Search

17 Jun 2019: G =. {(a bc d. ): a, b, c, d Fp, ad bc 6= 0. }. ... a (b c). Given that the vector a b b c c a is orthogonal to the plane Ψ of the faceABC, obtain an equation for Ψ.

17 Jun 2019: z. Hence show that b(z) and a(z) satisfy. b′ =b. cD. [. kbχ. a c2. ]. , a′ =kb. c,. where the prime denotes differentiation with respect to z. ... p aN2. V 2. ). (V bN) = NkT,. where a and b are constants.

17 Jun 2019: but immunity (from infection or vaccination) is lost at per capita rate b. ... b) Let K1 and K2 be algebraically closed fields of the same characteristic.

17 Jun 2019: Give a short exact sequence of chain complexes relating A , B, and C. ... 4 3. 16. a. b, B 1. 4+. 9. 16. a.

30 Aug 2019: Give a condition in terms of(X X, B B, µ µ, T T), which implies that (X, B, µ, T) is weak mixing. ... State a theorem without proof.]. Let (X, B, µ, T) be a weak mixing system.

30 Aug 2019: µ0( B) B ,. B. t= (u B) ,. B = 0 ,. 2Φ = 4πGρ. Part III, Paper 314. 3. 1. (a) In magnetohydrodynamics, the cross-helicity contained in a fixed volume V isdefined as. ... The basic state is in magnetostaticequilibrium, with density ρ(z), pressure p(z)

17 Jun 2019: iii) Let f : [a, b] R be continuous, and differentiable on (a, b). ... A, B] AB BA. Show that [A, A] = 0; [A, B] = [B, A]; and [A, λB] = λ[A, B] for λ C.

30 Aug 2019: i) Justify the assertion that the velocity u and induced magnetic field b (so thatthe total field is B0ẑb) are of the form u = (u(z), 0, 0), b = (b(z), ... A(2T)B(2T). ). =. (. cosh σT iσ sinh σTi. σsinh σT cosh σT. ) (.

30 Aug 2019: a path of open edges of B(n) connecting FL(n) to FR(n). ... Reff(a, b) 6 dG(a, b). (b) Let X be a simple random walk on G starting from a.

19 Jun 2019: STATISTICAL THEORY. Attempt FOUR questions, not more than TWO of which should be from Section B. ... For the particular choice. ψ(x) = min{b, max{x,b}}, b < :. (i) Find the asymptotic variance V (ψ, Φ), where Φ is the standard normal distri-bution;.