The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other rese...

The fractional diffusion equation is one of the important recent models that can efficiently characterize various complex processes, such as in inhomogeneous or heterogeneous media porous media. This article provides a method for numerical simulation time-fractional equations. proposed scheme combines local meshless based on radial basis function (RBF) with Laplace transform. first implements t...

Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎

Let J% exp(-PQf(t) dt = F(P) P > 0 where b > 0 is a given number. We give a formula for f (t) in terms of F (p) , p > 0. The object of this Letter is to give a formula for the inverse Laplace transform in which the data used are given on the semi-axis p > 0 only. Let P>O where b > 0 is a fixed number. We have (1, formula 4.14.1) where Jo is a Bessel function. It follows from (1) and (2) that s,...

Topological properties of the spaces of analytic test functions and distributions are investigated in the framework of the general theory of nonarchimedean locally convex spaces. The Laplace transform, topological isomorphism, is introduced and applied to the differential equations of nonarchimedean mathematical physics (Klein-Gordon and Dirac propagators).

A time-domain-reflectometry Smith-chart display is demonstrated to be a valuable diagnostic tool in a variety of situations in time-domain-reflectometry dielectric spectroscopy. A relative reflection coefficient is formed by dividing the Laplace transform of the reflected sample transient by the Laplace transform of the empty-sensor transient and displaying in the complex plane, with the approx...

The paper presents the simple and efficient analysis method of frequency-domain to control core power coolant temperature Nuclear Power Plants (NPPs). In order properly describe neutron kinetic thermal transmission NPPs, a one-dimensional dynamic model has been accomplished by using linearizing in time domain discretizing spatial domain, then transfer function matrix can be obtained through Lap...

This paper presents a time-domain formulation called Explicit Green’s approach (ExGA) linear method for the solution of the bioheat equation. Starting from the hyperbolic bioheat equation, which includes the parabolic one as a special case, the linear method is incorporated into the standard ExGA time marching scheme. The numerical Green’s function is firstly computed in the Laplace transform d...

Introduction: Transformations are vital to any engineering subject, in particular, to electrical engineering. Fourier series, Laplace transform, Fourier transform and their counterparts in the discrete-time domain, are the fundamental tools for signal processing, communication and control engineering. Recently, the discrete Pascal transform (DPT) has been introduced to process discrete signals ...