In this paper we present a nite di erence scheme for the discretization of the nonlinear PoissonBoltzmann(PB) equation over irregular domains that is second-order accurate. The interface is represented by a zero level set of a signed distance function using Octree data structure, allowing a natural and systematic approach to generate non-graded adaptive grids. Such a method guaranties computati...

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...

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

This paper presents nite-di erence solution and analytical solution of the nite-di erence approximations based on the standard explicit method to the one-dimensional Burgers equation which arises frequently in the mathematical modelling used to solve problems in uid dynamics. Results obtained by these ways for some modest values of viscosity have been compared with the exact (Fourier) one. It i...

The problem of estimating the di erence in arrival times of a noisy sinusoid received at two spatially separated sensors is considered. Given the sinusoidal frequency, a simple delay estimator using the phase di erence of the discrete time Fourier transforms (DTFTs) of the received signals is devised. With the use of periodogram, the algorithm is extended to estimate the delay when the frequenc...

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...

The nite di erence method is a numerical analysis technique used to solve problems involving irregular geometries, complicated boundary conditions, or both. The geometries are represented using partial di erential equations. The solutions to the partial di erential equations can be easily generated with the aid of a computer. As the geometries become increasingly complex, the solutions of the p...

Phase based methods for extracting binocular dispar ity are discussed including phase di erence methods and phase correlation A third method is also described that combines some of their properties and appears consistent with recent physiological data