In this paper we study in detail some spectral properties of the magnetic discrete Laplacian. We identify its form-domain, characterize the absence of essential spectrum and provide the asymptotic eigenvalue distribution.

Abstract. We study a general transition operator, generated by a random walk on a graph X ; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from l(X) into itself. Moreover we characterize compact operators and we relate this property to the behaviour of the associated random walk. We give a necessary ...

It is well known that, under certain circumstances, discrete plane waves can propagate through lattices. Waves can also be generated by oscillating one point in the lattice: the corresponding solution of the governing partial difference equations is the discrete Green’s function, gmn. The far-field behaviour of gmn is obtained using three methods: textbook derivations are corrected and a formul...

Transformation plays a much more important role in every science. In this research article, two parametric forms of SEE transformation have been explored and the fundamental properties transformations shown. Furthermore, transformed function some functions their time derivative rule has The application solving differential equations radioactive decay problem first-order linear solved article wh...

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

Mesh smoothing is a method to remove noise or small scale features from large meshes, while still preserving the basic overall shape and important features of the original model. Most sophisticated smoothing methods rely on ideas from differential geometry. In this lecture we discuss some basic geometric concepts and introduce some simple smoothing algorithms; the paper presented at this lectur...

The well-studied methods of current source density analysis use the Laplacian transform to identify locations and relative magnitudes of current sources and sinks. The method is typically used in reduced one-dimensional form for electrophysiological measures, due to technical limitations. The present paper outlines a two-dimensional method in which simultaneous samples are recorded from multipl...

We introduce a curvature function for planar graphs to study the connection of curvature and geometric and spectral properties of the graph. We show that non-positive curvature implies that the graph is infinite, locally similar to a tessellation and admits no cut locus. For negative curvature we prove empty interior of minimal bigons and explicit bounds for the growth of distance balls and Che...

Abstract We prove that (1) diagonal systems of hydrodynamic type are Darboux integrable if and only the corresponding for commuting flows integrable, (2) Laplace transformation sequences terminate, (3) necessarily semihamiltonian. give geometric interpretation integrability such in terms congruences lines solution orbits with respect to symmetry subalgebras, discuss known new examples.

Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.