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16 Nov 2005: c) P = 2. q(. 1. q cos p). sin p and Q = log(. ... q1 = Q1 cos λ P2 sin λ , q2 = Q2 cos λ P1 sin λ.

21 Feb 2005: sin(θ ψ) sin(θ ψ) = 2 sin θ cos ψ. We have. ... ρ(B) = cos. (. π. m 1. ). 1 π2. 2m2,.

15 Aug 2005: Denoting by θn. a(t, yn), it is clear that. F (x) = exA(tn,yn) =. (cos xθn θ. 1n sin xθn. θn sin xθn cos xθn. ),. ... 1](x) = ϕ1(x). (cos 2θnx. θ2n sin 2θnx. 2θ3nx x. θ2n+ sin 2θnx.

14 Feb 2005: Suppose |i〉a occurs ai times, |j〉b occurs bj times and|ij〉ab occurs cij times in Eab. ... V b) = RT. van der Waals’ equation. a N2 , b N , R = Nk.

26 Sep 2005: Smoothness is important: the torus. {(cos ψ ρ cos θ, sin ψ ρ sin θ,ρ cos θ) : 0 ψ,θ 2π}. ... Let us compute the commutator of twosuch vector fields F(A,a) and F(B,b).