(2) N elec = D p,q p,q χ q χ p dr = p,q D p,q S q,p Mulliken PA D Mull p = p = group A D p,p 1 + D p,q S q,p p q p [ r A D Mull p ] group χ p G Mull A

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "(2) N elec = D p,q p,q χ q χ p dr = p,q D p,q S q,p Mulliken PA D Mull p = p = group A D p,p 1 + D p,q S q,p p q p [ r A D Mull p ] group χ p G Mull A"

Transcription

1 7 - (Electron-Donor Acceptor) : Charge-Transfer ( CT) ( (Charge-Transfer) - (electron donor-electron acceptor) [1][2][3][4] Van der Waals CT [5] Population Analysis population analysis ( ), observable physical property population analysis - (electron donor-electron acceptor) population analysis 7.1 Population Analysis Population analysis(pa) Population analysis Mulliken PA[6] Löwdin PA[7] Weinhold Natural PA[8][9] PA 1 ( ) ρ(r) i = i n i ϕ i ϕ i (1) n i c p,i χ p χ q c q,i D p,q χ p χ q p,q (2) p,q D CΩ C, [Ω] i,j = n i δ ij ϕ i n i χ p D p,q D ( { χ p }) ρ(r) ρ(r)dr =N elec 138

2 (2) N elec = D p,q p,q χ q χ p dr = p,q D p,q S q,p Mulliken PA D Mull p = p = group A D p,p 1 + D p,q S q,p p q p [ r A D Mull p ] group χ p G Mull A A D Mull p (3) G Mull A (4) ( ( p A ( ) S q,p D Mull p D Mull p = χ p ρ(r) χ p PA χ p Löwdin PA Löwdin PA χ L = χs 1 2 (5) D Lw r = χ L r ρ(r) χ L r = D p,q χ L r χ p χ q χ L r p,q = p,q ] D p,q [S 1 2 s,t = D p,q [S 1 2 p,q [ ] = S DS 2 r,r ] r,p r,s S s,p S q,t [S 1 2 ] t,r [ ] S 1 2 = [ ] [ ] S 1 2 D p,q S 1 2 q,r r,p q,r p,q (6) (7) (8) S 1 2 DS Natural Population Analysis Weinhold Natural PA Natural Atomic Orbital Gaussian Gamess Weinhold know-how [10] ρ(r) χ NPA r [10] 1 139

3 { χ p } { χ A p } D A 1 pre-nao(natural Atomic Orbital) 1-1: (p x, y, z d x 2, y 2, z 2, xy, xz, yz) (l, m), χ sph = χt sph (9) C sph = T sph C (10) D sph = T sph DT sph = T sph CΩ CT sph = C sph Ω C sph (11) S sph = T sph ST sph (12) D sph (S sph ) A, (l, m) D (A,l,m) (S (A,l,m) ) 1-2: A m A (l = 0, 1, 2, ) M (A,l) [ D (A,l)] p,q 1 2l + 1 [ S (A,l)] p,q 1 2l + 1 l m= l l m= l [ D (A,l,m)] p,q [ S (A,l,m)] p,q D (A,l), S (A,l) M (A,l) (13) (14) D (A,l) U (A,l) = S (A,l) U (A,l) Ω (A,l) (15) M (A,l) pre-nao η (A,l,m) = χ sph(a,l,m) U (A,l) (16) Ω (A,l) pre-nao [ 1-3: ANO Ω (A,l)] k = 1,, M (A,l) pre-ano k,k pre-ano natural minimal basis (NMB) Li Be s (l = 0) 2 B Ne s (l = 0) 2 (1s 2s ) p (l = 1) 1 (2p ) M (A,l) NMB pre-ano natural Rydberg Basis (NRB) Weinhold NMB NRB 2 pre-ano Population analysis AO (weighted 140

4 interatomic orthogonalization) NMB NRB NRB NMB Schmidt µ = {µ i ; i = 1, M} ν = {ν i ; i = 1, M} ν= µv (17) νν= : NMB A l,m M (A,l) k [ M ν i µ i 2 = minimum (18) i M w i ν i µ i 2 = minimum (19) i Ω (A,l)] η (A,l,m) k k,k O M W NMB η (A,l,m) 2 = minimum (20) k χ ONMB = χt sph U (A,l) O M W (21) 2-2: NRB NMB Schmidt O S NRB NRB [ Ω (A,l)] NMB k,k 1-2,1-3 U (A,l) O S NRB T sph U (A,l) O S U (A,l) χ NRB = χt sph U (A,l) O S U (A,l) (22) χ ONRB = χ NRB O R W (23) 141

5 3 ( χ ONMB, χ ONRB) Natural AO 1-2,1-3 N restore ANO χ ANO χ ANO (6) χ NRB χ ONRB N restore (24) D ANO r = χ ANO ρ(r) χ ANO r r (25) Population analysis 7.2 Mulliken [4] Mulliken (Molecular Orbital Theory) Mulliken school 1966 Mulliken MO VB MO ( D A D + A DA (26) DA DA Mulliken DA Ψ N = aφ 0 (D A) + bφ 1 (D + A ) (27) (no-bond) (dative) resonance (2 2) Φ 0 Ĥ Φ 0 Φ 0 Ĥ Φ 1 Φ 1 Ĥ Φ 0 Φ 1 Ĥ Φ 1 a b = E 1 Φ 0 Φ 1 Φ 1 Φ 0 1 a b (28) W 0 Φ 0 H Φ 0, W 1 Φ 1 H Φ 1, W 01 Φ 1 H Φ 0 = Φ 0 H Φ 1, S Φ 1 Φ 0 = Φ 0 Φ 1 142

