1

Size: px
Start display at page:

Download "1"

Transcription

1

2 .....

3 .. XY XZ YZ

4

5 .....

6

7

8

9

10

11

12 ..

13

14

15

16

17

18

19 ..

20

21

22

untitled

untitled 20 7 1 22 7 1 1 2 3 7 8 9 10 11 13 14 15 17 18 19 21 22 - 1 - - 2 - - 3 - - 4 - 50 200 50 200-5 - 50 200 50 200 50 200 - 6 - - 7 - () - 8 - (XY) - 9 - 112-10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 -

More information

untitled

untitled 19 1 19 19 3 8 1 19 1 61 2 479 1965 64 1237 148 1272 58 183 X 1 X 2 12 2 15 A B 5 18 B 29 X 1 12 10 31 A 1 58 Y B 14 1 25 3 31 1 5 5 15 Y B 1 232 Y B 1 4235 14 11 8 5350 2409 X 1 15 10 10 B Y Y 2 X 1 X

More information

.....Z...^.[.......\..

.....Z...^.[.......\.. 15 10 16 42 55 55 56 60 62 199310 1995 134 10 8 15 1 13 1311 a s d f 141412 2 g h j 376104 3 104102 232 4 5 51 30 53 27 36 6 Y 7 8 9 10 8686 86 11 1310 15 12 Z 13 14 15 16 102193 23 1712 60 27 17 18 Z

More information

表紙

表紙 A B,BW C Rc No. h Rc C 2 3 4 M2 M3 M4 M5 M6 25 3.2 6.8 3.5 6.4 2.8 2.7 2.4 9.1 15.5 21.6 28.0 34.4 35 41 40 50 60 80 100 120 140 160 180 200 240 4.8 10.2 5.2 10.1 4.3 4.1 3.8 14.23 24.36 34.1 44.2 54.3

More information

1.1 1 A

1.1 1 A . A..2 2 2. () (xyz) ( xyz) ( xy z) = (x x)yz ( xy z) = yz ( xy z) = y(z ( x z)) = y((z x)(z z)) = y( x z) (2) (3) M aj (x, y, M aj ( x, ȳ, z)) = xy ȳm aj ( x, ȳ, z) M aj ( x, ȳ, z)x M aj (x, y, z) x =

More information

7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6

7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6 26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7

More information

応力とひずみ.ppt

応力とひずみ.ppt in yukawa@numse.nagoya-u.ac.jp 2 3 4 5 x 2 6 Continuum) 7 8 9 F F 10 F L L F L 1 L F L F L F 11 F L F F L F L L L 1 L 2 12 F L F! A A! S! = F S 13 F L L F F n = F " cos# F t = F " sin# S $ = S cos# S S

More information

ユニセフ表紙_CS6_三.indd

ユニセフ表紙_CS6_三.indd 16 179 97 101 94 121 70 36 30,552 1,042 100 700 61 32 110 41 15 16 13 35 13 7 3,173 41 1 4,700 77 97 81 47 25 26 24 40 22 14 39,208 952 25 5,290 71 73 x 99 185 9 3 3 3 8 2 1 79 0 d 1 226 167 175 159 133

More information

ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y

ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y 01 4 17 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy + r (, y) z = p + qy + r 1 y = + + 1 y = y = + 1 6 + + 1 ( = + 1 ) + 7 4 16 y y y + = O O O y = y

More information

( ) x y f(x, y) = ax

( ) x y f(x, y) = ax 013 4 16 5 54 (03-5465-7040) nkiyono@mail.ecc.u-okyo.ac.jp hp://lecure.ecc.u-okyo.ac.jp/~nkiyono/inde.hml 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy

More information

2

2 2007 8 12 1 Q&A Q1 A 2007 6 29 2008 1 1 14 1 12 1 2 3 1 1 13 1 2 15 1 1 2 Q2 A 627 1 20 1 1 3 15 2003 18 2 3 4 5 3 406 44 2 1997 7 16 5 1 1 15 4 52 1 31 268 17 5 60 55 50 1999 3 9 1999 3 39 40 44 100 1

More information

untitled

untitled 2 5 1 5 5.1 5.2 5.3 5.4 5.1 5.3 6 6.1 6.2 2 6.3 F 6.4 2 6.5 6.6 2 2 6.1 6.4 2 6.2 2 6.3 F 6.5 6.6 2 6.1 6.1 1 5 X N 2 /n Z X - / / n Z N 0 1 P -z /2 Z z /2 1- z P Z z = P X-z /2 / n X+ z /2 / n 100 % X-z

