* 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
|
|
|
- こうじ ことじ
- 5 years ago
- Views:
Transcription
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
2 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 x H 1 L 1 µ 1, µ, σ 1 x L 1 µ 1, µ, σ 1 x L 0 µ, σ 1 0 x 1 *3 1 L 1 µ 1, µ, σ 1 T = log x L 0 µ, σ 0 x χ * 4*5 χ H 0 H 1 H 0 : µ, σ H 1 : µ 1, µ, σ T > χ 1, 0.95 *6 *3 *4 n *5 T T = log L 0 µ, σ 0 x L 1 µ 1, µ, σ 1 x logx = log 1 x *6 χ 1, 0.95 χ t χ F χ
3 . x 11,, x 1n Nµ 1, σ x 1,, x n Nµ, σ H 0 µ 1 = µ = µ H 1 µ 1 µ α i H 0, H 1 *7 *8 ii i iii ii L 1 µ 1, µ, σ 1 T = log x L 0 µ, σ 0 x = l 1 µ 1, µ, σ 1 x l0 µ, σ 0 x *9 iv m= H 1 H 0 χ T > χ m, 1 α T χ H 1 H x 11,, x 15 Nµ 1, σ x 1,, x 5 Nµ, σ * 10 H 0 µ 1 = µ = µ H 1 µ 1 µ x 11 = 10, x 1 = 13, x 13 = 14, x 14 = 8, x 15 = 15 x 1 = 13, x = 1, x 3 = 18, x 4 = 5, x 5 = *7 µ σ *8 *9 l 1 µ 1, µ, σ 1 x, l0 µ, σ 0 x *
4 H 0 µ 1 = µ = µ 10 Nµ, σ * 11 µ = 1 10 σ 0 = 1 10 = 1 10 = 3. L 0 µ, σ x = 5 1 exp x ij µ πσ σ 10 1 = exp πσ 1 σ l 0 µ, σ x = 10 log πσ 1 σ x ij µ x ij µ x ij = = x ij µ { } l 0 µ, σ 0 x = 10 log π σ 0 1 σ 0 x ij µ σ 0 = 1 10 x ij µ x ij µ x ij µ = 10 σ 0 l 0 µ, σ 0 x = 10 log π σ σ σ 0 0 = 5 log 46.4π 5 *11 1 4
5 * 1 L 1 µ 1, µ, σ x = 5 { 1 exp x 1j µ 1 } πσ σ = exp 1 πσ σ x 1j µ 1 + l 1 µ 1, µ, σ x = 10 log πσ 1 σ µ 1 = 1 5 µ = 1 5 { 1 exp x j µ } πσ σ x j µ x 1j µ 1 + x 1j = = 1 5 x j = = 18 5 σ 1 = 1 x 1j µ = 1 10 = 14. x j µ x j µ 3 { } 3 l 1 µ 1, µ, σ 1 x = 10 log π σ 1 1 x 1j µ 1 + σ 1 σ 1 = 1 x 1j µ 1 + x j µ 10 x j µ 4 4 l 1 µ 1, µ, σ 1 x = 10 log π σ σ σ 1 1 = 5 log 8.4π 5 *1 5
6 L 1 µ 1, µ, σ 1 T = log x L 0 µ, σ 0 x = l 1 µ 1, µ, σ 1 x l0 µ, σ 0 x = { 5 log 8.4π 5 5 log 46.4π 5} 46.4π = 10 log 8.4π 46.4 = 10 log * 13 χ H 1 µ 1, µ, σ H 0 µ, σ χ 1, * 14 T 4.9 > 3.84 χ 1, i * 15 ii 4.1 i 1 x 1,, x n x 1,, x n * 16 x 1,, x n x 1,, x n * 17 * 18 * 19 *13 log PC *14 10 *15 *16 *17 *18 *19 6
7 4. ii 4..1 fx n, p = n C x p x 1 p n x 10 3 Lp 10, 3 = 10 C 3 p 3 1 p 7 5 p p = 0.1, 0.3, p p = 0.1 L0.1 10, 3 = 10 C p = 0.3 L0.3 10, 3 = 10 C p = 0.5 L0.5 10, 3 = 10 C p=0.1 p = p=0.3 p = p=0.5 p = p = 0.3 p = 0.1, 0.5 p = * p = 0.1, 0.3, 0.5 p = 0.3 p 0 1 Lp 10, 3 p p Lp 10, 3 p dlp 10, 3 dp = 0 6 *0 7
