We introduce the Laplace transform for an arbitrary time scale. Two particular choices of time scales, namely the reals and the integers, yield the concepts of the classical Laplace transform and of the classical Z-transform. Other choices of time scales yield new concepts of our Laplace transform, which can be applied to find solutions of higher order linear dynamic equations with constant coe...

Latent Gaussian models are flexible models that are applied in several statistical applications. When posterior marginals or full conditional distributions in hierarchical Bayesian inference from these models are not available in closed form, Markov chain Monte Carlo methods are implemented. The component dependence of the latent field usually causes increase in computational time and divergenc...

We compute the asymptotic determinant of the discrete Laplacian on a simplyconnected rectilinear region in R2. Specifically, for each > 0 let H be the subgraph of Z2 whose vertices lie in a fixed rectilinear polygon U . Let N (H ) denote the number of vertices of H and B(H ) the number of vertices on the boundary (the outer face). Then the log of the determinant of the Laplacian on H has the fo...

In this work we focus on approximations of continuous harmonic functions by discrete harmonic functions based on the discrete Laplacian in a triangulation of a point set. We show how the choice of edge weights based on generalized barycentric coordinates influences the approximation quality of discrete harmonic functions. Furthermore, we consider a varying point set to demonstrate that generali...

We prove an analogue of a classical asymptotic stability result of standing waves of the Schrödinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi [M1] and it involves a discrete Schrödinger operator H = −∆+q. The decay rates on the potential are less stringent than in [M1], since we require q ∈ l1,τ w...

There are a lot of researches on the spectrum of the discrete Laplacian on an infinite graph in various areas. One of main topics among them is to characterize the spectral structure in terms of a certain geometric property of the graph. We focus on the possibility of the absence of eigenvalues and give a criterion for this in terms of combinatorial property of a graph. A graph G is a connected...

We show stability in a Banach space framework of backward Euler and second order backward diierence timestepping methods for a parabolic equation with memory. The results are applied to derive maximum norm stability estimates for piecewise linear nite element approximations in a plane spatial domain, which is accomplished by a new resolvent estimate for the discrete Laplacian. Error estimates a...

Email: [email protected] Abstract: Biometrics deals with recognition of individuals based on their behavioral or biological features. The recognition of IRIS is one of the newer techniques of biometrics used for personal identification. It is one of the most widely used and reliable technique of biometrics. In this study a novel approach is presented for IRIS recognition. The proposed approach...

In this paper, we study a first order random coefficient autoregressive model with Laplace distribution as marginal. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, we develop a first order random coefficient autoregressive moving average model with Laplace marginal and discus...

The orbital dynamics of most planetary satellites is governed by the quadrupole moment from the equatorial bulge of the host planet and the tidal field from the Sun. On the Laplace surface, the long-term orbital evolution driven by the combined effects of these forces is zero, so that orbits have a fixed orientation and shape. The “classical” Laplace surface is defined for circular orbits, and ...