168. W rdrop. W rdrop ( ).. (b) ( ) OD W rdrrop r s x t f c q δ, 3.4 ( ) OD OD OD { δ, = 1 if OD 0
|
|
- みさえ すえたけ
- 5 years ago
- Views:
Transcription
1 167 p (n) im p(n+1) im p (n+1) im p(n) im < ε (3.264) ε p (n+1) im 1 4 [1],, :, Vol.43, pp.14-21, [2] Rust, J., Optiml Replcement of GMC Bus Engines: An Empiricl Model of Hrold Zurcher, Econometric, Vol.55,pp , [3] Hotz, V. J., nd R. A. Miller, Conditionl Choice Probbilities nd the Estimtion of Dynmic Models, Review of Economic Studies, Vol.60, pp , 1993 [4] V,Aguirregbiri., P,Mir., Swpping the Nested Fixed Point Algorithm: A Clss of Estimto for Discrete Mrov Decision Models ().. TDM ITS.
2 168. W rdrop. W rdrop ( ).. (b) ( ) OD W rdrrop r s x t f c q δ, 3.4 ( ) OD OD OD { δ, = 1 if OD 0
3 W rdrop (3.65). ( c u ) 0 c u = 0 (3.265) u OD. (3.65). OD q x. (3.66). min z (x) = x 0 t (ω) dω (3.266) x x = (..., x...). (3.70) (3.71). f = q (3.267) f 0 (3.268) (3.72) (3.73). x = r f δ, (3.269) s c = t δ, (3.270) (3.72) OD (3.73).
4 170 (c) (3.66) (3.70) (3.73). L (f, u) = z [x (f)] + u ( q f ) (3.271) f f = (..., f,...). u OD u = (..., u,...). (3.71). (3.73) (3.272). f L (f, u) = 0 nd f L (f, u) f 0 (3.272) (3.273). L (f, u) u = 0 (3.273) (3.273) (3.70) f (3.274). f mn l L (f, u) = f mn l z [x (f)] + f mn l (3.274) (3.275). ( u q ) f (3.274) f mn l z [x (f)] = z (x) x b x b f mn l (3.275) (3.275). (3.276). z (x) x b = x b x 0 t (ω) dω = t b (3.276)
5 (refue5) (3.275) (3.277). x b f mn l = δ mn b,l (3.277) (3.276) (3.277) (3.275) (3.73) (3.278). z [x (f)] f mn l b t b δ mn b,l = c mn l (3.278) OD mn l. (3.274). (3.279). f f mn l = { 1 if r = m, s = n nd = l 0 (3.279) q u fl mn. (3.274) (3.280) f mn l ( u q f ) = u mn (3.280) (3.278) (3.280) (3.274) (3.281). f mn l L (f, u) = c mn l u mn (3.281) (3.281) (3.272) (3.273) (3.71) (3.282). ( f c u ) = 0 c u 0 f = q f 0 (3.282) (3.282) (3.66) (3.70) (3.71).
6 () W rdrop. W rdrop. W rdrop. W rdrop... (3.283) (3.285). min z (x) = x t (x ) (3.283) (b) f = q (3.284) f 0 (3.285). ( ) q = 6. (3.286).
7 t 1 [x 1 ] = 50 + x 1 t 2 [x 2 ] = 50 + x 2 t 3 [x 3 ] = 10x 3 (3.286) t 4 [x 4 ] = 10x O 1 4 D O 3 2 D = (3.287). t 5 = 10 + x 5 (3.287) O 1 4 D O 3 2 D O D ()...
8 : 3.66 :. W rdrop... (b) ( )..OD V (3.288). V = c (3.288)
9 OD K P P (3.289). = exp ( ) θ c exp ( θ c ) (3.289) K θ. θ. θ θ. OD f f (3.291). = q P = q exp ( ) θ c exp ( θ c ) (3.290) K (3.291) (3.292). min z (x) = x 0 t (ω) dω Ω 1 θ q K ( f ln f ) q q (3.291) f K = q f 0 (3.292) Ω OD. (3.293). x = Ω f K δ, (3.293)
10 F rn W olfe. () F rn W olfe F rn W olfe.. u n n OD. 0: x 0 = 0 t0. ll or nothing ( 0 ) ( )x 1. n = 1. 1: x n tn. OD u n. 2: t n OD y n.dn = yn xn d n. 3: (3.294) x n+1 (3.66) α n. (3.295) α n. α n x n+1
11 t n+1 u n+1. OD x n+1 = x n + αn d n = x n + αn ( y n xn ) (3.294) min 0 α 1 4: x n +αn (y n xn ) 0 t (ω) dω (3.295) (3.296) ( ) n = n x n+1. (3.296) κ. u n+1 u n u n+1 κ (3.296) F rn W olfe. (MSA; MethodofSuccessiveAverges) SimplicilDecomposition. ().. (Dil )..
