The reaction cross section of a bimolecular reaction has been calculated from the corresponding rate constant by the inverse Laplace transform. In carrying out the inverse Laplace transform, the method of steepest-descent has been used. As applications, the reaction cross sections for the rate constant of k(T) = k' T(n)e(-E0/kT) and for the rate constant of the absolute reaction rate theory hav...

Based on recent results for 2-D continuous-discrete systems, this paper develops 2-D Laplace-z transform, which can be used to analyze 2-D continuous-discrete signals and system in Laplace-z hybrid domain. Current 1-D Laplace transformation and z transform can be combined into the new 2-D s-z transform. However, 2-D s-z transformation is not a simple extension of 1D transform, in 2-D case, we n...

It is often possible to e ectively calculate cumulative distribution functions and other quantities of interest by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable. In that event, we show that it is sometimes possible to nd continued-fr...

Laplace decomposition method is based on Laplace transform method and Adomian decomposition method. In this paper we show that the method is applicable to certain successive interval valued linear as well as nonlinear differential-difference equations of order (1, 2), that means the differential is of order one and the difference is of order two. It is also shown that the method gives exact sol...

Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...