Size: px
Start display at page:

Download ""

Transcription

1

2 2

3 1. 10/ / /23 ( ) 4. 10/ / 6 ( ) 6. 11/ /20 ( ) 8. 11/ / 4 ( ) / /18 skyline 12. 1/ 8 ALE 13. 1/15 ALE 14. 1/22 ALE 3

4 t + t M t+ t ü + C t+ t u + t+ t Q = t+ t F M C t t + t Newmark-β t M, C Q Newton-Raphson M t+ t ü (k) + C t+ t u (k) + t+ t K (k 1) u (k) = t+ t F t+ t Q (k 1) t+ t u (k) = t u (k 1) + u (k) t+ t u (k) = t u (k 1) + u (k) t+ tü (k) = t ü (k 1) + ü (k) u (k), u (k), ü (k) 4

5 t t + t t+τü = t ü + τ t (t+τ ü t ü) τ τ = t t+ t u = t u + t 2 ( t+ tü + t ü ) t+ t u = t u + t t u + t2 3 tü + t2 t+ tü 6 u (k) = t 2 ü(k) u (k) = t2 6 ü(k) 5

6 Newmark -β 1 Newmark-β 1959 Newmark,, t.,, t + t M t+ t ü + C t+ t u + t+ t Q = t+ t F Newmark-β, t + t t,. t+ t u = t u + t [ γ t+ t ü +(1 γ) t ü ] {( ) } 1 t+ t u = t u + t t u + t 2 2 β tü + β t+ t ü 6

7 Newmark -β 2 Newmark-β, t + t t,. t+ t u = t u + t [ γ t+ t ü +(1 γ) t ü ] {( ) 1 t+ t u = t u + t t u + t 2 2 β tü } + β t+ t ü, γ = 1 2, β = 1 6, γ = 1 2, β = 1 4, t+ t u t+ t u. t+ t u = t u + t 2 (t+ t ü + t ü) t+ t u = t u + t t u + t2 4 (t ü + t+ t ü) t t + t t+τü = 1 2 (t ü + t+ t ü) (0 τ t) (1),. γ = 1 2, β = 1 4 (trapezoidal rule) 7

8 Newmark -β 3 Newmark-β, t + t t,,, t + t,. t+ tü = 1 u t u) 1 ( ) 1 t u β t 2(t+ t β t 2β 1 tü { [ t+ t 1 u = t u + (1 γ) t ü + γ u t u) 1 t u ( 1 ]} β t 2(t+ t β t 2β 1)t ü t = t u + t(1 γ) t ü + γ β t (t+ t u t u) γ ( ) 1 t u γ β 2β 1 t t ü = γ ( β t (t+ t u t u)+ 1 γ ) ( t u + t 1 γ ) tü 2β 2β, K Q t+ t t+ t Q = K t+ t u Newmark-β ( 1 β t 2M + γ ) β t C + K t+ t u = t+ t F + M [ 1 β t 2 t u C ( ) 1 t u + β t 2β 1 [ ( ) γ γ t u + β t β 1 tü ] ( ) ] γ t u + 2β 1 t t ü (2) 8

9 Newmark-β ( 1 β t 2M + γ ) β t C + K Newmark -β 4 t+ t u = t+ t F + M [ 1 β t 2 t u + 1 ( ) 1 t u + β t 2β 1 [ ( ) γ γ + C t u + β t β 1 ] tü ( ) ] γ t u + 2β 1 t t ü ( ) 1 M + γ β t 2 β t C + K, γ = 1 2, β = 1 4, t., γ = 1 2, β = 1 t,, 6., γ>

10 Newmark -β 5,, Newton-Raphson (k =2, 3, ). M t+ t ü (k) + C t+ t u (k) + t+ t K (k 1) u (k) = t+ t F t+ t Q (k 1) t+ t u (k) = t+ t u (k 1) + u (k) t+ t u (k) = t+ t u (k 1) + u (k) t+ tü (k) = t+ t ü (k 1) + ü (k), (k) k., Newmark β,,, k k 1 u (k) = γ β t u(k) (3) u (k) ( 1 β t 2M + γ ) β t C + K u (k) ü (k) = 1 β t 2 u(k) (4) = t+ t F t+ t Q (k 1) M t+ t ü (k 1) C t+ t u (k 1) (5) 10

