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17 Jun 2019: c k cot ka = 0. Find the minimum value of V0 for this equation to have a solution. ... Giventhat. 〈x〉 =1. 2k(ka tan ka),. discuss briefly the possibility of 〈x〉 being greater than a.

17 Jun 2019: Let. KA = {X Mnn(R) | [A, X] = 0}LA = {[A, X] | X Mnn(R)}. ... Show that KA and LA are linear subspaces of Mnn(R). If A and B are similar, showthat KA = KB and LA = LB.

17 Jun 2019: Hence a 7 ax 7 S(Ka)I, so our fourth equation is. ... Level 1 k1 = K s1 = S(C(0),S0 = •) K1 = Ka S1 = Sab.

17 Jun 2019: A Killing vector field Ka of a metric gab satisfies. Ka;b Kb;a = 0. ... Hence show that a constant vector field Ka with one non-zero component, K4 say, is aKilling vector field if gab is independent of x4.

17 Jun 2019: Let. Q(k) = aR′ (a)R(a). kaj′ (ka)j(ka). Obtain the relation. tan δ =Q(k)j2(ka)ka. ... Q(k)n(ka)j(ka)ka 1. Suppose thattan δ. γ. k0 k,. for some , with all other δ small for k k0.

17 Jun 2019: What distinguishes a stationary metric from a“static” metric? A Killing vector field Ka of a metric gab satisfies. ... Ka;b Kb;a = 0. Show that this is equivalent to. gab,cKc gacKc,b gcbKc,a = 0.

17 Jun 2019: If Ka are the components of a contravariant vector field and gab the componentsof a metric tensor, let. ... In a particular co-ordinate system (x1,x2,x3,x4), it is given that Ka = (0, 0, 0, 1),Qab = 0.

17 Jun 2019: For all N, find integers ka(N) and kb(N)such that. kb(N). k=ka(N).

17 Jun 2019: cosh kx cosh ka),. where k is a constant such thatlk = 2 sinh ka.

17 Jun 2019: Let N(k) = aR′(a)/R(a). Show that. tan δ(k) =N(k) j(ka) kaj′(ka)N(k) n(ka) kan′(ka).