The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter ρ > 0. In previous work a convenient form of the inverse transformation was derived for the case ρ = 3/2. This paper generalizes that result to all ρ > 0. It is a well-known fact that the GST can be formulated as an iterated Laplace transform, and that therefore its inverse can be expressed as an iter...

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...

A Lagrangian analysis of the impact of transport and transformation on the ozone stratification observed in the free troposphere during the ESCOMPTE campaign A. Colette, G. Ancellet, L. Menut, and S. R. Arnold Service d’Aéronomie/Institut Pierre-Simon Laplace, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie, 4, place Jussieu, P.O. Box 102, 75 252 Paris Cedex 05, F...

Continuous-time quantum walk (CTQW) on a given graph is investigated by using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that, the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of t...

The main objective of this work is to introduce a novel generalization double transformations called the triple Laplace–ARA–Sumudu transform (TLARAST). This hybrid transformation extends concepts Laplace–Sumudu, Laplace–ARA and ARA–Sumudu transforms into transform. article provides definition TLARAST investigates its fundamental properties, including existence, inverses related theorems. Furthe...

An algorithm to compute a reduced-order model of a linear dynamic system is described. It is based on the rational Krylov method, which is an extension of the shift-and-invert Arnoldi method where several shifts (interpolation points) are used to compute an orthonormal basis for a sub-space. It is discussed how to generate a reduced-order model of a linear dynamic system, in such a way that the...

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a flat impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with ne...

A practical method to calculate time evolutions of magnetic field effects (MFEs) on photochemical reactions involving radical pairs is developed on the basis of the theory of the chemically induced dynamic spin polarization proposed by Pedersen and Freed. In theory, the stochastic Liouville equation (SLE), including the spin Hamiltonian, diffusion motions of the radical pair, chemical reactions...