Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotiv...

The aim of the article is to demonstrate the use of the Laplace transform to the evaluation of consols’ present value under different streams of returns (dividends). Consols (or perpetual bonds, perpetuities) are bonds with no maturity, which means that interest is paid to a bondholder perpetually (usually annually) forever. The present value of a consol, when constant interest is paid, is simp...

The spherical phylon group and invariants of the Laplace transform. Abstract We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of R d that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.

The present work is aimed at analyzing the thermoelastic disturbances in a circular plate of finite thickness and infinite extent subjected to constant initial temperature and axisymmetric heat supply. Integral transform technique is used. Analytic solutions for temperature, displacement and stresses are derived within the context of unified system of equations in generalized thermoelasticity i...

A time scale is any closed subset of the real line. Continuous time and discrete time are special cases. The unilateral Laplace transform of a signal on a time scale subsumes the continuous-time unilateral Laplace transform, and the discretetime unilateral z-transform as special cases. The regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s graininess....

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

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 ...

In this paper we will investigate the semi-markov random processes with positive tendency, negative jumps and delaying boundary at zero in this article. The Laplace transform on time, Laplace-Stieltjes transform on phase of the conditional and unconditional distributions and Laplace-Stieltjes transform of the ergodic distribution are defined. The characteristics of the ergodic distribution will...