12 178 0: x 0 = 0 t0. ( )x 1. n = 1. 1: x n tn. 2: t n OD y n.dn = yn xn d n. 3: α n (3.297). (3.294) x n+1. t n+1 4: α n = 1 n + 1 (3.297). (3.298) ( ) n = n x n+1. (3.298) κ. ( x n+1 x n x n x n (3.299). ) 2 < κ (3.298) x n = xn + xn 1 + x n x n m+1 m (3.299)
13 n n x n n + 1 xn+1. (3.299) m. (b) (=).. (3.291) 2 ( ) (3.300). ) q ( f q ln f q Ω K = { x r ln xr + ( ) ( ln r R j N I j x r I j x r )} (3.300) x r ( r ) R N I j j. (3.300).. 0: x 0 = 0 t0. OD ( )x r,1 n = 1.. 1: x n = tn. r R x r,n
14 180 2: t n OD y r,n.d r,n = y r,n x r,n d r,n. 3: α n (3.302). x r,n+1 = x r,n + α n d r,n (3.301) x r,n+1 α. (3.303) α. min 0 α 1 r R 4: (c) x n+1 t 0 (ω) dω ( x r,n + α n d r,n 1 + { ( x r,n θ j N I j { ( ln x r,n I j ) ln ( x r,n ) } + α n d r,n ) } + α n d r,n ) + α n d r,n (3.302) (3.296) ( ) n = n x n+1 SimplicilDecomposition. SimplicilDecomposition... 0: OD ˆK.
15 x 0 = 0 t0. ˆK. ll or nothing f,1 x 1. n = 1. 1: x n tn. ˆK. 2: f n+1 = (f,n+1 ) (3.303). min f n+1 Ω A x n+1 0 t (w) dw 1 θ q ˆK ( ) f,n+1 q ln f,n+1 q (3.303) (3.304). f,n+1 0 f,n+1 ˆK = q x n+1 = Ω f ˆK δ, (3.304). 2-0: g,1 = f,1 y 1 = x1. m = : (3.305) t m t m = t. ( ) y m (3.305)
16 182 t m OD h, z m (3.306) (3.307). ( ) h,m = q z m exp ˆK exp = Ω θ ( A θ e,m d m. δ, tm A h,m ˆK δ, tm ) (3.306) δ, (3.307) (3.308) (3.309) e,m = h,m 2-2: g,m (3.308) d,m = z m ym (3.309) η m (3.310) (3.311). g,m+1 = g,m + η m e,m (3.310) y m+1 = y m + ηm d m (3.311) g,m+1 y m+1 η. (3.312). min 0 η m 1 Ω A 1 θ q y m +ηm d m 0 t (w) dw ˆK ( g,m,m +η m e ln g,mq,m +η m e q ) (3.312)
17 : g m = h m f,n+1 = g,m+1 x n+1 = y m+1 3. m = m : (d) n = n x n+1 f,n+1. (Genetic Algorithm) ( GA ) DNA 1 ( ) GA 3.67 ( ) ( ) GA 3 0 : 10 3 (2, 3, 5) (3, 7) STEP2 ( )
18 184 STEP0: STEP1: STEP2: No STEP3: 3.67 Yes GA
19 / encode decode 1 1 : (t ) 1 STEP2: 3 ( )
20 186 2 ( ) A B C D E 1 A 2 3 D B C 4 E
21 : t t + 1. GA 2 GA GA ( ) GA GA
22 188 (e) (3.313). [ t 1 = ( x 1 ) ] 4 [ 2 t 2 = ( x 2 ) ] 4 [ 4 t 3 = ( x 3 ) ] 4 (3.313) 3 F rn W olfe x 1 = 3.58 x 2 = 4.62 x 3 = κ = F rn W olfe : 0 (f) Bell nd Cssir(2002)[5] n n
23 F rn W olfe : 3.73 F rn W olfe : 1 2 3, 4 1 OD n (i) Wrdrop h j = 0 g j (h) > min g (h)for ll pths j (3.314) h j > 0 g j (h) = min g (h) = g OD (h) (3.315) h g n h j = pj n h j = 0 p j = 0 p j j g j (h ) OD g OD (h) h p j = 0 (ii) n s π j π j j
24 190 s = j π j p j (3.316) p j j n s c = j p j c (s, π j ) (3.317) c (s, π j ) j n-1 s ( ) j p 1j = p 2j =... = p nj = p j (3.318) c 1 (s 1, π 1j ) = c 2 (s 2, π 2j ) =... = c n (s n, π nj ) (3.319) h p n j h j c (s, π j ) = g j (h) (3.320) j n h j n p j c (s, π j ) > min c (s, π ) = 0 (3.321) p j > 0 c (s, π j ) = min c (s, π ) (3.322) (Nsh, 1951) n
25 Networ demon n+1 demon demon 1 demon n+1 G 1 G 1 : solve simultnenously c (s, q) = p j q c (s, π j ) for ech networ user, (1,..., n) j c n+1 (s, q) = q c n+1, (s ) for the demon plyer n + 1 (3.323) q c (s, π j ) j n-1 s c n+1, (s) demon n s c n+1, (s) c n+1, (s) = p j c (s, π j ) = j c (s) (3.324) (Nsh(1951)) n B 1
26 192 B 1 : solve simultnenously U : mx c (s, q) = q g j (h) subject to q = 1, q 0 q j L : min c n+1 (s, q) = vu(h) q t u (x)dx (3.325) h u 0 subject to v u = uj h j, h j = n, h 0 j j g j (h) h j t u (v u ) u uj j u 1 0 n B 1 G 1 B 1 demon ( ) F or U : q = 0 j q > 0 j F or L : h j = 0 j h j > 0 j g j (h)h j < mx r g j (h)h j = mx r g j (h)q < min r g j (h)q = min r g jr (h)h j (3.326) j g jr (h)h j (3.327) j g r (h)q (3.328) g r (h)q (3.329) n g j (h)h j = cn+1, (s) (3.330) j
27 193 n q = 0 c n+1, (s) < mx c n+1,r (s) r (3.331) q > 0 c n+1, (s) = mx c n+1,r (s) r (3.332) n j n g j (h)q = c (s, π j )q = c (s, π j ) (3.333) h j = pj n = p j n p j = 0 c (s, π j ) < mx c (s, π r ) r (3.334) p j > 0 c (s, π j ) = mx c (s, π r ) r (3.335) n n+1 (Nsh, 1951)[6] n B 1 n+1 G 1 [1] : I,, 2003 [2] : 2,, 2006 [3] Yosef Sheffi: Urbn Trnsporttion Netwo: Equilibrium Anlysis With Mthemticl Progrmming Methods, Prentice Hll, 1985 [4] : D Vol.62 No.4 pp [5] Michel G. H. Bell, Chris Cssir: Trnsporttion Reserch Prt B,Vol.36,pp ,2002. [6] Nsh,J.:Non-coopertive gmes:annls of Mthemtics,Vol.54,pp.286?295,1951.
28
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 information85 4
85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V
More informationx E E E e i ω = t + ikx 0 k λ λ 2π k 2π/λ k ω/v v n v c/n k = nω c c ω/2π λ k 2πn/λ 2π/(λ/n) κ n n κ N n iκ k = Nω c iωt + inωx c iωt + i( n+ iκ ) ωx
x E E E e i ω t + ikx k λ λ π k π/λ k ω/v v n v c/n k nω c c ω/π λ k πn/λ π/(λ/n) κ n n κ N n iκ k Nω c iωt + inωx c iωt + i( n+ iκ ) ωx c κω x c iω ( t nx c) E E e E e E e e κ e ωκx/c e iω(t nx/c) I I
More information20 6 4 1 4 1.1 1.................................... 4 1.1.1.................................... 4 1.1.2 1................................ 5 1.2................................... 7 1.2.1....................................
More information(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1)
1. 1.1...,. 1.1.1 V, V x, y, x y x + y x + y V,, V x α, αx αx V,, (i) (viii) : x, y, z V, α, β C, (i) x + y = y + x. (ii) (x + y) + z = x + (y + z). 1 (iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y
More informationB
B YES NO 5 7 6 1 4 3 2 BB BB BB AA AA BB 510J B B A 510J B A A A A A A 510J B A 510J B A A A A A 510J M = σ Z Z = M σ AAA π T T = a ZP ZP = a AAA π B M + M 2 +T 2 M T Me = = 1 + 1 + 2 2 M σ Te = M 2 +T
More informationuntitled
0 ( L CONTENTS 0 . sin(-x-sinx, (-x(x, sin(90-xx,(90-xsinx sin(80-xsinx,(80-x-x ( sin{90-(ωφ}(ωφ. :n :m.0 m.0 n tn. 0 n.0 tn ω m :n.0n tn n.0 tn.0 m c ω sinω c ω c tnω ecω sin ω ω sin c ω c ω tn c tn ω
More informationわが国企業による資金調達方法の選択問題
* takeshi.shimatani@boj.or.jp ** kawai@ml.me.titech.ac.jp *** naohiko.baba@boj.or.jp No.05-J-3 2005 3 103-8660 30 No.05-J-3 2005 3 1990 * E-mailtakeshi.shimatani@boj.or.jp ** E-mailkawai@ml.me.titech.ac.jp
More information, 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
More informationi 18 2H 2 + O 2 2H 2 + ( ) 3K
i 18 2H 2 + O 2 2H 2 + ( ) 3K ii 1 1 1.1.................................. 1 1.2........................................ 3 1.3......................................... 3 1.4....................................
More informationhttp://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
More information: , 2.0, 3.0, 2.0, (%) ( 2.
2017 1 2 1.1...................................... 2 1.2......................................... 4 1.3........................................... 10 1.4................................. 14 1.5..........................................