11 Newmark -β 6 Newmark-β. 1. (a) M C. (b). a 0 = 1 a β t 2 1 = γ a β t 2 = 1 β t a 3 = 1 2β 1 a 4 = γ β 1 a 5 = γ 2β 1 a 6 = γ t a 7 =(1 γ) t 2. (a) t + t. K eff = a 0 M + a 1 C + K (b) t + t. t+ t F eff = t+ t F t Q + M(a 2t u + a 3tü)+C(a 4t u + a5ü) (c) t + t t+ t u. K eff u = t F t+ t eff u = t u + u (d),. i. U (0) = U, i =0. ii. i = i +1 iii. i 1. 11

12 t+ t F (i 1) eff = t+ t F M t+ t ü (i 1) C t+ t u (i 1) t+ t Q (i 1) iv. i. K eff u (i) = t+ t F (i 1) eff v.. u = u + u (i) vi., t + t,,. t+ t ü = a 3 u + a 4t u + a 5tü t+ t u = t u + a 6tü + a t+ tü 7 t+ t u = t u + u 12

13 1 t t + t t t + t,,,,. [t, t + t], u t+ t/2 u, u ü. t u t u t+ t/2 = ut+ t u t t ü t = ut+ t/2 u t t/2 t u t = ut+ t/2 + u t t/2 t (6) 13

14 2 M tü + C t u + t Q = t F, u t+ t/2. ( M u t+ t/2 = t + C ) 1 [ ( M (F t Q t (u t )) + 2 t C 2 u t+ t = u t + t u t+ t/2 ) u t t/2 ] (7) t + t u t+ t t ü t. (7), M t + C 2,, u t+ t/2.,, M (lumped mass matrix),.,,,., 1. 14

15 t. t., u t/2, t =0 u 0. u 0 = 0 u t/2 = u t/2 (8) u t/2 = tm 1 (F t Q t (u t ))/2 (9) 15

16 3. 1. (a) M C. (b) t. (c). M eff = M t + C 2 (d) 0 0 u, 0 u 0 ü, t. 2. (a) t. F t eff = F t Q t (u t )+ ( M t C 2 ) u t t/2 (b) t + t/2 u t+ t/2. u t+ t/2 = M 1 eff F t eff (c) t + t u t+ t. t ü t.,, t. 16

17 1, consistant (lumped).. consistant, ρ 0, ρ t 0,t δu ρ 0 üdv = δu ρ t üd t v = δu t MÜ (10) V t v. (10),, consistant. (lumped),, consistant,, lumped.,,, lumped. 17

18 1 lumped,, V e N i dv e. lumped 1. V e N (i) dv i 2. V e N (i) N (i) dv i serendipity 5. consistent 18

19 1 MK Ax = λx Kx = λmx MK L M = LL T Kx = λmx Kx = λll T x L 1 Kx = λl T x L T x = y x = L T y L 1 KL T y = λy MK 19

20 2 R = xt Ax x T x = xt λx x T x = λ 20

i

i 14 i ii iii iv v vi 14 13 86 13 12 28 14 16 14 15 31 (1) 13 12 28 20 (2) (3) 2 (4) (5) 14 14 50 48 3 11 11 22 14 15 10 14 20 21 20 (1) 14 (2) 14 4 (3) (4) (5) 12 12 (6) 14 15 5 6 7 8 9 10 7

More information

i ii iii iv v vi vii ( ー ー ) ( ) ( ) ( ) ( ) ー ( ) ( ) ー ー ( ) ( ) ( ) ( ) ( ) 13 202 24122783 3622316 (1) (2) (3) (4) 2483 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 11 11 2483 13

More information

262014 3 1 1 6 3 2 198810 2/ 198810 2 1 3 4 http://www.pref.hiroshima.lg.jp/site/monjokan/ 1... 1... 1... 2... 2... 4... 5... 9... 9... 10... 10... 10... 10... 13 2... 13 3... 15... 15... 15... 16 4...

