This paper is concerned with the asymptotic behavior of the trav-eling wave fronts in Lotka-Volterra competition system. By Laplacian transform, we prove that the traveling wave fronts of the system grow exponentially when the traveling coordinate tends to negative infinity.

We introduce the matrix sums that represent a discrete analog of the matrix integrals of random matrix theory. The summation runs over the set Γn of all possible n-vertex graphs γn weighted by exp{−β Tr∆n}, β > 0, where ∆n = ∆(γn) is the analog of the Laplace operator determined on γn. Corresponding probability measure on Γn reproduces the well-known Erdős-Rényi ensemble of random graphs. Here ...

All methods presented in textbooks for computing inverse -transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence whose -transform is ; 2) computation using the inversion integral method becomes labored when has poles at the origin of the complex plane; 3...

We consider selection of nested and non-nested semiparametric models. Using profile likelihood we can define both a likelihood ratio statistic and an Akaike information for models with nuisance parameters. Asymptotic quadratic expansion of the log profile likelihood allows derivation of the asymptotic null distribution of the likelihood ratio statistic including the boundary cases, as well as u...

The recently introduced correntropy function is an interesting and useful similarity measure between two random variables which has found myriad applications in signal processing. A series expansion for correntropy in terms of higher-order moments of the difference between the two random variables has been used to try to explain its statistical properties for uses such as deconvolution. We exam...

Free quantal motion on group manifolds is considered. The Hamiltonian is given by the Laplace – Beltrami operator on the group manifold, and the purpose is to get the (Feynman’s) evolution kernel Kt. The spectral expansion, which produced a series of the representation characters for Kt in the compact case, does not exist for non-compact group, where the spectrum is not bounded. In this work re...

In this dissertation, we study the Karhunen-Loève (KL) expansion and the exact L small ball probability for Gaussian processes. The exact L small ball probability is connected to the Laplace transform of the Gaussian process via Sytaja Tauberian theorem. Using this technique, we solved the problem of finding the exact L small ball estimates for the Slepian process S(t) defined as S(t) = W (t+a)...

We determine the log-Sobolev constant of multi-urn Bernoulli–Laplace diffusion model with arbitrary parameters, up to a small universal multiplicative constant. Our result extends classical estimate Lee and Yau (1998) confirms conjecture Filmus, O’Donnell Wu (2018). Among other applications, we completely quantify small-set expansion phenomenon on multislice, obtain sharp mixing-time estimates ...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...