More information4................................. 4................................. 4 6................................. 6................................. 9.................................................... 3..3..........................
More information(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
More informationOnsager SOLUTION OF THE EIGENWERT PROBLEM (O-29) V = e H A e H B λ max Z 2 Onsager (O-77) (O-82) (O-83) Kramers-Wannier 1 1 Ons
Onsager 2 9 207.2.7 3 SOLUTION OF THE EIGENWERT PROBLEM O-29 V = e H A e H B λ max Z 2 OnsagerO-77O-82 O-83 2 Kramers-Wannier Onsager * * * * * V self-adjoint V = V /2 V V /2 = V /2 V 2 V /2 = 2 sinh 2H
More informationuntitled
. x2.0 0.5 0 0.5.0 x 2 t= 0: : x α ij β j O x2 u I = α x j ij i i= 0 y j = + exp( u ) j v J = β y j= 0 j j o = + exp( v ) 0 0 e x p e x p J j I j ij i i o x β α = = = + +.. 2 3 8 x 75 58 28 36 x2 3 3 4
More information03.Œk’ì
HRS KG NG-HRS NG-KG AIC Fama 1965 Mandelbrot Blattberg Gonedes t t Kariya, et. al. Nagahara ARCH EngleGARCH Bollerslev EGARCH Nelson GARCH Heynen, et. al. r n r n =σ n w n logσ n =α +βlogσ n 1 + v n w
More information1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
More information30
3 ............................................2 2...........................................2....................................2.2...................................2.3..............................
More informationCVMに基づくNi-Al合金の
CV N-A (-' by T.Koyama ennard-jones fcc α, β, γ, δ β α γ δ = or α, β. γ, δ α β γ ( αβγ w = = k k k ( αβγ w = ( αβγ ( αβγ w = w = ( αβγ w = ( αβγ w = ( αβγ w = ( αβγ w = ( αβγ w = ( βγδ w = = k k k ( αγδ
More information() Remrk I = [0, ] [x i, x i ]. (x : ) f(x) = 0 (x : ) ξ i, (f) = f(ξ i )(x i x i ) = (x i x i ) = ξ i, (f) = f(ξ i )(x i x i ) = 0 (f) 0.
() 6 f(x) [, b] 6. Riemnn [, b] f(x) S f(x) [, b] (Riemnn) = x 0 < x < x < < x n = b. I = [, b] = {x,, x n } mx(x i x i ) =. i [x i, x i ] ξ i n (f) = f(ξ i )(x i x i ) i=. (ξ i ) (f) 0( ), ξ i, S, ε >
More information( )
7..-8..8.......................................................................... 4.................................... 3...................................... 3..3.................................. 4.3....................................
More informationI ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
More information2009 IA I 22, 23, 24, 25, 26, a h f(x) x x a h
009 IA I, 3, 4, 5, 6, 7 7 7 4 5 h fx) x x h 4 5 4 5 1 3 1.1........................... 3 1........................... 4 1.3..................................... 6 1.4.............................. 8 1.4.1..............................
More information艥尾
1 1960 Holt Modigliani Muth Simon 1960 HMMS HMMS 2 recovery reuse reverse Thierry 1995 direct reuse repair recycling remanufacturing 4 container Minner 2003 2 Kistner Dobos 2000 2 Minner Kleber 2001 Dobos
More information1 (Contents) (1) Beginning of the Universe, Dark Energy and Dark Matter Noboru NAKANISHI 2 2. Problem of Heat Exchanger (1) Kenji
8 4 2018 6 2018 6 7 1 (Contents) 1. 2 2. (1) 22 3. 31 1. Beginning of the Universe, Dark Energy and Dark Matter Noboru NAKANISHI 2 2. Problem of Heat Exchanger (1) Kenji SETO 22 3. Editorial Comments Tadashi
More informationP.1P.3 P.4P.7 P.8P.12 P.13P.25 P.26P.32 P.33
: : P.1P.3 P.4P.7 P.8P.12 P.13P.25 P.26P.32 P.33 27 26 10 26 10 25 10 0.7% 331 % 26 10 25 10 287,018 280,446 6,572 30,236 32,708 2,472 317,254 313,154 4,100 172,724 168,173 4,551 6,420 6,579 159 179,144
More informationohpmain.dvi
fujisawa@ism.ac.jp 1 Contents 1. 2. 3. 4. γ- 2 1. 3 10 5.6, 5.7, 5.4, 5.5, 5.8, 5.5, 5.3, 5.6, 5.4, 5.2. 5.5 5.6 +5.7 +5.4 +5.5 +5.8 +5.5 +5.3 +5.6 +5.4 +5.2 =5.5. 10 outlier 5 5.6, 5.7, 5.4, 5.5, 5.8,
More informationKorteweg-de Vries
Korteweg-de Vries 2011 03 29 ,.,.,.,, Korteweg-de Vries,. 1 1 3 1.1 K-dV........................ 3 1.2.............................. 4 2 K-dV 5 2.1............................. 5 2.2..............................
