The so-called ”acoustic revival mechanism” of core-collapse supernova proposed recently by the Arizona group is an interesting new possibility. Aiming to understand the elementary processes involved in the mechanism, we have calculated the eigen frequencies and eigen functions for the g-mode oscillations of a non-rotating proto neutron star. The g-modes have relatively small eigen frequencies. ...

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 show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions. Mathematics Subject Classifications (2000): 31C20, 35C15, 47G20, 60J45, 46A55.

in this paper, one of the numerical solution method of one- particle, one dimensional timeindependentschrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function v(x).for each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. the paper ended with a comparison ...

The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-sect...

A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of du-ality: a dual model with inverse Planck constant exists such that the eigen-functions of its Hamiltonians coincide with the eigen-functions of Hamiltonians of the original model. We explain that this duality can be considered as duality bet...

Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and together they provide the eigen-decomposition of a matrix which analyzes the structure of this matrix. Even though the eigen-decomposition does not exist for all square matrices, it has a particularly simple expression for a class of matrices often used in multivariate analysis such as correlation, covarianc...

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...

in this paper, the numerical solution methods of one- particale, one – dimensional time- independentschrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function v(x). these methods included the fem(finite element method), cooly, numerov and others. here we considered the numerov method inmore details...