More information

178 5 I 1 ( ) ( ) 10 3 13 3 1 8891 8 3023 6317 ( 10 1914 7152 ) 16 5 1 ( ) 6 13 3 13 3 8575 3896 8 1715 779 6 (1) 2 7 4 ( 2 ) 13 11 26 12 21 14 11 21

178 5 I 1 ( ) ( ) 10 3 13 3 1 8891 8 3023 6317 ( 10 1914 7152 ) 16 5 1 ( ) 6 13 3 13 3 8575 3896 8 1715 779 6 (1) 2 7 4 ( 2 ) 13 11 26 12 21 14 11 21 I 178 II 180 III ( ) 181 IV 183 V 185 VI 186 178 5 I 1 ( ) ( ) 10 3 13 3 1 8891 8 3023 6317 ( 10 1914 7152 ) 16 5 1 ( ) 6 13 3 13 3 8575 3896 8 1715 779 6 (1) 2 7 4 ( 2 ) 13 11 26 12 21 14 11 21 4 10 (

More information

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2)

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2) (1) I 44 II 45 III 47 IV 52 44 4 I (1) ( ) 1945 8 9 (10 15 ) ( 17 ) ( 3 1 ) (2) 45 II 1 (3) 511 ( 451 1 ) ( ) 365 1 2 512 1 2 365 1 2 363 2 ( ) 3 ( ) ( 451 2 ( 314 1 ) ( 339 1 4 ) 337 2 3 ) 363 (4) 46

More information

i ii i iii iv 1 3 3 10 14 17 17 18 22 23 28 29 31 36 37 39 40 43 48 59 70 75 75 77 90 95 102 107 109 110 118 125 128 130 132 134 48 43 43 51 52 61 61 64 62 124 70 58 3 10 17 29 78 82 85 102 95 109 iii

More information

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-7 O1-8 O1-9 O1-10 O1-11 O1-12 O1-13 O1-14 O1-15 O1-16 O1-17 O1-18 O1-19 O1-20 O1-21 O1-22 O1-23 O1-24 O1-25 O1-26 O1-27 O1-28 O1-29 O1-30 O1-31 O1-32 O1-33 O1-34 O1-35

More information

untitled

untitled i ii iii iv v 43 43 vi 43 vii T+1 T+2 1 viii 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 38 39 40 41 42 43 44 45 46 47 48 49 50 a) ( ) b) ( ) 51

More information

AccessflÌfl—−ÇŠš1

AccessflÌfl—−ÇŠš1 ACCESS ACCESS i ii ACCESS iii iv ACCESS v vi ACCESS CONTENTS ACCESS CONTENTS ACCESS 1 ACCESS 1 2 ACCESS 3 1 4 ACCESS 5 1 6 ACCESS 7 1 8 9 ACCESS 10 1 ACCESS 11 1 12 ACCESS 13 1 14 ACCESS 15 1 v 16 ACCESS

More information

2

2 1 2 3 4 5 6 7 8 9 10 I II III 11 IV 12 V 13 VI VII 14 VIII. 15 16 17 18 19 20 21 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 VII 51 52 53 54 55 56 57 58 59

More information

I II III IV V

I II III IV V I II III IV V N/m 2 640 980 50 200 290 440 2m 50 4m 100 100 150 200 290 390 590 150 340 4m 6m 8m 100 170 250 µ = E FRVβ β N/mm 2 N/mm 2 1.1 F c t.1 3 1 1.1 1.1 2 2 2 2 F F b F s F c F t F b F s 3 3 3

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 31 32 33 () - 1 - - 2 - - 3 - - 4 - - 5 - 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

More information

86 7 I ( 13 ) II ( )

86 7 I ( 13 ) II ( ) 10 I 86 II 86 III 89 IV 92 V 2001 93 VI 95 86 7 I 2001 6 12 10 2001 ( 13 ) 10 66 2000 2001 4 100 1 3000 II 1988 1990 1991 ( ) 500 1994 2 87 1 1994 2 1000 1000 1000 2 1994 12 21 1000 700 5 800 ( 97 ) 1000

More information

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.   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

More information

入門ガイド

入門ガイド ii iii iv NEC Corporation 1998 v P A R 1 P A R 2 P A R 3 T T T vi P A R T 4 P A R T 5 P A R T 6 P A R T 7 vii 1P A R T 1 2 2 1 3 1 4 1 1 5 2 3 6 4 1 7 1 2 3 8 1 1 2 3 9 1 2 10 1 1 2 11 3 12 1 2 1 3 4 13

