|
|
- あきとし たかはし
- 5 years ago
- Views:
Transcription
1 Game Theory( 0) Masato Shimura
2
3 MAXMIN = Sharplay Example J
4 Game one-shot/ / / /
5 ( ) A= , B = J cr=:%.}:"1 a +b = 10 a +c = 10 b +c = 0 a=:3 4 $ a cr a ( 0 )
6
7
8 gmatrix GH _1 _1 _5 0 A _5 _3 _3 A B0 B1 ( ), ( ) gmatrix GN ( )
9 gmatrix GN A A B0 B1 ( 1 2 ) 3 2 ( ) ( ) ( 2 3, 1 3 ) ( 1 3, 2 3 ) 1.2 MAXMIN A B A B shihai GM NB. A-> 0 B-> 2 (0-2)
10 NB. (5 7) (6 8) (5 7) A (4 5) B (4 5) 2 maxmin0 GM NB. 2 (4 5) maxmin
11 x y y x 1.3 ( ) A\B y 1 y x xy x(1 y) 1 x (1 x)y (1 x)(1 y) A\B y 1 y x xy x xy 1 x y xy x y + xy J 2 xy x,y xy + x,y + x 0 x y + + +
12 y Working Example , = +/ = =+/ 3 12= =+/ 9 12= , x = 15 45y = 21, 2 xy A (x, 1 x) = 0.47, 0.53 B (y, 1 y) = 0.33, 0.67 mix_2s GH _ _
13 AB AB mix_2 GN NB. MAN NB. LADY A B set of game 1, 1 2, , 0 mix_2 1 1 ;2 2 ;0 3;3 0
14 _4 _ _4 0 _ A 1 2 B set of game nash
15 A,B 3
16 A\B y v 1 y v x xy xv x(1 y v) u uy uv u(1 y v) 1 x u y(1 x u) v(1 x u) (1 x u)(1 y v) ( ) A\B y v 1 y v x xy xv x xy xv u uy uv u uy uv 1 x u y xy uy y vx uv) 1 x y u v + xy + xv + uy + uv x, y, u, v x, y, u, v x 0 x y u v y
17 u v A\B y v 1 y v x u x u $ GH _ ( ) mix_3s GH _5 0 _ _8 0 _32 0 _ _32 0 _32 _ _32 0 _ A B
18
19 2 2.1 A\B gmatrix GN : combi_2 i tree_game GN
20 NB NB NB. A NB. B : 20{. 0.1 parrot0 GN NB. Score A NB. Score B NB. cumrative A NB. cumrative B : 20{. 0.1 parrot1 GN1 NB. both panish -> eternal panish
21 3 3.1 ( )
22
23 4 = 4.1 ( ) Working Example ( ) A 5 B,C 15!3 = 6? (ABC)=10 (AB)=10 (AC)=10 (A)=(B)=(C)=(BC)=0
24 cr=. %.}:"1 a=. 3 4 $ cr a a A 10 B,C 0 a, b > 10 a, c > 10 b, c > Sharplay ( ) Working Example A B C ABC 120 : mk_sharplay_index VAL NB. number a b c ab ac bc abc NB. combination of player NB. Value ABC 6 (sh_sub P1) { L: abc
25 abc bac bca acb cab cba bac abc acb bca cba cab cab acb abc cba bca bac NB. A NB. B NB. C A 6 A (abc,acb) a a v(a) v(π) = 10 0 = 10 (bac,cab) (ab,ac) v(ab) v(b) = = 40,v(ac) v(c) = = 40 (bca,cba) A A v(abc) v(bc) = = 40 A 6 calc_sharplay3 VAL NB. A NB. B NB. C Working Example -fee of Taxi Taxi ABC COST : mk_sharplay_index VAL
26 a b c ab ac bc abc sharplay Value calc_sharplay3 VAL NB. A NB. B NB. C Working Example ABC 3 3 ( ) a0,.({:"1 a1),.({:"1 a2),.{:"1 a3 NR/combi/P1/P2/P3/Total a b c ab
27 ac bc abc ABC3 calc_sharplay3 VAL50 NB. Project NB. A NB NB. B NB. C calc_sharplay3 VAL51 NB. Project calc_sharplay3 VAL52 NB. Project
28 calc_sharplay3 VAL53 NB. Total 3 projects NB. A NB. B NB. C Sharplay-Shubic Reference ( ) 12/ Tree.1 (a + b) n pascal
29 τ 0 rw _1 2 0 _2 3 1 _1 _ _2 _ _1 _3 _5
48 * *2
374-1- 17 2 1 1 B A C A C 48 *2 49-2- 2 176 176 *2 -3- B A A B B C A B A C 1 B C B C 2 B C 94 2 B C 3 1 6 2 8 1 177 C B C C C A D A A B A 7 B C C A 3 C A 187 187 C B 10 AC 187-4- 10 C C B B B B A B 2 BC