8 * 1 5 p 10 log * lp 10, 3 = log Lp 10, 3 lp 10, 3 p dlp 10, 3 dp = 0 7 * 3 p p p 5 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 H 0 H 0 H 1 µ 1, µ, σ x L 0 µ, σ 0 x L 1 µ 1, µ, σ 1 x *1 y = fx f x = 0 f x = 0 fx = x 3 x = 0 6 * Lp 10, 3 = 10 C 3 p 3 1 p 7 lp 10, 3 = log 10 C log p + 7 log 1 p p dl dp p = 0, dl p = 0 dp *3 x = 0, n 8
9 5.1 i H 0 L 0 µ, σ 0 x ii H 0, H 1 L 1 µ 1, µ, σ 1 x H 0 H 0, H 1 a b a H 0 µ 1 = µ = µ H 0 H 1 µ 1, µ H 0 µ 1 = µ µ 1 µ µ σ 0 = 1 n n x ij µ σ 1 = 1 n x 1j µ 1 + n n x j µ H 0 H 0 H 1 L 1 µ 1, µ, σ 1 x L 0 µ, σ 0 x 1 b H 1 µ 1 µ H 1 µ 1 µ µ 1 µ H 0 µ L 0 µ, σ 0 x H 0 H 1 H 1 µ 1, µ L 1 µ 1, µ, σ 1 x L0 µ, σ 0 x L 1 µ 1, µ, σ 1 x L 0 µ, σ 0 x >> 1 * 4 *4 9
10 6 6.1 log L 1 µ 1, µ, σ 1 T = log x L 0 µ, σ 0 x = l 1 µ 1, µ, σ 1 x l0 µ, σ 0 x * 5 6. * 6 T = l 1 µ 1, µ, σ 1 x l0 µ, σ 0 x χ 1 χ H 1 H 0 H 1 µ 1, µ, σ H 0 µ, σ α T = l 1 µ 1, µ, σ 1 x l0 µ, σ 0 x > χ 1, 1 α H 0 H 0 H 0 H 1 a H 0 H 0 H 1 b H 0 T c T H 0 c H 0 H 0 H 1 a H 0 H 0 H 1 b T H 0 H 1 *5 T 0 *6 10
11 7 7.1 X 1, X X = X X1 X, µ = µ1 µ, Σ = X N µ, Σ σ 1 ρσ 1 σ ρσ 1 σ σ ρ 0 X 1, X = x 1, x Lµ 1, µ, ρ, σ1, σ x 1 1, x = πσ 1 σ exp 1 x1 µ 1 1 ρ 1 ρ σ 1 ρx 1 µ 1 x µ + x µ σ 1 σ σ X 1 Nµ 1, σ1, X Nµ, σ fx 1 µ 1, σ1 fx µ, σ 1 = exp x 1 µ 1 1 exp x µ πσ 1 πσ = σ 1 1 exp x 1 µ 1 πσ σ1 x µ σ Lµ 1, µ, ρ, σ 1, σ x 1, x σ * 7 µ µ µ *7 11
12 * 8 x 1,, x n Nµ, σ σ ML = 1 n σ = 1 n 1 n x i x i=1 n x i x i=1 * 9 σ σ ML n n = 10 x i x = 70 i=1 σ ML = = 7, σ = 70 9 = 30 σ ML * σ ML µ = x µ µ * 31 µ = x µ 9,999 µ 1,, µ 9999 µ 10,000 10,000 µ µ + µ µ 9999 µ µ µ µ µ 1,, µ 100 µ µ *8 µ µ = x µ µ µ *9 *30 *31 UMVU 1
13 10,000 σ ML + σ ML, σ ML,9999 < σ * 3 µ * 33 σ = 1 n x i µ 8 n i=1 σ µ µ = x σ ML = 1 n x i µ 9 n i=1 8 9 µ µ 8 µ σ * 34 9 µ µ µ µ * 36 * H 0, H 1 H 1 H 0 H 1 x 11, x 1, x 13 Nµ 1, σ, x 1, x, x 3 Nµ, σ *3 σ ML *33 *34 *35 *36 µ 13
14 H 0 : µ 1 = µ = µ H 1 : µ 1 µ x 11 = 0, x 1 = 30, x 13 = x 1 = 5, x = 18, x 3 = 9 H 1 µ 1 = = 4, µ = = 4 3 µ 1 µ H 1 µ 1 µ H 0 H 1 µ 1 = µ H 0 µ 1 = µ µ 1 = µ H 0 µ 1 = µ * 37 H 1 H 0 H 1 8 Holmes Sharlock Holmes * 38 * 39 we balance the probabilies and choose the most likely * p = 0.1, 0.3, 0.5 * 41 * =1 L 1 µ 1, µ, σ 1 x L 0 µ, σ 0 x 1 *38 *39 *40 Holmes A B C *41 Holmes Bayes 14
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.
