Costas J. Efthimiou Department of Physics University of Central Florida Orlando, FL 32816 USA Introduction In another NOTE in this MAGAZINE, the author presented a method [2] that uses the Laplace transform and allows one to find exact values for a large class of convergent series of rational terms. Recently, in this MAGAZINE too, Lesko and Smith [3] revisited the method and demonstrated an ext...

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?‎

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical ...

This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of (FT). The Unilateral Laplace (LT) observed to be special case GFT. GFT, as proposed in this work, contributes significantly scholarly literature. There are many salient contribution work. Firstly, GFT applicable a much larger class signals, some which cannot analyzed with FT and LT. For examp...

other areas. 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. In this dissertation, we construct efficient algorithms for the evaluation of the singular value decomposition (SVD) of such operators. The approach of this dissertation is somewhat simila...

other areas. 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. In this dissertation, we construct efficient algorithms for the evaluation of the singular value decomposition (SVD) of such operators. The approach of this dissertation is somewhat simila...

We give some precisions on the Fourier-Laplace transform theorem for tempered ultrahyperfunctions introduced by Sebastião e Silva and Hasumi, by considering the theorem in its simplest form: the equivalence between support properties of a distribution in a closed convex cone and the holomorphy of its Fourier-Laplace transform in a suitable tube with conical basis. We establish a generalization ...

a dynamic two dimensional problem of thermoelasticity with double porous structure has been considered to investigate the disturbance due to normal force and thermal source. laplace and fourier transform technique is applied to the governing equations to solve the problem. the transformed components of stress and temperature distribution are obtained .the resulting expressions are obtained in t...

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued...