ( ( ( ( ( ( ( ( ( ( ( l l l l, : l l, : l l l l: l, : l, + RT y y + y y + y y + y y ( ( ( ( ( ( ( ( ( l l ( l l y y y ( l ( ( l ( ( ( = yl l: l + y l: + RT( yl + ( ( ( ( ( + y ( yl y ( yl + y y + y + y y + y y y ( ( 0 ( 0 ( ( 0 ( ( ( 0 l l, : l l, : l l: l, l l, : l, ( ( ( = yl : l + y : + RT( y + ( ( ( ( ( + yl ( yl y ( yl + y + y y ( y y ( ( ( ( ( l, : l l, : l l l: l, + y y + y + y y + y y y ( ( 0 ( 0 ( ( 0 ( ( ( 0 l l l, : l l, : l : l, l l l, : l, ( ( ( = yl l: l + y : l + RT( yl + + y + y y ( y y ( ( ( ( ( l, : l l, : l l : l, ( (0 ( (0 (0 ( ( (0 + yl y l, : l + y ( yl l: l, + y : l, + yl y y l, : l, ( ( ( ( + yl y ( yl y ( ( ( ( ( (, : ( ll+ y yl y yl ll :, + y l :,

6 y ( ( ( ( = yl l: + y : + RT( y + ( (0 ( (0 (0 ( ( (0 + yl y l, : + yl ( yl l: l, + y : l, + yl y yl l, : l, ( ( ( ( + yl y ( yl y ( ( ( ( ( (, : ( l+ yl yl y yl ll :, + y l :, = y + y, 0 = +, = = y + y, 0 = +, = x = y + y, 0 = +, = ( ( ( x = y + y, 0= +, = ( ( ( ( ( ( l l l ( ( ( ( ( ( l l l ( ( ( ( ( ( l l l l l l l y ( l ( ( ( y = y ( ( l ( ( yl = xl yl y = y = x + y ( ( ( l l l y ( l y ( l d ( ( ( ( = ( l + ( + ( l + ( yl y yl y d y y ( ( ( l = ( + + ( ( ( ( ( + ( ( l l l l yl y l = 0 ( + ( + ( ( = yl y yl y ( ( = ( yl y yl y ( 5

7 ( ( = ( ( yl y yl y ( ( ( yl l: l + y : l + RT( yl + + y y + y ( y + y + y y y ( ( ( ( ( ( ( ( ( + y y ( y y, : + y ( y y y :, + y :, ( ( ( yl l: + y : + RT( y + ( (0 ( (0 (0 ( ( (0 + y y + y ( y + y + y y y ( ( ( ( ( ( ( ( ( + yl y ( yl y l, : + yl ( yl y yl l: l, + y ( ( ( yl l: l + y l: + RT( yl + ( ( 0 ( 0 ( ( 0 ( ( ( 0 = + y ( y + y + y y + y y y ( ( ( ( ( ( ( ( ( + y ( yl y ( yl l, : l + y + y y ( y y ( ( ( yl : l + y : + RT( y + ( ( 0 ( 0 ( ( 0 ( ( ( 0 + yl ( yl l, : l + y l, : + yl y : l, + y y y ( ( ( ( ( ( ( ( ( + y ( y y ( y + y + y y ( y y ( ( 0 ( ( 0 ( 0 ( ( ( 0 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, - y ( j = x i i 6

8 xll: l + x : l + RT( xl + + x x + x x + x + x x x + x x ( x x + x ( x x x + x xll: + x : + RT( x x x + x ( x + x + x x x xl x ( xl x l, : xl ( xl x xl l: l, + x xll: l + xl: + RT( xl = + x ( x + x + x x + x x x + x ( xl x ( xl l, : l + x l, : + x x ( x x xl: l + x : + RT( x x ( x + x + x x + x x x + xl ( xl x ( xl l, : + x + x x ( x x (, : ( :, :, 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, xll: l + x : l + x x + x ( x + x + x x x + xl x ( xl x l, : l + x ( xl x ( xl l: l, + x : l, l l, : l l l: l, : l, l : l, l l, : l, xll: + x : + x x + x ( x + x + x x x + xl x ( xl x l, : + xl ( xl x ( xl l: l, + x : l, l l, : l l: l, l: l, : l, l l l, : l, xll: l + xl: = + x ( x + x + x x + x x x + x ( xl x ( xl l, : l + x l, : + xl x ( xl x l: l, l l, : l l, : l l, : l l: l, l l, : l, xl : l + x : + x ( x + x + x x + x x x + xl ( xl x ( xl l, : l + x l, : + xl x ( xl x : l, l l, : l l, : l l, : l : l, l l l, : l, 7

9 0 0 xl ( l: l l: l: l, + x ( : l + : l, : xl x ( l, : l + l: l, : l, l, : + l: l, : l, 0 + xl x ( x xl l, : l, + xl x ( xl x ( l, : l l, : + x ( x x x + x x ( x x x + x ( :, :, ( :, :, l l l l l l l l l l l 0 xl ( l: l : l 0 l, : l + x ( l: + l, : : xl x ( l, : l l, : + l: l, + l, : l l, : : l, 0 = + xl x ( x xl l, : l, + x ( xl x xl l, : l + x x ( x x x + x + xl x ( xl x ( l: l, : l, ( l, : l l ( l l, : l l, : 0 0 xl ( l: l l: l: l, + x ( : l + : l, : xl x ( l, : l l, : + l: l, : l, + xl x ( x xl l, : l, + xl x ( xl x ( l, : l l, : + ( xl x x x xl xl ( xl l: l, + x : l, 0 0 xl ( l: l : l l, : l + x ( l: + l, : : 0 0 = + xl x ( l: l, : l, + ll, : l, : + xlx( x xl ll, :, + ( xl x x x xl xl ( xl l, : l + x l, : + xl x ( xl x ( l: l, : l, x ( + x ( l l: l l: l: l, : l : l, : x ( x ( l l: l : l l, : l l: l, : : + x x ( ( 0 + x x x x 0 0 l l, : l l, : l: l, : l, l l l, : l, x x ( + x x ( x x l l: l, : l, l, : l l, : l l l, : l, + x x ( x x ( + ( x x x x x x (x + x l l l, : l l, : l l l l l: l, : l, ( x x x x x x ( x + x x x ( x x ( = 0 l l l l l, : l l, : l l l: l, : l, x ( ( x + l l: : l l: l l: l, l, : l : l l: : : l, l, : + x x ( l l, : l l, : l: l, : l, + x x ( x x ( + 0 l l l, : l l: l, l, : : l, l, : l, + ( x x x x { x ( + x ( } = 0 l l l l: l, l, : l : l, l, : 8

10 + = l: : l l: l l: l, l, : l + = : l l: : : l, l, : = l, : l l, : l: l, : l, l, : l 0 l: l, l, : : l, l, : l, = 0 l: l, l, : l = 0 : l, l, : + = 0 = = 0 l: l : = l: = : l = + = 0 l: l, l: l, = : l, l, : l = = : l, l, : = l, : l l, : : l, + 0 l, : l l: l, l, : : l, l, : l, = 0 l, : l = 0 5 l, : = : l, = 0 0 : l, = + 0 l, : l = + + = + + = + = + + = l, : : l, 9

11 = l, : l = l, : 5 = ( + = ( = ( 5 0 l, : l, l, : l l: l, l, : : l, = = 0 l: l : = l: = : l = + + = = = = 0 l, : l 0 l, : 0 l: l, 0 : l, l: l, = : l, 5 = ( 0 l, : l, 5 = = = l: : l =, = l, : l l, : l: l, : l, 0

12 l: l : l: : l 0 l, : l 0 l, : 0 l: l, 0 : l, l: l, = = 0 = = = + + = + + = + w = + + = + + = + w = = + = w + = w = = : l, 5 = ( 0 l, : l, 5

2.

2. 2. 10 2. 2. 1995/12006/111995/42006/12 2. 10 1995120061119954200612 02505 025 05 025 02505 0303 02505 250100 250 200 100200 5010050 100200 100 100 50100 100200 50100 10 75100100 0250512 02505 1 025051205

More information

土壌環境行政の最新動向(環境省 水・大気環境局土壌環境課)

土壌環境行政の最新動向(環境省 水・大気環境局土壌環境課) 201022 1 18801970 19101970 19201960 1970-2 1975 1980 1986 1991 1994 3 1999 20022009 4 5 () () () () ( ( ) () 6 7 Ex Ex Ex 8 25 9 10 11 16619 123 12 13 14 5 18() 15 187 1811 16 17 3,000 2241 18 19 ( 50

More information

syuryoku

syuryoku 248 24622 24 P.5 EX P.212 2 P271 5. P.534 P.690 P.690 P.690 P.690 P.691 P.691 P.691 P.702 P.702 P.702 P.702 1S 30% 3 1S 3% 1S 30% 3 1S 3% P.702 P.702 P.702 P.702 45 60 P.702 P.702 P.704 H17.12.22 H22.4.1

More information

ID POS F

ID POS F 01D8101011L 2005 3 ID POS 2 2 1 F 1... 1 2 ID POS... 2 3... 4 3.1...4 3.2...4 3.3...5 3.4 F...5 3.5...6 3.6 2...6 4... 8 4.1...8 4.2...8 4.3...8 4.4...9 4.5...10 5... 12 5.1...12 5.2...13 5.3...15 5.4...17

More information

- 1 - - 0.5%5 10 10 5 10 1 5 1

- 1 - - 0.5%5 10 10 5 10 1 5 1 - - - 1 - - 0.5%5 10 10 5 10 1 5 1 - 2 - - - - A B A A A B A B B A - 3 - - 100 100 100 - A) ( ) B) A) A B A B 110 A B 13 - 4 - A) 36 - - - 5 - - 1 - 6-1 - 7 - - 8 - Q.15 0% 10% 20% 30% 40% 50% 60% 70%

More information

1

1 1 - 2 - ... - 4 -... - 4 -... - 4 -... - 4 -... - 5 -... - 5 -... - 8 -... - 9 -... - 9 -... - 9 -... - 9 -... - 9 -... - 9 -... - 10 -... - 10 -... - 10 -... - 10 -... - 10 -... - 11 -... - 11 -... -

More information

弾性定数の対称性について

弾性定数の対称性について () by T. oyama () ij C ij = () () C, C, C () ij ji ij ijlk ij ij () C C C C C C * C C C C C * * C C C C = * * * C C C * * * * C C * * * * * C () * P (,, ) P (,, ) lij = () P (,, ) P(,, ) (,, ) P (, 00,

More information

II 2 II

II 2 II II 2 II 2005 yugami@cc.utsunomiya-u.ac.jp 2005 4 1 1 2 5 2.1.................................... 5 2.2................................. 6 2.3............................. 6 2.4.................................

More information

2 2.1 2 2.1.1 2.1.1 4060 4060 *1 3550 3550 3550 *2 4060 4060 1520 7095 6090 4060 4060 4060 4080 3070 3001500 200400 40200 - - 5002000 15003500 60200 *1 *2 6 2.1.1 1 2 3 2.1.2 1 7 2 3 4 180 5 2 6 3,000K

More information

2

2 1 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234

More information

○01 那覇市(7月変更)

○01 那覇市(7月変更) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 H26,2 H28.2 9 9 38 39 40 41 42 43 l ll 44 45 46 47 48 49 50 51 52 53 54 55 2733 14,500 56 57 58 59

More information

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)

