行列代数2010A
|
|
|
- ひろみ かつもと
- 5 years ago
- Views:
Transcription
1 (,) A (,) B C = AB a 11 a 1 a 1 b 11 b 1 b 1 c 11 c 1 c a A = 1 a a, B = b 1 b b, C = AB = c 1 c c a 1 a a b 1 b b c 1 c c i j ij a i1 a i a i b 1j b j b j c ij = a ik b kj
2 b 1j b j AB = a i1 a i a ik a i = b kj a ik b kj = C b j (,) AO = O A = O AE = A, E A = A O O E A = , B = AB BA AB BA AB = 1 1 1, BA =
3 i j a ij = 1 a ij = 0 a ij (i, j) A A A = A = = A (i, j) (i, j) A A 3 A 3 a i1 a 1j + a i a j + a i3 a 3j + a i4 a 4 j i j i j A = = =
4 A A A = A = = k a 11 a 1 a 1 a A = 1 a a a 1 a a 1 = a 1t = a 11 + a 1 ++ a 1 t =1 = a t = a 1 + a ++ a t =1 = a t = a 1 + a ++ a t =
5 s = t t =1 = A 1 = a s1 = a 11 + a 1 ++ a 1 = a s = a 1 + a ++ a = a s = a 1 + a ++ a a st = a st t =1 t =1 = A A = ( 1) +1 ( 1) + ( 1) + 3 s = a st s t =1 t = a st t t =1 s = t t =1
6 a st = (s 1) + t s = a st = ((s 1) + t) = (s 1) + t =1 t =1 s = (s 1) + ( +1) ) = 3 ( 1) ( * t = a st = ((s 1) + t) = ( 1) + t * t = t =1 t =1 ( 1) + t) = 3 ( 1) ( + s = * t t =1 ( +1) + ( +1) + ( +1) = ( + +1) = ) = ( +1) = ( +1) C (,) (,) (A + B)C = AC + BC C (,) (,) A(B + C) = AB + BC A = [ aij ], B = [ b ij ], A + B = [ ij ] = [ a ij + b ij ], C = [ c ij ] {(A + B)C} ij = ik c kj = (a ik + b ik )c kj = (a ik c kj + b ik c kj ) = a ik c kj + b ik c kj = AC (A + B)C = AC + BC { } ij + { BC} ij A(B + C) = AB + BC
7 (,) (,) (,p) (AB)C = A(BC) A = a ij, B = b ij, AB = ij = a b is sj ( ), {(AB)C} ij = it c tj = a is b * + st -. c ), tj = a is b st c * + tj -. t=1 t=1 t=1 ), ), = a is b st c * + tj -. = a is b st c * + tj -. t=1 t=1 = { A(BC) } ij A = [ x 1 x x 3 ] A = x y c [ ] a c y 1 y y 3 0 a b A = 0 0 a a b x A = 0 0 a b y A = x 1 y 1 + x y + x 3 y 3 A = ax + cxy + by 0 0 a A = A = = O
8 E A = (E A)(E + A) E A 3 = (E A)(E + A + A ) (E A)(E + A) = E(E + A) A(E + A) = E + EA AE A = E + A A A = E A (E A)(E + A + A ) = E(E + A + A ) A(E + A + A ) = E + EA + EA AE A A 3 = E + A + A A A A 3 = E A 3 A + B = B + A AB BA (,) E Kroecker s delta ij = 1 0 i = j i j E = [ ij ] = 0 0 1
9 A E A = [ a ij ], E = ij AE = EA = ) AE = EA = A [ ] a ik kj ( ( = a i1 1j + a i j +a i j [ ] = [ a ij ] = A ik a kj ( ( = i1 a 1j + i a j + i a j [ ] = [ a ij ] = A X 1 0 X = X A = X = = (E + A) A = 0 0 0, A 3 = = O, A = O for ( x, y (x + y) = x k y (k, k k= 0 = k C k = ( ( k)k A,B (A + B) = A k B (k, k k= 0 = k C k = ( ( k)k
10 E A X = (E + A) = ) (E) (k A k = E + (1 A + 1 k ( (1) ( A + ca 3 + k= 0 = E + (1 A + 1 ( (1) ( A * (1 1 (-, ( (1) /, = 0 (1 /, /, 0 0 / +,./ A = 0 0 1, B = 0 1 0, X = A + B = AB = 0 0 0, BA = 0 0, A = 0 0 0, B = X = A + AB + BA + B = 0, X = A + AB + B = X = 0 1, X = 0, X 3 = 0 3 3, X 4 = (1 1 ( ( (1) X = 0 ( ( 1) ( ( +1) 1 1 ( +1) ( X +1 = X X = 0 1 ( ( ( 0 1 ( = 0 +1 ( +1) ( ( 0 0 ( 0 0 ( ( ( (
11 X = X = 0 a 1 a 13 a a 3 a a (1) a 1 a 13 a a 3 a a (1) = 0 0 * * * * * 0 0 * = = 1 X +1 = X 1 X = 0 a 1 a 13 a a 3 a a (1) * * * * * 0 0 * * * * * * X +1 = X 1 X = 0 0 * = X = X = O
12 A t A trasposed a 11 a 1 a 1 a A = 1 a a a 1 a a a 11 a 1 a 1 t a A = 1 a a a 1 a a (,) t ( t A) = A t (A + B)= t A+ t B t (A) = t A
