I present an example of a discrete Schrödinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously iden...

this paper presents time domain fundamental solutions for the extended biot's dynamic formulations of two-dimensional (2d) unsaturated poroelasticity. unsaturated porous media is considered as a porous media in which the voids are saturated with two immiscible fluids, i.e. liquid and gas. at first, the corresponding explicit laplace transform domain fundamental solution is obtained in term...

For simplicity, we follow the rules: x, y are sets, N is an element of N, c, i, j, k, m, n are natural numbers, D is a non empty set, s is an element of 2Set Seg(n + 2), p is an element of the permutations of n-element set, p1, q1 are elements of the permutations of (n+ 1)-element set, p2 is an element of the permutations of (n+ 2)-element set, K is a field, a, b are elements of K, f is a finit...

February 2, 2008 Abstract. Recently, Breiter et al.(2004) reported the computation of Hansen coefficients X k for non integer values of γ. In fact, the Hansen coefficients are closely related to the Laplace b (m) s , and generalized Laplace coefficients b (m) s,r (Laskar and Robutel, 1995) that do not require s, r to be integers. In particular, the coefficients X 0 have very simple expressions ...

In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Hölder inequalities. They are showed be to of exponential order, which are nece...

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component φ 4 theory ABSTRACT Modified Laplace transformation method is applied to N component φ 4 theory and the finite temperature problem in the massless limit is reexamined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orde...

other fields. However, the spectral properties of the Laplace Transform tend to complicate its numerical treatment; therefore, the closely related “Truncated” Laplace Transforms are often used in applications. We have constructed efficient algorithms for the evaluation of the left singular functions and singular values of the Truncated Laplace Transform. Together with the previously introduced ...