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 informationChap11.dvi
. () x 3 + dx () (x )(x ) dx + sin x sin x( + cos x) dx () x 3 3 x + + 3 x + 3 x x + x 3 + dx 3 x + dx 6 x x x + dx + 3 log x + 6 log x x + + 3 rctn ( ) dx x + 3 4 ( x 3 ) + C x () t x t tn x dx x. t x
More informationx, 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 informationi
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
More informationI A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google
I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59
More informationN cos s s cos ψ e e e e 3 3 e e 3 e 3 e
3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >
More information2012 IA 8 I p.3, 2 p.19, 3 p.19, 4 p.22, 5 p.27, 6 p.27, 7 p
2012 IA 8 I 1 10 10 29 1. [0, 1] n x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 2. 1 x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 1 0 f(x)dx 3. < b < c [, c] b [, c] 4. [, b] f(x) 1 f(x) 1 f(x) [, b] 5.
More information() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (
3 n nc k+ k + 3 () n C r n C n r nc r C r + C r ( r n ) () n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (4) n C n n C + n C + n C + + n C n (5) k k n C k n C k (6) n C + nc
More information.. F x) = x ft)dt ), fx) : PDF : probbility density function) F x) : CDF : cumultive distribution function F x) x.2 ) T = µ p), T : ) p : x p p = F x
203 7......................................2................................................3.....................................4 L.................................... 2.5.................................
More informationマイクロメカニクスの基礎と応用
by.koyama ( ij ijk k ( (,, ijk jik ijk ijk ijk kij ( * * * * * * ( ( * k uk u + x x k u i (4 Estr ijkij k (5 (5 (5 * * * * 0 0 0 0 0 0 0 0 0 * * 0 0 0 (6 (7 Estr ijkijk ( + + + + + + + + + + + + + + +
More information廃棄物処理施設生活環境影響調査指針
- - 0.04ppm 0.1ppm 10ppm 0ppm 0.10mg/m 3 0.0 mg/m 3 0.06ppm 0.04ppm 0.06ppm 0.003 mg/m 3 0. mg/m 3 0. mg/m 3 0.15 mg/m 3 - -1 - 0.6pg-TEQ/m 3 53 3 1 0.10.ppm 0.0ppm 5 6 16 136 0.0ppm 7 15 7 31 0.04g-Hg/m
More information) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4
1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev
More informationuntitled
18 1 2,000,000 2,000,000 2007 2 2 2008 3 31 (1) 6 JCOSSAR 2007pp.57-642007.6. LCC (1) (2) 2 10mm 1020 14 12 10 8 6 4 40,50,60 2 0 1998 27.5 1995 1960 40 1) 2) 3) LCC LCC LCC 1 1) Vol.42No.5pp.29-322004.5.
More informationCV CV CV --
30 4 30 0 30 60 V/Hz V/Hz CV CV -- CV CV CV -- CV 3 AVR -3- 5m/ 0.5G 3m/ 0.3G 3 0.5Hz 0Hz 0.5Hz 0Hz 3 54kV 3 5 m/ 0.5G 3 3 5m/ 0.5G -4- V & bc 0.0VPT Z & G Z & L V& bc Z & L j0.50 0.0 0.0 5.7 V Z & + Z
More informationHanbury-Brown Twiss (ver. 2.0) van Cittert - Zernike mutual coherence
Hanbury-Brown Twiss (ver. 2.) 25 4 4 1 2 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 4 3 Hanbury-Brown Twiss ( ) 5 3.1............................................