13 (,) (,) t (AB)= t B t A A = [ a ij ], B = [ b ij ], a ij = A { } ij, b ij = { B} ij { t (AB)} = a jk b ki ij = b ki a jk = { t B} t A = t B t A ik t (AB)= t B t A k { } kj { } ij A= t A A = t A a 11 = a = = a = 0 a ii = a ii a ii = 0 AB= t (AB) AB= t (AB)= t B t A = BA AB = BA AB = BA AB = BA= t B t A= t (AB) AB= t (AB)
14 A = 1 (A+t A) + 1 (At A) P = 1 (A+t A), Q = 1 (At A) t P = 1 ( t A+ t ( t (A))) = 1 (A+t A) = P t Q = 1 ( t A t ( t (A))) = 1 (At A) = Q A = P + Q t A = t P+ t Q = P Q P = 1 (A+t A) Q = 1 (At A) A = 1 (A+t A) + 1 (At A) a 11 a 1 a 1 a 1 a a A = a 1 a a a 11 a 1 a 1 a A = 1 a a = a 1 a a = [ a 1 a a ] b 1 b b a 11 a 1 a a 1 = 1 a, a =,a = a 1 a b 1 = a 11 a 1 a 1 [ ] [ ] b = a 1 a a [ ] b = a 1 a a a 1 a a E = 0, e 1 =, e = 1,e =
15 (,) (,) B = [ b 1 b b ] AB = [ Ab 1 Ab Ab ] { AB} ij = a ik b kj [ Ab 1 Ab Ab ] ij = (Ab j ) i = a ik b kj AB = [ Ab 1 Ab Ab ]
行列代数2010A
a ij i j 1) i +j i, j) ij ij 1 j a i1 a ij a i a 1 a j a ij 1) i +j 1,j 1,j +1 a i1,1 a i1,j 1 a i1,j +1 a i1, a i +1,1 a i +1.j 1 a i +1,j +1 a i +1, a 1 a,j 1 a,j +1 a, ij i j 1,j 1,j +1 ij 1) i +j a
弾性定数の対称性について
() by T. oyama () ij C ij = () () C, C, C () ij ji ij ijlk ij ij () C C C C C C * C C C C C * * C C C C = * * * C C C * * * * C C * * * * * C () * P (,, ) P (,, ) lij = () P (,, ) P(,, ) (,, ) P (, 00,
II 2 3.,, A(B + C) = AB + AC, (A + B)C = AC + BC. 4. m m A, m m B,, m m B, AB = BA, A,, I. 5. m m A, m n B, AB = B, A I E, 4 4 I, J, K
II. () 7 F 7 = { 0,, 2, 3, 4, 5, 6 }., F 7 a, b F 7, a b, F 7,. (a) a, b,,. (b) 7., 4 5 = 20 = 2 7 + 6, 4 5 = 6 F 7., F 7,., 0 a F 7, ab = F 7 b F 7. (2) 7, 6 F 6 = { 0,, 2, 3, 4, 5 },,., F 6., 0 0 a F
linearal1.dvi
19 4 30 I 1 1 11 1 12 2 13 3 131 3 132 4 133 5 134 6 14 7 2 9 21 9 211 9 212 10 213 13 214 14 22 15 221 15 222 16 223 17 224 20 3 21 31 21 32 21 33 22 34 23 341 23 342 24 343 27 344 29 35 31 351 31 352
all.dvi
5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0
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
(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
![(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y](/thumbs/98/136512264.jpg "(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y")
(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
) 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
140 120 100 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
さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n
1 1.1 1.1.1 A 2 P Q 3 R S T R S T P 80 50 60 Q 90 40 70 80 50 60 90 40 70 8 5 6 1 1 2 9 4 7 2 1 2 3 1 2 m n m n m n n n n 1.1 8 5 6 9 4 7 2 6 0 8 2 3 2 2 2 1 2 1 1.1 2 4 7 1 1 3 7 5 2 3 5 0 3 4 1 6 9 1
(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
![(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y](/thumbs/101/151465237.jpg "(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y")
(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y
PSCHG000.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
(, Goo Ishikawa, Go-o Ishikawa) ( ) 1
(, Goo Ishikawa, Go-o Ishikawa) ( ) 1 ( ) ( ) ( ) G7( ) ( ) ( ) () ( ) BD = 1 DC CE EA AF FB 0 0 BD DC CE EA AF FB =1 ( ) 2 (geometry) ( ) ( ) 3 (?) (Topology) ( ) DNA ( ) 4 ( ) ( ) 5 ( ) H. 1 : 1+ 5 2