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

More information

( : December 27, 2015) CONTENTS I. 1 II. 2 III. 2 IV. 3 V. 5 VI. 6 VII. 7 VIII. 9 I. 1 f(x) f (x) y = f(x) x ϕ(r) (gradient) ϕ(r) (gradϕ(r) ) ( ) ϕ(r)

( : December 27, 2015) CONTENTS I. 1 II. 2 III. 2 IV. 3 V. 5 VI. 6 VII. 7 VIII. 9 I. 1 f(x) f (x) y = f(x) x ϕ(r) (gradient) ϕ(r) (gradϕ(r) ) ( ) ϕ(r) ( : December 27, 215 CONTENTS I. 1 II. 2 III. 2 IV. 3 V. 5 VI. 6 VII. 7 VIII. 9 I. 1 f(x f (x y f(x x ϕ(r (gradient ϕ(r (gradϕ(r ( ϕ(r r ϕ r xi + yj + zk ϕ(r ϕ(r x i + ϕ(r y j + ϕ(r z k (1.1 ϕ(r ϕ(r i

More information

6.1 (P (P (P (P (P (P (, P (, P.101

6.1 (P (P (P (P (P (P (, P (, P.101 (008 0 3 7 ( ( ( 00 1 (P.3 1 1.1 (P.3.................. 1 1. (P.4............... 1 (P.15.1 (P.15................. (P.18............3 (P.17......... 3.4 (P................ 4 3 (P.7 4 3.1 ( P.7...........

More information

DocuPrint C2424 取扱説明書(詳細編)

DocuPrint C2424 取扱説明書(詳細編) 3 4 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1.1 1 1 2 3 4 5 30 1.2 1 31 1.3 1 32 33 1 1.4 1 1.4.1 34 1.4.2 1 2 35 1 1.5 1 1 2 3 4 36 5 6 7 8 9 37 1 1 10 11 12 13 38 14 15

More information

untitled

untitled 1 ( 14 1517 18 20 24 2 3 4 5 1947H18536H23 5,2332,155 12H22-H25.3 209144H22-H25.3 H23.4 KI 24,090H25.5 H24.3 5,233H25.5 2,155H22-H23 1,068H22-H23 1.2%H224.1%H24 1947H18536H23 1.34H171.55H22 1H23 553,059

More information

特許侵害訴訟における無効の主張を認めた判決─半導体装置事件−

特許侵害訴訟における無効の主張を認めた判決─半導体装置事件− [*1847] 12 4 11 10 364 54 4 1368 1710 68 1032 120 X Y 6.8.31 29 3 875 X Y 9.9.10 29 3 819 Y 320275 391468 46 12 21 35 2 6 3513745 39 1 30 320249 1) 1 39 1 [*1848] 2) 3) Y 10 51 2 4 39 5 39 1 3 139 7 2

More information

プリント

プリント l l l l ll l l l l l l l l l l l 𩸽 l l l l l ll l l l l l l l l l ll l l l l l l l l ll ll l l l l l l ll ll ll l

More information

X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2

More information

sec13.dvi

sec13.dvi 13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:

More information

6.1 (P (P (P (P (P (P (, P (, P.

6.1 (P (P (P (P (P (P (, P (, P. (011 30 7 0 ( ( 3 ( 010 1 (P.3 1 1.1 (P.4.................. 1 1. (P.4............... 1 (P.15.1 (P.16................. (P.0............3 (P.18 3.4 (P.3............... 4 3 (P.9 4 3.1 (P.30........... 4 3.

More information

表紙オモテ

表紙オモテ 1 2 http://www.mlit.go.jp/kankocho/shisaku/sangyou/taiou_manual.html 3 4 . 5 . 6 . 7 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 18 . EX). 19 . 20 . 21 . 22 . 23 . 24 25. 26. . 27 28 . pork 29 . 30 .

