Size: px
Start display at page:

Download ""

Transcription

1

2

3 causs # & /) & = k'"( 1+ (2n)!/o!') rod p, (16v.),p=4n+l,n=l-2500

4 provtbility p e 3n:+3n+l y'= x1k Cruss P-n1l y' = x,+k

5

6 2nl.2r+y t -y, -xx-21+ y t+ y - lt -

7 y1 = z1+ (x1-2) z+ I (rr z"+ t, n = ^ 6

8 f(x) = D., ax = a,+a,x+tux,+... +r,ix',+&,,x"1 f(x) [ql (x) = ( l-x'') (f,,.",."/ ( l-q'x) +a",) eigen value eigen vectors [-r, l, l, r, o] [o,o.o.o. r] [0, -r, o l, o] cigcn valuc [-r, r, r, t, o] [o,o,o,o,r]

9 value projector ( l+tx-xl-rx!) /4 focl, sensc hop, will family of curvas polynomial Euler,'= 1(x,+qx+r) y'=x(x-l)(x{) F (tn,tn,t,x) P ' 4n+l p - 4n-l

10

11

12

13

14 I I r.. I 0 I p p' d' o t p'... p'..p'''" o I pp'p:'rr'.. pd,fr 0 I00..0-r

15

16

17 0, l, 0, 0, 0, x',0,0,0, x',0,0 l,0,0, 0, 0, 0, l, 0,0,0,0,0 0, l, 0, 0, 0, 0, 0, x,0,0,0,0 0, 0, r, 0, 0, 0, 0, 0, x2, 0, 0,0 0, 0. 0, I, 0, 0, 0, 0, 0, xr, 0,0 0, 0, 0, 0, r, 0, 0, 0, 0, 0, xr,0 0, 0, 0, 0, 0, l, 0, 0, 0, 0, 0, x' l,0,0, 0,0,0. x'. 0. 0, 0, , l, 0, 0, 0, 0, 0, x',0,0,0,0 0, 0. l, 0, 0, 0, 0, 0, xr, 0, 0,0 0, 0, 0, l, 0, 0, 0, 0, 0, x',0,0 0, 0, 0, 0, r, 0, 0, 0, o, 0, x'd, 0 0, 0, 0, 0, 0, l, 0, 0, 0, 0, 0, x" r, 0, 0, 0, 0, 0, l, 0, 0, 0, 0, 0 0, l, 0, 0, 0, 0, 0, x',0, o,0,0 0, 0, l, 0, 0, 0, 0, 0, x', 0, 0.0 I, 0, 0, 0, 0, 0, x', 0, O, 0, 0,0 0, l, 0, 0, 0, 0. 0, xr,0, 0, 0,0 0, 0, l. 0, 0, 0. 0,0, xro, , 0, 0, l,0,0,0,0.0. r,0,0 0, 0, 0, 0, t, 0, 0, 0, 0, 0, x:,0 0, 0, 0, 0, 0, l, 0, 0, 0. 0,0. x' 0, 0, 0, t. 0, 0, 0, 0, 0, x'. 0, o 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, x" 0 0, 0, 0, 0, 0, r, 0, 0, 0, 0, 0, x' 0, r,0, 0,0, x',0,0,0. x' , 0, l,0.0.0, r,0,0,0, t,0 0, 0, l, 0,0,0, x',0,0,0, xr,0 0, 0, l, 0, 0,0, x',0,0,0, xr,0 0, 0, 0, t, 0,0,0, l, 0, 0, 0, t 0, 0, 0, 1, 0, 0, 0, x',0,0,0, xl 0, 0, 0, l, 0, 0, 0, x',0,0,0, x' B,- l, 0, 0, 0, t, 0, 0, 0, l, 0,0,0 0, l, 0, 0, 0, xr,0,0, O, x',0,0 l, 0, 0, 0, x', 0,0, 0, xt, O, O, O 0, l, 0, 0, 0, x',0,0,0, 1.0,0 l, 0, 0, 0, xr,0, 0, 0, xr. 0. O. O 0, 1, 0, 0, 0, x'",0.0.0, x'.0,0 0, 0, l,0,0,0, r,0,0,0, l,0