More information

koji07-01.dvi

koji07-01.dvi 2007 I II III 1, 2, 3, 4, 5, 6, 7 5 10 19 (!) 1938 70 21? 1 1 2 1 2 2 1! 4, 5 1? 50 1 2 1 1 2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 3 1, 2 1, 3? 2 1 3 1 2 1 1, 2 2, 3? 2 1 3 2 3 2 k,l m, n k,l m, n kn > ml...?

More information

<4D6963726F736F667420506F776572506F696E74202D208376838C835B83938365815B835683878393312E707074205B8CDD8AB78382815B83685D>

<4D6963726F736F667420506F776572506F696E74202D208376838C835B83938365815B835683878393312E707074205B8CDD8AB78382815B83685D> i i vi ii iii iv v vi vii viii ix 2 3 4 5 6 7 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 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

More information

SC-85X2取説

SC-85X2取説 I II III IV V VI .................. VII VIII IX X 1-1 1-2 1-3 1-4 ( ) 1-5 1-6 2-1 2-2 3-1 3-2 3-3 8 3-4 3-5 3-6 3-7 ) ) - - 3-8 3-9 4-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 5-10 5-11

More information

untitled

untitled 23 12 10 12:55 ~ 18:45 KKR Tel0557-85-2000 FAX0557-85-6604 12:55~13:00 13:00~13:38 I 1) 13:00~13:12 2) 13:13~13:25 3) 13:26~13:38 13:39~14:17 II 4) 13:39~13:51 5) 13:52 ~ 14:04 6) 14:05 ~ 14:17 14:18 ~

More information

第1部 一般的コメント

第1部 一般的コメント (( 2000 11 24 2003 12 31 3122 94 2332 508 26 a () () i ii iii iv (i) (ii) (i) (ii) (iii) (iv) (a) (b)(c)(d) a) / (i) (ii) (iii) (iv) 1996 7 1996 12

More information

o 2o 3o 3 1. I o 3. 1o 2o 31. I 3o PDF Adobe Reader 4o 2 1o I 2o 3o 4o 5o 6o 7o 2197/ o 1o 1 1o

o 2o 3o 3 1. I o 3. 1o 2o 31. I 3o PDF Adobe Reader 4o 2 1o I 2o 3o 4o 5o 6o 7o 2197/ o 1o 1 1o 78 2 78... 2 22201011... 4... 9... 7... 29 1 1214 2 7 1 8 2 2 3 1 2 1o 2o 3o 3 1. I 1124 4o 3. 1o 2o 31. I 3o PDF Adobe Reader 4o 2 1o 72 1. I 2o 3o 4o 5o 6o 7o 2197/6 9. 9 8o 1o 1 1o 2o / 3o 4o 5o 6o

More information

表1票4.qx4

表1票4.qx4 iii iv v 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 22 23 10 11 24 25 26 27 10 56 28 11 29 30 12 13 14 15 16 17 18 19 2010 2111 22 23 2412 2513 14 31 17 32 18 33 19 34 20 35 21 36 24 37 25 38 2614

More information

第1章 国民年金における無年金

第1章 国民年金における無年金 1 2 3 4 ILO ILO 5 i ii 6 7 8 9 10 ( ) 3 2 ( ) 3 2 2 2 11 20 60 12 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 14 15 8 16 2003 1 17 18 iii 19 iv 20 21 22 23 24 25 ,,, 26 27 28 29 30 (1) (2) (3) 31 1 20

More information

微分積分 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, 初版 1 刷発行時のものです.

微分積分 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, 初版 1 刷発行時のものです. 微分積分 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. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)

More information

gr09.dvi

gr09.dvi .1, θ, ϕ d = A, t dt + B, t dtd + C, t d + D, t dθ +in θdϕ.1.1 t { = f1,t t = f,t { D, t = B, t =.1. t A, tdt e φ,t dt, C, td e λ,t d.1.3,t, t d = e φ,t dt + e λ,t d + dθ +in θdϕ.1.4 { = f1,t t = f,t {

More information

20 15 14.6 15.3 14.9 15.7 16.0 15.7 13.4 14.5 13.7 14.2 10 10 13 16 19 22 1 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 2,500 59,862 56,384 2,000 42,662 44,211 40,639 37,323 1,500 33,408 34,472

More information

I? 3 1 3 1.1?................................. 3 1.2?............................... 3 1.3!................................... 3 2 4 2.1........................................ 4 2.2.......................................