More information

II 2 3.,, A(B + C) = AB + AC, (A + B)C = AC + BC. 4. m m A, m m B,, m m B, AB = BA, A,, I. 5. m m A, m n B, AB = B, A I E, 4 4 I, J, K

II 2 3.,, A(B + C) = AB + AC, (A + B)C = AC + BC. 4. m m A, m m B,, m m B, AB = BA, A,, I. 5. m m A, m n B, AB = B, A I E, 4 4 I, J, K II. () 7 F 7 = { 0,, 2, 3, 4, 5, 6 }., F 7 a, b F 7, a b, F 7,. (a) a, b,,. (b) 7., 4 5 = 20 = 2 7 + 6, 4 5 = 6 F 7., F 7,., 0 a F 7, ab = F 7 b F 7. (2) 7, 6 F 6 = { 0,, 2, 3, 4, 5 },,., F 6., 0 0 a F

More information

- 1 - - 2 - - 3 - - 4 - - 5 - - 6 - - 7 - - 8 - - 9 - - 10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 - - 17 - - 18 - - 19 - - 20 - - 21 - - 22 - - 23 - - 24 - - 25 - - 26 - - 27 - - 28 - - - - 29 - - 30

More information

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2 1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2

More information

untitled

untitled 131 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 7. 1 71 71 71 71 71 71 71 71 71 7 1 71 71 71 71 71 71 71 71 71 71 71 71 71

More information

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63> Visual Basic でわかるやさしい有限要素法の基礎 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/092001 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. URL http://www.morikita.co.jp/soft/92001/ horibe@mx.ibaraki.ac.jp

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

2017 II 1 Schwinger Yang-Mills 5. Higgs 1

2017 II 1 Schwinger Yang-Mills 5. Higgs 1 2017 II 1 Schwinger 2 3 4. Yang-Mills 5. Higgs 1 1 Schwinger Schwinger φ 4 L J 1 2 µφ(x) µ φ(x) 1 2 m2 φ 2 (x) λφ 4 (x) + φ(x)j(x) (1.1) J(x) Schwinger source term) c J(x) x S φ d 4 xl J (1.2) φ(x) m 2

More information

( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1

( )/2   hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1 ( )/2 http://www2.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html 1 2011 ( )/2 2 2011 4 1 2 1.1 1 2 1 2 3 4 5 1.1.1 sample space S S = {H, T } H T T H S = {(H, H), (H, T ), (T, H), (T, T )} (T, H) S

More information

6 6.1 L r p hl = r p (6.1) 1, 2, 3 r =(x, y, z )=(r 1,r 2,r 3 ), p =(p x,p y,p z )=(p 1,p 2,p 3 ) (6.2) hl i = jk ɛ ijk r j p k (6.3) ɛ ijk Levi Civit

6 6.1 L r p hl = r p (6.1) 1, 2, 3 r =(x, y, z )=(r 1,r 2,r 3 ), p =(p x,p y,p z )=(p 1,p 2,p 3 ) (6.2) hl i = jk ɛ ijk r j p k (6.3) ɛ ijk Levi Civit 6 6.1 L r p hl = r p (6.1) 1, 2, 3 r =(x, y, z )=(r 1,r 2,r 3 ), p =(p x,p y,p z )=(p 1,p 2,p 3 ) (6.2) hl i = jk ɛ ijk r j p k (6.3) ɛ ijk Levi Civita ɛ 123 =1 0 r p = 2 2 = (6.4) Planck h L p = h ( h

More information

Part () () Γ Part ,

Part () () Γ Part , Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35

More information

Chap9.dvi

Chap9.dvi .,. f(),, f(),,.,. () lim 2 +3 2 9 (2) lim 3 3 2 9 (4) lim ( ) 2 3 +3 (5) lim 2 9 (6) lim + (7) lim (8) lim (9) lim (0) lim 2 3 + 3 9 2 2 +3 () lim sin 2 sin 2 (2) lim +3 () lim 2 2 9 = 5 5 = 3 (2) lim

More information

Q E Q T a k Q Q Q T Q =

Q E Q T a k Q Q Q T Q = i 415 q q q q Q E Q T a k Q Q Q T Q = 10 30 j 19 25 22 E 23 R 9 i i V 25 60 1 20 1 18 59R1416R30 3018 1211931 30025R 10T1T 425R 11 50 101233 162 633315 22E1011 10T q 26T10T 12 3030 12 12 24 100 1E20 62

More information

( )

( ) 7..-8..8.......................................................................... 4.................................... 3...................................... 3..3.................................. 4.3....................................