More informationn 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m
1 1 1 + 1 4 + + 1 n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m a n < ε 1 1. ε = 10 1 N m, n N a m a n < ε = 10 1 N
More informationchap10.dvi
. q {y j } I( ( L y j =Δy j = u j = C l ε j l = C(L ε j, {ε j } i.i.d.(,i q ( l= y O p ( {u j } q {C l } A l C l
More information7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
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 information2011de.dvi
211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37
More informationSO(3) 7 = = 1 ( r ) + 1 r r r r ( l ) (5.17) l = 1 ( sin θ ) + sin θ θ θ ϕ (5.18) χ(r)ψ(θ, ϕ) l ψ = αψ (5.19) l 1 = i(sin ϕ θ l = i( cos ϕ θ l 3 = i ϕ
SO(3) 71 5.7 5.7.1 1 ħ L k l k l k = iϵ kij x i j (5.117) l k SO(3) l z l ± = l 1 ± il = i(y z z y ) ± (z x x z ) = ( x iy) z ± z( x ± i y ) = X ± z ± z (5.118) l z = i(x y y x ) = 1 [(x + iy)( x i y )
More information01.Œk’ì/“²fi¡*
AIC AIC y n r n = logy n = logy n logy n ARCHEngle r n = σ n w n logσ n 2 = α + β w n 2 () r n = σ n w n logσ n 2 = α + β logσ n 2 + v n (2) w n r n logr n 2 = logσ n 2 + logw n 2 logσ n 2 = α +β logσ
More information4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
More information2 G(k) e ikx = (ik) n x n n! n=0 (k ) ( ) X n = ( i) n n k n G(k) k=0 F (k) ln G(k) = ln e ikx n κ n F (k) = F (k) (ik) n n= n! κ n κ n = ( i) n n k n
. X {x, x 2, x 3,... x n } X X {, 2, 3, 4, 5, 6} X x i P i. 0 P i 2. n P i = 3. P (i ω) = i ω P i P 3 {x, x 2, x 3,... x n } ω P i = 6 X f(x) f(x) X n n f(x i )P i n x n i P i X n 2 G(k) e ikx = (ik) n
More information2D-RCWA 1 two dimensional rigorous coupled wave analysis [1, 2] 1 ε(x, y) = 1 ε(x, y) = ϵ mn exp [+j(mk x x + nk y y)] (1) m,n= m,n= ξ mn exp [+j(mk x
2D-RCWA two dimensional rigoros copled wave analsis, 2] εx, εx, ϵ mn exp +jmk x x + nk ] m,n m,n ξ mn exp +jmk x x + nk ] 2 K x K x Λ x Λ ϵ mn ξ mn K x 2π Λ x K 2π Λ ϵ mn ξ mn Λ x Λ x Λ x Λ x Λx Λ Λx Λ
More informationuntitled
17 5 13 1 2 1.1... 2 1.2... 2 1.3... 3 2 3 2.1... 3 2.2... 5 3 6 3.1... 6 3.2... 7 3.3 t... 7 3.4 BC a... 9 3.5... 10 4 11 1 1 θ n ˆθ. ˆθ, ˆθ, ˆθ.,, ˆθ.,.,,,. 1.1 ˆθ σ 2 = E(ˆθ E ˆθ) 2 b = E(ˆθ θ). Y 1,,Y
More information2009 IA 5 I 22, 23, 24, 25, 26, (1) Arcsin 1 ( 2 (4) Arccos 1 ) 2 3 (2) Arcsin( 1) (3) Arccos 2 (5) Arctan 1 (6) Arctan ( 3 ) 3 2. n (1) ta
009 IA 5 I, 3, 4, 5, 6, 7 6 3. () Arcsin ( (4) Arccos ) 3 () Arcsin( ) (3) Arccos (5) Arctan (6) Arctan ( 3 ) 3. n () tan x (nπ π/, nπ + π/) f n (x) f n (x) fn (x) Arctan x () sin x [nπ π/, nπ +π/] g n
More informationZ: Q: R: C:
0 Z: Q: R: C: 3 4 4 4................................ 4 4.................................. 7 5 3 5...................... 3 5......................... 40 5.3 snz) z)........................... 4 6 46 x
More informationuntitled
( ) l 1991 1) 4) 5),6) 7) 8) 31) 39) 46) : () + +θ (c) l h A - : θ A () (d) 1 ε=/l=θ/cot 1(d) 1 () =tn( ) h + 1 u F m N F m =Ntn N N N F m N F m =Ntn N S α S1 R α+ R = tn( ) = tn = tn( + ) R R d = d ()
More information弾性論(Chen)
Phase-field by T.Koyama Phase-field da da a( ) a + { } a d + d δ (-) δ (-) eigen a a a ε ε δ δ (-) da ε (-4) a d ε ε + δε ( ) (-5) δε d (-6) V u ul δεl + l (-7) eigen el ε ε ε (-8) σ el C ε el C { ε ε
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 information2
2013 Vol.18 No.2 3 24 25 8 22 2 23 26 9 15 20 2 3 4 5 6 7 8 point1 point 2 point3 point4 10 11 point1 point 2 point 3 point 4 12 13 14 15 16 17 18 19 20 http://www.taishukan.co.jp/kateika/ 21 22 23 24
More informationVol.171 2004.9.15 14 100 5 10 15 52 53 55 1 7 55 58 63 3 26 53 3 6 9 2 3 6 9 6 52 53 55 3 9 5 1 7 10 14 4 12 8 11
Vol.170 2004.9.9 9 17 9 17 1000 8 10 9 17 14:00 17:00 30 28 Vol.171 2004.9.15 14 100 5 10 15 52 53 55 1 7 55 58 63 3 26 53 3 6 9 2 3 6 9 6 52 53 55 3 9 5 1 7 10 14 4 12 8 11 9.17 10 15 38 51 53 55 6 2
More informationkou05.dvi
2 C () 25 1 3 1.1........................................ 3 1.2..................................... 4 1.3..................................... 7 1.3.1................................ 7 1.3.2.................................