More information

- 2 -

- 2 - - 2 - - 3 - (1) (2) (3) (1) - 4 - ~ - 5 - (2) - 6 - (1) (1) - 7 - - 8 - (i) (ii) (iii) (ii) (iii) (ii) 10 - 9 - (3) - 10 - (3) - 11 - - 12 - (1) - 13 - - 14 - (2) - 15 - - 16 - (3) - 17 - - 18 - (4) -

More information

2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1

2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1 1 1979 6 24 3 4 4 4 4 3 4 4 2 3 4 4 6 0 0 6 2 4 4 4 3 0 0 3 3 3 4 3 2 4 3? 4 3 4 3 4 4 4 4 3 3 4 4 4 4 2 1 1 2 15 4 4 15 0 1 2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4

More information

1 (1) (2)

1 (1) (2) 1 2 (1) (2) (3) 3-78 - 1 (1) (2) - 79 - i) ii) iii) (3) (4) (5) (6) - 80 - (7) (8) (9) (10) 2 (1) (2) (3) (4) i) - 81 - ii) (a) (b) 3 (1) (2) - 82 - - 83 - - 84 - - 85 - - 86 - (1) (2) (3) (4) (5) (6)

More information

211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,

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

これわかWord2010_第1部_100710.indd

これわかWord2010_第1部_100710.indd i 1 1 2 3 6 6 7 8 10 10 11 12 12 12 13 2 15 15 16 17 17 18 19 20 20 21 ii CONTENTS 25 26 26 28 28 29 30 30 31 32 35 35 35 36 37 40 42 44 44 45 46 49 50 50 51 iii 52 52 52 53 55 56 56 57 58 58 60 60 iv

More information

パワポカバー入稿用.indd

パワポカバー入稿用.indd i 1 1 2 2 3 3 4 4 4 5 7 8 8 9 9 10 11 13 14 15 16 17 19 ii CONTENTS 2 21 21 22 25 26 32 37 38 39 39 41 41 43 43 43 44 45 46 47 47 49 52 54 56 56 iii 57 59 62 64 64 66 67 68 71 72 72 73 74 74 77 79 81 84

More information

これでわかるAccess2010

これでわかるAccess2010 i 1 1 1 2 2 2 3 4 4 5 6 7 7 9 10 11 12 13 14 15 17 ii CONTENTS 2 19 19 20 23 24 25 25 26 29 29 31 31 33 35 36 36 39 39 41 44 45 46 48 iii 50 50 52 54 55 57 57 59 61 63 64 66 66 67 70 70 73 74 74 77 77

More information

平成18年版 男女共同参画白書

平成18年版 男女共同参画白書 i ii iii iv v vi vii viii ix 3 4 5 6 7 8 9 Column 10 11 12 13 14 15 Column 16 17 18 19 20 21 22 23 24 25 26 Column 27 28 29 30 Column 31 32 33 34 35 36 Column 37 Column 38 39 40 Column 41 42 43 44 45

More information

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 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

More information

ÿþ

ÿþ I O 01 II O III IV 02 II O 03 II O III IV III IV 04 II O III IV III IV 05 II O III IV 06 III O 07 III O 08 III 09 O III O 10 IV O 11 IV O 12 V O 13 V O 14 V O 15 O ( - ) ( - ) 16 本 校 志 望 の 理 由 入 学 後 の

More information

provider_020524_2.PDF

provider_020524_2.PDF 1 1 1 2 2 3 (1) 3 (2) 4 (3) 6 7 7 (1) 8 (2) 21 26 27 27 27 28 31 32 32 36 1 1 2 2 (1) 3 3 4 45 (2) 6 7 5 (3) 6 7 8 (1) ii iii iv 8 * 9 10 11 9 12 10 13 14 15 11 16 17 12 13 18 19 20 (2) 14 21 22 23 24