More information

.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(

.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,

More information

all.dvi

all.dvi 5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0

More information

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 (

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 ( 1 1.1 (1) (1 + x) + (1 + y) = 0 () x + y = 0 (3) xy = x (4) x(y + 3) + y(y + 3) = 0 (5) (a + y ) = x ax a (6) x y 1 + y x 1 = 0 (7) cos x + sin x cos y = 0 (8) = tan y tan x (9) = (y 1) tan x (10) (1 +

More information

- 1 - 2 ç 21,464 5.1% 7,743 112 11,260 2,349 36.1% 0.5% 52.5% 10.9% 1,039 0.2% 0 1 84 954 0.0% 0.1% 8.1% 91.8% 2,829 0.7% 1,274 1,035 496 24 45.0% 36.6% 17.5% 0.8% 24,886 5.9% 9,661 717 6,350 8,203 38.8%

More information

IPA... 3... 4... 7... 8... 8... 10... 11... 13... 14... 21... 21... 23... 27 2

IPA... 3... 4... 7... 8... 8... 10... 11... 13... 14... 21... 21... 23... 27 2 IPA 1 IPA... 3... 4... 7... 8... 8... 10... 11... 13... 14... 21... 21... 23... 27 2 IPA 2011103 3 1 139 2 4 10 4 5 6 7 8 9 2 ID 10 11 12 13 14 15 16 17 18 19 20 http://www.jpcert.or.jp/research/2008/inoculation_200808.pdf

More information

layout_H1-H4

layout_H1-H4 KI GOODS CATALOGUE 2012.8 304,500 77,700 7,350 174,700 156,700 71,400 9,450 6,970 7,350 389,550 269,870 251,870 71,400 133,400 9,450 6,970 787 787 294,000 9,450 303,450 612,270 178,500 77,700 140,700 203,700

More information

untitled

untitled 1 4 4 6 8 10 30 13 14 16 16 17 18 19 19 96 21 23 24 3 27 27 4 27 128 24 4 1 50 by ( 30 30 200 30 30 24 4 TOP 10 2012 8 22 3 1 7 1,000 100 30 26 3 140 21 60 98 88,000 96 3 5 29 300 21 21 11 21

More information

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y [ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)

More information

O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0

O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0 9 O y O ( O ) O (O ) 3 y O O v t = t = 0 ( ) O t = 0 t r = t P (, y, ) r = + y + (t,, y, ) (t) y = 0 () ( )O O t (t ) y = 0 () (t) y = (t ) y = 0 (3) O O v O O v O O O y y O O v P(, y,, t) t (, y,, t )

More information

ssp2_fixed.dvi

ssp2_fixed.dvi 13 12 30 2 1 3 1.1... 3 1.2... 4 1.3 Bravais... 4 1.4 Miller... 4 2 X 5 2.1 Bragg... 5 2.2... 5 2.3... 7 3 Brillouin 13 3.1... 13 3.2 Brillouin... 13 3.3 Brillouin... 14 3.4 Bloch... 16 3.5 Bloch... 17

More information

I S /I SO 1.04 C T S D 0.38 I SO =0.70

I S /I SO 1.04 C T S D 0.38 I SO =0.70 I S /I SO 1.01 C T S D 0.63 I SO =0.75 U=1.25 I S /I SO 1.00 C T S D 0.63 I SO =0.75 U=1.25 I S /I SO 1.01 C T S D 0.77 I SO =0.75 U=1.25 I S /I SO 1.03 C TU S D 0.32 I S /I SO 1.08 C TU S D 0.66 I S /I

