Baker and Schubert (1998) NOTE 1 Baker and Schubert(1998) 1 (subsolar point) 177.4, ( 1). Sp dig subsolar point equator 2.7 dig Np Sun V
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1 Baker and Schubert (1998) NOTE 1 Baker and Schubert(1998) 1 (subsolar point) 177.4, ( 1). Sp dig subsolar point equator 2.7 dig Np Sun Venus 1:. 2 (Rayleigh number), ρ u i t + ρu u i j = p + x j x i x i { ( ui µ + u j x j 2 )} u k δ ij ρge z. (1) x i 3 x k u i x j = 0 (2)
2 Baker and Schubert (1998) NOTE 2 (1) (2) u i t + u u i j = 1 p ν 2 u i ge z. (3) x j ρ x i, ν = µ/ρ. ( )., ρ ρ 0 ρ (x, y, z, t)., p ρ 0 p 0, p (x, y, z, t)., (3) 2, 3, 1 ρ ge z = 1 p 0 + p ρ 0 + ρ x i ρ = ρ 0 + ρ, (4) p = p 0 + p. (5) = 1 ρ 0 p 0 x i + ρ ρ 2 0 ge z p 0 x i 1 ρ 0 p x i ge s.,, p 0 x i = ρ 0 ge s (6).,, 1 ρ ge z = ge z 1 ρ 0 p x i ρ ρ 0 ge s ge z = 1 ρ 0 p x i ρ ρ 0 ge z u i t = 1 ρ 0 p x i ρ ρ 0 ge z + ν 2 u i. (7)
3 Baker and Schubert (1998) NOTE 3 (16). x = d x, t = d2 ν t, u = L τ ũ = d d 2 /ν ũ = ν dũ, p = ρ 0 U 2 ν 2 = ρ 0 d, 2 T = Γd T. (8),. d, L, Γ., (16),, ν ν ũ i d 2 d t = αt ge z ρ 0 ν 2 p + ν2 ρ 0 d 3 x i d 2 ũ 3 i = αγd T e z ν2 p + ν2 d 3 x i d 2 ũ 3 i ũ i t = αγgd4 T ez p + ν 2 x 2 ũ i i,., = Ra P r T e z p x i + 2 ũ i. (9) Ra = αγgd4 νκ, (10) P r = ν (11) κ, (Rayleigh number) (Prandtl number)... ( ),.,..
4 Baker and Schubert (1998) NOTE 4, T t + v T = κ 2 T (12),,, 2 T = 0. z,, A, B,, Γ,. T = Az + B. T = T 1 T 2 z + T 2. d Γ = dt dz = T 1 T 2 d = const.. C. q, T. C V, S, [ ] = [ ]., ρc p T dv = t V = S V q ds div q dv.
5 Baker and Schubert (1998) NOTE 5,., c p, ρ., 1 ) q = k T, ρc p T dv = k 2 T dv. t V V, T t = k ρc p 2 T = κ 2 T.,,. κ = k ρc p V (T, p)., ( ) ( ) V V V = T + P T p p T, V V = 1 V ( ) V T + 1 T p V ( ) V P p T. 2. α, α = 1 ( ) V V T p = 1 R V p = 1 T. 1 ),,, (q), (dt/dx) (S)., q = ks dt dx., S = 1.
6 Baker and Schubert (1998) NOTE 6 BS1998 (maximam internally heated Rayligh numbers)., (10),.,, (10), T = Γd. T = q 0d k. Γd = dq 0 ρ 0 c p κ. Ra q = gq 0d 4 T 0 ρ 0 c p νκ 2. BS1998, Ra q = gq 0d 5 T 0 ρ 0 c p νκ 2 (13)., (13) q 0,., BS1998 d 7 km Ra q., Ra q,, 100% ). 2 ),.. ν = κ m κ = κ θ
7 Baker and Schubert (1998) NOTE 7 g 8.87 m s 2 R J kg 1 K 1 c p 891 J kg 1 K 1 κ m 155 m 2 s 1 κ θ 155 m 2 s 1 d 20.0 km ρ kg m 3 T K q 0 (60%) W m 3 (80%) W m 3 (100%) W m 3 P r 1.00 γ 1.27 C g C k C q ,, 100%,,. Ra q = gq 0d 5 T 0 ρ 0 c p νκ = = ,. ( )..