More information140 120 100 80 60 40 20 0 115 107 102 99 95 97 95 97 98 100 64 72 37 60 50 53 50 36 32 18 H18 H19 H20 H21 H22 H23 H24 H25 H26 H27 1 100 () 80 60 40 20 0 1 19 16 10 11 6 8 9 5 10 35 76 83 73 68 46 44 H11
More information7 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 information1 1 MM nm M1234n M4 ABAB nab ABz AB nabna AB AB nabnan B ABz nab nabnan B 202A3B B na10nb66 AB61218 n AB106 2 UUA A AA AA e AB na B na nbna B ABz na B
1 2 3 4 5 6 7 8 9 10 10 1 1 MM nm M1234n M4 ABAB nab ABz AB nabna AB AB nabnan B ABz nab nabnan B 202A3B B na10nb66 AB61218 n AB106 2 UUA A AA AA e AB na B na nbna B ABz na B na nb n(a( B) n(a ( )n(b)n(a
More informationPSCHG000.PS
a b c a ac bc ab bc a b c a c a b bc a b c a ac bc ab bc a b c a ac bc ab bc a b c a ac bc ab bc de df d d d d df d d d d d d d a a b c a b b a b c a b c b a a a a b a b a
More informationuntitled
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 informationuntitled
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 information10 4 2
1 10 4 2 92 11 3 8 20 10 2 10 20 10 28 3 B 78 111 104 1021 95 10 2 4 10 8 95 18 10 30 11 13 104 20 105 105 105 105 107 5 1 11 26 13301500 6 GH 1 GH 34 7 11 27 9301030 8 4 9 GH 1 23 10 20 60 --------------------------------------------------------------------------------------------------------------------------
More information1 (1) vs. (2) (2) (a)(c) (a) (b) (c) 31 2 (a) (b) (c) LENCHAR
() 601 1 () 265 OK 36.11.16 20 604 266 601 30.4.5 (1) 91621 3037 (2) 20-12.2 20-13 (3) ex. 2540-64 - LENCHAR 1 (1) vs. (2) (2) 605 50.2.13 41.4.27 10 10 40.3.17 (a)(c) 2 1 10 (a) (b) (c) 31 2 (a) (b) (c)
More information1. 2 P 2 (x, y) 2 x y (0, 0) R 2 = {(x, y) x, y R} x, y R P = (x, y) O = (0, 0) OP ( ) OP x x, y y ( ) x v = y ( ) x 2 1 v = P = (x, y) y ( x y ) 2 (x
. P (, (0, 0 R {(,, R}, R P (, O (0, 0 OP OP, v v P (, ( (, (, { R, R} v (, (, (,, z 3 w z R 3,, z R z n R n.,..., n R n n w, t w ( z z Ke Words:. A P 3 0 B P 0 a. A P b B P 3. A π/90 B a + b c π/ 3. +
More information1 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 informationEPSON VP-1200 取扱説明書
4020178-01 w p s 2 p 3 4 5 6 7 8 p s s s p 9 p A B p C 10 D p E 11 F G H H 12 p G I s 13 p s A D p B 14 C D E 15 F s p G 16 A B p 17 18 s p s 19 p 20 21 22 A B 23 A B C 24 A B 25 26 p s p s 27 28 p s p
More informationA(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6
1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67
More information26 2 3 4 5 8 9 6 7 2 3 4 5 2 6 7 3 8 9 3 0 4 2 4 3 4 4 5 6 5 7 6 2 2 A B C ABC 8 9 6 3 3 4 4 20 2 6 2 2 3 3 4 4 5 5 22 6 6 7 7 23 6 2 2 3 3 4 4 24 2 2 3 3 4 4 25 6 2 2 3 3 4 4 26 2 2 3 3 27 6 4 4 5 5
More informationmogiJugyo_slide_full.dvi