More information.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T
NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977
More information211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
More information1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
More informationuntitled
- k k k = y. k = ky. y du dx = ε ux ( ) ux ( ) = ax+ b x u() = ; u( ) = AE u() = b= u () = a= ; a= d x du ε x = = = dx dx N = σ da = E ε da = EA ε A x A x x - σ x σ x = Eε x N = EAε x = EA = N = EA k =
More informationTitle 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue Date Type Technical Report Text Version publisher URL
Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue 2012-06 Date Type Technical Report Text Version publisher URL http://hdl.handle.net/10086/23085 Right Hitotsubashi University Repository
More information0226_ぱどMD表1-ol前
No. MEDIA DATA 0 B O O K 00-090-0 0 000900 000 00 00 00 0000 0900 000900 AREA MAP 0,000 0,000 0,000 0,000 00,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 00,000 0,000
More informationt 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.
More information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!
More informationI, II 1, A = A 4 : 6 = max{ A, } A A 10 10%
1 2006.4.17. A 3-312 tel: 092-726-4774, e-mail: hara@math.kyushu-u.ac.jp, http://www.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html Office hours: B A I ɛ-δ ɛ-δ 1. 2. A 1. 1. 2. 3. 4. 5. 2. ɛ-δ 1. ɛ-n
More informationall.dvi
I 1 Density Matrix 1.1 ( (Observable) Ô :ensemble ensemble average) Ô en =Tr ˆρ en Ô ˆρ en Tr  n, n =, 1,, Tr  = n n  n Tr  I w j j ( j =, 1,, ) ˆρ en j w j j ˆρ en = j w j j j Ô en = j w j j Ô j emsemble
More information() [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () ) m/s 4. ) 4. AMEDAS
() [REQ] 4. 4. () [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () 0 0 4. 5050 0 ) 00 4 30354045m/s 4. ) 4. AMEDAS ) 4. 0 3 ) 4. 0 4. 4 4.3(3) () [REQ] () [REQ] (3) [POS] () ()() 4.3 P = ρ d AnC DG ()
More informationX G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
More informationMathematical Logic I 12 Contents I Zorn
Mathematical Logic I 12 Contents I 2 1 3 1.1............................. 3 1.2.......................... 5 1.3 Zorn.................. 5 2 6 2.1.............................. 6 2.2..............................
More informationf(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f
22 A 3,4 No.3 () (2) (3) (4), (5) (6) (7) (8) () n x = (x,, x n ), = (,, n ), x = ( (x i i ) 2 ) /2 f(x) R n f(x) = f() + i α i (x ) i + o( x ) α,, α n g(x) = o( x )) lim x g(x) x = y = f() + i α i(x )
More information17 ( ) II III A B C(100 ) 1, 2, 6, 7 II A B (100 ) 2, 5, 6 II A B (80 ) 8 10 I II III A B C(80 ) 1 a 1 = 1 2 a n+1 = a n + 2n + 1 (n = 1,
17 ( ) 17 5 1 4 II III A B C(1 ) 1,, 6, 7 II A B (1 ), 5, 6 II A B (8 ) 8 1 I II III A B C(8 ) 1 a 1 1 a n+1 a n + n + 1 (n 1,,, ) {a n+1 n } (1) a 4 () a n OA OB AOB 6 OAB AB : 1 P OB Q OP AQ R (1) PQ
More information2 2 MATHEMATICS.PDF 200-2-0 3 2 (p n ), ( ) 7 3 4 6 5 20 6 GL 2 (Z) SL 2 (Z) 27 7 29 8 SL 2 (Z) 35 9 2 40 0 2 46 48 2 2 5 3 2 2 58 4 2 6 5 2 65 6 2 67 7 2 69 2 , a 0 + a + a 2 +... b b 2 b 3 () + b n a
More informationω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
More informationy = x x R = 0. 9, R = σ $ = y x w = x y x x w = x y α ε = + β + x x x y α ε = + β + γ x + x x x x' = / x y' = y/ x y' =
y x = α + β + ε =,, ε V( ε) = E( ε ) = σ α $ $ β w ( 0) σ = w σ σ y α x ε = + β + w w w w ε / w ( w y x α β ) = α$ $ W = yw βwxw $β = W ( W) ( W)( W) w x x w x x y y = = x W y W x y x y xw = y W = w w
More informationSFGÇÃÉXÉyÉNÉgÉãå`.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
More informationW u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
More information半 系列における記号の出現度数の対称性
l l 2018 08 27 2018 08 28 FFTPRSWS18 1 / 20 FCSR l LFSR NLFSR NLFSR Goresky Klapper FCSR l word-based FCSR l l... l 2 / 20 LFSR FCSR l a m 1 a m 2... a 1 a 0 q 1 q 2... q m 1 q m a = (a n) n 0 R m LFSR
More informationKroneher Levi-Civita 1 i = j δ i j = i j 1 if i jk is an even permutation of 1,2,3. ε i jk = 1 if i jk is an odd permutation of 1,2,3. otherwise. 3 4
[2642 ] Yuji Chinone 1 1-1 ρ t + j = 1 1-1 V S ds ds Eq.1 ρ t + j dv = ρ t dv = t V V V ρdv = Q t Q V jdv = j ds V ds V I Q t + j ds = ; S S [ Q t ] + I = Eq.1 2 2 Kroneher Levi-Civita 1 i = j δ i j =
More information基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............