18 0, 0, 0, 1,0,0,0, x',0,0,0, x' 0, 0, 1, 0, 0, 0, x',0,0,0, x',0 0, 0, 0, l, 0, 0, 0, x",0,0,0, I 0, 0, l, 0, 0, 0, x', 0, 0, 0, x', 0 0, 0, 0, l, 0, 0, 0, xro,0,0,0, x' c,= r, 0, 0, 0, 0, 0, l,0,0,0,0,0 0, I,0,0,0,0,0, x', 0, 0, 0, 0 l, 0, 0, 0, 0, 0, x!,0,0,0,0,0 0, 1, 0, 0, 0, 0, 0, x",0,0,0,0 0, 0, t, 0, 0, 0, 0, 0, 1, 0,0,0 0, 0, 0, r, 0,0, 0,0, 0, xr, o, 0 0, 0, r, 0, 0, 0, 0, 0, x" 0,0,0 0, 0, 0, 1,0,0,0,0,0, xt,0,0 0, 0, 0, 0, 1, 0, 0 0,0, 0, 1, 0 0, 0, 0, 0, 0, t, 0, 0, x' 0, 0, 0, 0, t, 0, 0,0, 0, 0, x" 0 0, 0, 0, 0, 0, t, 0, 0, 0, 0, 0, x' Cr= l, 0, 0, 0, 0, 0, r, 0, 0, 0, 0, 0 l, 0, 0, 0, 0, 0, x',0, 0, 0, 0, 0 0, t, 0, 0, 0,0, 0, t,0, 0, 0, 0 0, l, 0, 0, 0, 0, O, xd, 0,0, 0,0 0, 0, r, 0, 0, 0,0, 0, r, 0, 0, 0 0, 0, l, 0, 0, 0, 0, 0, x" 0,0,0 l, 0, 0, 0, l, 0, 0, 0, 1, 0, 0,0 0, l, 0, 0, O, x, 0, 0, 0, x1, O, O 0, 0, 1,0, 0, 0, x':, 0,0,0, x', 0 0, 0, 0, 1,0,0,0, x.,0,0,0, x' l, 0, 0, 0, x',0,0,0, x',0,0,0 0, l, 0, o, 0, x', 0, 0, o, x'", 0,0 0, 0, 1.0.0,0, x'.0,0,0, r,0 0, 0, 0, I, O, O, O, x', 0, 0, 0, x' l, 0, 0, 0, x',0, 0, 0, x', 0, 0, 0 0, l,0, 0,0, x", 0, 0, 0, x" 0, 0 0, 0, 0, r, 0, 0, 0, 0,0, t, 0, 0 0, 0, 0, l,0,0, 0, 0,0. x" , 0, 0, 0,!,0, 0, 0, 0, 0. l. 0 0,0,0,0, l,0,0,0,0,0, x" 0 0, q 0, 0, 0, 1,0, 0, 0, 0, 0, I 0, 0, 0, 0, 0, t, 0.0, 0, 0, Q x'

19 Euclid-Vandcmonde factorization theorcn t-et V - (x"), and x'-l = 0, xtu (n. > I ) b ary r pr sentation of n 'lhen there cxisr degr e n natrix A,, A,,.,A' such thar A,A,.. Au * 'A,. 'A,'A, = V, non zero elcntcnls in each row and column ofa, are n,

20 ij = i(j,xsxaxl+ j,xax3+jrx3+j,) mod n t95,4,31 t85,4,31 tz,ss:l 192,s,31 iz,s,lfll

21

II

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 +

More information

SOWC04....

SOWC04.... 99 100 101 2004 284 265 260 257 235 225 222 211 207 205 200 197 192 190 183 183 183 183 180 176 171 169 166 165 156 152 149 143 141 141 138 138 136 126 126 125 123 123 122 118 110 109 108 107 107 105 100

More information

2012 A, N, Z, Q, R, C

2012 A, N, Z, Q, R, C 2012 A, N, Z, Q, R, C 1 2009 9 2 2011 2 3 2012 9 1 2 2 5 3 11 4 16 5 22 6 25 7 29 8 32 1 1 1.1 3 1 1 1 1 1 1? 3 3 3 3 3 3 3 1 1, 1 1 + 1 1 1+1 2 2 1 2+1 3 2 N 1.2 N (i) 2 a b a 1 b a < b a b b a a b (ii)

More information

A A = a 41 a 42 a 43 a 44 A (7) 1 (3) A = M 12 = = a 41 (8) a 41 a 43 a 44 (3) n n A, B a i AB = A B ii aa

A A = a 41 a 42 a 43 a 44 A (7) 1 (3) A = M 12 = = a 41 (8) a 41 a 43 a 44 (3) n n A, B a i AB = A B ii aa 1 2 21 2 2 [ ] a 11 a 12 A = a 21 a 22 (1) A = a 11 a 22 a 12 a 21 (2) 3 3 n n A A = n ( 1) i+j a ij M ij i =1 n (3) j=1 M ij A i j (n 1) (n 1) 2-1 3 3 A A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33

More information

1 1 n 0, 1, 2,, n n 2 a, b a n b n a, b n a b (mod n) 1 1. n = (mod 10) 2. n = (mod 9) n II Z n := {0, 1, 2,, n 1} 1.

1 1 n 0, 1, 2,, n n 2 a, b a n b n a, b n a b (mod n) 1 1. n = (mod 10) 2. n = (mod 9) n II Z n := {0, 1, 2,, n 1} 1. 1 1 n 0, 1, 2,, n 1 1.1 n 2 a, b a n b n a, b n a b (mod n) 1 1. n = 10 1567 237 (mod 10) 2. n = 9 1567 1826578 (mod 9) n II Z n := {0, 1, 2,, n 1} 1.2 a b a = bq + r (0 r < b) q, r q a b r 2 1. a = 456,

More information

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy

More information

0181898_dks-NONIONIC.indd

0181898_dks-NONIONIC.indd NONIONIC SURFACTANTS LF-40X 12.4 20 31.3 21 3 1 LF-41X 12.8 28 29.9 20 9 2 LF-42X 13.0 34 28.9 14 18 3 LF-40X LF-41X LF-42X 0 S-90 13.6 67 28.3 18 120 92 X-140 14.4 82 20 37.3 200 115 60 S-90 X-140 EA-017

More information

198 Column 1 201512/1-20164/30 Column 1 199 201512/1-20164/30 12/1-4/30 Coupon 2015 2016 1 12 2 3 4

198 Column 1 201512/1-20164/30 Column 1 199 201512/1-20164/30 12/1-4/30 Coupon 2015 2016 1 12 2 3 4 198 Column 1 201512/1-20164/30 Column 1 199 201512/1-20164/30 12/1-4/30 Coupon 2015 2016 1 12 2 3 4 201512/1-20164/30 201512/1-20164/30 12 1 2 3 4 12 1 2 3 4, 201 200 202 201512/1-20164/30, 1 12 2 3 4

More information

FX ) 2

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

More information

程蘊(ていうん).indd

程蘊(ていうん).indd 1963 1964 3 1963 1 2 3 1 2 3 1963 1964 1962 LT 1963 4 5 9 30 6 7 10 8 9 10 26 10 10 27 11 12 13 14 15 1 2 34 16 1963 10 7 17 18 19 10 8 20 8 9 10 16 21 22 17 22 10 24 23 10 27 24 28 25 30 26 27 11 20 UNHCR

More information

1. 52

1. 52 51 1. 52 5 2. 1 2 54 4 55 5 1 56 2 57 . 1 1 58 2 1 59 2 4 60 61 62 6 64 4. 65 66 67 5 1 2 4 68 1 69 2 70 1 2 71 72 1 2 7 1 2 74 75 1 76 2 77 1 2 78 4 79 5 80 6. 1 81 2 82 8 84 85 86 87 7. 88 89 8. column

More information

1 2 2 36 8 1212 15 16 20 22 24 26 28 8 14 21 1 31 32 32 3335 37 39 43 45 48 49 5051 54 56 58 6264 6669 43 50 58 2 73 74 7779 8183 85 88 91 93 9698 100 102103 74 85 93 106 106 108 110 112 3 115 116 116