「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)
(iii) x, x N(µ, ) z = x µ () N(0, ) () 0 (y,, y 0 ) (σ = 6) *3 0 y y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y ( ) *4 H 0 : µ
t 2 Armitage t t t χ 2 F χ 2 F 2 µ, N(µ, ) f(x µ, ) = ( ) exp (x µ)2 2πσ 2 2 0, N(0, ) (00 α) z(α) t * 2. t (i)x N(µ, ) x µ σ N(0, ) 2 (ii)x,, x N(µ, ) x = x + +x ( N µ, σ2 ) (iii) (i),(ii) x,, x N(µ,
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,
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
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
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
() 3 3 2 5 3 6 4 2 5 4 2 (; ) () 8 2 4 0 0 2 ex. 3 n n =, 2,, 20 : 3 2 : 9 3 : 27 4 : 8 5 : 243 6 : 729 7 : 287 8 : 656 9 : 9683 0 : 59049 : 7747 2 : 5344 3 : 594323 4 : 4782969 5 : 4348907 6 : 4304672
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,
分散分析・2次元正規分布
2 II L10(2016-06-30 Thu) : Time-stamp: 2016-06-30 Thu 13:55 JST hig F 2.. http://hig3.net ( ) L10 2 II(2016) 1 / 24 F 2 F L09-Q1 Quiz :F 1 α = 0.05, 2 F 3 H 0, : σ 2 1 /σ2 2 = 1., H 1, σ 2 1 /σ2 2 1. 4
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
untitled
1 th 1 th Dec.2006 1 1 th 1 th Dec.2006 103 1 2 EITC 2 1 th 1 th Dec.2006 3 1 th 1 th Dec.2006 2006 4 1 th 1 th Dec.2006 5 1 th 1 th Dec.2006 2 6 1 th 1 th Dec.2006 7 1 th 1 th Dec.2006 3 8 1 th 1 th Dec.2006
ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.
24(2012) (1 C106) 4 11 (2 C206) 4 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%)
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
³ÎΨÏÀ
2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p
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
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)
- 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) -
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
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
I? 3 1 3 1.1?................................. 3 1.2?............................... 3 1.3!................................... 3 2 4 2.1........................................ 4 2.2.......................................
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!
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
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)
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
D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j
![D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j](/thumbs/103/158001152.jpg "D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j")
6 6.. [, b] [, d] ij P ij ξ ij, η ij f Sf,, {P ij } Sf,, {P ij } k m i j m fξ ij, η ij i i j j i j i m i j k i i j j m i i j j k i i j j kb d {P ij } lim Sf,, {P ij} kb d f, k [, b] [, d] f, d kb d 6..
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
( )/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
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 {
.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
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 (
,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = , ( ) : = F 1 + F 2 + F 3 + ( ) : = i Fj j=1 2
6 2 6.1 2 2, 2 5.2 R 2, 2 (R 2, B, µ)., R 2,,., 1, 2, 3,., 1, 2, 3,,. () : = 1 + 2 + 3 + (6.1.1).,,, 1 ,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = 1 + 2 + 3 +,
研修コーナー
l l l l l l l l l l l α α β l µ 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 l l l l l l l l l l l l l l l l l
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.