a 2 + b 2 = c 2 (a, b, c) a 2 a 2 = a a a 1/ 78 2/ 78 3/ 78 4/ 78 180 5/ 78 http://www.kaijo.ed.jp/ 6/ 78 a, b, c ABC C a b B c A C 90 a 2 + b 2 = c 2 7/ 78 C a b a 2 +b 2 = c 2 B c A a 2 a a 2 = a a 8/
More information1 2 3 4 5 6 X Y ABC A ABC B 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 13 18 30 P331 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 51 52 53 54 55 56 57 58 59
More information) 9 81
4 4.0 2000 ) 9 81 10 4.1 natural numbers 1, 2, 3, 4, 4.2, 3, 2, 1, 0, 1, 2, 3, integral numbers integers 1, 2, 3,, 3, 2, 1 1 4.3 4.3.1 ( ) m, n m 0 n m 82 rational numbers m 1 ( ) 3 = 3 1 4.3.2 3 5 = 2
More information70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 informationH27 28 4 1 11,353 45 14 10 120 27 90 26 78 323 401 27 11,120 D A BC 11,120 H27 33 H26 38 H27 35 40 126,154 129,125 130,000 150,000 5,961 11,996 6,000 15,000 688,684 708,924 700,000 750,000 1300 H28
More information0.6 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 information70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
More informationuntitled
1 2 3 4 5 6 7 8 9 10 11 ( ) 12 13 14 15 0.95 0.90 0.85 0.90 0.97 0.90 0.80 0.80 0.75 0.65 0.60 0.61 0.63 0.50 0.32 0.26 0.20 16 17 18 19 20 21 22 23 24 25 26 27 28 29 ( ) 30 ( ) 31 () () 32 33 34 ( ) ()
More information新たな基礎年金制度の構築に向けて
[ ] 1 1 4 60 1 ( 1 ) 1 1 1 4 1 1 1 1 1 4 1 2 1 1 1 ( ) 2 1 1 1 1 1 1 1996 1 3 4.3(2) 1997 1 65 1 1 2 1/3 ( )2/3 1 1/3 ( ) 1 1 2 3 2 4 6 2.1 1 2 1 ( ) 13 1 1 1 1 2 2 ( ) ( ) 1 ( ) 60 1 1 2.2 (1) (3) ( 9
More informationEPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D
More informationありがとうございました
- 1 - - 2 - - 3 - - 4 - - 5 - 1 2 AB C A B C - 6 - - 7 - - 8 - 10 1 3 1 10 400 8 9-9 - 2600 1 119 26.44 63 50 15 325.37 131.99 457.36-10 - 5 977 1688 1805 200 7 80-11 - - 12 - - 13 - - 14 - 2-1 - 15 -
More informationEPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D
More information公務員人件費のシミュレーション分析
47 50 (a) (b) (c) (7) 11 10 2018 20 2028 16 17 18 19 20 21 22 20 90.1 9.9 20 87.2 12.8 2018 10 17 6.916.0 7.87.4 40.511.6 23 0.0% 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2.0% 4.0% 6.0% 8.0%
More informationQ1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 A B (A/B) 1 1,185 17,801 6.66% 2 943 26,598 3.55% 3 3,779 112,231 3.37% 4 8,174 246,350 3.32% 5 671 22,775 2.95% 6 2,606 89,705 2.91% 7 738 25,700 2.87% 8 1,134
More information橡hashik-f.PDF
1 1 1 11 12 13 2 2 21 22 3 3 3 4 4 8 22 10 23 10 11 11 24 12 12 13 25 14 15 16 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 144 142 140 140 29.7 70.0 0.7 22.1 16.4 13.6 9.3 5.0 2.9 0.0
More information198
197 198 199 200 201 202 A B C D E F G H I J K L 203 204 205 A B 206 A B C D E F 207 208 209 210 211 212 213 214 215 A B 216 217 218 219 220 221 222 223 224 225 226 227 228 229 A B C D 230 231 232 233 A
More informationネットショップ・オーナー2 ユーザーマニュアル
