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...

It is well known that the Green function of the standard discrete Laplacian on l2(Zd), ∆stψ(n) = (2d) −1 ∑ |n−m|=1 ψ(m), exhibits a pathological behavior in dimension d ≥ 3. In particular, the estimate 〈δ0|(∆st − E − i0)δn〉 = O(|n|− d−1 2 ) fails for 0 < |E| < 1 − 2/d. This fact complicates the study of the scattering theory of discrete Schrödinger operators. Molchanov and Vainberg suggested th...

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.

A'transputer-based multiprocessor system for visual communication applications is presented. H.261, the encoding/decoding standard for video telephones recommended by CCITT, is implemented in this system for demonstration. Fundamental video processing operators, such as 3 x 3 discrete Laplacian, are also implemented. Up to 20.4 frames per second (fps) video replaying rate and about 7.2 fps proc...

The migration section is the reflectivity distribution modulated by the discrete Green’s function for migration. For a poorly sampled trace distribution, the Green’s function introduces noise into the migration image that can obscure its interpretation. Using this migration Green’s function and assuming shift invariance, we propose an economical method to deconvolve the Green’s function from th...

We consider traveling wave solutions to a class of diierential-diierence equations. Our interest is in understanding propagation failure, directional dependence due to the discrete Laplacian, and the relationship between traveling wave solutions of the spatially continuous and spatially discrete limits of this equation. The diierential-diierence equations that we study include damped and undamp...

We study the properties of a discrete Schrödinger operator. We prove that if its spectrum is discrete in the complement of [−2d, 2d], then it contains [−2d, 2d].

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...