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
( ) 2002 1 1 1 1.1....................................... 1 1.1.1................................. 1 1.1.2................................. 1 1.1.3................... 3 1.1.4......................................
( 28 ) ( ) ( ) 0 This note is c 2016, 2017 by Setsuo Taniguchi. It may be used for personal or classroom purposes, but not for commercial purp
( 28) ( ) ( 28 9 22 ) 0 This ote is c 2016, 2017 by Setsuo Taiguchi. It may be used for persoal or classroom purposes, but ot for commercial purposes. i (http://www.stat.go.jp/teacher/c2epi1.htm ) = statistics
2010 II / y = e x y = log x = log e x 2. ( e x ) = e x 3. ( ) log x = 1 x 1.2 Warming Up 1 u = log a M a u = M a 0
2010 II 6 10.11.15/ 10.11.11 1 1 5.6 1.1 1. y = e x y = log x = log e x 2. e x ) = e x 3. ) log x = 1 x 1.2 Warming Up 1 u = log a M a u = M a 0 log a 1 a 1 log a a a r+s log a M + log a N 1 0 a 1 a r
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...?
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
ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.
(1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..
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
‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í
Markov 2009 10 2 Markov 2009 10 2 1 / 25 1 (GA) 2 GA 3 4 Markov 2009 10 2 2 / 25 (GA) (GA) L ( 1) I := {0, 1} L f : I (0, ) M( 2) S := I M GA (GA) f (i) i I Markov 2009 10 2 3 / 25 (GA) ρ(i, j), i, j I
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...........
newmain.dvi
数論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published
no35.dvi
p.16 1 sin x, cos x, tan x a x a, a>0, a 1 log a x a III 2 II 2 III III [3, p.36] [6] 2 [3, p.16] sin x sin x lim =1 ( ) [3, p.42] x 0 x ( ) sin x e [3, p.42] III [3, p.42] 3 3.1 5 8 *1 [5, pp.48 49] sin
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..................................................
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)
64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k
63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5
<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
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
function2.pdf
2... 1 2009, http://c-faculty.chuo-u.ac.jp/ nishioka/ 2 11 38 : 5) i) [], : 84 85 86 87 88 89 1000 ) 13 22 33 56 92 147 140 120 100 80 60 40 20 1 2 3 4 5 7.1 7 7.1 1. *1 e = 2.7182 ) fx) e x, x R : 7.1)
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
FX ) 2
(FX) 1 1 2009 12 12 13 2009 1 FX ) 2 1 (FX) 2 1 2 1 2 3 2010 8 FX 1998 1 FX FX 4 1 1 (FX) () () 1998 4 1 100 120 1 100 120 120 100 20 FX 100 100 100 1 100 100 100 1 100 1 100 100 1 100 101 101 100 100
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
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
SFGÇÃÉXÉyÉNÉgÉãå`.pdf
SFG 1 SFG SFG I SFG (ω) χ SFG (ω). SFG χ χ SFG (ω) = χ NR e iϕ +. ω ω + iγ SFG φ = ±π/, χ φ = ±π 3 χ SFG χ SFG = χ NR + χ (ω ω ) + Γ + χ NR χ (ω ω ) (ω ω ) + Γ cosϕ χ NR χ Γ (ω ω ) + Γ sinϕ. 3 (θ) 180
II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re
![II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re](/thumbs/94/118770263.jpg "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
Exif Viewer, DPOF Editor 使用説明書
Exif Viewer DP Editor 2 3 I 4 II III 5 I 6 I 7 I 8 I 9 I 10 I 11 I 12 I 13 I 14 I 15 I 16 I 17 I 18 I 19 I 20 I 21 I 22 I 23 I 24 25 I 26 I 27 I 28 I 29 I Windows 30 I 31 I 32 I 33 I 34 35 II II 36 II
A, B, C. (1) A = A. (2) A = B B = A. (3) A = B, B = C A = C. A = B. (3)., f : A B g : B C. g f : A C, A = C. 7.1, A, B,. A = B, A, A A., A, A
91 7,.,, ( ).,,.,.,. 7.1 A B, A B, A = B. 1), 1,.,. 7.1 A, B, 3. (i) A B. (ii) f : A B. (iii) A B. (i) (ii)., 6.9, (ii) (iii).,,,. 1), Ā = B.. A, Ā, Ā,. 92 7 7.2 A, B, C. (1) A = A. (2) A = B B = A. (3)
ii p ϕ x, t = C ϕ xe i ħ E t +C ϕ xe i ħ E t ψ x,t ψ x,t p79 やは時間変化しないことに注意 振動 粒子はだいたい このあたりにいる 粒子はだいたい このあたりにいる p35 D.3 Aψ Cϕdx = aψ ψ C Aϕ dx
i B5 7.8. p89 4. ψ x, tψx, t = ψ R x, t iψ I x, t ψ R x, t + iψ I x, t = ψ R x, t + ψ I x, t p 5.8 π π π F e ix + F e ix + F 3 e 3ix F e ix + F e ix + F 3 e 3ix dx πψ x πψx p39 7. AX = X A [ a b c d x
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
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
基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 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
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...