8 Baker and Schubert (1998) NOTE 8 ν κ m κ κ θ ν u i u i x u j = κ ū i m j x j κ θ θ x u j = κ θ θ j x j, ( ).,.. θ z. z w, z. z, ( θ + θ w ) = θ w (14).,., w., l., l /2 3 ). l /2, θ l d θ 2 dz,, ] [ θ(z) l d θ w 2 dz.,, ] [ θ(z) + l d θ w 2 dz., z,, 3 ). θ w = l d θ dz w l d θ w 2 dz
9 Baker and Schubert (1998) NOTE 9. θ w, l w 2. κ θ l w 2. x ρu z ρu w, ρu w ρl dū w 2 dz, κ m l w 2., ū ± l dū/dz, ū u, u 2 w 2, u 2 w 2 l dū dz., ρu w = ρl 2 dū dū dz dz..
10 Baker and Schubert (1998) NOTE 10 Mariner10, PioneerVenus, Gallileo, km km (Belton et al. 1976, 1991; Rossow et al. 1980; Covey and Schubert 1981; Baker and Schubert 1992; Murray et al. 1974; Toigo et al. 1994). 2. 2: (Baker and Schubert 1992). Mariner10, Magellan Mariner10 (Howard et al. 1974) Magellan (Jenkins et al. 1994) 4 ), km, km. Pioneer Venus Pioneer, km, km (Seiff et al. 1980). Vega (Young et al. 1987). Vega km 1 3 km s 1 (Linkin et al. 1986). 4 ),,..
11 Baker and Schubert (1998) NOTE 11 3: Vega1 (Linkin et al. 1992)., (A), (B), (C), (D). ( / ) 10 2, 1 (Agee 1987). 2 (Tritton 1975).,. Tritton.
12 Baker and Schubert (1998) NOTE 12, 100 (Covey and Schubert 1981)., wave-convection (Baker and Schubert 1992). 60km convective layer If a convection occures only in this layer, the aspecto ratio is about km 30km 18km static layer (In this layer, only wave can propagate.) convective layer wave If a convection occures in whole reasion, the aspecto ratio is about 10, then it seems to be Earth-like ratio. 4:. 100.,, 10,. (Schubert 1983; Schubert and Walterscheid 1984; Schinder et al. 1990; Baker and Schubert 1992; Seiff et al. 1992; Leroy 1994; Leroy and Ingersoll 1995, 1996). Pioneer (Seiff et al. 1980) Magellan (Jenkins etal. 1994; Hinson and Jenkins 1995)..,.,.
13 Baker and Schubert (1998) NOTE 13 5 )., 2. Baker and Schubert ,., 3., 100%, 80%, 60%., 2. u, w, ρ, θ., d, ρ 0, T 0, q 0, d/(rt 0 ) 1/2,. R, 60 km. ρ t = ρu i, (15) x i ρu i = (ρu t x iu j + p δ ij σc k τ ij) C g ρ δ i3, (16) j θ t = [( θ + θ )u x i] + ( θ + θ ) u i + C ) k (ρκ θ i x i ρ x i x i + γ 1 σc k γ ρ τ u ij j + C q x i ρ Q. (17), u i x i, p, ρ, θ, t, κ, Q, τ ij. τ ij, ( ) u τ ij = ρκ i + u j x j x i., (18) p = (ρθ) γ (19). 5 ),,,.
14 Baker and Schubert (1998) NOTE 14,. x = dˆx (20) t = d ˆt RT0 (21) u = x τ û = RT 0 û (22) p = ρu 2ˆp = ρrt 0ˆp (23) ˆ., ( ) d. (19) ρ, p ρ = γ(ρθ)γ 1 θ. = γrt 0, T 0 c 2 s = p ρ = γrt 0. γ 1, d τ τ = d RT0.,, ρ = ρ + ρ, ρ t + (ρu) = 0 (24) ρ t = ρu i x i (25).