More information

「産業上利用することができる発明」の審査の運用指針(案)

「産業上利用することができる発明」の審査の運用指針(案) 1 1.... 2 1.1... 2 2.... 4 2.1... 4 3.... 6 4.... 6 1 1 29 1 29 1 1 1. 2 1 1.1 (1) (2) (3) 1 (4) 2 4 1 2 2 3 4 31 12 5 7 2.2 (5) ( a ) ( b ) 1 3 2 ( c ) (6) 2. 2.1 2.1 (1) 4 ( i ) ( ii ) ( iii ) ( iv)

More information

OHP.dvi

OHP.dvi 7 2010 11 22 1 7 http://www.sml.k.u-tokyo.ac.jp/members/nabe/lecture2010 nabe@sml.k.u-tokyo.ac.jp 2 1. 10/ 4 2. 10/18 3. 10/25 2, 3 4. 11/ 1 5. 11/ 8 6. 11/15 7. 11/22 8. 11/29 9. 12/ 6 skyline 10. 12/13

More information

エクセルカバー入稿用.indd

エクセルカバー入稿用.indd i 1 1 2 3 5 5 6 7 7 8 9 9 10 11 11 11 12 2 13 13 14 15 15 16 17 17 ii CONTENTS 18 18 21 22 22 24 25 26 27 27 28 29 30 31 32 36 37 40 40 42 43 44 44 46 47 48 iii 48 50 51 52 54 55 59 61 62 64 65 66 67 68

More information

2011de.dvi

2011de.dvi 211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37

More information

1 c Koichi Suga, ISBN

1 c Koichi Suga, ISBN c Koichi Suga, 4 4 6 5 ISBN 978-4-64-6445- 4 ( ) x(t) t u(t) t {u(t)} {x(t)} () T, (), (3), (4) max J = {u(t)} V (x, u)dt ẋ = f(x, u) x() = x x(t ) = x T (), x, u, t ẋ x t u u ẋ = f(x, u) x(t ) = x T x(t

More information

(報告書まとめ 2004/03/  )

(報告書まとめ 2004/03/  ) - i - ii iii iv v vi vii viii ix x xi 1 Shock G( Invention) (Property rule) (Liability rule) Impact flow 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 (

More information

1... 1... 1... 3 2... 4... 4... 4... 4... 4... 6... 10... 11... 15... 30

1... 1... 1... 3 2... 4... 4... 4... 4... 4... 6... 10... 11... 15... 30 1 2420128 1 6 3 2 199103 189/1 1991031891 3 4 5 JISJIS X 0208, 1997 1 http://www.pref.hiroshima.lg.jp/site/monjokan/ 1... 1... 1... 3 2... 4... 4... 4... 4... 4... 6... 10... 11... 15... 30 1 3 5 7 6 7

More information

ii iii iv CON T E N T S iii iv v Chapter1 Chapter2 Chapter 1 002 1.1 004 1.2 004 1.2.1 007 1.2.2 009 1.3 009 1.3.1 010 1.3.2 012 1.4 012 1.4.1 014 1.4.2 015 1.5 Chapter3 Chapter4 Chapter5 Chapter6 Chapter7

More information

untitled

untitled I...1 II...2...2 III...3...3...7 IV...15...15...20 V...23...23...24...25 VI...31...31...32...33...40...47 VII...62...62...67 VIII...70 1 2 3 4 m 3 m 3 m 3 m 3 m 3 m 3 5 6 () 17 18 7 () 17 () 17 8 9 ()

More information

01_.g.r..