More information

ユニセフ表紙_CS6_三.indd

ユニセフ表紙_CS6_三.indd 16 179 97 101 94 121 70 36 30,552 1,042 100 700 61 32 110 41 15 16 13 35 13 7 3,173 41 1 4,700 77 97 81 47 25 26 24 40 22 14 39,208 952 25 5,290 71 73 x 99 185 9 3 3 3 8 2 1 79 0 d 1 226 167 175 159 133

More information

2005

2005 20 30 8 3 190 60 A,B 67,2000 98 20 23,600 100 60 10 20 1 3 2 1 2 1 12 1 1 ( ) 340 20 20 30 50 50 ( ) 6 80 5 65 17 21 5 5 12 35 1 5 20 3 3,456,871 2,539,950 916,921 18 10 29 5 3 JC-V 2 ( ) 1 17 3 1 6

More information

xyr x y r x y r u u

xyr x y r x y r u u xyr x y r x y r u u y a b u a b a b c d e f g u a b c d e g u u e e f yx a b a b a b c a b c a b a b c a b a b c a b c a b c a u xy a b u a b c d a b c d u ar ar a xy u a b c a b c a b p a b a b c a

More information

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, 変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +

More information

untitled

untitled 1 ( 12 11 44 7 20 10 10 1 1 ( ( 2 10 46 11 10 10 5 8 3 2 6 9 47 2 3 48 4 2 2 ( 97 12 ) 97 12 -Spencer modulus moduli (modulus of elasticity) modulus (le) module modulus module 4 b θ a q φ p 1: 3 (le) module

More information

42,955 27,585 6,696 53,020 44,577 2,198 43,625 25,917 16,007 12,213 12,062 11,788 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000

42,955 27,585 6,696 53,020 44,577 2,198 43,625 25,917 16,007 12,213 12,062 11,788 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 Disclosure 2005 TOMAKOMAI SHINKIN BANK 11 350,000 300,000 250,000 200,000 150,000 100,000 50,000 24,281 21,469 22,693 66,792 67,769 73,165 216,099 222,407 228,456 0 7 42,955 27,585 6,696 53,020 44,577

More information

p q p q p q p q p q p q p q p q p q x y p q t u r s p q p p q p q p q p p p q q p p p q P Q [] p, q P Q [] P Q P Q [ p q] P Q Q P [ q p] p q imply / m

p q p q p q p q p q p q p q p q p q x y p q t u r s p q p p q p q p q p p p q q p p p q P Q [] p, q P Q [] P Q P Q [ p q] P Q Q P [ q p] p q imply / m P P N p() N : p() N : p() N 3,4,5, L N : N : N p() N : p() N : p() N p() N p() p( ) N : p() k N : p(k) p( k ) k p(k) k k p( k ) k k k 5 k 5 N : p() p() p( ) p q p q p q p q p q p q p q p q p q x y p q

More information

II 1 3 2 5 3 7 4 8 5 11 6 13 7 16 8 18 2 1 1. x 2 + xy x y (1 lim (x,y (1,1 x 1 x 3 + y 3 (2 lim (x,y (, x 2 + y 2 x 2 (3 lim (x,y (, x 2 + y 2 xy (4 lim (x,y (, x 2 + y 2 x y (5 lim (x,y (, x + y x 3y

More information

A

A A05-132 2010 2 11 1 1 3 1.1.......................................... 3 1.2..................................... 3 1.3..................................... 3 2 4 2.1............................... 4 2.2

More information

平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2

平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2 3 90 2006 1. V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2 = xz y 2 = 0} V (x,y) n = 1 n = 2 (x,y) V n = 1 n = 2 (3/5,4/5),(5/13,12/13)... n 3 V (0,±1),(±1,0) ( ) n 3 x n + y n = z n,

More information

プラズマ・核融合学会誌

プラズマ・核融合学会誌 5. Validation and Application of a Numerical Tool for Lifetime Evaluation of Ion Thruster s Ion Optics Japan Aerospace Exploration Agency, Sagamihara, KANAGAWA 252-5210, Japan μ10pm author s e-mail: watanabe.hiroki@jaxa.jp

More information

7-12.dvi

7-12.dvi 26 12 1 23. xyz ϕ f(x, y, z) Φ F (x, y, z) = F (x, y, z) G(x, y, z) rot(grad ϕ) rot(grad f) H(x, y, z) div(rot Φ) div(rot F ) (x, y, z) rot(grad f) = rot f x f y f z = (f z ) y (f y ) z (f x ) z (f z )