11夏特集号初校.indd
1 2 3 5 50 40 7 6 3 ABC 3 5 A 5% B C 100 3 1 2 3 A 5% 5% 5% B 10% 5% 0% C 20% 10% 15% A 15.8% 15.0% 0.8% B 15.5% 15.0% 0.5% C 12.2% 15.0% 2.8% 2,000 1,500 1,000 500 0 10% 5% 3% 1% 01 5 10 15 20 25 30
1. 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. +
+ 1 ( ) I IA i i i 1 n m a 11 a 1j a 1m A = a i1 a ij a im a n1 a nj a nm.....
+ http://krishnathphysaitama-uacjp/joe/matrix/matrixpdf 1 ( ) I IA i i i 1 n m a 11 a 1j a 1m A = a i1 a ij a im a n1 a nj a nm (1) n m () (n, m) ( ) n m B = ( ) 3 2 4 1 (2) 2 2 ( ) (2, 2) ( ) C = ( 46
A(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
ver Web
ver201723 Web 1 4 11 4 12 5 13 7 2 9 21 9 22 10 23 10 24 11 3 13 31 n 13 32 15 33 21 34 25 35 (1) 27 4 30 41 30 42 32 43 36 44 (2) 38 45 45 46 45 5 46 51 46 52 48 53 49 54 51 55 54 56 58 57 (3) 61 2 3
> > <., 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 >
2002.N.x.h.L.......g9/20
1 2 3 4 5 6 1 2 3 4 5 8 9 1 11 11 12 13 k 14 l 16 m 17 n 18 o 19 k 2 l 2 m 21 n 21 o 22 p 23 q 23 r 24 24 25 26 27 28 k 28 l 29 m 29 3 31 34 42 44 1, 8, 6, 4, 2, 1,2 1, 8 6 4 2 1, 8, 6, 4, 2, 1,2 1, 8
untitled
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/
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
HITACHI 液晶プロジェクター CP-AX3505J/CP-AW3005J 取扱説明書 -詳細版- 【技術情報編】
B A C E D 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 H G I F J M N L K Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01
A E A A A A E A E EAE EAE EA AE E AE E A AE EA AE EA AE EA AE EA AE EAE EAE EAE EAE E AE E A AE EA AE EAE E AE EA AE E AE E A AE E E A AE E E A AE EA
A E A A A A E A E EAE EAE EA AE E AE E A AE EA AE EA AE EA AE EA AE EAE EAE EAE EAE E AE E A AE EA AE EAE E AE EA AE E AE E A AE E E A AE E E A AE EA AE EAE EA E AE EA AE EA AE EAE E AE EAE E AE EA AE
取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ
B A C D E F K I M L J H G N O Q P Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01 00 00 60 01 00 BE EF 03 06 00 19 D3 02 00
<4D F736F F D2095BD90AC E937890B68A888F4B8AB E397C394EF82CC93AE8CFC82C98AD682B782E992B28DB895AA90CD2E646F6378>
29 5 IT 1,234 1,447 2,130 1,200 3,043 2 9,275 2,818 ICD-10 p.2 27 3 7,848 1,234 10 4,291 11.3% 10 33.3% 32.4%12.9% 32.2%26.9%18.5% 1,095 874 339 490 189 178 6,358 5,279 3,380 2,345 1,994 1,693 37.6 34.9
ad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign(
I n n A AX = I, YA = I () n XY A () X = IX = (YA)X = Y(AX) = YI = Y X Y () XY A A AB AB BA (AB)(B A ) = A(BB )A = AA = I (BA)(A B ) = B(AA )B = BB = I (AB) = B A (BA) = A B A B A = B = 5 5 A B AB BA A
1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :
9 ( ) 9 5 I II III A B (0 ) 5 I II III A B (0 ), 6 8 I II A B (0 ), 6, 7 I II A B (00 ) OAB A B OA = OA OB = OB A B : P OP AB Q OA = a OB = b () OP a b () OP OQ () a = 5 b = OP AB OAB PAB a f(x) = (log
０４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
HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語
A B C D E F G H I 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 K L J Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C RS-232C RS-232C Cable (cross) LAN cable (CAT-5 or greater) LAN LAN LAN LAN RS-232C BE