More information

W810 QX100 QX30 QX10 W810 QX100 QX30 QX10 RX100 RX100 WX500 WX350 RX100 RX100 HX400V HX90V HX60V RX100 RX100 RX100 RX100 HX400V HX90V HX60V WX500 WX350 RX100 RX100 WX500 WX350 RX100 RX100 HX400V HX90V

More information

1 2

1 2 1 2 4 3 5 6 8 7 9 10 12 11 0120-889-376 r 14 13 16 15 0120-0889-24 17 18 19 0120-8740-16 20 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58

More information

3 5 6 7 7 8 9 5 7 9 4 5 6 6 7 8 8 8 9 9 3 3 3 3 8 46 4 49 57 43 65 6 7 7 948 97 974 98 99 993 996 998 999 999 4 749 7 77 44 77 55 3 36 5 5 4 48 7 a s d f g h a s d f g h a s d f g h a s d f g h j 83 83

More information

a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p

a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p a a a a y y ax q y ax q q y ax y ax a a a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p y a xp q y a x p q p p x p p q p q y a x xy xy a a a y a x

More information

200608094-101

200608094-101 94 A O D 1 A 1 A A 1 AO 1 95 A OA 1 a r A A 1 r A R 1 A R 1 A R 1 a a A OA R 1 96 F AO 1 A O 1 A 1 A O 1 A 1 O A 1 97 b O AO 1 O AO 1 A 1 A OA 1 AO 1 AA 1 98 A AO 1 A AO 1 b b 1 b b B B A 1 Q 1 rr 1 99

More information

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

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

More information

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

A11 (1993,1994) 29 A12 (1994) 29 A13 Trefethen and Bau Numerical Linear Algebra (1997) 29 A14 (1999) 30 A15 (2003) 30 A16 (2004) 30 A17 (2007) 30 A18

A11 (1993,1994) 29 A12 (1994) 29 A13 Trefethen and Bau Numerical Linear Algebra (1997) 29 A14 (1999) 30 A15 (2003) 30 A16 (2004) 30 A17 (2007) 30 A18 2013 8 29y, 2016 10 29 1 2 2 Jordan 3 21 3 3 Jordan (1) 3 31 Jordan 4 32 Jordan 4 33 Jordan 6 34 Jordan 8 35 9 4 Jordan (2) 10 41 x 11 42 x 12 43 16 44 19 441 19 442 20 443 25 45 25 5 Jordan 26 A 26 A1

More information

2016 3/1-7/31 2016 3/1-7/31 Column 1 P, 263 262

2016 3/1-7/31 2016 3/1-7/31 Column 1 P, 263 262 2016 3/1-7/31 2016 3/1-7/31 Column 1 P, 263 262 2016 3/1-7/31 2016 3/1-7/31,,, 265 264 2016 3/1-7/31 2016 3/1-7/31 Column 2,, 3/21, 3/21 3/21, 3/27, 267 266 3/1-7/31 2016 3/1-7/31 2016 3/1-7/31,, 269 268

More information

308 ( ) p.121

308 ( ) p.121 307 1944 1 1920 1995 2 3 4 5 308 ( ) p.121 309 10 12 310 6 7 ( ) ( ) ( ) 50 311 p.120 p.142 ( ) ( ) p.117 p.124 p.118 312 8 p.125 313 p.121 p.122 p.126 p.128 p.156 p.119 p.122 314 p.153 9 315 p.142 p.153

More information

日経テレコン料金表(2016年4月)

日経テレコン料金表(2016年4月) 1 2 3 4 8,000 15,000 22,000 29,000 5 6 7 8 36,000 42,000 48,000 54,000 9 10 20 30 60,000 66,000 126,000 166,000 50 100 246,000 396,000 1 25 8,000 7,000 620 2150 6,000 4,000 51100 101200 3,000 1,000 201

More information

73 p.1 22 16 2004p.152

73 p.1 22 16 2004p.152 1987 p.80 72 73 p.1 22 16 2004p.152 281895 1930 1931 12 28 1930 10 27 12 134 74 75 10 27 47.6 1910 1925 10 10 76 10 11 12 139 p.287 p.10 11 pp.3-4 1917 p.284 77 78 10 13 10 p.6 1936 79 15 15 30 80 pp.499-501

More information

122011pp.139174 18501933

122011pp.139174 18501933 122011pp.139174 18501933 122011 1850 3 187912 3 1850 8 1933 84 4 1871 12 1879 5 2 1 9 15 1 1 5 3 3 3 6 19 9 9 6 28 7 7 4 1140 9 4 3 5750 58 4 3 1 57 2 122011 3 4 134,500,000 4,020,000 11,600,000 5 2 678.00m

More information

2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226. 1893 B pp. 1 2. p. 3.