More information

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0,

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0, .1.1 Y K L Y = K 1 3 L 3 L K K (K + ) 1 1 3 L 3 K 3 L 3 K 0 (K + K) 1 3 L 3 K 1 3 L 3 lim K 0 K = L (K + K) 1 3 K 1 3 3 lim K 0 K = 1 3 K 3 L 3 z = f(x, y) x y z x-y-z.1 z = e x +xy y 3 x-y ( ) z 0 f(x,

More information

73

73 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

More information

96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A

96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A 7 Lorentz 7.1 Ampère I 1 I 2 I 2 I 1 L I 1 I 2 21 12 L r 21 = 12 = µ 0 2π I 1 I 2 r L. (7.1) 7.1 µ 0 =4π 10 7 N A 2 (7.2) magnetic permiability I 1 I 2 I 1 I 2 12 21 12 21 7.1: 1m 95 96 7 1m =2 10 7 N

More information

取扱説明書 [F-07E]

取扱説明書 [F-07E] 2 3 4 5 6 7 8 9 0 2 3 4 5 a b c d a b c d 6 a b cd e a b c d e 7 8 9 20 a b a a b b 2 22 a c b d 23 24 a b ef ghi j k cd l m n op q w xy z r s t u v A B a b c d e f g h i j k l m n o p q r s 25 t u v

More information

untitled

untitled 1 Hitomi s English Tests 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 2 0 0 1 1 0 0 0 0 0 1 1 1 1 0 3 1 1 0 0 0 0 1 0 1 0 1 0 1 1 4 1 1 0 1 0 1 1 1 1 0 0 0 1 1 5 1 1 0 1 1 1 1 0 0 1 0

More information

数学Ⅲ立体アプローチ.pdf

数学Ⅲ立体アプローチ.pdf Ⅲ Ⅲ DOLOR SET AMET . cos x cosx = cos x cosx = (cosx + )(cosx ) = cosx = cosx = 4. x cos x cosx =. x y = cosx y = cosx. x =,x = ( y = cosx y = cosx. x V y = cosx y = sinx 6 5 6 - ( cosx cosx ) d x = [

More information

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

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 ),

More information

40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x,

40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x, 9.. x + y + 0. x,y, x,y, x r cos θ y r sin θ xy x y x,y 0,0 4. x, y 0, 0, r 0. xy x + y r 0 r cos θ sin θ r cos θ sin θ θ 4 y mx x, y 0, 0 x 0. x,y 0,0 x x + y x 0 x x + mx + m m x r cos θ 5 x, y 0, 0,

More information

剛塑性FEM入門.ppt

剛塑性FEM入門.ppt 2 3 4 5 DEFORM-2D, -3D Altan, Ohio State Univ. SFTC FORGE 23 Chenot, CEMEF VirtualForging QForm Quantor Ltd. RIPLS-FORGE FS DD 6 7 ! "#%*+,-.0123456789:;?@! EF567! AB! "# x "x + " yx "y + F x = 0 "

More information

III No (i) (ii) (iii) (iv) (v) (vi) x 2 3xy + 2 lim. (x,y) (1,0) x 2 + y 2 lim (x,y) (0,0) lim (x,y) (0,0) lim (x,y) (0,0) 5x 2 y x 2 + y 2. xy x2 + y

III No (i) (ii) (iii) (iv) (v) (vi) x 2 3xy + 2 lim. (x,y) (1,0) x 2 + y 2 lim (x,y) (0,0) lim (x,y) (0,0) lim (x,y) (0,0) 5x 2 y x 2 + y 2. xy x2 + y III No (i) (ii) (iii) (iv) (v) (vi) x 2 3xy + 2. (x,y) (1,0) x 2 + y 2 5x 2 y x 2 + y 2. xy x2 + y 2. 2x + y 3 x 2 + y 2 + 5. sin(x 2 + y 2 ). x 2 + y 2 sin(x 2 y + xy 2 ). xy (i) (ii) (iii) 2xy x 2 +

More information

0 (1 ) 0 (1 ) 01 Excel Excel ( ) = Excel Excel =5+ 5 + 7 =5-5 3 =5* 5 10 =5/ 5 5 =5^ 5 5 ( ), 0, Excel, Excel 13E+05 13 10 5 13000 13E-05 13 10 5 0000

0 (1 ) 0 (1 ) 01 Excel Excel ( ) = Excel Excel =5+ 5 + 7 =5-5 3 =5* 5 10 =5/ 5 5 =5^ 5 5 ( ), 0, Excel, Excel 13E+05 13 10 5 13000 13E-05 13 10 5 0000 1 ( S/E) 006 7 30 0 (1 ) 01 Excel 0 7 3 1 (-4 ) 5 11 5 1 6 13 7 (5-7 ) 9 1 1 9 11 3 Simplex 1 4 (shadow price) 14 5 (reduced cost) 14 3 (8-10 ) 17 31 17 3 18 33 19 34 35 36 Excel 3 4 (11-13 ) 5 41 5 4