6 W 0 E W 01 SE W 01 SE W 1 E E (W 01 SW 0 ) SE (W 01 SW 0 ) SE E = 0 (29) = 0, E E W 0 (30) E ± = 1 W 0 + W 1 (1 S 2 SW 01 ± ) 2 ( ) 2 + β 0 β 1 2 W 1 W 0 β 0 W 01 W 0 S, β 1 W 01 W 1 S β 0, β W 0 < W 1 Ψ N Φ 0 (D A) Ψ V Φ 1 (D + A ) Charge-transfer transition 3 Φ 1 (D + A ) Ĥ Φ 1 (D + A ) Φ 0 (D A) Ĥ Φ 0(D A) [ Φ(D + ) Ĥ D Φ(D + ) Φ(D) Φ(D) ] ĤD [ Φ(A + ) Ĥ A Φ(A ) ] Φ(A) ĤA Φ(A) + [ V (D + A ) V (D A) ] (31) H D (H A ) D(A) V (D + A ), V (D A) D + A D A D I E (D) I E (D) = Φ(D + ) Ĥ D Φ(D + ) Φ(D) ĤD Φ(D) 143

7 A A E (A) A E (A) = Φ(A) ĤA Φ(A) Φ(A ) Ĥ A Φ(A ) C(D + A ) [ V (D + A ) V (D A) ] (32) 1 R(D A) (33) I E (D) A E (A) C(D + A ) β 0 (β 1 ) (4 29) v QP P S Φ 1 Φ 0 S ( ) 2 β 0 β 1 2 ( ) 2 ( ) [ ] + β 0 β β 0β ( ) 2 2 ( ) W1 W 0 = + β 0β 1 2 W 1 W 0 β 0 β 1 = β 0 (W 01 W 1 S) = β 0 {W 01 W 0 S + (W 0 W 1 ) S} = β 2 0 β 0 (W 1 W 0 ) S = β β 1 (W 1 W 0 ) S E N E W 0 β2 0 E V E + W 1 + β2 1 (34) (35) hν CT = E V E N = W 1 W 0 + β2 1 + β 2 0 = I E (D) A E (A) C(D + A ) + β β 2 0 I E (D) A E (A) C(D + A ) (36) A D I E 1 I E A E 144

8 a, b (28) b N a N = W 0 E N W 01 SE N (37) a V b V = W 1 E V W 01 SE V (38) 34 (35) b N a N = β2 0 β 0 (1 + S β2 0 ) = (a 2 N + b2 N + 2a N b N S = 1) β 0 + Sβ 0 β 0 > 0 (39) a V β 1 = β 1 b V Sβ 1 < 0 (40) a N = 1 1 β, b 0 N = β 0 a V = β β1 1 1 β 0 b V = β1 (x ) (41) (42) x Ψ N x Ψ N = a 2 N Φ 0 x Φ 0 + b 2 N Φ 1 x Φ 1 + 2a N b N Φ 0 x Φ 1 D A x D A x ( β 0 x b 2 N Φ1 (D + A ) x Φ 1 (D + A ) ( ) 2 ( ) 2 β 0 1 β0 1 β R 0 D A R D A (43) ) 2 1 R 1 β 0 D A Ψ V x Ψ N b N b V Φ1 (D + A ) x Φ 1 (D + A ) ( β0 ( ) β0 ) R D A (44) 7.3 EDA(CT) DA 145

9 [11] 7-2 tetracyano-benzene 1:N,N,N N -tetramethyl-p-phenylene-diamine(tmpd), 2 N,N-dimethyl-aniline, 3:hexamethyl-benzene tetracyano-benzene(tcnb) 7-3 [11] TCNB trinitro-benzene(tnb) TCNB ( 36 1 I E ( ) 36 A E 146

10 7-3 trinitro-benzene(tnb) tetracyano-benzene(tcnb) ( I 2 C=O N=O 7-4 I 2 N (C 5 H 5 NO) CCl 4 1 I 2 2,3, C 5 H 5 NO 490nm( mµ (isobestic point) (σ σ ) ( ) 380nm 7-4 I 2 C 5 H 5 NO CCl 4 1 I 2 2,3, C 5 H 5 NO 147

11 [12] 7-5 Cl 2 Cl-Cl I E 10.13eV HF/6-31 () [12] N Cl-Cl 7-6 C 2 H 4 C-C [13] 148

12 7-6 C=C [13] 43 Q s Q s 2 x Q s 2β 0R D A 2 β 0 Q s (45) Q s C=C D-A 7.4 EDA(CT) Horváth [14] Lewis 149

13 7-1 BH 3 NH 3 [14] 7-8 N-B B-H N-H 7-7 BH 3 NH3 N-H [14] [14] 7-2 LP MO 3rdSPT + dispersion [15] [16] NH 3 -SO 2 ) E 3SPT+Disp CCSD(T)/CBS 1kcal mol E 3SPT E 3SPT ( 150

