Search

15 Oct 2021: b. a) Show that the sequences (f(xj. )). 1j=0. and (f(yj. )). ... 0. 1X. k=1. (a. k. cos kx b. k. sin kx) ,. where ak. , b. k. 2 R. Show that ifP1. k=1.

15 Oct 2021: Res[F,i] = cosh(π θ)4 sinh π. , Res[F,n] =cos(nθ). 2π(1 n2). ... b) Show that if φ attains a minimum at θ0 R, then φ(θ0) 0.

8 Jul 2021: Using spherical coordinates, wefollow ref. [12], and prescribe the tangential surface veloc-ity, us, as us = (3U0/2)(sin θ β sin θ cos θ)eθ, where U0. ... For a given value ofthe dipole strength, the maximum growth rate is obtainedfor cos k = 1, i.e.

20 Jul 2021: i) Show that θ(t) satisfies the following equation of motion. θ̈ =(ω2 cos θ g. ... SP dS =. VE JdV. t. V. |E|2 |B|22. dV. (). (b) Suppose J = 0 and consider an electromagnetic wave. E = E0 ŷ cos(kxωt) and B = B0 ẑ cos(kxωt) ,.

20 Jul 2021: M =. (f(θ). 2 i sinθ2f(θ) sinθ2f(θ)sinθ2f(θ). f(θ)2. i sinθ2f(θ). ), f(θ) =. 1 cos θ,. where θ R. (ii) Now consider an element of ... Rab = cos θδab (1 cos θ)nanb sin θabcnc,. where a,b,c = 1, 2, 3, nana = 1 and abc is the 3-dimensional

20 Jul 2021: b). (i) Consider two states ρ1 = |0〉〈0|, ρ2 = |θ〉〈θ|, where |θ〉 = cos(θ)|0〉 sin(θ)|1〉,θ (0,π/2). ... c,d (0, 1), a < b < c < d and〈φ1|φ1〉 = 〈φ2|φ2〉 = 1.

6 Nov 2021: 0 = ma22(sin θ cos θ sin φ cos φ) mga(sin θ sin φ). ... 1. 2π. g/a cos θ0 2 cos 2θ0,. and find the other normal frequency.

16 Dec 2021: θ. [4]. (b) For u(r,θ) of the form. u(r,θ) = rn cos(nθ) ,. where n is a positive integer, use the Cauchy-Riemann equations from part (a) and ... T [z] =12gR. θ2θ1. R2 z′2. cos θdθ ,. where g is the acceleration due to gravity.

8 Jul 2021: θ ),. ξx (t ) = ξ0 {[A(R) B(R) cos2 θ ]eiωt } and ξy (t ) = ξ0 {B(R) cos θ sin θ eiωt }. (17). B. Low-frequency limit of Lissajous figures. The ... 1 cos2θ )2 ξ2x. 2 tan θ cos φ. 1 cos2θ ξxξy 1.

11 Feb 2021: Li = log. (eWyixicos(θyi,i)byi. j eWjxicos(θ j,i)b j. )(3.8). NormalizingWj in each iteration and zeroing the biases, the posterior probability becomes. ... Taking binary classificationas example, the modified softmax loss requires cos(θ1) > cos(θ2)