1 (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)
1,000 700-1 -
23 9 () - 0 - 1,000 700-1 - 2 3 ( 16:0017:00 ( 8:15 8:30 10:3010:50 8:00 8:10 8:10 9:30 11:0011:20 11:3015:30 16:0016:40 16:0016:10 16:50 21:00 4:00 4:006:00 6:00 6:1511:00 11:3012:00 12:3014:30 (1) ()
R 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
SO(2)
TOP URL http://amonphys.web.fc2.com/ 1 12 3 12.1.................................. 3 12.2.......................... 4 12.3............................. 5 12.4 SO(2).................................. 6
13,825,228 3,707,995 26.8 4.9 25 3 8 9 1 50,000 0.29 1.59 70,000 0.29 1.74 12,500 0.39 1.69 12,500 0.55 10,000 20,000 0.13 1.58 30,000 0.00 1.26 5,000 0.13 1.58 25,000 40,000 0.13 1.58 50,000 0.00 1.26
TOP URL 1
TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
... 1... 2... 9... 20... 23 - i - ... 30... 34... 38 - ii - - 1 - - 2 - - 3 - - 4 - - 5 - - 6 - - 7 - - 8 - - 9 - - 10 - 10 (A) (B) (A)(B) (C) (E) (C)(E) 16 3,096 3,700 6,796 975 5,821 17 3,002 4,082 7,084
EPSON 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
.1 A cos 2π 3 sin 2π 3 sin 2π 3 cos 2π 3 T ra 2 deta T ra 2 deta T ra 2 deta a + d 2 ad bc a 2 + d 2 + ad + bc A 3 a b a 2 + bc ba + d c d ca + d bc +
.1 n.1 1 A T ra A A a b c d A 2 a b a b c d c d a 2 + bc ab + bd ac + cd bc + d 2 a 2 + bc ba + d ca + d bc + d 2 A a + d b c T ra A T ra A 2 A 2 A A 2 A 2 A n A A n cos 2π sin 2π n n A k sin 2π cos 2π
untitled
351 351 351 351 13.0 0.0 25.8 1.0 0.0 6.3 92.9 0.0 80.5 0.0 1.5 15.9 0.0 3.5 13.1 0.0 30.0 54.8 18.0 0.0 27.5 1.0 0.0 2.5 94.7 0.0 91.7 0.0 1.3 14.7 0.0 3.8 14.4 0.0 25.0 50.5 16.0 0.0 27.5 2.0 0.0 2.5
H27 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
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
26 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
mogiJugyo_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/
1 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
untitled
18 18 8 17 18 8 19 3. II 3-8 18 9:00~10:30? 3 30 3 a b a x n nx n-1 x n n+1 x / n+1 log log = logos + arithmos n+1 x / n+1 incompleteness theorem log b = = rosário Euclid Maya-glyph quipe 9 number digits
2
2 3 4 5 6 4 2 2 2 7 17 10 FM7 11 generalist specialist specialist specialist 12 3 4 3 IC -- Win Win KJ 13 1955 14 1969 1999 32 20 2001 15 16 1 3 3 8 6 17 18 3 3 15 23 19 J () 20 5500 21 2000 23 () (KI)
漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト
https://www.hmg-gen.com/tuusin.html https://www.hmg-gen.com/tuusin1.html 1 2 OK 3 4 {a n } (1) a 1 = 1, a n+1 a n = 2 (2) a 1 = 3, a n+1 a n = 2n a n a n+1 a n = ( ) a n+1 a n = ( ) a n+1 a n {a n } 1,
2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l
ABCDEF a = AB, b = a b (1) AC (3) CD (2) AD (4) CE AF B C a A D b F E (1) AC = AB + BC = AB + AO = AB + ( AB + AF) = a + ( a + b) = 2 a + b (2) AD = 2 AO = 2( AB + AF) = 2( a + b) (3) CD = AF = b (4) CE
i I II I II II IC IIC I II ii 5 8 5 3 7 8 iii I 3........................... 5......................... 7........................... 4........................ 8.3......................... 33.4...................