14 7-2 Hobza (ref.31 [16]) LP MO [15] kj mol 1. π tetracyanoethylene(tcne) acenaphtylene [17] 7-9 TCNE-Acenaphtylene[17] DFT [18] π T π 151

15 7.5 2 π Pulay [19] aug-pvqz CCSD(T), QCISD(T) coupled cluster T Parallel displaced (PD) 2 Note µ = {µ i ; i = 1, M} µ = χu µµ =ŨSU T (46) ν={ν i ; i = 1, M} = µv ν i = µ i v i 152

16 νν =ṼŨSUV =ṼTV = 1 (19) I = i,.j [δ ij w i (ṽ i µ i )(v i µ i ) + λ ji ṽ i v j ] ṽ i I = w i (v i µ i ) + ṽ i.j λ ji v j = 0 i = 1, M µ i w i =.j v j (δ ji w i + λ ji ) = 0 µ i w i =.j v j w j λ ji (47) λ ji λ ji δ jiw i + λ ji 21 µω = µvωλ µ TΩ = TVΩΛ (48) Λ ṼTV = 1 ṼTΩ = ṼTVΩΛ = ΩΛ 22 TΩ = TVṼTΩ V = Ω(ΩTΩ) 1/ [1][2][3] 4. ( β 0, β 1 W 0, W 1 (W 0, W 1 β 0, β 1 β i = Φ 1 Ĥ Φ 0 S Φ i Ĥ Φ i 153

17 Ω ) ) β i = Φ 1 (Ĥ Ω Φ 0 S Φ i (Ĥ Ω Φ i ( ) ( ) = Φ 1 Ĥ Φ 0 ΩS S Φ i Ĥ Φ i SΩ Ω W i = Φ i Ĥ Φ i SW i S β i Φ i H Ĥ Φ i = W i Φ i + Υ i i Υ i i β 0 = Φ 1 Ĥ Φ 0 S Φ 0 Ĥ Φ 0 = Φ 1 Υ 0 0 β 1 = Φ 0 Υ 1 1 [1] R. S. Mulliken, J. Am. Chem. Soc., 72, 600 (1950). [2] R. S. Mulliken, J. Am. Chem. Soc., 74, 811 (1952). [3] R. S. Mulliken, J. Phys. Chem., 56, 801 (1952). [4] R. S. Mulliken, Willis B. Person, Molecular Complexes, Wiley Interscience, (1969). [5] Noboru Mataga, Tanekazu Kubota, Molecular Interactions and Electronic Spectra, Marcel Dekker Inc., (1970). [6] R. S. Mulliken, J. Chem. Phys., 23, 1833 (1952). [7] P. O. Lowdin, Phys. Rev., 97, 1474 (1955). [8] A. E. Reed, L.. A. Curtis, F. Weinhold, Chem. Rev., 88, 899 (1988). 154

18 [9] F. Weinhold, Encyclopedia of Computational Chemistry Edited by von Schleyer, 3, 1792 (1998). [10] A. E. Reed, R. B. Weinstock, F. Weinhold, J. Chem, Phys., 83, 735 (1985). [11] S. Iwata, J.Tanaka, S. Nagakura, J. Am. Chem. Soc., 88, 894 (1966). [12] H. Matsuzawa, S. Iwata, Chem. Phys., 163, 297 (1992). [13] H. Matsuzawa, H. Yamashita, M. Ito, S. Iwata, Chem. Phys., 147, 77 (1990). [14] V. Horvth, A. Kovcs, I. Hargittai, J. Phy. Chem., 107, 1197 (2003). [15] S. Iwata, Phys. Chem. Phys. Chem., 14, 7787 (2012). [16] S. Karthikeyan, R. Sedlak, P. Hobza, J. Phys. Chem. A, 115, 9422 (2011). [17] H.-B. Yi, X.-Y. Li, S.-Y. Yang, X.-H. Duan, Int. J. Quant. Chem, 94, 23 (2003). [18] M.-S. Liao, Y. Lu, S. Scheiner, J. Comp. Chem., 24, 624 (2003). [19] T. Janowski, P. Pulay, Chem. Phys. Letters, 447, 27 (2007). 155

42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =

42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 = 3 3.1 3.1.1 kg m s J = kg m 2 s 2 MeV MeV [1] 1MeV=1 6 ev = 1.62 176 462 (63) 1 13 J (3.1) [1] 1MeV/c 2 =1.782 661 731 (7) 1 3 kg (3.2) c =1 MeV (atomic mass unit) 12 C u = 1 12 M(12 C) (3.3) 41 42 3 u

More information

『共形場理論』

『共形場理論』 T (z) SL(2, C) T (z) SU(2) S 1 /Z 2 SU(2) (ŜU(2) k ŜU(2) 1)/ŜU(2) k+1 ŜU(2)/Û(1) G H N =1 N =1 N =1 N =1 N =2 N =2 N =2 N =2 ĉ>1 N =2 N =2 N =4 N =4 1 2 2 z=x 1 +ix 2 z f(z) f(z) 1 1 4 4 N =4 1 = = 1.3

More information

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e 7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z

More information

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B 9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A

More information

= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds

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 information

量子力学A

量子力学A c 1 1 1.1....................................... 1 1............................................ 4 1.3.............................. 6 10.1.................................. 10......................................