15 Baker and Schubert (1998) NOTE 15, u i t + u u i j = 1 p + 1 [ ( ui ρκ + u )] j gδ i3 x j ρ x i ρ x j x j x i = 1 p + 1 (τ ij ) gδ i3 (26) ρ x i ρ x j, ( ui τ ij = ρκ + u ) j. (27) x j x i (26) ρ+ (25) u i ρu i t + (ρu i u j ) = p + (τ ij ) ρgδ i3 (28) x j x i x j, ρu i t = x i (ρu i u j + pδ ij τ ij ) ρgδ i3 (29). (29), ρu i t = ( ) ρu x i u j + p δ ij τ ij ρ gδ i3 i 6 )., ( ρ 0 RT 0 ˆρû i = 1 ρ 0 ˆρRT 0 û i û j + ρ 0 RT 0ˆp δ ij ρ ) 0κ m RT0 τ ij ρ 0 ˆρ gδ i3. d ˆt d ˆx i d,, ˆρû i ˆt ( ) = ˆρû i û j + ˆp δ ij κ m ˆx i d τ ij RT 0 dg RT 0 ˆρ δ i3. σ = κ m κ θ κ θ C k = d RT 0 C g = dg RT 0, ˆ (16). 6 ),.
16 Baker and Schubert (1998) NOTE 16, 7 )., (24), c p dθ dt = θ T Q (30) c p ( t (ρθ) + (ρθu) ) = θ T Q. 8 ) ( ) c p t (ρ θ) + (ρ θū + ρθ u ) = θ T Q., ( ) c p t (ρ θ) + (ρ θū) = θ T Q c p ρθ u., θ u i κ, θ u i = κ θ x i. (2) (24),, ( θ c p t + ū θ ) j = 1 [ ( ρ θ x j ρ T Q c p ρκ θ )] x j x j (31)., θ θ. θ θ = θ + θ, (31), ( ) θ c p t + u j ( θ + θ ) = 1 [ ) c p (ρκ θ + ρθ ] x j ρ x j x i T Q. 7 ) GFD 2011,. 8 ).,,. ā = 0, a + b = ā + b, a b = ā b, ab = a b, ab = ā b + a b.
17 Baker and Schubert (1998) NOTE 17,., ρθ T Q = τ ij u i + Q. x j, Q.,. ( ) θ c p t + u j ( θ θ ) = 1 [ ) ] c p (ρκ θ + τ u i ij + Q. (32) x j ρ x j x i x j, Q. (32),,,. T 0 RT0 d θ t = [( θ + θ )u x i] + ( θ + θ ) u i i x i + 1 ) (ρκ θ + 1 ρ x i x i c p ρ τ u ij j + 1 x j c p ρ Q. ˆθ t = 1 d T 0 RT0 [(ˆ θ + ˆθ x )û i ] + T 0 ( i + κ θt 0 1 ˆρˆκ ˆθ ) + κ mrt 0 d 2 ˆρ ˆx i ˆx i ˆθ t = [(ˆ θ + ˆθ x )û i ] + (ˆ θ + ˆθ ) û i i ˆx i ( + κ θ d 1 RT 0 ˆρ ˆx i ˆρˆκ ˆθ ˆx i RT0 d 1 d 2 c p ˆρ ˆ τ ij û j ) + κ m RT0 1 τ dc p T 0 ˆρ ˆ ij û j + ˆx i γ = c p c v C q = dq 0 ρ 0 c p T 0 RT0, ˆ (17) 9 ). 9 ), c p c v = R. R = γ 1 c p γ (ˆ θ + ˆθ ) û i ˆx i ˆx i + q 0 c p ρ 0 1 ˆρ ˆQ. dq 0 1 ρ 0 c p T 0 RT0 ˆρ ˆQ
18 Baker and Schubert (1998) NOTE 18 σ 10 ). γ. C g d, d. C k. C q. (15), (16), (17). 2.,, -,. 10 ), τ A t = A κ 2 x 2 τ = L2 κ. L. τ θ, τ m,,, σ = κ m κ θ = τ θ τ m.,.,,,.