01_.g.r.. I II III IV V VI VII VIII IX X XI I II III IV V I I I II II II I I YS-1 I YS-2 I YS-3 I YS-4 I YS-5 I YS-6 I YS-7 II II YS-1 II YS-2 II YS-3 II YS-4 II YS-5 II YS-6 II YS-7 III III YS-1 III YS-2

More information

2002 11 21 1 http://www.sml.k.u-tokyo.ac.jp/members/nabe/lecture2002 http://www.sml.k.u-tokyo.ac.jp/members/nabe/lecture nabe@sml.k.u-tokyo.ac.jp 2 1. 10/10 2. 10/17 3. 10/24 4. 10/31 5. 11/ 7 6. 11/14

More information

活用ガイド (ソフトウェア編)

活用ガイド (ソフトウェア編) (Windows 95 ) ii iii iv NEC Corporation 1999 v P A R T 1 vi P A R T 2 vii P A R T 3 P A R T 4 viii P A R T 5 ix x P A R T 1 2 3 1 1 2 4 1 2 3 4 5 1 1 2 3 4 6 5 6 7 7 1 1 2 8 1 9 1 1 2 3 4 5 6 1 2 3 4

More information

21 1 11 11 11 11 13 13 13 14 14 14 211 216 217 2118 221 222 222 223 225 226 226 227 2 228 229 229 2210 2211 2213 2216 2228 2229 2230 2231 2232 2233 2233 2234 2234 2236 2237 2238 2238 2239 2240 2241 3

More information

3 5 18 3 5000 1 2 7 8 120 1 9 1954 29 18 12 30 700 4km 1.5 100 50 6 13 5 99 93 34 17 2 2002 04 14 16 6000 12 57 60 1986 55 3 3 3 500 350 4 5 250 18 19 1590 1591 250 100 500 20 800 20 55 3 3 3 18 19 1590

More information

困ったときのQ&A

困ったときのQ&A ii iii iv NEC Corporation 1997 v P A R T 1 vi vii P A R T 2 viii P A R T 3 ix x xi 1P A R T 2 1 3 4 1 5 6 1 7 8 1 9 1 2 3 4 10 1 11 12 1 13 14 1 1 2 15 16 1 2 1 1 2 3 4 5 17 18 1 2 3 1 19 20 1 21 22 1

More information

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =

More information

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............

More information

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,. 9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,

More information

http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................

More information

III

III III 1 1 2 1 2 3 1 3 4 1 3 1 4 1 3 2 4 1 3 3 6 1 4 6 1 4 1 6 1 4 2 8 1 4 3 9 1 5 10 1 5 1 10 1 5 2 12 1 5 3 12 1 5 4 13 1 6 15 2 1 18 2 1 1 18 2 1 2 19 2 2 20 2 3 22 2 3 1 22 2 3 2 24 2 4 25 2 4 1 25 2

More information

iii iv v vi vii viii ix 1 1-1 1-2 1-3 2 2-1 3 3-1 3-2 3-3 3-4 4 4-1 4-2 5 5-1 5-2 5-3 5-4 5-5 5-6 5-7 6 6-1 6-2 6-3 6-4 6-5 6 6-1 6-2 6-3 6-4 6-5 7 7-1 7-2 7-3 7-4 7-5 7-6 7-7 7-8 7-9 7-10 7-11 8 8-1

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

最新耐震構造解析 ( 第 3 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 3 版 1 刷発行時のものです.

最新耐震構造解析 ( 第 3 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 3 版 1 刷発行時のものです. 最新耐震構造解析 ( 第 3 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/052093 このサンプルページの内容は, 第 3 版 1 刷発行時のものです. i 3 10 3 2000 2007 26 8 2 SI SI 20 1996 2000 SI 15 3 ii 1 56 6

More information

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+ R 3 R n C n V??,?? k, l K x, y, z K n, i x + y + z x + y + z iv x V, x + x o x V v kx + y kx + ky vi k + lx kx + lx vii klx klx viii x x ii x + y y + x, V iii o K n, x K n, x + o x iv x K n, x + x o x

More information

4 5.............................................. 5............................................ 6.............................................. 7......................................... 8.3.................................................4.........................................4..............................................4................................................4.3...............................................

More information

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....

More information

all.dvi

all.dvi 38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t

More information

.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

.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

More information

活用ガイド (ソフトウェア編)

活用ガイド (ソフトウェア編) (Windows 98 ) ii iii iv v NEC Corporation 1999 vi P A R T 1 P A R T 2 vii P A R T 3 viii P A R T 4 ix P A R T 5 x P A R T 1 2 3 1 1 2 4 1 2 3 4 5 1 1 2 3 4 5 6 6 7 7 1 1 2 8 1 9 1 1 2 3 4 5 6 1 2 3 10

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