1 1-1 1-2 1-3 1-4 1 1-5 2 2-1 A C 2-2 A 2 C D E F G H I 2-3 2-4 2 C D E E A 3 3-1 A 3 A A 3 3 3 3-2 3-3 3-4 3 C 4 4-1 A A 4 B B C D C D E F G 4 H I J K L 4-2 4 C D E B D C A C B D 4 E F B E C 4-3 4
More information1
1 2 3 4 5 (2,433 ) 4,026 2710 243.3 2728 402.6 6 402.6 402.6 243.3 7 8 20.5 11.5 1.51 0.50.5 1.5 9 10 11 12 13 100 99 4 97 14 A AB A 12 14.615/100 1.096/1000 B B 1.096/1000 300 A1.5 B1.25 24 4,182,500
More information05[ ]戸田(責)村.indd
147 2 62 4 3.2.1.16 3.2.1.17 148 63 1 3.2.1.F 3.2.1.H 3.1.1.77 1.5.13 1 3.1.1.05 2 3 4 3.2.1.20 3.2.1.22 3.2.1.24 3.2.1.D 3.2.1.E 3.2.1.18 3.2.1.19 2 149 3.2.1.23 3.2.1.G 3.1.1.77 3.2.1.16 570 565 1 2
More information/9/ ) 1) 1 2 2) 4) ) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x ) x 2 8x + 10 = 0
1. 2018/9/ ) 1) 8 9) 2) 6 14) + 14 ) 1 4 8a 8b) 2 a + b) 4) 2 : 7 = x 8) : x ) x ) + 1 2 ) + 2 6) x + 1)x + ) 15 2. 2018/9/ ) 1) 1 2 2) 4) 2 + 6 5) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x 2 15 12
More informationAC-2
AC-1 AC-2 AC-3 AC-4 AC-5 AC-6 AC-7 AC-8 AC-9 * * * AC-10 AC-11 AC-12 AC-13 AC-14 AC-15 AC-16 AC-17 AC-18 AC-19 AC-20 AC-21 AC-22 AC-23 AC-24 AC-25 AC-26 AC-27 AC-28 AC-29 AC-30 AC-31 AC-32 * * * * AC-33
More informationエンジョイ北スポーツ
28 3 20 85132 http://www.kita-city-taikyo.or.jp 85 63 27 27 85132 http://www.kita-city-taikyo.or.jp 2 2 3 4 4 3 6 78 27, http://www.kita-city-taikyo.or.jp 85132 3 35 11 8 52 11 8 2 3 4 1 2 4 4 5 4 6 8
More information8 OR (a) A A 3 1 B 7 B (game theory) (a) (b) 8.1: 8.1(a) (b) strategic form game extensive form game 1
8 OR 8.1 8.1.1 8.1(a) A A 3 1 B 7 B (game theory) (a) (b) 8.1: 8.1(a) (b) strategic form game extensive form game 1 2 [5] player 2 1 noncooperative game 2 cooperative game8.4 8.1.2 2 8.1.1 ( ). A B A B
More information案内(最終2).indd
1 2 3 4 5 6 7 8 9 Y01a K01a Q01a T01a N01a S01a Y02b - Y04b K02a Q02a T02a N02a S02a Y05b - Y07b K03a Q03a T03a N03a S03a A01r Y10a Y11a K04a K05a Q04a Q05a T04b - T06b T08a N04a N05a S04a S05a Y12b -
More informationR R 16 ( 3 )
(017 ) 9 4 7 ( ) ( 3 ) ( 010 ) 1 (P3) 1 11 (P4) 1 1 (P4) 1 (P15) 1 (P16) (P0) 3 (P18) 3 4 (P3) 4 3 4 31 1 5 3 5 4 6 5 9 51 9 5 9 6 9 61 9 6 α β 9 63 û 11 64 R 1 65 13 66 14 7 14 71 15 7 R R 16 http://wwwecoosaka-uacjp/~tazak/class/017
More information13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x
More information( ) 2002 1 1 1 1.1....................................... 1 1.1.1................................. 1 1.1.2................................. 1 1.1.3................... 3 1.1.4......................................
More informationGmech08.dvi
63 6 6.1 6.1.1 v = v 0 =v 0x,v 0y, 0) t =0 x 0,y 0, 0) t x x 0 + v 0x t v x v 0x = y = y 0 + v 0y t, v = v y = v 0y 6.1) z 0 0 v z yv z zv y zv x xv z xv y yv x = 0 0 x 0 v 0y y 0 v 0x 6.) 6.) 6.1) 6.)