More information

dy + P (x)y = Q(x) (1) dx dy dx = P (x)y + Q(x) P (x), Q(x) dy y dx Q(x) 0 homogeneous dy dx = P (x)y 1 y dy = P (x) dx log y = P (x) dx + C y = C exp

dy + P (x)y = Q(x) (1) dx dy dx = P (x)y + Q(x) P (x), Q(x) dy y dx Q(x) 0 homogeneous dy dx = P (x)y 1 y dy = P (x) dx log y = P (x) dx + C y = C exp + P (x)y = Q(x) (1) = P (x)y + Q(x) P (x), Q(x) y Q(x) 0 homogeneous = P (x)y 1 y = P (x) log y = P (x) + C y = C exp{ P (x) } = C e R P (x) 5.1 + P (x)y = 0 (2) y = C exp{ P (x) } = Ce R P (x) (3) αy

More information

オートマトンと言語理論 テキスト 成蹊大学理工学部情報科学科 山本真基 ii iii 1 1 1.1.................................. 1 1.2................................ 5 1.3............................. 5 2 7 2.1..................................

More information

dvipsj.8449.dvi

dvipsj.8449.dvi 9 1 9 9.1 9 2 (1) 9.1 9.2 σ a = σ Y FS σ a : σ Y : σ b = M I c = M W FS : M : I : c : = σ b

More information

JKR Point loading of an elastic half-space 2 3 Pressure applied to a circular region Boussinesq, n =

JKR Point loading of an elastic half-space 2 3 Pressure applied to a circular region Boussinesq, n = JKR 17 9 15 1 Point loading of an elastic half-space Pressure applied to a circular region 4.1 Boussinesq, n = 1.............................. 4. Hertz, n = 1.................................. 6 4 Hertz

More information

II Time-stamp: <05/09/30 17:14:06 waki> ii

II Time-stamp: <05/09/30 17:14:06 waki> ii II waki@cc.hirosaki-u.ac.jp 18 1 30 II Time-stamp: ii 1 1 1.1.................................................. 1 1.2................................................... 3 1.3..................................................

More information

2.4 ( ) ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) Minoru TANAKA (Osaka Univ.) I(2011), Sec p. 1/30

2.4 ( ) ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) Minoru TANAKA (Osaka Univ.) I(2011), Sec p. 1/30 2.4 ( ) 2.4.1 ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) I(2011), Sec. 2. 4 p. 1/30 (2) Γ f dr lim f i r i. r i 0 i f i i f r i i i+1 (1) n i r i (3) F dr = lim F i n i r i. Γ r i 0 i n i

More information

ii

ii ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................

More information

SEG SEG

SEG   SEG SEG http://www.seg.co.jp/ http://www.seg.co.jp/i/ SEG (4cm3cm) Web http://www.seg.co.jp/ Web Web http://www.seg.co.jp/ Web Web http://www.seg.co.jp/ Web http://www.seg.co.jp/ Web Web Extreme http://www.seg.co.jp/i/

More information

6 BV17057 30 2 7 1 1 1.1.................................................... 1 1.2.................................................. 1 1.3 6............................... 1 1.4....................................................

More information

2

2 D 1 2 3 XX XY ( ) 4 5 GID ( ) ( ) ( ) ( ) WHO( ) ( ) ( ) WHO ( ) WHO ( ) 6 7 8 9 X Y XX XY XO XXY XXXY Y Y SRY Y SRY X XX XY SRY XY XX Y Y X Y Y DNA DNA 10 XY XY 11 12 13 F M T 14 U H R 15 K N F 16 M T

More information

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

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

More information

s s U s L e A = P A l l + dl dε = dl l l

s s U s L e A = P A l l + dl dε = dl l l P (ε) A o B s= P A s B o Y l o s Y l e = l l 0.% o 0. s e s B 1 s (e) s Y s s U s L e A = P A l l + dl dε = dl l l ε = dε = l dl o + l lo l = log l o + l =log(1+ e) l o Β F Α E YA C Ο D ε YF B YA A YA

More information

4 1 Ampère 4 2 Ampere 31

4 1 Ampère 4 2 Ampere 31 4. 2 2 Coulomb 2 2 2 ( ) electricity 2 30 4 1 Ampère 4 2 Ampere 31 NS 2 Fleming 4 3 B I r 4 1 0 1.257 10-2 Gm/A µ 0I B = 2πr 4 1 32 4 4 A A A A 4 4 10 9 1 2 12 13 14 4 1 16 4 1 CH 2 =CH 2 28.0313 28 2

More information

1

1 PalmGauss SC PGSC-5G Instruction Manual PalmGauss SC PGSC-5G Version 1.01 PalmGauss SC PGSC5G 1.... 3 2.... 3 3.... 3 3.1... 3 3.2... 3 3.3 PalmGauss... 4 3.4... 4 3.4.1 (Fig. 4)... 4 3.4.2 (Fig. 5)...

