The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differential geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior algebra...

The notion of a Laplace ladder for a discrete analogue of the Laplace equation is presented. The adjoint of the discrete Moutard equation and a discrete counterpart of the nonlinear form of Goursat equation are introduced. 1 Notation Value of functions of continuous variables we denote by f(u, v) i.e. f : R ∋ (u, v) 7→ f(u, v) ∈ R while functions of discrete variables by f(m1, m2) i.e. f : Z 2 ...

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].

It is known that the Laplace transform is frequently used to solve fractional-order differential equations. Unlike integer-order differential equations, fractional-order differential equations always lead to difficulties in calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the fractional-order differential equations, we investigated the validity ...