In this paper the effect of window shape parameter „α‟ in Kaiser-Hamming and Cosh-Hamming window functions on the signal to noise ratio (SNR) values of the Indian Mesosphere-Stratosphere-Troposphere (MST) radar is computed. The six parts of multibeam observations of the lower atmosphere made by the MST radar are utilized for the analysis of results. Prior to the Fourier transformation, the in-p...

The use of Gaussian quadrature formulae is explored for the computation of the Macdonald function Kν(x) = ∫ ∞ 0 e cosh t cosh νt dt when x > 0 and ν is complex, ν = α+ iβ. It is shown that Gaussian quadrature with weight function w(t) = exp(−et) on [0,∞] is a viable approach, unless x is small and/or β large, but in combination with Gauss–Legendre quadrature, even in these latter cases.

We consider an eigenvalue problem for a system in [0, 1]:        0 1 1 0 d dx + p11(x) p12(x) p21(x) p22(x) ϕ (1) (x) ϕ (2) (x) = λ ϕ (1) (x) ϕ (2) (x) ϕ (2) (0) cosh µ − ϕ (1) (0) sinh µ = ϕ (2) (1) cosh ν + ϕ (1) (1) sinh ν = 0 with constants µ, ν ∈ C. Under the assumption that p21, p22 are known, we prove a uniqueness theorem and provide a reconstruction formula for p11 and p12 from t...

Unitary irreducible representation of the group SO(1,2) is obtained in the mixed basis, i.e. between the compact and noncompact basis and the new addition theorems are derived which are required in path integral applications involving the positively signed potential. The Green function for the potential barrier V = cosh −2 ωx is evaluated from the path integration over the coset space SO(1,2)/K...

We introduce and study a new Ma–Minda subclass of starlike functions $${\mathcal {S}}^*_{\varrho },$$ defined as $$\begin{aligned} {\mathcal {S}}^{*}_{\varrho }:=\left\{ f\in {A}}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho (z), z\in {\mathbb {D}} \right\} , \end{aligned}$$ associated with an analytic univalent function $$\cosh \sqrt{z},$$ where we choose the branch square root so that \s...

Recommended by Stephen L. Clark For any n, the contour integral y cosh x ∮ C cosh zs / sinh z − sinhx n 1 dz, s2 −λ, is associated with differential equation d2y x /dx2 λ n n 1 /coshx y x 0. Explicit solutions for n 1 are obtained. For n 1, eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored. This differential equation which does have solution in terms of t...

This thesis is about multidominance or sharing in syntax. The term sharing is used in a technical sense, to refer to a situation where a syntactic node has more than one mother. I assume that multidominance is allowed by the grammar. I argue that sharing configurations are more diverse than it has been proposed. I identify two kinds of sharing: bulk sharing and non-bulk sharing. A string of mul...