More information

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP 1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

More information

untitled

untitled (a) (b) (c) (d) Wunderlich 2.5.1 = = =90 2 1 (hkl) {hkl} [hkl] L tan 2θ = r L nλ = 2dsinθ dhkl ( ) = 1 2 2 2 h k l + + a b c c l=2 l=1 l=0 Polanyi nλ = I sinφ I: B A a 110 B c 110 b b 110 µ a 110

More information

* 1 2014 7 8 *1 iii 1. Newton 1 1.1 Newton........................... 1 1.2............................. 4 1.3................................. 5 2. 9 2.1......................... 9 2.2........................

More information

Γ Ec Γ V BIAS THBV3_0401JA THBV3_0402JAa THBV3_0402JAb 1000 800 600 400 50 % 25 % 200 100 80 60 40 20 10 8 6 4 10 % 2.5 % 0.5 % 0.25 % 2 1.0 0.8 0.6 0.4 0.2 0.1 200 300 400 500 600 700 800 1000 1200 14001600

More information

C 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

C 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

2 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 information

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t 6 6.1 6.1 (1 Z ( X = e Z, Y = Im Z ( Z = X + iy, i = 1 (2 Z E[ e Z ] < E[ Im Z ] < Z E[Z] = E[e Z] + ie[im Z] 6.2 Z E[Z] E[ Z ] : E[ Z ] < e Z Z, Im Z Z E[Z] α = E[Z], Z = Z Z 1 {Z } E[Z] = α = α [ α ]

More information

2 FIG. 1: : n FIG. 2: : n (Ch h ) N T B Ch h n(z) = (sin ϵ cos ω(z), sin ϵ sin ω(z), cos ϵ), (1) 1968 Meyer [5] 50 N T B Ch h [4] N T B 10 nm Ch h 1 µ

2 FIG. 1: : n FIG. 2: : n (Ch h ) N T B Ch h n(z) = (sin ϵ cos ω(z), sin ϵ sin ω(z), cos ϵ), (1) 1968 Meyer [5] 50 N T B Ch h [4] N T B 10 nm Ch h 1 µ : (Dated: February 5, 2016), (Ch), (Oblique Helicoidal) (Ch H ), Twist-bend (N T B ) I. (chiral: ) (achiral) (n) (Ch) (N ) 1996 [1] [2] 2013 (N T B ) [3] 2014 [4] (oblique helicoid) 2016 1 29 Electronic

More information

AHPを用いた大相撲の新しい番付編成

AHPを用いた大相撲の新しい番付編成 5304050 2008/2/15 1 2008/2/15 2 42 2008/2/15 3 2008/2/15 4 195 2008/2/15 5 2008/2/15 6 i j ij >1 ij ij1/>1 i j i 1 ji 1/ j ij 2008/2/15 7 1 =2.01/=0.5 =1.51/=0.67 2008/2/15 8 1 2008/2/15 9 () u ) i i i

More information

1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e

1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e No. 1 1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e I X e Cs Ba F Ra Hf Ta W Re Os I Rf Db Sg Bh

More information

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1 1 1.1......... 1............. 1.3... 1.4......... 1.5.............. 1.6................ Bownian Motion.1.......... Einstein.............. 3.3 Einstein........ 3.4..... 3.5 Langevin Eq.... 3.6................

More information

p.2/76

p.2/76 kino@info.kanagawa-u.ac.jp p.1/76 p.2/76 ( ) (2001). (2006). (2002). p.3/76 N n, n {1, 2,...N} 0 K k, k {1, 2,...,K} M M, m {1, 2,...,M} p.4/76 R =(r ij ), r ij = i j ( ): k s r(k, s) r(k, 1),r(k, 2),...,r(k,

More information

[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization)

[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization) . D............................................... : E = κ ............................................ 3.................................................

More information

Z: Q: R: C: 3. Green Cauchy

Z: Q: R: C: 3. Green Cauchy 7 Z: Q: R: C: 3. Green.............................. 3.............................. 5.3................................. 6.4 Cauchy..................... 6.5 Taylor..........................6...............................

More information

nsg04-28/ky208684356100043077

nsg04-28/ky208684356100043077 δ!!! μ μ μ γ UBE3A Ube3a Ube3a δ !!!! α α α α α α α α α α μ μ α β α β β !!!!!!!! μ! Suncus murinus μ Ω! π μ Ω in vivo! μ μ μ!!! ! in situ! in vivo δ δ !!!!!!!!!! ! in vivo Orexin-Arch Orexin-Arch !!

More information

(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law

(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law I (Radom Walks ad Percolatios) 3 4 7 ( -2 ) (Preface),.,,,...,,.,,,,.,.,,.,,. (,.) (Basic of Proability Theory). (Probability Spacees ad Radom Variables...............2, (Expectatios, Meas).............................