meiji_resume_1.PDF
β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E
ito.dvi
1 2 1006 214 542 160 120 160 1 1916 49 1710 55 1716 1 2 1995 1 2 3 4 2 3 1950 1973 1969 1989 1 4 3 3.1 3.1.1 1989 2 3.1.2 214 542 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
10:30 12:00 P.G. vs vs vs 2
1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B
α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β *3 2.3 * *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P + 10) 15 (µ A = µ P +
Armitage 1 1.1 2 t *1 α β 1.2 µ x µ 2 2 2 α β 2.1 1 α β α ( ) β *1 t t 1 α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β 1 0 0 1 1 5 2.5 *3 2.3 *4 3 3.1 1 1 1 *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P
- - - - - - - - - - - - - - - - - - - - - - - - - -1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2...2...3...4...4...4...5...6...7...8...
取 扱 説 明 書 - - - - - - - - - - - - - - - - - - - - - - - - - -1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2...2...3...4...4...4...5...6...7...8...9...11 - - - - - - - - - - - - - - - - -
.. ( )T p T = p p = T () T x T N P (X < x T ) N = ( T ) N (2) ) N ( P (X x T ) N = T (3) T N P T N P 0
20 5 8..................................................2.....................................3 L.....................................4................................. 2 2. 3 2. (N ).........................................
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
2 7 ( ) µ BayesfiI‡É“ÅfiK‡È−w‘K‡Ì‡½‡ß‡ÌChow-Liu…A…‰…S…−…Y…•
1 / 21 Kruscal V : w i,j R: w i,j = w j,i i j Kruscal (w i,j 0 ) 1 E {{i, j} i, j V, i i} 2 E {} 3 while(e = ϕ) for w i,j {i, j} E 1 E E\{i, j} 2 G = (V, E {i, j}) = E E {i, j} G {i,j} E w i,j 2 / 21 w
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
1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l
1 1 ϕ ϕ ϕ S F F = ϕ (1) S 1: F 1 1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l : l r δr θ πrδr δf (1) (5) δf = ϕ πrδr
, 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x
![, 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x](/thumbs/93/113428934.jpg ", 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x")
1 1.1 4n 2 x, x 1 2n f n (x) = 4n 2 ( 1 x), 1 x 1 n 2n n, 1 x n n 1 1 f n (x)dx = 1, n = 1, 2,.. 1 lim 1 lim 1 f n (x)dx = 1 lim f n(x) = ( lim f n (x))dx = f n (x)dx 1 ( lim f n (x))dx d dx ( lim f d
Dirac 38 5 Dirac 4 4 γ µ p µ p µ + m 2 = ( p µ γ µ + m)(p ν γ ν + m) (5.1) γ = p µ p ν γ µ γ ν p µ γ µ m + mp ν γ ν + m 2 = 1 2 p µp ν {γ µ, γ ν } + m
Dirac 38 5 Dirac 4 4 γ µ p µ p µ + m 2 p µ γ µ + mp ν γ ν + m 5.1 γ p µ p ν γ µ γ ν p µ γ µ m + mp ν γ ν + m 2 1 2 p µp ν {γ µ, γ ν } + m 2 5.2 p m p p µ γ µ {, } 10 γ {γ µ, γ ν } 2η µν 5.3 p µ γ µ + mp