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16 May 2019: SIGMAA. Calculate phase probabilities from |F. O. |, |F. C. |,. C. Combine MIR phase information using Hendrickson-Lattman coefficients. p(. ). exp[A cos(. ) ... B sin(. ) C cos(2. ) D sin(2. )]. Produce 4 types of map coefficients:.

30 Aug 2019: cos a = cos b cos c sin b sin c cos A. ... sin a cos B = cos b sin c sin b cos c cos A.

17 Jun 2019: cos α =(a b) (a c)|a b||a c|. Using identities (1) and (2), prove that. ... cos δ(B, C) = cos δ(A, B) cos δ(A, C) sin δ(A, B) sin δ(A, C) cos α.

23 Nov 2019: The. Hamiltonian felt by the protons will then be. H = µ (B b cos(ωt) ) = 2µ. ... The TDSE for this system is thus(ȧ. ḃ. )= i. (B b cos(ωt).

17 Jun 2019: 1]. (b). J = π/2. 0. sin x cos x dx. ... 4]. (d) The surface S of an ellipsoid is defined parametrically byx = (b sin θ cos φ, b sin θ sin φ, a cos θ), where 0 6 θ 6 π

1 May 2019: χ2i wi. λab. (Kab K0)2 (18). C00 = 1 (19). C10 = cos θ (20). ... C20 =12(3 cos. 2 θ 1) (21). 2. Table 1: Parameters of PAH anisotropic atom-atom potential in a.u.Atom Pair laκa lbκb ρ α C6C C 00 00

16 May 2019: A cos(αφ. 1. ) B cos(αφ. 2. ). This is where the vector representation of waves becomes very useful. ... i (cosα. 1. sinα. 2. cosα. 2. sinα. 1. ). = cos(α. 1. α. 2. ) i sin(α. 1. α. 2. ).

6 Nov 2019: A cos(ka) B sin(ka) = 0 (4.23). and hence. A cos(ka) = 0 and B sin(ka) = 0. ... or B = 0 , cos(ka) = 0 ,. ψ(x) = A cos(kx) , k =nπ.

8 Nov 2019:   cos φ sin φ 0sin φ cos φ 00 0 1. ... ψ̇ φ̇ cos θ. . (b) [optional extra] Calculate the matrix B = R>Ṙ and verify that it is antisymmetric.

17 Jun 2019: 1]. B C. A. D. 2. 5. Solve for x in the interval 0 6 x 6 π: cos 2x = sinx. ... 1]. Natural Sciences IA, Paper 1. 5. SECTION B. 11Z. (a) Use De Moivre’s theorem to express 8 cos(6θ) 15 sin(4θ) sin(2θ) in terms of cos θand

17 Jun 2019: Prove the Pythagorean theorem for spherical geometry in the form. cos c = cos a cos b. ... E = (E0 cos(kz ωt), 0, 0) B = (0,B0 cos(kz ωt), 0),.

30 Aug 2019: 6|1〉B, sin. π. 6|0〉B cos. π. 6|1〉B. ). ,(. sinπ. 6|0〉B cos. ... π. 6|1〉B, cos. π. 6|0〉B sin. π. 6|1〉B. ). determine the condition, which α and β must satisfy in order for the measurementstatistics to violate the

16 May 2019: Can you remember how to work with the following expression? A cos(αφ. ... 1. ) B cos(αφ. 2. ). This is where the vector representation of waves becomes very useful.

17 Jun 2019: 2]. 3 Differentiate(a) ln(x3);. [1]. (b) x cos(2x). [1]. 4 Integrate. ... a) y = (ln x)2 for 0 < x < ;. [1]. (b) y = sin(x) cos(x) for π 6 x 6 π.

27 May 2019: 1, 2), B = B(r){cos(ot),sin(ot),0}is the background magnetic field, ẑ is the normal to the air–water interface, B(r) is the strength of the ... 4h2sintyðtÞ; (18). where n̂ = {sin[c(t)],cos[c(t)],0}, b 3mB0ðC

17 Jun 2019: sationσ(u, v) =. ((a b cos u) cos v, (a b cos u) sin v, b sin u. ),. ... 2π. 0. sin2 θdθ. a b cos θ=. 2π. b2. [a.

30 Aug 2019: X(θ) = b(cos θ, sin θ, θ tan φ), 0 6 θ 6 L cos φ/b, (). where φ is the pitch of the helix (i.e. the constant angle ... between dX/dθ and the xy-plane)and L cos φ b.

17 Jun 2019: π2. 8=. n=1. 1(2n 1)2. [17]. 3B Consider the matrix. A =(. cos θ sin θsin θ cos θ. ). (a) Determine the eigenvalues of A. ... r = (a cos φ sin θ, b sin φ sin θ, c cos θ).

17 Jun 2019: cos α =(a b) (a c)|a b||a c|. Using identities (1) and (2), prove that. ... cos δ(B, C) = cos δ(A, B) cos δ(A, C) sin δ(A, B) sin δ(A, C) cos α.

30 Aug 2019: χ =(A cos αr. B sin αrr. cr2). sin2 θ. Find conditions on A,B,C and α for which B = 0 on the sphere r = a, and givean expression for ... πc(τ) sin 2πz,. χ =1k. [πd(τ). ( 8p. )1/2sin kx cos πz e(τ) sin 2kx. ],.