The Finite-Diierence Time Domain (FDTD) method has received considerable attention recently. The popularity of the FDTD method stems from the fact that it is not limited to a speciic geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However,...

We give several eecient transformations for manipulating the statistical diierence (variation distance) between a pair of probability distributions. The eeects achieved include increasing the statistical diierence, decreasing the statistical diierence, \polarizing" the statistical relationship, and \reversing" the statistical relationship. We also show that a boolean formula whose atoms are sta...

Finite diierence schemes for singularly perturbed convection problems are studied in the limit case in which the viscosity approaches zero with the mesh-size. The error estimates allow choosing in advance appropriate schemes and mesh-resolutions for both boundary layer problems and circulating ow problems.

We sketch a BDD-like structure for representing unions of simple convex polyhedra, describing the legal values of a set of clocks given bounds on the values of clocks and clock di erences.

A system of diierence constraints consists of a set of inequalities of the form x i ? x j b i;j. Such systems occur in many applications, e.g., temporal reasoning. The best known algorithm to determine if a system of diierence constraints is feasible (i.e., if it has a solution) and to compute a solution if the system is feasible runs in (mn) time, where n is the number of variables and m is th...

We establish the connections between finite projective planes admitting a collineation group of Lenz–Barlotti type I.3 or I.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the Dembowski– Piper classification; our main tool is an equivalent description by a certain type of di¤erence set relative to disjoint ...

In this paper, we present Clock Diierence Diagrams, a new BDD-like data-structure for eeective representation and manipulation of certain non-convex subsets of the Euclidean space, notably those encountered in veriication of timed automata. It is shown that all set-theoretic operations including inclusion checking may be carried out eeciently on Clock Diierence Diagrams. Other central operation...

We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite di↵erence schemes. By studying the Fourier series expansions of the source discretization and the finite di↵erence operator, we derive su cient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in F...

This paper presents and analyzes four explicit, two implicit and four semi-implicit finite difference algorithms for the linear shape from shading problem. Comparisons of accuracy, solvability, stability and convergence of these schemes indicate that the weighted semi-implicit scheme and the box scheme are better than the other ones because they can be calculated more easily, they are more accu...

On q-Di®erence Equations Moemen H. Abu-Risha Department of Mathematics Cairo University, Eygpt E-mail: [email protected] We give an investigation of some properties of solutions of linear q¡di®erence equations de ̄ned on an interval [a;1): The cases a = 0 and a > 0 are essentially di®erent. The study of the latter case is necessary for the derivation of asymptotic formulae and oscil...