More information

-2-

-2- -1-2009 3 2 2 HP http://homepage3.nifty.com/office-wada/ -2- -3-1 01 X Y 100 Y Y 02 A B B C A -4- 2 03 X Y Y X XY Y X Y X Y Z XY Z Z X 261 24 14 49 41 77 1 48 6 21 27 6 712 11 1 53 9 14 906 88 X1 X2 X3

More information

d dt P = d ( ) dv G M vg = F M = F (4.1) dt dt M v G P = M v G F (4.1) d dt H G = M G (4.2) H G M G Z K O I z R R O J x k i O P r! j Y y O -

d dt P = d ( ) dv G M vg = F M = F (4.1) dt dt M v G P = M v G F (4.1) d dt H G = M G (4.2) H G M G Z K O I z R R O J x k i O P r! j Y y O - 44 4 4.1 d P = d dv M v = F M = F 4.1 M v P = M v F 4.1 d H = M 4.2 H M Z K I z R R J x k i P r! j Y y - XY Z I, J, K -xyz i, j, k P R = R + r 4.3 X Fig. 4.1 Fig. 4.1 ω P [ ] d d = + ω 4.4 [ ] 4 45 4.3

More information

Microsoft Word - 計算力学2007有限要素法.doc

Microsoft Word - 計算力学2007有限要素法.doc 95 2 x y yz = zx = yz = zx = { } T = { x y z xy } () {} T { } T = { x y z xy } = u u x y u z u x x y z y + u y (2) x u x u y x y x y z xy E( ) = ( + )( 2) 2 2( ) x y z xy (3) E x y z z = z = (3) z x y

More information

2012専門分科会_new_4.pptx

2012専門分科会_new_4.pptx d dt L L = 0 q i q i d dt L L = 0 r i i r i r r + Δr Δr δl = 0 dl dt = d dt i L L q i q i + q i i q i = q d L L i + q i i dt q i i q i = i L L q i L = 0, H = q q i L = E i q i i d dt L q q i i L = L(q

More information

Image Browser Ver3.5 Manual. Zeiss Image Browser Ver3.5 p2. p3. p5. p7. p9. p13. p17. p19. p23 Appendix 1. p25 Appendix 2. p27 LSM Image Browser http:

Image Browser Ver3.5 Manual. Zeiss Image Browser Ver3.5 p2. p3. p5. p7. p9. p13. p17. p19. p23 Appendix 1. p25 Appendix 2. p27 LSM Image Browser http: Image Browser Ver3.5 Manual 200505av10 Image Browser Ver3.5 Manual. Zeiss Image Browser Ver3.5 p2. p3. p5. p7. p9. p13. p17. p19. p23 Appendix 1. p25 Appendix 2. p27 LSM Image Browser http://www.zeiss.de/imagebrowser

More information

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b) 2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................

More information

70の法則

70の法則 70 70 1 / 27 70 1 2 3 4 5 6 2 / 27 70 70 70 X r % = 70 2 r r r 10 72 70 72 70 : 1, 2, 5, 7, 10, 14, 35, 70 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 3 / 27 r = 10 70 r = 10 70 1 : X, X 10 = ( X + X

More information

6

6 000 (N =000) 50 ( N(N ) / = 499500) μm.5 g cm -3.5g cm 3 ( 0 6 µm) 3 / ( g mo ) ( 6.0 0 3 mo ) =.3 0 0 0 5 (0 6 ) 0 6 0 6 ~ 0 000 000 ( 0 6 ) ~ 0 9 q R q, R q q E = 4πε 0 R R (6.) -6 (a) (b) (c) (a) (b)

More information

k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i σ ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m σ A σ σ σ σ f i x

k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i σ ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m σ A σ σ σ σ f i x k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m A f i x i B e e e e 0 e* e e (2.1) e (b) A e = 0 B = 0 (c) (2.1) (d) e

More information

13 6 2 68 34 JIS S0026 JIS JIS S0026 50000 2550mm 2550mm 2550mm 12 1 4 15 ( ) 3000 1 1 H17 ttp://www.isuzu.co.jp/product/bus/gala_ss/approach.html