More information

ms.dvi

ms.dvi ( ) 2010 11 21 1 review Onsager [1] 2 2 1 1 PPM 2010-09 図 1: 実験装置の図 写真中央にある円筒形の容器が超電導コイルで囲まれた真空 容器で この中に電子を閉じ込める 左側の四角い箱の中には光学系が設置されて おり 電子の像を箱左端の CCD カメラへ導く役割を担う このようにして超電導マ グネットから CCD カメラを遠ざけないと 強磁場の影響を受け正しい撮像が行え

More information

nsg02-13/ky045059301600033210

nsg02-13/ky045059301600033210 φ φ φ φ κ κ α α μ μ α α μ χ et al Neurosci. Res. Trpv J Physiol μ μ α α α β in vivo β β β β β β β β in vitro β γ μ δ μδ δ δ α θ α θ α In Biomechanics at Micro- and Nanoscale Levels, Volume I W W v W

More information

2 σ γ l σ ο 4..5 cos 5 D c D u U b { } l + b σ l r l + r { r m+ m } b + l + + l l + 4..0 D b0 + r l r m + m + r 4..7 4..0 998 ble4.. ble4.. 8 0Z Fig.4.. 0Z 0Z Fig.4.. ble4.. 00Z 4 00 0Z Fig.4.. MO S 999

More information

3/4/8:9 { } { } β β β α β α β β

3/4/8:9 { } { } β β β α β α β β α β : α β β α β α, [ ] [ ] V, [ ] α α β [ ] β 3/4/8:9 3/4/8:9 { } { } β β β α β α β β [] β [] β β β β α ( ( ( ( ( ( [ ] [ ] [ β ] [ α β β ] [ α ( β β ] [ α] [ ( β β ] [] α [ β β ] ( / α α [ β β ] [ ] 3

More information

橡博論表紙.PDF

橡博論表紙.PDF Study on Retaining Wall Design For Circular Deep Shaft Undergoing Lateral Pressure During Construction 2003 3 Study on Retaining Wall Design For Circular Deep Shaft Undergoing Lateral Pressure During Construction

More information

本組よこ/根間:文11-029_P377‐408

本組よこ/根間:文11-029_P377‐408 377 378 a b c d 379 p M NH p 380 p 381 a pp b T 382 c S pp p 383 p M M 384 a M b M 385 c M d M e M 386 a M b M a M 387 b M 388 p 389 a b c 390 391 a S H p p b S p 392 a T 393 b S p c S 394 A a b c d 395

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

gr09.dvi

gr09.dvi .1, θ, ϕ d = A, t dt + B, t dtd + C, t d + D, t dθ +in θdϕ.1.1 t { = f1,t t = f,t { D, t = B, t =.1. t A, tdt e φ,t dt, C, td e λ,t d.1.3,t, t d = e φ,t dt + e λ,t d + dθ +in θdϕ.1.4 { = f1,t t = f,t {

More information

プラズマ核融合学会誌1月【83-2】/講座2-3

プラズマ核融合学会誌1月【83-2】/講座2-3 2.3 Plasma Flow Measurements Spectroscopic Methods KADO Shinichiro author s e-mail: kado@q.t.u-tokyo.ac.jp Czerny-Turner GN: grating normalmn: mount normalfn: facet normal. f L L Fig. 3 μ μ in-situ μ

More information

LHC ALICE (QGP) QGP QGP QGP QGP ω ϕ J/ψ ALICE s = ev + J/ψ

LHC ALICE (QGP) QGP QGP QGP QGP ω ϕ J/ψ ALICE s = ev + J/ψ 8 + J/ψ ALICE B597 : : : 9 LHC ALICE (QGP) QGP QGP QGP QGP ω ϕ J/ψ ALICE s = ev + J/ψ 6..................................... 6. (QGP)..................... 6.................................... 6.4..............................

More information

2

2 th 37 ICh Theoretical Examination - - - - 5 - - : - ( ): ( ) - : 279 - - - - - - - G D L U C K 1 2 1 amu = 1.6605 10-27 kg N = 6.02 10 23 mol -1 k = 1.3806503 10-23 J K -1 e = 1.6022 10-19 C F = 9.6485

More information

Note5.dvi

Note5.dvi 12 2011 7 4 2.2.2 Feynman ( ) S M N S M + N S Ai Ao t ij (i Ai, j Ao) N M G = 2e2 t ij 2 (8.28) h i μ 1 μ 2 J 12 J 12 / μ 2 μ 1 (8.28) S S (8.28) (8.28) 2 ( ) (collapse) j 12-1 2.3 2.3.1 Onsager S B S(B)

More information

CKY CKY CKY 4 Kerr CKY

CKY CKY CKY 4 Kerr CKY ( ) 1. (I) Hidden Symmetry and Exact Solutions in Einstein Gravity Houri-Y.Y: Progress Supplement (2011) (II) Generalized Hidden Symmetries and Kerr-Sen Black Hole Houri-Kubiznak-Warnick-Y.Y: JHEP (2010)

More information

untitled

untitled . 96. 99. ( 000 SIC SIC N88 SIC for Windows95 6 6 3 0 . amano No.008 6. 6.. z σ v σ v γ z (6. σ 0 (a (b 6. (b 0 0 0 6. σ σ v σ σ 0 / v σ v γ z σ σ 0 σ v 0γ z σ / σ ν /( ν, ν ( 0 0.5 0.0 0 v sinφ, φ 0 (6.