2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226. 1893 B pp. 1 2. p. 3. 1 73 72 1 1844 11 9 1844 12 18 5 1916 1 11 72 1 73 2 1862 3 1870 2 1862 6 1873 1 3 4 3 4 7 2 3 4 5 3 5 4 2007 p. 117. 2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226.

More information

29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23

29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23 29 2011 3 pp.55 86 19 1886 2 13 1 1 21 1888 1 13 2 3,500 3 5 5 50 4 1959 6 p.241 21 1 13 2 p.14 1988 p.2 21 1 15 29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23 1

More information

Microsoft Word - 映画『東京裁判』を観て.doc

Microsoft Word - 映画『東京裁判』を観て.doc 1 2 3 4 5 6 7 1 2008. 2 2010, 3 2010. p.1 4 2008 p.202 5 2008. p.228 6 2011. 7 / 2008. pp.3-4 1 8 1 9 10 11 8 2008, p.7 9 2011. p.41 10.51 11 2009. p. 2 12 13 14 12 2008. p.4 13 2008, p.7-8 14 2008. p.126

More information

() L () 20 1

() L () 20 1 () 25 1 10 1 0 0 0 1 2 3 4 5 6 2 3 4 9308510 4432193 L () 20 1 PP 200,000 P13P14 3 0123456 12345 1234561 2 4 5 6 25 1 10 7 1 8 10 / L 10 9 10 11 () ( ) TEL 23 12 7 38 13 14 15 16 17 18 L 19 20 1000123456

More information

戦後の補欠選挙

戦後の補欠選挙 1 2 11 3 4, 1968, p.429., pp.140-141. 76 2005.12 20 14 5 2110 25 6 22 7 25 8 4919 9 22 10 11 12 13 58154 14 15 1447 79 2042 21 79 2243 25100 113 2211 71 113 113 29 p.85 2005.12 77 16 29 12 10 10 17 18

More information

17 17 17 17 11 21 28 1 24 12 36 2,000 2 22 11 3.67 3.38 22 2.97 21 10 1.7 1.12 22 10 13 2.75 11 10 15 24 10 12 14 3 17 17 2006 4 17 10 24 12 17 5 15 17 17 11 40 6 17 40 17 11 7 24 17 24 17 8 40 17 17 9

More information

untitled

untitled ,337 37 35 0,349,09 35 55 988 3 0 0 3,387 7 90 0,369,46 5 57 5 0 90 38 8,369 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 0 3 4 5 6 8 9 30 3 3 5,400 7,00 9,000 0,800,600 4,400 6,00 8,000 9,800,600 3,400 5,00 7,000 8,800

More information

,877 61,524 33, ,292, ,653 57,601 95,188 2,416 1,767,

,877 61,524 33, ,292, ,653 57,601 95,188 2,416 1,767, 02 02 02 180,771 07 02 01 1,377 07 02 02 1,051,703 07 02 05 220,099 07 03 01 926,597 08 02 04 1,877,566 08 04 02 2,973,603 08 05 03 672,950 10 06 03 778,433 10 06 04 735,789 10 06 06 225,392 10 06 07 365,442

More information

PowerPoint Presentation

PowerPoint Presentation 2 9/ 3 3 9/ 9 4 5 , PR () 6 ,,, (11) 7 PR 8 9 10 11 TEL. 106 8/131512/291/3 TEL. 107 12/291/3 12 http://www.f-turn.jp/ 13 21 4 21 14 200910 U 200911 U 200911 20102 15 20102 PR 20103 20103 16 20103 20104