More informationuntitled
07H9) 0050 (30) w0xy w+ =x+y i w R R>w R xy (x, y ) () a 0a w a xy (x, y ) w=r (cosa +isia )0(a w+ w =R (cosa +isia )+ R 0cos a + isia cos a isia =R (cosa +isia )+ R 0cos a + isia 0cosa isia cosa isia
More information(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n
. 99 () 0 0 0 () 0 00 0 350 300 () 5 0 () 3 {a n } a + a 4 + a 6 + + a 40 30 53 47 77 95 30 83 4 n S n S n = n = S n 303 9 k d 9 45 k =, d = 99 a d n a n d n a n = a + (n )d a n a n S n S n = n(a + a n
More information2
Bradley-Terry 1 2 3 paired comparison 4 paired comparison 1860 Landau 5 6 A B B C A C 7 n 0.5n(n-1) n 2 0.5n(n-1) 3 8 9 A B B C A C 10 0.5n(n-1) (n-1) 11 Kendall coefficient of consistence ζ (1940) null
More informationuntitled
1 17 () BAC9ABC6ACB3 1 tan 6 = 3, cos 6 = AB=1 BC=2, AC= 3 2 A BC D 2 BDBD=BA 1 2 ABD BADBDA ABC6 BAD = (18 6 ) / 2 = 6 θ = 18 BAD = 12 () AD AD=BADCAD9 ABD ACD A 1 1 1 1 dsinαsinα = d 3 sin β 3 sin β
More information/02/18
3 09/0/8 i III,,,, III,?,,,,,,,,,,,,,,,,,,,,?,?,,,,,,,,,,,,,,!!!,? 3,,,, ii,,,!,,,, OK! :!,,,, :!,,,,,, 3:!,, 4:!,,,, 5:!,,! 7:!,,,,, 8:!,! 9:!,,,,,,,,, ( ),, :, ( ), ( ), 6:!,,, :... : 3 ( )... iii,,
More information225 225 232528 152810 225 232513 -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-
More information232528 152810 232513 -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-
More information> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3
13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >
More information2 / 5 Auction: Theory and Practice 3 / 5 (WTO) 1 SDR 27 1,6 Auction: Theory and Practice 4 / 5 2
stakagi@econ.hokudai.ac.jp June 22, 212 2................................................................ 3...................................................... 4............................................................
More information1
005 11 http://www.hyuki.com/girl/ http://www.hyuki.com/story/tetora.html http://www.hyuki.com/ Hiroshi Yuki c 005, All rights reserved. 1 1 3 (a + b)(a b) = a b (x + y)(x y) = x y a b x y a b x y 4 5 6
More information8 i, III,,,, III,, :!,,,, :!,,,,, 4:!,,,,,,!,,,, OK! 5:!,,,,,,,,,, OK 6:!, 0, 3:!,,,,! 7:!,,,,,, ii,,,,,, ( ),, :, ( ), ( ), :... : 3 ( )...,, () : ( )..., :,,, ( ), (,,, ),, (ϵ δ ), ( ), (ˆ ˆ;),,,,,,!,,,,.,,
More informationS K(S) = T K(T ) T S K n (1.1) n {}}{ n K n (1.1) 0 K 0 0 K Q p K Z/pZ L K (1) L K L K (2) K L L K [L : K] 1.1.
() 1.1.. 1. 1.1. (1) L K (i) 0 K 1 K (ii) x, y K x + y K, x y K (iii) x, y K xy K (iv) x K \ {0} x 1 K K L L K ( 0 L 1 L ) L K L/K (2) K M L M K L 1.1. C C 1.2. R K = {a + b 3 i a, b Q} Q( 2, 3) = Q( 2
More informationuntitled
yoshi@image.med.osaka-u.ac.jp http://www.image.med.osaka-u.ac.jp/member/yoshi/ II Excel, Mathematica Mathematica Osaka Electro-Communication University (2007 Apr) 09849-31503-64015-30704-18799-390 http://www.image.med.osaka-u.ac.jp/member/yoshi/
More informationEPSON LP-8900ユーザーズガイド
3 4 5 6 7 8 abc ade w p s 9 10 s s 11 p 12 p 13 14 p s 15 p s A B 16 w 17 C p 18 D E F 19 p w G H 20 A B 21 C s p D 22 E s p w 23 w w s 24 p w s 25 w 26 p p 27 w p s 28 w p 29 w p s 30 p s 31 A s B 32
More information1 B64653 1 1 3.1....................................... 3.......................... 3..1.............................. 4................................ 4..3.............................. 5..4..............................