More information_0212_68<5A66><4EBA><79D1>_<6821><4E86><FF08><30C8><30F3><30DC><306A><3057><FF09>.pdf
More information
ohpr.dvi
2003/12/04 TASK PAF A. Fukuyama et al., Comp. Phys. Rep. 4(1986) 137 A. Fukuyama et al., Nucl. Fusion 26(1986) 151 TASK/WM MHD ψ θ ϕ ψ θ e 1 = ψ, e 2 = θ, e 3 = ϕ ϕ E = E 1 e 1 + E 2 e 2 + E 3 e 3 J :
More informationδ ij δ ij ˆx ˆx ŷ ŷ ẑ ẑ 0, ˆx ŷ ŷ ˆx ẑ, ŷ ẑ ẑ ŷ ẑ, ẑ ˆx ˆx ẑ ŷ, a b a x ˆx + a y ŷ + a z ẑ b x ˆx + b
23 2 2.1 n n r x, y, z ˆx ŷ ẑ 1 a a x ˆx + a y ŷ + a z ẑ 2.1.1 3 a iˆx i. 2.1.2 i1 i j k e x e y e z 3 a b a i b i i 1, 2, 3 x y z ˆx i ˆx j δ ij, 2.1.3 n a b a i b i a i b i a x b x + a y b y + a z b
More informationC p (.2 C p [[T ]] Bernoull B n,χ C p p q p 2 q = p p = 2 q = 4 ω Techmüller a Z p ω(a a ( mod q φ(q ω(a Z p a pz p ω(a = 0 Z p φ Euler Techmüller ω Q
p- L- [Iwa] [Iwa2] -Leopoldt [KL] p- L-. Kummer Remann ζ(s Bernoull B n (. ζ( n = B n n, ( n Z p a = Kummer [Kum] ( Kummer p m n 0 ( mod p m n a m n ( mod (p p a ( p m B m m ( pn B n n ( mod pa Z p Kummer
More information(Bessel) (Legendre).. (Hankel). (Laplace) V = (x, y, z) n (r, θ, ϕ) r n f n (θ, ϕ). f n (θ, ϕ) n f n (θ, ϕ) z = cos θ z θ ϕ n ν. P ν (z), Q ν (z) (Fou
(Bessel) (Legendre).. (Hankel). (Laplace) V = (x, y, z) n (r, θ, ϕ) r n f n (θ, ϕ). f n (θ, ϕ) n f n (θ, ϕ) z = cos θ z θ ϕ n ν. P ν (z), Q ν (z) (Fourier) (Fourier Bessel).. V ρ(x, y, z) V = 4πGρ G :.
More informationCOE-RES Discussion Paper Series Center of Excellence Project The Normative Evaluation and Social Choice of Contemporary Economic Systems Graduate Scho
COE-RES Discussion Paper Series Center of Excellence Project The Normative Evaluation and Social Choice of Contemporary Economic Systems Graduate School of Economics and Institute of Economic Research
More informationMicrosoft Word - ip38.doc
交通ネットワーク均衡モデル求解アルゴリズムと収束判定 Algorithms for ilibrim Trnsporttion Networ Models nd vltion of Their Convergence rror 井上紳一 By hin-ichi INOU 1. はじめに 2. 収束判定指標 利用者均衡配分モデルを代表とする交通ネットワーク均衡モデルは 数理問題としては非線形計画問題 非線形相補性問題
More information(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37
4. 98 () θ a = 5(cm) θ c = 4(cm) b = (cm) () D 0cm 0 60 D 99 () 0m O O 7 sin 7 = 0.60 cos 7 = 0.799 tan 7 = 0.754 () xkm km R km 00 () θ cos θ = sin θ = () θ sin θ = 4 tan θ = () 0 < x < 90 tan x = 4 sin
More information2 ID POS 1... 1 2... 2 2.1 ID POS... 2 2.2... 3 3... 5 3.1... 5 3.2... 6 3.2.1... 6 3.2.2... 7 3.3... 7 3.3.1... 7 3.3.2... 8 3.3.3... 8 3.4... 9 4... 11 4.1... 11 4.2... 15 4.3... 27 5... 35... 36...
More informationuntitled
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}, {}.
More informationタイトル
Flud Flow Smulton wth Cellulr Automt 00N2100008J 2002 225 1. cellulr utomton n t+ 1 t t = f( r, L, + r (1 t t+ 1 f t r t +1 Prllel Vrtul Mchne Messge-Pssng Interfce 1 2. 2. 1 t t 0 t = 1 = 1 = t = 2 2
More information