More information

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

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)

More information

弾性論(Chen)

弾性論(Chen) Phase-field by T.Koyama Phase-field da da a( ) a + { } a d + d δ (-) δ (-) eigen a a a ε ε δ δ (-) da ε (-4) a d ε ε + δε ( ) (-5) δε d (-6) V u ul δεl + l (-7) eigen el ε ε ε (-8) σ el C ε el C { ε ε

More information

5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6 cos π 6.7 MP 4 P P N i i i i N i j F j ii N i i ii F j i i N ii li i F j i ij li i i i

5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6 cos π 6.7 MP 4 P P N i i i i N i j F j ii N i i ii F j i i N ii li i F j i ij li i i i i j ij i j ii,, i j ij ij ij (, P P P P θ N θ P P cosθ N F N P cosθ F Psinθ P P F P P θ N P cos θ cos θ cosθ F P sinθ cosθ sinθ cosθ sinθ 5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6

More information

) 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 = 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

More information

untitled

untitled 17 5 13 1 2 1.1... 2 1.2... 2 1.3... 3 2 3 2.1... 3 2.2... 5 3 6 3.1... 6 3.2... 7 3.3 t... 7 3.4 BC a... 9 3.5... 10 4 11 1 1 θ n ˆθ. ˆθ, ˆθ, ˆθ.,, ˆθ.,.,,,. 1.1 ˆθ σ 2 = E(ˆθ E ˆθ) 2 b = E(ˆθ θ). Y 1,,Y

More information

5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )

5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j ) 5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y

More information

0.1 I I : 0.2 I

0.1 I I : 0.2 I 1, 14 12 4 1 : 1 436 (445-6585), E-mail : sxiida@sci.toyama-u.ac.jp 0.1 I I 1. 2. 3. + 10 11 4. 12 1: 0.2 I + 0.3 2 1 109 1 14 3,4 0.6 ( 10 10, 2 11 10, 12/6( ) 3 12 4, 4 14 4 ) 0.6.1 I 1. 2. 3. 0.4 (1)

More information

151021slide.dvi

151021slide.dvi : Mac I 1 ( 5 Windows (Mac Excel : Excel 2007 9 10 1 4 http://asakura.co.jp/ books/isbn/978-4-254-12172-8/ (1 1 9 1/29 (,,... (,,,... (,,, (3 3/29 (, (F7, Ctrl + i, (Shift +, Shift + Ctrl (, a i (, Enter,

More information

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2 II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh

More information

1 食品安全を主な目的とする取組

1 食品安全を主な目的とする取組 --a 2003 7 26 3. 3.1-1- 16 2 27 0227012-2-a 23 7 1 82 2 1 7 9 2 ( ) -2- -2-b 19 3 28 18 14701-2-c ) 15 5 2-3- 26 21 7 2 2 7 2 3 7 2 4 10 83 23 3 1 7 2 5 7 2 5-2-d -4- -5 - -3-a -6- -4-a -7- -4-b -8- -5-a

More information

Auerbach and Kotlikoff(1987) (1987) (1988) 4 (2004) 5 Diamond(1965) Auerbach and Kotlikoff(1987) 1 ( ) ,

Auerbach and Kotlikoff(1987) (1987) (1988) 4 (2004) 5 Diamond(1965) Auerbach and Kotlikoff(1987) 1 ( ) , ,, 2010 8 24 2010 9 14 A B C A (B Negishi(1960) (C) ( 22 3 27 ) E-mail:fujii@econ.kobe-u.ac.jp E-mail:082e527e@stu.kobe-u.ac.jp E-mail:iritani@econ.kobe-u.ac.jp 1 1 1 2 3 Auerbach and Kotlikoff(1987) (1987)

More information

0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (,

0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (, [ ], IC 0. A, B, C (, 0, 0), (0,, 0), (,, ) () CA CB ACBD D () ACB θ cos θ (3) ABC (4) ABC ( 9) ( s090304) 0. 3, O(0, 0, 0), A(,, 3), B( 3,, ),. () AOB () AOB ( 8) ( s8066) 0.3 O xyz, P x Q, OP = P Q =

More information

st.dvi

st.dvi 9 3 5................................... 5............................. 5....................................... 5.................................. 7.........................................................................