More information

1 n =3, 2 n 3 x n + y n = z n x, y, z 3 a, b b = aq q a b a b b a b a a b a, b a 0 b 0 a, b 2

1 n =3, 2 n 3 x n + y n = z n x, y, z 3 a, b b = aq q a b a b b a b a a b a, b a 0 b 0 a, b 2 n =3, 200 2 10 1 1 n =3, 2 n 3 x n + y n = z n x, y, z 3 a, b b = aq q a b a b b a b a a b a, b a 0 b 0 a, b 2 a, b (a, b) =1a b 1 x 2 + y 2 = z 2, (x, y) =1, x 0 (mod 2) (1.1) x =2ab, y = a 2 b 2, z =

More information

IS2 ISP2 IS2 ISP2 X-Y 2 軸 組 合 せ 単 軸 2 軸 組 合 せ IS2/ISP2- -93 IS2/ISP2- -95 IS2/ISP2- -97 IS2/ISP2- -99 IS2/ISP2- -101 IS2/ISP2- -103 IS2/ISP2- -105 IS2

IS2 ISP2 IS2 ISP2 X-Y 2 軸 組 合 せ 単 軸 2 軸 組 合 せ IS2/ISP2- -93 IS2/ISP2- -95 IS2/ISP2- -97 IS2/ISP2- -99 IS2/ISP2- -101 IS2/ISP2- -103 IS2/ISP2- -105 IS2 防 滴 4 I2 I3 IS(P)2 IS(P)2 IS(P)3 IS(P)3 選 定 上 の 注 意 事 項 -5 4 I2 パルスモータ 高 速 型 4-1RT -9 4-1PR -11 4-1 -13 ロボシリンダ 2 軸 組 合 せ I2-PX1 S -15 I2-PX1-17 I2-PX2 S -19 I2-PX2-21 I2-PX1 S -23 I2-PX1-25 I2-PX2 S -27

More information

, = = 7 6 = 42, =

, = = 7 6 = 42, = http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8

More information

untitled

untitled F(r)=QE(r) Q ρ( r ') 3 E= ke 3 ( r r ') d r ' V r r' () Er () = Fr Q E E x y Ez ρ = x y z ε E E z y Ex E E z y Ex =, =, = y z z x x y A A x y Az diva = x y z A A z y A A x A z y Ax rot A =,, y z z x x

More information

B line of mgnetic induction AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B = B ds 2π A B P P O s s Q PQ R QP AB θ 0 <θ<π

B line of mgnetic induction AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B = B ds 2π A B P P O s s Q PQ R QP AB θ 0 <θ<π 8 Biot-Svt Ampèe Biot-Svt 8.1 Biot-Svt 8.1.1 Ampèe B B B = µ 0 2π. (8.1) B N df B ds A M 8.1: Ampèe 107 108 8 0 B line of mgnetic induction 8.1 8.1 AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B

More information

ParametricPlot [5] In[5]:= Out[5]= m1.v1 axby, cxdy [6] pr In[6]:= Out[6]= pr = m1.m 3ab, ab,3cd, cd [7] In[7]:= Out[7]//MatrixForm= pr //Matri

ParametricPlot [5] In[5]:= Out[5]= m1.v1 axby, cxdy [6] pr In[6]:= Out[6]= pr = m1.m 3ab, ab,3cd, cd [7] In[7]:= Out[7]//MatrixForm= pr //Matri Chapter 6 1 ParametricPlot 3 ParametricPlot ParametricPlot3D 6.1 [1] *1 In[1]:= v1 = {x, y}; v = {z, w}; [] In[]:= m1 = {{a, b}, {c, d}}; m = {{3, }, {1, }}; [3] 3 3.3 In[3]:= Out[3]//MatrixForm= [] m1

More information

pdf

pdf http://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg

More information

nakata/nakata.html p.1/20

nakata/nakata.html p.1/20 http://www.me.titech.ac.jp/ nakata/nakata.html p.1/20 1-(a). Faybusovich(1997) Linear systems in Jordan algebras and primal-dual interior-point algorithms,, Euclid Jordan p.2/20 Euclid Jordan V Euclid

More information

05›ª“è†E‘¼›Y”†(P47-P62).qx

05›ª“è†E‘¼›Y”†(P47-P62).qx z z z z z pz z x ux z ux z subject Ixp z I p z z z z z L ux z Ixp z L u u i p z i u x z i I xp z x z u u ux z uip z z u u z ui z z u u z z z z u ui z Iuz u u i u z u x x z i z i Ix u x u x z i z i x z