More information

CVMに基づくNi-Al合金の

CVM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

1 P2 P P3P4 P5P8 P9P10 P11 P12

1 P2 P P3P4 P5P8 P9P10 P11 P12 1 P2 P14 2 3 4 5 1 P3P4 P5P8 P9P10 P11 P12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 & 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1! 3 2 3! 4 4 3 5 6 I 7 8 P7 P7I P5 9 P5! 10 4!! 11 5 03-5220-8520

More information

研修コーナー

研修コーナー l l l l l l l l l l l α α β l µ l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

More information

(Basics of Proability Theory). (Probability Spacees ad Radom Variables,, (Ω, F, P ),, X,. (Ω, F, P ) (probability space) Ω ( ω Ω ) F ( 2 Ω ) Ω σ (σ-fi

(Basics of Proability Theory). (Probability Spacees ad Radom Variables,, (Ω, F, P ),, X,. (Ω, F, P ) (probability space) Ω ( ω Ω ) F ( 2 Ω ) Ω σ (σ-fi I (Basics of Probability Theory ad Radom Walks) 25 4 5 ( 4 ) (Preface),.,,,.,,,...,,.,.,,.,,. (,.) (Basics of Proability Theory). (Probability Spacees ad Radom Variables...............2, (Expectatios,

More information

c a a ca c c% c11 c12

c a a ca c c% c11 c12 c a a ca c c% c11 c12 % s & % c13 c14 cc c16 c15 %s & % c211 c21% c212 c21% c213 c21% c214 c21% c215 c21% c216 c21% c23 & % c24 c25 c311 c311 % c% c % c312 %% a c31 c315 c32 c33 c34 % c35 c36 c411 c N

More information

1. Introduction Palatini formalism vierbein e a µ spin connection ω ab µ Lgrav = e (R + Λ). 16πG R µνab µ ω νab ν ω µab ω µac ω νcb + ω νac ω µcb, e =

1. Introduction Palatini formalism vierbein e a µ spin connection ω ab µ Lgrav = e (R + Λ). 16πG R µνab µ ω νab ν ω µab ω µac ω νcb + ω νac ω µcb, e = Chiral Fermion in AdS(dS) Gravity Fermions in (Anti) de Sitter Gravity in Four Dimensions, N.I, Takeshi Fukuyama, arxiv:0904.1936. Prog. Theor. Phys. 122 (2009) 339-353. 1. Introduction Palatini formalism

More information

(Basics of Proability Theory). (Probability Spacees ad Radom Variables,, (Ω, F, P ),, X,. (Ω, F, P ) (probability space) Ω ( ω Ω ) F ( 2 Ω ) Ω σ (σ-fi

(Basics of Proability Theory). (Probability Spacees ad Radom Variables,, (Ω, F, P ),, X,. (Ω, F, P ) (probability space) Ω ( ω Ω ) F ( 2 Ω ) Ω σ (σ-fi II (Basics of Probability Theory ad Radom Walks) (Preface),.,,,.,,,...,,.,.,,.,,. (Basics of Proability Theory). (Probability Spacees ad Radom Variables...............2, (Expectatios, Meas).............................

More information

Fig. Division of unbounded domain into closed interior domain and its eterior domain. Zienkiewicz [5, 6] Burnett [7, 8] [3] The conjugated Ast

Fig. Division of unbounded domain into closed interior domain and its eterior domain. Zienkiewicz [5, 6] Burnett [7, 8] [3] The conjugated Ast 7 6 pp. 635 643 635 43..Rz; 43.4.Rj * 3 3 Unbounded problems, Finite element method, Infinite element, Hybrid variational principle, Fourier series. Boundary Element Method: BEM BEM Finite Element Method:

More information

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1. 1.1 1. 1.3.1..3.4 3.1 3. 3.3 4.1 4. 4.3 5.1 5. 5.3 6.1 6. 6.3 7.1 7. 7.3 1 1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N

More information

本組よこ/根間:文11-11_P131-158

本組よこ/根間:文11-11_P131-158 131 132 pp 133 134 a b 135 S pp S 136 a p b p S 137 p S p p H a p b 138 p H p p 139 T T pp pp a b c S a Sp a 140 b c d Sp a b c d e Spp a 141 b c d S a b c d S pp a b 142 c d e S S S S S S S 143 S S S

More information

(a) (b) X Ag + + X AgX F < Cl < Br < I Li + + X LiX F > Cl > Br > I (a) (b) (c)

(a) (b) X Ag + + X AgX F < Cl < Br < I Li + + X LiX F > Cl > Br > I (a) (b) (c) ( 13 : 30 16 : 00 ) (a) (b) X Ag + + X AgX F < Cl < Br < I Li + + X LiX F > Cl > Br > I (a) (b) (c) (a) CH 3 -Br (b) (c),2,4- (d) CH 3 O-CH=CH-CH 2 (a) NH 2 CH 3 H 3 C NH 2 H CH 3 CH 3 NH 2 H 3 C CH 3

More information

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t 1 1.1 sin 2π [rad] 3 ft 3 sin 2t π 4 3.1 2 1.1: sin θ 2.2 sin θ ft t t [sec] t sin 2t π 4 [rad] sin 3.1 3 sin θ θ t θ 2t π 4 3.2 3.1 3.4 3.4: 2.2: sin θ θ θ [rad] 2.3 0 [rad] 4 sin θ sin 2t π 4 sin 1 1

More information

EOS Kiss X4 使用説明書

EOS Kiss X4 使用説明書 J J 2 3 6 V U 0 S 0 9 7 8 3 M M M 1 4 1 2 3 4 5 6 7 8 9 10 11 5 6 1 2 Q 3 1 1 7 2 3 4 5 6 C x 3 4 d Z D E S i j A s f a 8 q Oy A A A A B 2 7 8 5 6 7 8 A B f HI u y b X 9 10 11 K L B w W 9 i j s f D 7 A

