Our interest in this paper is to study and develop oscillation conditions for solutions of a class neutral differential equations with damping terms. New criteria were obtained by using Riccati transforms. The we improved completed some the previous studies mentioned literature. Examples are provided illustrate applicability our results.

Two new transforms with piecewise linear kernels are introduced. These analogues of the classical Laplace transform and Z-transform. Properties these investigated applications to ordinary differential equations integral provided. This article is ideal for study as a foundational project in an undergraduate course and/or equations.

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certai...

It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random N × N Hermitian matrices. Our main goal is to investigate the issue of universality of large N asymptotics for those Cauchy transforms for a wide class of weight functions. Our analysis covers three different...

In the research, special type of linear volterra integro-differential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a Homotopy with an imbedding parameter p that is considered as a small parameter...