More information

: , 2.0, 3.0, 2.0, (%) ( 2.

: , 2.0, 3.0, 2.0, (%) ( 2. 2017 1 2 1.1...................................... 2 1.2......................................... 4 1.3........................................... 10 1.4................................. 14 1.5..........................................

More information

tokei01.dvi

tokei01.dvi 2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN

More information

2

2 1 2 2005 15 17 21 22 24 25 67 95 3 1 2 3 4 17 4 5 6 7 8 9 PR PR PR 10 11 12 PR 419 844 1,490 950 590 20 12 50 13 12/20 2/28 3/30 14 17 349 666 15 59 6 11 15 17 14 15 15 17 3,525,992 15 59 15 17 18 910

More information

『保守の比較政治学』

『保守の比較政治学』 v vi vii viii ix x xi xii xiii xiv 3 3 3 9 20 25 25 27 30 32 37 xvi 43 47 57 57 60 66 72 74 81 81 83 86 91 xvii 98 101 111 111 111 115 118 125 128 135 135 136 143 151 157 xviii 163 163 167 173 179 185

More information

Color MultiWriter 9900C/9800C ユーザーズマニュアル

Color MultiWriter 9900C/9800C ユーザーズマニュアル l l l l l i ii iii iv v vi vii viii ix x xi xii xiii xiv xv xvi xvii xviii xix xx xxi xxii xxiii xxiv xxv xxvi 1.1 1 2 3 1 1 4 5 1 1 6 7-1 1.2 1 8 1.3 1 9 1 1.3.1 10 1 2 11 1 1 1.3.2 12 13 1 1 14 1.4

More information

[] x < T f(x), x < T f(x), < x < f(x) f(x) f(x) f(x + nt ) = f(x) x < T, n =, 1,, 1, (1.3) f(x) T x 2 f(x) T 2T x 3 f(x), f() = f(t ), f(x), f() f(t )

[] x < T f(x), x < T f(x), < x < f(x) f(x) f(x) f(x + nt ) = f(x) x < T, n =, 1,, 1, (1.3) f(x) T x 2 f(x) T 2T x 3 f(x), f() = f(t ), f(x), f() f(t ) 1 1.1 [] f(x) f(x + T ) = f(x) (1.1), f(x), T f(x) x T 1 ) f(x) = sin x, T = 2 sin (x + 2) = sin x, sin x 2 [] n f(x + nt ) = f(x) (1.2) T [] 2 f(x) g(x) T, h 1 (x) = af(x)+ bg(x) 2 h 2 (x) = f(x)g(x)

More information

_;-TIL._ I J --' ) /'. (t -/. a rlr. l 111!' Ir': i " b "It'_1_; -1r-_.-- I'!f' I :;(: 1 '1' 1 ' 't'l] S I) I "' :h "'t t-1-i ' J ilt'tt't 1 Jf(i - 7J_.1 _ f F FT'II 1 ' ft - JI '- ll i" ': "'1l li l!

More information

1 I p2/30

1 I p2/30 I I p1/30 1 I p2/30 1 ( ) I p3/30 1 ( ), y = y() d = f() g(y) ( g(y) = f()d) (1) I p4/30 1 ( ), y = y() d = f() g(y) ( g(y) = f()d) (1) g(y) = f()d I p4/30 1 ( ), y = y() d = f() g(y) ( g(y) = f()d) (1)

More information

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H 199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)

More information