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

P.3 P.4 P.9 P.11

P.3 P.4 P.9 P.11 MOST is the best! P.3 P.4 P.9 P.11 P. P.6 P.7 P.8 P.19 P.14 1 2 P.14 1 2 12,036 P.14 4 13,40 P.14 3 P.12P.14 P.12P.14 6 P.12 P.1 7 P.1 7 P.1 8 P.1 9 P.16 11 P.12 P.1 P.1 P.16 12 P.16 13 P.16-13 P.12 P.16

More information

JIS Z803: (substitution method) 3 LCR LCR GPIB

JIS Z803: (substitution method) 3 LCR LCR GPIB LCR NMIJ 003 Agilent 8A 500 ppm JIS Z803:000 50 (substitution method) 3 LCR LCR GPIB Taylor 5 LCR LCR meter (Agilent 8A: Basic accuracy 500 ppm) V D z o I V DUT Z 3 V 3 I A Z V = I V = 0 3 6 V, A LCR meter

More information

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4 20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d

More information

?

? 240-8501 79-2 Email: nakamoto@ynu.ac.jp 1 3 1.1...................................... 3 1.2?................................. 6 1.3..................................... 8 1.4.......................................

More information

ii-03.dvi

ii-03.dvi 2005 II 3 I 18, 19 1. A, B AB BA 0 1 0 0 0 0 (1) A = 0 0 1,B= 1 0 0 0 0 0 0 1 0 (2) A = 3 1 1 2 6 4 1 2 5,B= 12 11 12 22 46 46 12 23 34 5 25 2. 3 A AB = BA 3 B 2 0 1 A = 0 3 0 1 0 2 3. 2 A (1) A 2 = O,

More information

newmain.dvi

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

More information

2Column / / / /31 3,, Column , /1-1/ Coupon

2Column / / / /31 3,, Column , /1-1/ Coupon 2Column 1 20159/1-20161/31 20159/1-20161/31 3,, Column 1 9 10 11 12 1, 2015 9/1-1/31 2016 Coupon 4 20159/1-20161/31 20159/1-20161/31 Column 2 5, 9/27, 10/12, Column 2 9/27, 10/12, 6 20159/1-20161/31 20159/1-20161/31

More information

XX data 03.xls sheet(1) data 03.xls sheet(1) 2 1. n 1 2. m 1 3. O 11 O

XX data 03.xls sheet(1) data 03.xls sheet(1) 2 1. n 1 2. m 1 3. O 11 O 1 5 2017 5 8 4 : website: email: http://www3.u-toyama.ac.jp/kkarato/ kkarato@eco.u-toyama.ac.jp 1 2 1.1............................. 2 1.2 IF.................................... 3 1.3...............................

More information

J1-a.dvi

J1-a.dvi 4 [ ] 4. ( ) (x ) 3 (x +). f(x) (x ) 3 x 3 3x +3x, g(x) x + f(x) g(x) f(x) (x 3)(x +)+x+ (x 3)g(x)+x+ g(x) r(x) x+ g(x) x (x+)+ x r(x)+ g(x) x x 4x+5 r(x) g(x) x (f(x) (x 3)g(x)) g(x) x f(x) f(x)g(x) 4

More information

??

?? ( ) 2014 2014 1/119 = (ISS) ISS ISS ISS iss-clf iss-clf ISS = (ISS) FB 2014 2/119 = (ISS) ISS ISS ISS iss-clf iss-clf ISS R + : 0 K: γ: R + R + K γ γ(0) = 0 K : γ: R + R + K γ K γ(r) (r ) FB K K K K R

More information

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

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

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

13 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

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

More information

109

109 108 1 2 3 109 110 111 112 1 c c < c c< B N a d 1 2 3 5 8 9 0 ; 2c< rc a h 3c 113 1p 2c< 3c< a r 4cc 1p 2 c 3c< c p a c 4p 5 c rr c c Cr m e 114 1 c c < c< B N d a 1 3 5 9 0 ; 2c< B ; p c< BN50; ar h 3c