More information

Stereoelectronic Effect

Stereoelectronic Effect node anti bonding M ( σ* ) A A : bonding M ( σ ) A: atomic orbital M: molecular orbital node anti bonding M filled orbital of molecular 1 M bonding M vacant orbital of molecular 2 LUM LUM (lowest unoccupied

More information

I 1 V ( x) = V (x), V ( x) = V ( x ) SO(3) x = R x: R SO(3) Lorentz R t JR = J: J = diag(1, 1, 1, 1) x = x + a Poincarré ( ) 2

I 1 V ( x) = V (x), V ( x) = V ( x ) SO(3) x = R x: R SO(3) Lorentz R t JR = J: J = diag(1, 1, 1, 1) x = x + a Poincarré ( ) 2 III 1 2005 Jan 30th, 2006 I : II : I : [ I ] 12 13 9 (Landau and Lifshitz, Quantum Mechanics chapter 12, 13, 9: Pergamon Pr.) [ ] ( ) (H. Georgi, Lie algebra in particle physics, Perseus Books) [ ] II

More information

H J

H J H J qt q w e r t qt q w e r t qt q w e r t qt q w e r t qt q w e r t qt q w e r t qt q w e r t H qt q w e r t qt q w e r t J qt q w e r t D qt q w e r t qt q w e r t qt q w e r t qt D q w e r t qy q w

More information

mains.dvi

mains.dvi 8 Λ MRI.COM 8.1 Mellor and Yamada (198) level.5 8. Noh and Kim (1999) 8.3 Large et al. (1994) K-profile parameterization 8.1 8.1: (MRI.COM ) Mellor and Yamada Noh and Kim KPP (avdsl) K H K B K x (avm)

More information

176 B B.1: ( ) ( ) ( ) (2 2 ) ( ) ( ) ( ) (quantitative nondestructive evaluation:qnde) (1) X X X X CT(computed tomography)

176 B B.1: ( ) ( ) ( ) (2 2 ) ( ) ( ) ( ) (quantitative nondestructive evaluation:qnde) (1) X X X X CT(computed tomography) B 1) B.1 B.1.1 ( ) B.1 1 50 100 m B.1.2 (nondestructive testing:ndt) (nondestructive inspection:ndi) (nondestructive evaluation:nde) 175 176 B B.1: ( ) ( ) ( ) (2 2 ) ( ) ( ) ( ) (quantitative nondestructive

More information

Microsoft Word - 5MS.doc

Microsoft Word - 5MS.doc 5 5.1 mass spectrometer electron impact, EI 5.1 :;"< 789 =>? *!"#$%& '%&(),,,-./ 0.12%3456 :;"@AB CDEFG:;"HIJK@LMN :;"@HIOPQ0RST6 5.1. 70 ev molecular ion #"$%& M M e!"!"'() #" m/z ; m = z = 1 mass spectrum,

More information

1

1 016 017 6 16 1 1 5 1.1............................................... 5 1................................................... 5 1.3................................................ 5 1.4...............................................

More information

第122号.indd

第122号.indd -1- -2- -3- 0852-36-5150 0852-36-5163-4- -5- -6- -7- 1st 1-1 1-2 1-3 1-4 1-5 -8- 2nd M2 E2 D2 J2 C2-9- 3rd M3 E3 D3 J3 C3-10- 4th M4 E4 D4 J4 C4-11- -12- M5 E5 J5 D5 C5 5th -13- -14- NEWS NEWS -15- NEWS

More information

10:30 12:00 P.G. vs vs vs 2

10:30 12:00 P.G. vs vs vs 2 1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B

More information

3章 問題・略解

3章 問題・略解 S S W R S O( l) O( ) c Jg g J Jg S R J 7. K.9 JK S W S R S JK S S R J 7. K.9JK 4 (a) -Tice 7.K T ice T N 77 K S R.9 JK 4. JK T T ice N.6JK S W S R S JK S S.6JK R (b) S R JK S.6 JK T T ice N 6 O( c) O(

More information

d dt A B C = A B C d dt x = Ax, A 0 B 0 C 0 = mm 0 mm 0 mm AP = PΛ P AP = Λ P A = ΛP P d dt x = P Ax d dt (P x) = Λ(P x) d dt P x =

d dt A B C = A B C d dt x = Ax, A 0 B 0 C 0 = mm 0 mm 0 mm AP = PΛ P AP = Λ P A = ΛP P d dt x = P Ax d dt (P x) = Λ(P x) d dt P x = 3 MATLAB Runge-Kutta Butcher 3. Taylor Taylor y(x 0 + h) = y(x 0 ) + h y (x 0 ) + h! y (x 0 ) + Taylor 3. Euler, Runge-Kutta Adams Implicit Euler, Implicit Runge-Kutta Gear y n+ y n (n+ ) y n+ y n+ y n+

More information

1. 2. C2

1. 2. C2 2000 7 6 (I) (II) ( 47, 1999) C1 1. 2. C2 1 ˆk AIC T C3 1.1 ( : 3 ) Y N ( µ(x a,x b,x c ),σ 2) µ(x a,x b,x c )=β 0 + β a x a + β b x b + β c x c x a,x b,x c α α {a, b, c} Θ α = {(σ, β) σ >0,β i =0,i α

More information

èCémò_ï (1Å`4èÕ).pdf

èCémò_ï (1Å`4èÕ).pdf Simulation of Magnetization Process in Antiferromagnetic Exchange-Coupled Films 19 1...1 1-1...1 1-2...1 1-2-1... 1 1-2-2 HDD...2 1-2-3 ( )...3 1-3 GMR... 4 1-4 ( )...5 1-5 SFMedia...5 1-6 (HAMR)...6 1-6-1...