More information

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

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

More information

Microsoft Word - K-ピタゴラス数.doc

Microsoft Word - K-ピタゴラス数.doc - ピタゴラス数の代数と幾何学 津山工業高等専門学校 菅原孝慈 ( 情報工学科 年 ) 野山由貴 ( 情報工学科 年 ) 草地弘幸 ( 電子制御工学科 年 ) もくじ * 第 章ピタゴラス数の幾何学 * 第 章ピタゴラス数の代数学 * 第 3 章代数的極小元の幾何学の考察 * 第 章ピタゴラス数の幾何学的研究の動機 交点に注目すると, つの曲線が直交しているようにみえる. これらは本当に直交しているのだろうか.

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

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 = 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

More information

座標変換におけるテンソル成分の変換行列

座標変換におけるテンソル成分の変換行列 座標変換におけるテンソル成分の変換行列 座標変換におけるテンソル成分の変換関係は 次元数によらず階数によって定義される変換行列で整理することができる 位置ベクトルの変換行列を D としてそれを示そう D の行列式を ( = D ) とするとき 鏡映や回映といった pseudo rotation に対しては = -1 である が問題になる基底は 対称操作に含まれる pseudo rotation に依存する

More information

<4D F736F F D B B BB2D834A836F815B82D082C88C60202D B2E646F63>

<4D F736F F D B B BB2D834A836F815B82D082C88C60202D B2E646F63> 例題で学ぶはじめての塑性力学 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/066721 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. http://www.morikita.co.jp/support/ 03 3817 5670 FAX 03 3815 8199 i 1

More information

1 1 2 1 3 1 4 2 4.1 AKB............................................... 2 4.2......................................... 6 4.3...........................

1 1 2 1 3 1 4 2 4.1 AKB............................................... 2 4.2......................................... 6 4.3........................... 24 3 28 : 1 1 2 1 3 1 4 2 4.1 AKB............................................... 2 4.2......................................... 6 4.3............................................. 9 5 9 5.1.........................................

More information

Microsoft Word - 触ってみよう、Maximaに2.doc

Microsoft Word - 触ってみよう、Maximaに2.doc i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x

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

m dv = mg + kv2 dt m dv dt = mg k v v m dv dt = mg + kv2 α = mg k v = α 1 e rt 1 + e rt m dv dt = mg + kv2 dv mg + kv 2 = dt m dv α 2 + v 2 = k m dt d

m dv = mg + kv2 dt m dv dt = mg k v v m dv dt = mg + kv2 α = mg k v = α 1 e rt 1 + e rt m dv dt = mg + kv2 dv mg + kv 2 = dt m dv α 2 + v 2 = k m dt d m v = mg + kv m v = mg k v v m v = mg + kv α = mg k v = α e rt + e rt m v = mg + kv v mg + kv = m v α + v = k m v (v α (v + α = k m ˆ ( v α ˆ αk v = m v + α ln v α v + α = αk m t + C v α v + α = e αk m

More information

2005 1

2005 1 2005 1 1 1 2 2 2.1....................................... 2 2.2................................... 5 2.3 VSWR................................. 6 2.4 VSWR 2............................ 7 2.5.......................................

More information

Fermat s Last Theorem Hajime Mashima November 19, 2018 Abstract About 380 years ago, Pierre de Fermat wrote the following idea to Diophantus s Arithme

Fermat s Last Theorem Hajime Mashima November 19, 2018 Abstract About 380 years ago, Pierre de Fermat wrote the following idea to Diophantus s Arithme Fermat s Last Theorem Hajime Mashima November 19, 2018 Abstract About 380 years ago, Pierre de Fermat wrote the following idea to Diophantus s Arithmetica. Cubum autem in duos cubos, aut quadratoquadratum

More information

MS3D.book

MS3D.book Corel MotionStudio 3D................. 1 3D................. 2............................. 4..................................... 5............................... 6 Corel VideoStudio Pro.........................

More information

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t 1 1.1 sin 2π [rad] 3 ft 3 sin 2t π 4 3.1 2 1.1: sin θ 2.2 sin θ ft t t [sec] t sin 2t π 4 [rad] sin 3.1 3 sin θ θ t θ 2t π 4 3.2 3.1 3.4 3.4: 2.2: sin θ θ θ [rad] 2.3 0 [rad] 4 sin θ sin 2t π 4 sin 1 1

More information

1 28 6 12 7 1 7.1...................................... 2 7.1.1............................... 2 7.1.2........................... 2 7.2...................................... 3 7.3...................................