More information

1 UTF Youtube ( ) / 30

1 UTF Youtube ( ) / 30 2011 11 16 ( ) 2011 11 16 1 / 30 1 UTF 10 2 2 16 2 2 0 3 Youtube ( ) 2011 11 16 2 / 30 4 5 ad bc = 0 6 7 (a, b, a x + b y) (c, d, c x + d y) (1, x), (2, y) ( ) 2011 11 16 3 / 30 8 2 01001110 10100011 (

More information

14 (x a x x a f(x x 3 + 2x 2 + 3x + 4 (x 1 1 y x 1 x y + 1 x 3 + 2x 2 + 3x + 4 (y (y (y y 3 + 3y 2 + 3y y 2 + 4y + 2 +

14 (x a x x a f(x x 3 + 2x 2 + 3x + 4 (x 1 1 y x 1 x y + 1 x 3 + 2x 2 + 3x + 4 (y (y (y y 3 + 3y 2 + 3y y 2 + 4y + 2 + III 2005 1 6 1 1 ( 11 0 0, 0 deg (f(xg(x deg f(x + deg g(x 12 f(x, g(x ( g(x 0 f(x q(xg(x + r(x, r(x 0 deg r(x < deg g(x q(x, r(x q(x, r(x f(x g(x r(x 0 f(x g(x g(x f(x g(x f(x g(x f(x 13 f(x x a q(x,

More information

kou05.dvi

kou05.dvi 2 C () 25 1 3 1.1........................................ 3 1.2..................................... 4 1.3..................................... 7 1.3.1................................ 7 1.3.2.................................

More information

(check matrices and minimum distances) H : a check matrix of C the minimum distance d = (the minimum # of column vectors of H which are linearly depen

(check matrices and minimum distances) H : a check matrix of C the minimum distance d = (the minimum # of column vectors of H which are linearly depen Hamming (Hamming codes) c 1 # of the lines in F q c through the origin n = qc 1 q 1 Choose a direction vector h i for each line. No two vectors are colinear. A linearly dependent system of h i s consists

More information

LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University

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

More information

¹₄ ³₈ ³₈ ¹₂ ¹₂ ¹₂ ³₄ ³₄

¹₄ ³₈ ³₈ ¹₂ ¹₂ ¹₂ ³₄ ³₄ 33 4 5 2 63 2 1 3 1 4 2 5 6 19 ¹₄ ³₈ ³₈ ¹₂ ¹₂ ¹₂ ³₄ ³₄ 1 1 5 6 6 7 1 1 1 1 1 1 35 GDC LB 1 1 Y 2 A54 2 1 2 1 1 5 1 1 21 1 2 2 2 53 512 53 53 512 3 12 2 2 4 5 63 1 1 2 4 5 63 1 1 2 45 1 5 2 3 4 4 3 4 4

More information

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

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

More information

25 7 18 1 1 1.1 v.s............................. 1 1.1.1.................................. 1 1.1.2................................. 1 1.1.3.................................. 3 1.2................... 3

More information

( [1]) (1) ( ) 1: ( ) 2 2.1,,, X Y f X Y (a mapping, a map) X ( ) x Y f(x) X Y, f X Y f : X Y, X f Y f : X Y X Y f f 1 : X 1 Y 1 f 2 : X 2 Y 2 2 (X 1

( [1]) (1) ( ) 1: ( ) 2 2.1,,, X Y f X Y (a mapping, a map) X ( ) x Y f(x) X Y, f X Y f : X Y, X f Y f : X Y X Y f f 1 : X 1 Y 1 f 2 : X 2 Y 2 2 (X 1 2013 5 11, 2014 11 29 WWW ( ) ( ) (2014/7/6) 1 (a mapping, a map) (function) ( ) ( ) 1.1 ( ) X = {,, }, Y = {, } f( ) =, f( ) =, f( ) = f : X Y 1.1 ( ) (1) ( ) ( 1 ) (2) 1 function 1 ( [1]) (1) ( ) 1:

More information

AS1161 : K21

AS1161 : K21 2012 AUTUMN & WINTER CATALOG AS1161 : K21 AS3432 : A28 AS1157 : S83 AS1842 : K23 AS3433 : K25 AS1953 : A28 AS1730 : K25 AS3435 : K27 AS3434 : S83 AS3431 : N27 AS1159 : L04 AX1029 : C02 RX0044 : W06 AX1031

More information