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
1 2 3 4 5 1 1:30 NPO 16 1 19 16 2 17-6 - 10 2008 2010 120 150 IT( ) 60 21 40-7 - - 8-10 ( ) NPO 2 10 16:40-9 - 10 ii NPO NPO ( ) ( ) 11 12 13 14 15 22 26 27 28 29 30 31 32 33 34 m3 m3
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
/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
EPSON 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
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 -
EPSON 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
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%
Q1 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
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
198
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
1
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
05[ ]戸田(責)村.indd
![05[ ]戸田(責)村.indd](/thumbs/91/106164845.jpg "05[ ]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
, = = 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
( 9 1 ) 1 2 1.1................................... 2 1.2................................................. 3 1.3............................................... 4 1.4...........................................
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
AC-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
II
II 16 16.0 2 1 15 x α 16 x n 1 17 (x α) 2 16.1 16.1.1 2 x P (x) P (x) = 3x 3 4x + 4 369 Q(x) = x 4 ax + b ( ) 1 P (x) x Q(x) x P (x) x P (x) x = a P (a) P (x) = x 3 7x + 4 P (2) = 2 3 7 2 + 4 = 8 14 +
untitled
c 1. 2 2011 2012 0.248 0.252 1 Data Envelopment Analysis DEA 4 2 180 8633 3 3 1 IT DHARMA Ltd. 272 0122 1 14 12 13.10.7 14.5.27 DEA-AR (Assurance Region) 1 DEA 1 1 [1] 2011 2012 220 446 [2] 2. [2] 1 1
190 87 28 1 212 77 1777 77 219 1 171 28 201 1 1 16 102 17 10 1 16 99 1 1 1 1 960 1 1 1 1 1 2 168 1 12 2 18 100 2 1 6 1 61 7 16 18 20 2 961 2 11 6 2 6 6 0 17 86 1 2 16 1 1 9 2 1 1 1 1 1 1 0 2 17 16 6 1
v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) 3 R ij R ik = δ jk (4) i=1 δ ij Kronecker δ ij = { 1 (i = j) 0 (i
1. 1 1.1 1.1.1 1.1.1.1 v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) R ij R ik = δ jk (4) δ ij Kronecker δ ij = { 1 (i = j) 0 (i j) (5) 1 1.1. v1.1 2011/04/10 1. 1 2 v i = R ij v j (6) [
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...?
17 18 2
17 18 2 18 2 8 17 4 1 8 1 2 16 16 4 1 17 3 31 16 2 1 2 3 17 6 16 18 1 11 4 1 5 21 26 2 6 37 43 11 58 69 5 252 28 3 1 1 3 1 3 2 3 3 4 4 4 5 5 6 5 2 6 1 6 2 16 28 3 29 3 30 30 1 30 2 32 3 36 4 38 5 43 6
untitled
0. =. =. (999). 3(983). (980). (985). (966). 3. := :=. A A. A A. := := 4 5 A B A B A B. A = B A B A B B A. A B A B, A B, B. AP { A, P } = { : A, P } = { A P }. A = {0, }, A, {0, }, {0}, {}, A {0}, {}.
!!! 10 1 110 88 7 9 91 79 81 82 87 6 5 90 83 75 77 12 80 8 11 89 84 76 78 85 86 4 2 32 64 10 44 13 17 94 34 33 107 96 14 105 16 97 99 100 106 103 98 63 at 29, 66 at 58 12 16 17 25 56
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 ) i ii i ii 45 46 47 2 48 49 50 51 52 53 54 55 56 57 58
untitled
i ii (1) (1) (2) (1) (3) (1) (1) (2) (1) (3) (1) (1) (2) (1) (3) (2) (3) (1) (2) (3) (1) (1) (1) (1) (2) (1) (3) (1) (2) (1) (3) (1) (1) (1) (2) (1) (3) (1) (1) (2) (1) (3)
23 15961615 1659 1657 14 1701 1711 1715 11 15 22 15 35 18 22 35 23 17 17 106 1.25 21 27 12 17 420,845 23 32 58.7 32 17 11.4 71.3 17.3 32 13.3 66.4 20.3 17 10,657 k 23 20 12 17 23 17 490,708 420,845 23