More information

(I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 Typeset by Akio Namba usig Powerdot. 2 / 47

(I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 Typeset by Akio Namba usig Powerdot. 2 / 47 4 Typeset by Akio Namba usig Powerdot. / 47 (I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 Typeset by Akio Namba usig Powerdot. 2 / 47 (I) (II) 2 (I) 2 (II) 2 (III) (I) (II) (II) : 2 (radom variable):

More information

09基礎分析講習会

09基礎分析講習会 データ解析の意味を理解しないでパソコンで計算して 序論 誤差解析 何のために も意味がない 以下の本でちゃんと勉強しよう R. A. Millikan ミリカン 水滴の蒸発 大学院生H. Fletcher 水滴を油滴に 博士論文単名 140の観測のうち49個除外 データ削除 実験データを正しく扱うために 化学同人編集部編 油滴実験 Regener がもともとThompsonの実験室(Cambridge

More information

寄稿論文 規則性無機ナノ空間が創り出す新しい触媒能 | 東京化成工業

寄稿論文 規則性無機ナノ空間が創り出す新しい触媒能 | 東京化成工業 MCM-41 M41 MCM-41 M41 2 3 m 2 /g nm nm Mn Ti Ti H N 2 S Ti-MCM-41, H H N H H 2 2 -Urea, CH 2 Cl 2, H 2 S + S 1b 2b 3b 54%, 58% ee Ti M41 H 2 As 4 ZP 4 ZP ZS ZS 5 Me Me Me Me M41 / 15 mg MeH 1.0 mmol 89%

More information

* ἅ ὅς 03 05(06) 0 ἄβιος,-ον, ἄβροτον ἄβροτος ἄβροτος,-ον, 08 17(01)-03 0 ἄβυσσος,-ου (ἡ), 08 17(01)-03 0 ἀβύσσου ἄβυ

* ἅ ὅς 03 05(06) 0 ἄβιος,-ον, ἄβροτον ἄβροτος ἄβροτος,-ον, 08 17(01)-03 0 ἄβυσσος,-ου (ἡ), 08 17(01)-03 0 ἀβύσσου ἄβυ Complete Ancient Greek 2010 (2003 ) October 15, 2013 * 25 04-23 0 ἅ ὅς 03 05(06) 0 ἄβιος,-ον, 15 99-02 0 ἄβροτον ἄβροτος 15 99-02 0 ἄβροτος,-ον, 08 17(01)-03 0 ἄβυσσος,-ου (ἡ), 08 17(01)-03 0 ἀβύσσου ἄβυσσος

More information

( ) g 900,000 2,000,000 5,000,000 2,200,000 1,000,000 1,500, ,000 2,500,000 1,000, , , , , , ,000 2,000,000

( ) g 900,000 2,000,000 5,000,000 2,200,000 1,000,000 1,500, ,000 2,500,000 1,000, , , , , , ,000 2,000,000 ( ) 73 10,905,238 3,853,235 295,309 1,415,972 5,340,722 2,390,603 890,603 1,500,000 1,000,000 300,000 1,500,000 49 19. 3. 1 17,172,842 3,917,488 13,255,354 10,760,078 (550) 555,000 600,000 600,000 12,100,000

More information

86 6 r (6) y y d y = y 3 (64) y r y r y r ϕ(x, y, y,, y r ) n dy = f(x, y) (6) 6 Lipschitz 6 dy = y x c R y(x) y(x) = c exp(x) x x = x y(x ) = y (init

86 6 r (6) y y d y = y 3 (64) y r y r y r ϕ(x, y, y,, y r ) n dy = f(x, y) (6) 6 Lipschitz 6 dy = y x c R y(x) y(x) = c exp(x) x x = x y(x ) = y (init 8 6 ( ) ( ) 6 ( ϕ x, y, dy ), d y,, dr y r = (x R, y R n ) (6) n r y(x) (explicit) d r ( y r = ϕ x, y, dy ), d y,, dr y r y y y r (6) dy = f (x, y) (63) = y dy/ d r y/ r 86 6 r (6) y y d y = y 3 (64) y

More information

,, Mellor 1973),, Mellor and Yamada 1974) Mellor 1973), Mellor and Yamada 1974) 4 2 3, 2 4,

,, Mellor 1973),, Mellor and Yamada 1974) Mellor 1973), Mellor and Yamada 1974) 4 2 3, 2 4, Mellor and Yamada1974) The Turbulence Closure Model of Mellor and Yamada 1974) Kitamori Taichi 2004/01/30 ,, Mellor 1973),, Mellor and Yamada 1974) Mellor 1973), 4 1 4 Mellor and Yamada 1974) 4 2 3, 2

More information