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18 Jan 2011: b(k) = d t cos(Á(k) µ)n (1). where b(k) is the observed intensity in the kth direction, d is the diffuse component which isindependent of insonification direction ... b(k) = d te. n. cos1. sin µcos µ cos Ψ cos µ sin Ψ.

21 Feb 2011: and a b c < 2π. Conversely, show that for any three positive numbers a,b,c lessthan π satisfying the above conditions, we have cos(b c) < cos a < cos(bc), ... Deduce theformula. sin α sin β cos c = cos γ cos α cos β.

25 Oct 2011: ϕ(s,v) = α(s) r(n(s) cos v b(s) sin v. ),. where n = n(s) and b = b(s) are the normal and binormal vectors of α. ... 9. Consider a surface of revolution parametrized by ϕ : (0, 2π) (a,b) R3, whereϕ(u,v) =. (f(v) cos u,f(v) sin u,g(v). ). Suppose f

25 Nov 2011: u(1, t) = ν(t) = eω2t cos ω b. ω2. (1 eω. ... p0(1, t) = ν(t) = eω2t cos ω b. ω2. (1 eω.

22 Jun 2011: cos x. (x2 a2)(x2 b2)dx. Also evaluate. cos x. (x2 a2)2dx. ... a)12π. eax2. eiωxdx (b)12π. sin x. xeiωxdx. (c). 12π. eiωx. x2 a2dx.

31 Oct 2011: ϕ(s,v) = α(s) r(n(s) cos v b(s) sin v. ),. where n = n(s) and b = b(s) are the normal and binormal vectors of α. ... 9. Consider a surface of revolution parametrized by ϕ : (0, 2π) (a,b) R3, whereϕ(u,v) =. (f(v) cos u,f(v) sin u,g(v). ). Suppose f

21 Feb 2011: ϕ(s,v) = α(s) r(n(s) cos v b(s) sin v. ),. where n = n(s) and b = b(s) are the normal and binormal vectors of α. ... 10. Consider a surface of revolution parametrized by ϕ : (0, 2π) (a,b) R3, whereϕ(u,v) =. (f(v) cos u,f(v) sin u,g(v). ). Suppose f

22 Nov 2011: 1! 1!cos##"". F B µµ–. e+ e–. µµ++. F B e.g. ... backward hemisphere. Prof. M.A. Thomson Michaelmas 2011 506. -1! 1!cos##"". F B!

13 Jan 2011: Algebraically,. 1. ap1 = 1, 0, 0 , 3. 1. ap2 =. b. acos , sin , 0 , 4. 1. ap3 =. c. acos , cos sin , sin sin , 5. where a, b, and c are the lengths ... 1. b/a0, 1sin , cos sin sin , 11av3 =. u1 u2u1 u2 u3.

21 Oct 2011: Freundt. where h̃ = h di tan θ and d = δd di / cos θ. ... t. (hi /g)1/2. =FT (0, φ) tan φ. (cos θ )1/2 (tan φ tan θ ). (5.2). Figure 8(b) reveals that this solution is a poor representation