More information

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

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

More information

システムの概要

システムの概要 - i - - ii - 1 Excel BCS.CSV Excel BCS.CSV Excel A B C D Excel BCS.CSV - 1 - 2 Excel (V) (T) AB AB - 2 - 3 A B A B B C B C 1 B A - 3 - 1 C B 4 1 5 6 BCS - 4 - 4 1 Excel - 5 - 32 30 Excel Alt+Enter 1-6

More information

koji07-02.dvi

koji07-02.dvi 007 I II III 1,, 3, 4, 5, 6, 7 5 4 1 ε-n 1 ε-n ε-n ε-n. {a } =1 a ε N N a a N= a a

More information

x ( ) x dx = ax

x ( ) x dx = ax x ( ) x dx = ax 1 dx = a x log x = at + c x(t) = e at C (C = e c ) a > 0 t a < 0 t 0 (at + b ) h dx = lim x(t + h) x(t) h 0 h x(t + h) x(t) h x(t) t x(t + h) x(t) ax(t) h x(t + h) x(t) + ahx(t) 0, h, 2h,

More information

untitled

untitled 1 2 HUMAN( Socrates ) HUMAN( x) MORTAL( x) σ = { x Socrates} HUMAN( Socrates) MORTAL( Socrates) MORTAL(Socrates) x x x Socrates HUMAN(Socrates) HUMAN(Socrates) MORTAL(Socrates) x Socrates HUMAN(Socrates)

More information

17 ( :52) α ω 53 (2015 ) 2 α ω 55 (2017 ) 2 1) ) ) 2 2 4) (α β) A ) 6) A (5) 1)

17 ( :52) α ω 53 (2015 ) 2 α ω 55 (2017 ) 2 1) ) ) 2 2 4) (α β) A ) 6) A (5) 1) 3 3 1 α ω 53 (2015 ) 2 α ω 55 (2017 ) 2 1) 2000 2) 5 2 3 4 2 3 5 3) 2 2 4) (α β) 2 3 4 5 20 A 12 20 5 5 5) 6) 5 20 12 5 A (5) 1) Évariste Galois(1811-1832) 2) Joseph-Louis Lagrange(1736-1813) 18 3),Niels

More information

15228 98441 IMT- 2International Mobile Telecommunication 2 FBFront to Back IMT-2 H E 8 2/15 (2mm)H 5/4 (187mm)E 1 (15mm) FB 24.8dB E 3dB FB (H ) H 45 FB 23.8dB -6.2dB i 1 1 2 6 2.1.....................................

More information

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 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,

More information

: LES Energy RANS Kawai & Lele JCP (2010) Wavenumber Accuracy LES, DNS RANS 1970 s Efficiency

: LES Energy RANS Kawai & Lele JCP (2010) Wavenumber Accuracy LES, DNS RANS 1970 s Efficiency 2013 2 18 MHD (ISAS), (JAXA) kawai@flab.isas.jaxa.jp hp://flab.eng.isas.jaxa.jp/member/kawai JAXA : LES Energy RANS Kawai & Lele JCP (2010) Wavenumber Accuracy LES, DNS RANS 1970 s Efficiency FDS, FVS,

More information

(MRI) 10. (MRI) (MRI) : (NMR) ( 1 H) MRI ρ H (x,y,z) NMR (Nuclear Magnetic Resonance) spectrometry: NMR NMR s( B ) m m = µ 0 IA = γ J (1) γ: :Planck c

(MRI) 10. (MRI) (MRI) : (NMR) ( 1 H) MRI ρ H (x,y,z) NMR (Nuclear Magnetic Resonance) spectrometry: NMR NMR s( B ) m m = µ 0 IA = γ J (1) γ: :Planck c 10. : (NMR) ( 1 H) MRI ρ H (x,y,z) NMR (Nuclear Magnetic Resonance) spectrometry: NMR NMR s( B ) m m = µ 0 IA = γ J (1) γ: :Planck constant J: Ĵ 2 = J(J +1),Ĵz = J J: (J = 1 2 for 1 H) I m A 173/197 10.1

More information

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

More information

(w) F (3) (4) (5)??? p8 p1w Aさんの 背 中 が 壁 を 押 す 力 垂 直 抗 力 重 力 静 止 摩 擦 力 p8 p

(w) F (3) (4) (5)??? p8 p1w Aさんの 背 中 が 壁 を 押 す 力 垂 直 抗 力 重 力 静 止 摩 擦 力 p8 p F 1-1................................... p38 p1w A A A 1-................................... p38 p1w 1-3................................... p38 p1w () (1) ()?? (w) F (3) (4) (5)??? -1...................................

More information

a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552

a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552 3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n

More information

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

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

More information