Cylindrically symmetric inhomogeneous string cosmological model of the universe in presence of electromagnetic field is investigated. We have assumed that F12 is the only non-vanishing component of electromagnetic field tensor Fij . The Maxwell’s equations show that F12 is the function of x alone whereas the magnetic permeability is the function of x and t both. To get the deterministic solutio...

In the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. The cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axis...

In this paper we proposes a generalized spectral theory for tensors. Our proposed factorization decomposes a symmetric tensor into a product of an orthogonal and a diagonal tensor. In the same time, our factorization offers an expansion of a tensor as a summation of lower rank tensors that are obtained through an outer product defined on matrices. Our proposed factorization shows the relationsh...

in the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. the cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axisymmetrically on the boundary surfaces. m...

We examine the generating function of moments of the Minkowski question mark function ?(x), which describes the distribution of rationals according to their continued fraction expansion. It appears that the generating function possesses certain modular properties and is defined in C \ R≥1. The exponential generating function satisfies the integral equation, with kernel being the Bessel function...

We study the asymptotic behavior of a singular potential that arises under several frequently occurring analytic behaviors of the eigen functions (of the Schrödinger eigenvalue problem) without introducing cut-offs. Instead, in our analyses we focus on power behaviors of eigen functions. We find that the asymptotic behavior of the singular potential crucially depends on the analytic property of...

P. DALY, B.Sc, Ph.D.f Summary: A finite-element method based on a function minimization technique is developed for analysing homogeneous waveguide problems. The continuous eigen-value operator as in the Ritz finite-difference method is replaced by a matrix operator. The resulting equations are, however, matrix eigen-value equations. Relevant properties of the matrices are discussed. It is demon...

The eigenvalues of a symmetric matrix depend on the matrix nons-moothly. This paper describes the nonsmooth analysis of these eigen-values. In particular, I present a simple formula for the approximate (limiting Fr echet) subdiierential of an arbitrary function of the eigen-values, subsuming earlier results on convex and Clarke subgradients. As an example I compute the subdiierential of the k't...