For a skip-free Markov process on Z + with generator matrix Q, we evaluate the joint Laplace transform of the occupation times before hitting the state n (starting at 0). This Laplace transform has a very straightforward and familiar expression. We investigate the properties of this Laplace transform, especially the conditions under which the occupation times form a Markov chain.

Multidimensional NMR techniques used in the measurement of molecular displacements, whether by diffusion or advection, and in the measurement of nuclear spin relaxation times are categorised. Fourier-Fourier, Fourier-Laplace and Laplace-Laplace methods are identified, and recent developments discussed in terms of the separation, correlation and exchange perspective of multidimensional NMR spect...

We prove C regularity for a thin obstacle problem for the p-laplace equation. Due to the nonlinearity of the p-laplace operator we can not use the same methods used for the Laplace case, instead we use techniques developed by E. de Giorgi. AMS Classification: 35R35, 35J60, 35B65.

Structural learning with forgetting is an established method of using Laplace regularization to generate skeletal artificial neural networks. In this paper we develop a continuous dynamical system model of regularization in which the associated regularization parameter is generalized to be a time-varying function. Analytic results are obtained for a Laplace regularizer and a quadratic error sur...

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...

Discrete Laplace–Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of the weak Laplace–Beltrami operator are well-studied, less is known about the strong form. We present a principle for constructing strongly consistent discrete Laplace–Beltrami o...

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x, t) of finding the walker at position x at time t is completely determined by the Lapla...

Microarrays allow the study of the expression profile of hundreds to thousands of genes simultaneously. These expressions could be from treated samples and the healthy controls. The Esscher transformed Laplace distribution is used to fit microarray expression data as compared to Normal and Laplace distributions. The Maximum Likelihood Estimation procedure is used to estimate the parameters of t...

In this paper we first modify a widely used discrete Laplace Beltrami operator proposed by Meyer et al over triangular surfaces, and then establish some convergence results for the modified discrete Laplace Beltrami operator over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace Beltra...