More informationäÓíÍÇ ÉLÉÉÉâÉNÉ^Å[ÉeÅ[ÉuÉã.pdf
1 V 2 D 3 Y 4 W (a, b, c D SHG SFG Y CARS, CSRS, THG W SFG SHG CARS 4 2 D W D abba D ab * SFG (page point group) (page point group) 2 C s *, C i, C 2 * 12 D 4h 3 C 2v, * C 2h * 13 D 6h 4 D 2, D 2h 14 C
More information1 [ 1] (1) MKS? (2) MKS? [ 2] (1) (42.195k) k 2 (2) (3) k/hr [ 3] t = 0 10 ( 1 velocity [/s] 8 4 O
: 2014 4 10 1 2 2 3 2.1...................................... 3 2.2....................................... 4 2.3....................................... 4 2.4................................ 5 2.5 Free-Body
More informationall.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 information2/50 Auction: Theory and Practice 3 / 50 (WTO) 10 SDR ,600 Auction: Theory and Practice 4 / 50 2
stakagi@econ.hokudai.ac.jp June 24, 2011 2.... 3... 4... 7 8... 9.... 10... 11... 12 IPV 13 SPSB... 15 SPSB.... 17 SPSB.... 19 FPSB... 20 FPSB.... 22 FPSB.... 23... 24 Low Price Auction.... 27 APV 29...
More information1 + 1 + 1 + 1 + 1 + 1 + 1 = 0? 1 2003 10 8 1 10 8, 2004 1, 2003 10 2003 10 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 ( )?, 1, 8, 15, 22, 29?, 1 7, 1, 8, 15, 22,
More information18 5 10 1 1 1.1 1.1.1 P Q P Q, P, Q P Q P Q P Q, P, Q 2 1 1.1.2 P.Q T F Z R 0 1 x, y x + y x y x y = y x x (y z) = (x y) z x + y = y + x x + (y + z) = (x + y) + z P.Q V = {T, F } V P.Q P.Q T F T F 1.1.3
More information熊本県数学問題正解
00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (
More information1 1.1 [ 1] velocity [/s] 8 4 (1) MKS? (2) MKS? 1.2 [ 2] (1) (42.195k) k 2 (2) (3) k/hr [ 3] t = 0
: 2016 4 1 1 2 1.1......................................... 2 1.2................................... 2 2 2 2.1........................................ 2 2.2......................................... 3 2.3.........................................
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)
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 information2 1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a 2 + b 2 α (norm) N(α) = a 2 + b 2 = αα = α 2 α (spure) (trace) 1 1. a R aα =
1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a + b α (norm) N(α) = a + b = αα = α α (spure) (trace) 1 1. a R aα = aα. α = α 3. α + β = α + β 4. αβ = αβ 5. β 0 6. α = α ( ) α = α
More information( )
18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................
More information5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P
p P 1 n n n 1 φ(n) φ φ(1) = 1 1 n φ(n), n φ(n) = φ()φ(n) [ ] n 1 n 1 1 n 1 φ(n) φ() φ(n) 1 3 4 5 6 7 8 9 1 3 4 5 6 7 8 9 1 4 5 7 8 1 4 5 7 8 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 19 0 1 3 4 5 6 7
More information04年度LS民法Ⅰ教材改訂版.PDF
?? A AB A B C AB A B A B A B A A B A 98 A B A B A B A B B A A B AB AB A B A BB A B A B A B A B A B A AB A B B A B AB A A C AB A C A A B A B B A B A B B A B A B B A B A B A B A B A B A B A B
More informationuntitled
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 informationa (a + ), a + a > (a + ), a + 4 a < a 4 a,,, y y = + a y = + a, y = a y = ( + a) ( x) + ( a) x, x y,y a y y y ( + a : a ) ( a : a > ) y = (a + ) y = a
[] a x f(x) = ( + a)( x) + ( a)x f(x) = ( a + ) x + a + () x f(x) a a + a > a + () x f(x) a (a + ) a x 4 f (x) = ( + a) ( x) + ( a) x = ( a + a) x + a + = ( a + ) x + a +, () a + a f(x) f(x) = f() = a
More informationiii 1 1 1 1................................ 1 2.......................... 3 3.............................. 5 4................................ 7 5................................ 9 6............................
More informationCase 1 a,b,α, β α α + β β α = ua + vb β = sa + tb α α + β β = (ua + vb (ua + vb + (sa + tb (sa + tb = (u a a + uva b + uvb a + v b b + (s a a + sta b
Bogoliubov H = a a + aa < 0 H 0 >, < 1 H 1 >, < H > < H 0 > a H = α α α α, α = 1, α, α = α, α = 0 α α α H = α α Postulate( a,b α, β a, a = b, b = 1, a, b = b, a = 0 α, α = β, β = 1, α, β = β, α = 0 α,
More information(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
More information案内最終.indd
1 2 3 4 5 6 IC IC R22 IC IC http://www.gifu-u.ac.jp/view.rbz?cd=393 JR JR JR JR JR 7 / JR IC km IC km IC IC km 8 F HPhttp://www.made.gifu-u.ac.jp/~vlbi/index.html 9 Q01a N01a X01a K01a S01a T01a Q02a N02a
More informationOABC OA OC 4, OB, AOB BOC COA 60 OA a OB b OC c () AB AC () ABC D OD ABC OD OA + p AB + q AC p q () OABC 4 f(x) + x ( ), () y f(x) P l 4 () y f(x) l P
4 ( ) ( ) ( ) ( ) 4 5 5 II III A B (0 ) 4, 6, 7 II III A B (0 ) ( ),, 6, 8, 9 II III A B (0 ) ( [ ] ) 5, 0, II A B (90 ) log x x () (a) y x + x (b) y sin (x + ) () (a) (b) (c) (d) 0 e π 0 x x x + dx e
More informationさくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1
... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =
More information( ) ( ) 1729 (, 2016:17) = = (1) 1 1
1729 1 2016 10 28 1 1729 1111 1111 1729 (1887 1920) (1877 1947) 1729 (, 2016:17) 12 3 1728 9 3 729 1729 = 12 3 + 1 3 = 10 3 + 9 3 (1) 1 1 2 1729 1729 19 13 7 = 1729 = 12 3 + 1 3 = 10 3 + 9 3 13 7 = 91
More information学習の手順
NAVI 2 MAP 3 m 17 13 19 12 17 24 1 20 18 23 18 12 1 12 17 11 14 16 19 22 m 12 16 A 16 20 B 20 24 24 28 C 20 AC 40 cm AD A 0.20 12 0.300 B 0.200 0.12 12 C D 40 1.000 20 2 2 0 20 30 cm 14 1 1 160 160 16
More information7. 1 max max min f g h h(x) = max{f(x), g(x)} f g h l(x) l(x) = min{f(x), g(x)} f g 1 f g h(x) = max{f(x), g(x)} l(x) = min{f(x), g(x)} h(x) = 1 (f(x)
7. 1 ma ma min f g h h() = ma{f(), g()} f g h l() l() = min{f(), g()} f g 1 f g h() = ma{f(), g()} l() = min{f(), g()} h() = 1 (f() + g() + f() g() ) 2 1 1 l() = 1 (f() + g() f() g() ) 2 2 1 45 = 2 e 1
More information新・明解C言語で学ぶアルゴリズムとデータ構造
第 1 章 基本的 1 n 141 1-1 三値 最大値 algorithm List 1-1 a, b, c max /* */ #include int main(void) { int a, b, c; int max; /* */ List 1-1 printf("\n"); printf("a"); scanf("%d", &a); printf("b"); scanf("%d",
More informationuntitled
3-1 ( sit ) (stead state vibratio) (trasiet vibratio) sit(a)w s ( W s ) W / g C (b) sit ( + s ) ( + s ) c + W + sit W s si t + s + c + si t (3.1) si t (3.1) a C W b sit(respose) () 3- acost+ bsit a sit+
More information18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
More information1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C
0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,
More informationTaro10-名張1審無罪判決.PDF
-------------------------------------------------------------------------------- -------------------------------------------------------------------------------- -1- 39 12 23 36 4 11 36 47 15 5 13 14318-2-
More informationma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d
A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9
More informationx = 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