A new distance dA on Laplace transformations of probability distributions on R+ is given. The new complete metric space is shown to be homeomorphic to the topological probability distributions space on R+ with weak convergence. A new estimator for the fluorescence source distribution is described. c © 2005 Elsevier Ltd. All rights reserved.

*Correspondence: Rudolf A. Treumann, International Space Science Institute, ISSI, Hallerstrasse 6, CH-3012 Bern, Switzerland e-mail: [email protected] A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equat...

In this paper we solve the Laplace equation by solving a boundary integral equation in a wavelet basis. In wavelet basis the discretized equations preserve their good conditioning while their sparse structures speed up iterative solvers. We analyze the behavior of GCR algorithms under wavelet transformations and in non-standard form, the optimal choice of Daubechies lters and truncation strateg...

We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations of second-order hyperbolic equations in the plane and is based on an idea given by Ulisse Dini in 1902.

We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of general invariants are studied and some examples are presented. We also show that classical Laplace invariants correspond to some particular cases of general i...

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...

In classical signal processing, it is common to analyze and process signals in the frequency domain, by representing the signal in the Fourier basis, and filtering it by applying a transfer function on the Fourier coefficients. In some applications, it is possible to design an optimal filter. A classical example is the Wiener filter that achieves a minimum mean squared error estimate for signal...

In this paper, in the class of smooth functions, integration and differentiation operators connected with fractional conformable derivatives are introduced. The mutual reversibility these is proved, properties functions studied. Using transformations generalizing involutive transformations, a nonlocal analogue Laplace operator For corresponding Poisson equation, solvability some boundary value ...

This paper investigates the reliability characteristics of a complex system having nine subsystems arranged in the form of 3x3 matrix in which each row contains three subsystems. The configuration of the row is of the type 2-out-of-3: F. Each subsystem has n units connected in series. The system fails if any one row containing three subsystems fails. The considered system analyzed incorporating...