19 Baker and Schubert (1998) NOTE (Asselin 1972) ).. ( ) ( ) (z zl ) 2 (z zu ) 2 Q sub (z) = c L exp + c U exp 2σ 2 L 2σ 2 U (33), c L = Wm 3 z L = 27km σ L = 13km c U = Wm 3 z U = 67km σ U = 7.5km, z. Tomasko 1985,, Hou and Goody 1989 ( 5).. 11 ) GFD.
20 Baker and Schubert (1998) NOTE 20 5: (33) ( ). + Pioneer Venus (Tomasko et al. 1985), Hou and Goody (1989). g 8.87 m s 2 R J kg 1 K 1 c p 891 J kg 1 K 1 κ m 155 m 2 s 1 κ θ 155 m 2 s 1 d 20.0 km ρ kg m 3 T K q 0 (60%) W m 3 (80%) W m 3 (100%) W m 3 P r 1.00 γ 1.27 C g C k C q
21 Baker and Schubert (1998) NOTE 21 g, R, c p, κ m, κ θ 60 km. c p 350 K, 50 km (Seiff 1983) km, 180 km. 168, 1000.,..,., 5 km. 80%,. 60%, 100% 80%., CFL s. 60%, 100%, 15.6, % 50.,, % θ. 6, km, 1 2 km..,,.
22 Baker and Schubert (1998) NOTE 22 6: 100% km, km, km km. d dz (F c + F e + F k + F p + F v + F q ) (W b W p ) = 0. (34) F c, F e, F k, F p, F v, F q, W b, W p., (34),.
23 Baker and Schubert (1998) NOTE 23,. F c =< ρθ > (35) F e = C k ρκ dθ (36) dz F k = 1 (γ 1) < ρu 2 γ iu iw > (37) (γ 1) F p = < p w > γ (38) (γ 1) F v = σc k < u γ iτ iz > (39) F q = C q < F Q > (40) (γ 1) W b = C g < ρ w > (41) γ (γ 1) W p = p u j (42) γ x j, <>,. z, w., F Q Q..,,. d dz (F k + F p ) (W b + W p W v ) = 0. (43), W v,. W v = (γ 1) γ τ ij σc k u i x j (44)
24 Baker and Schubert (1998) NOTE 24 4: 7:. a) 60%, b) 80%, c) 100%. 7.,., 60%, 80%, 100% 115, 117, % 8.16 J m 3, (Emanuel 1994) J m 3, 12 ). 12 ) [1] p217.
25 Baker and Schubert (1998) NOTE 25 5: 54 km 8: 54 km. (a) t = 15.0 h 60% (b) t = 24.1 h 80%, (b) t = 13.8 h 100%.. 54 km. 1 3 km s 1 (Linkin et al. 1986). 3. (km s 1 ) (km s 1 ) 60% % %
26 Baker and Schubert (1998) NOTE 26,.,,. 6: 100% 9: 100%. (a), (b). F c ( ), F e ( ), F k ( ), F p ( ), F v (2 ), F q ( ). F q F c. F c, 13 ). 13 ) [1]p.156.
27 Baker and Schubert (1998) NOTE 27 w = ( ) 1/3 Fs gl (45) ρc p T. l = 7 km, 51.5 km, F s = 216 W m 2, ρ = 1.29 kg m 3,T = 335 K, 100% 3.27 m s 1.,.. 100% 4 14 km s 1, 10 m s ,,.,., 7 km, 7.2 km.,,., 10.,.,,.
28 Baker and Schubert (1998) NOTE 28 10: 100%,,. (43),,,,.
29 Baker and Schubert (1998) NOTE 29 11, % : 100%. 20 km < x < 70 km, 12.4.
30 Baker and Schubert (1998) NOTE 30 12: 8.
31 Baker and Schubert (1998) NOTE 31 11(a) 11(b) 12(c) 12(d, e) t = 21.4, x = 36 km z = 47 km 12, z = 44 km. (x = 41 km, z = 46 km )., 45 km. 4 K. 12, 43 km..,.., x = 35 km. 12 ( 12(d)),, ( 12(e))., :,. ( ), 60% ( ), 80% ( ), 100% (2 ). 13,,.,
32 Baker and Schubert (1998) NOTE 32. 3, 43.2 km, 43.1 km 42.7 km. 16.,. 14: 100% F c., W 2 m 4 Hz W 2 m 4 Hz 1., -. 14, F c., F c 30, 46, 105., F c 11, 13, 16, 105.
33 Baker and Schubert (1998) NOTE 33 11, 12,. 1 2 km s km, 5 30 km. 40 km. 10 m s 1,., m s 1., 58 km km. 40, 60 km,.. 5 km.,,., 40 km,.,,.,. 15
34 Baker and Schubert (1998) NOTE 34 15: 52 km.. ( ), ( ) km km.,.
35 Baker and Schubert (1998) NOTE 35 [1], 1984:,, 305pp
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6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
![6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2](/thumbs/92/109118076.jpg "6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2")
1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
chap10.dvi
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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.
8 300 mm 2.50 m/s L/s ( ) 1.13 kg/m MPa 240 C 5.00mm 120 kpa ( ) kg/s c p = 1.02kJ/kgK, R = 287J/kgK kPa, 17.0 C 118 C 870m 3 R = 287J
26 1 22 10 1 2 3 4 5 6 30.0 cm 1.59 kg 110kPa, 42.1 C, 18.0m/s 107kPa c p =1.02kJ/kgK 278J/kgK 30.0 C, 250kPa (c p = 1.02kJ/kgK, R = 287J/kgK) 18.0 C m/s 16.9 C 320kPa 270 m/s C c p = 1.02kJ/kgK, R = 292J/kgK
July 28, H H 0 H int = H H 0 H int = H int (x)d 3 x Schrödinger Picture Ψ(t) S =e iht Ψ H O S Heisenberg Picture Ψ H O H (t) =e iht O S e i
July 8, 4. H H H int H H H int H int (x)d 3 x Schrödinger Picture Ψ(t) S e iht Ψ H O S Heisenberg Picture Ψ H O H (t) e iht O S e iht Interaction Picture Ψ(t) D e iht Ψ(t) S O D (t) e iht O S e ih t (Dirac
m(ẍ + γẋ + ω 0 x) = ee (2.118) e iωt P(ω) = χ(ω)e = ex = e2 E(ω) m ω0 2 ω2 iωγ (2.119) Z N ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.120)
2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [
![H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [](/thumbs/99/141438442.jpg "H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [")
3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e
液晶の物理１：連続体理論（弾性，粘性）
The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers
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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
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基礎からの冷凍空調 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/067311 このサンプルページの内容は, 初版 1 刷発行当時のものです. http://www.morikita.co.jp/support. 03-3817-5670FAX 03-3815-8199 i () () Q&A
中央大学セミナー.ppt
String Gas Cosmology References Brandenberger & Vafa, Superstrings in the early universe, Nucl.Phys.B316(1988) 391. Tseytlin & Vafa, Elements of string cosmology, Nucl.Phys.B372 (1992) 443. Brandenberger,
高知工科大学電子 光システム工学科
卒業研究報告 題 目 量子力学に基づいた水素分子の分子軌道法的取り扱いと Hamiltonian 近似法 指導教員 山本哲也 報告者 山中昭徳 平成 14 年 月 5 日 高知工科大学電子 光システム工学科. 3. 4.1 4. 4.3 4.5 6.6 8.7 10.8 11.9 1.10 1 3. 13 3.113 3. 13 3.3 13 3.4 14 3.5 15 3.6 15 3.7 17
September 25, ( ) pv = nrt (T = t( )) T: ( : (K)) : : ( ) e.g. ( ) ( ): 1
September 25, 2017 1 1.1 1.2 p = nr = 273.15 + t : : K : 1.3 1.3.1 : e.g. 1.3.2 : 1 intensive variable e.g. extensive variable e.g. 1.3.3 Equation of State e.g. p = nr X = A 2 2.1 2.1.1 Quantity of Heat
[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt
![[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt](/thumbs/101/152334931.jpg "[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt")
3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 =.69 +.9 =7.74 [.]
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