We study the weak approximation error of a skew diffusion with bounded measurable drift and Hölder diffusion coefficient by an Euler-type scheme, which consists of iteratively simulating skew Brownian motions with constant drift. We first establish two sided Gaussian bounds for the density of this approximation scheme. Then, a bound for the difference between the densities of the skew diffusion...

This paper is concerned with the numerical approximation of viability kernels. The method described here provides an alternative approach to the usual viability algorithm. We first consider a characterization of the viability kernel as the value function of a related optimal control problem, and then use a specially relevant numerical scheme for its approximation. Since this value function is d...

The [Formula: see text] and [Formula: see text]-approximation schemes are introduced to approximate the popular generalized Cornu spirals with the help of the parametric rational cubic trigonometric Bézier curves. The [Formula: see text]-approximation scheme has two free parameters whereas [Formula: see text]-approximation scheme has four free parameters. To approximate the generalized Cornu sp...

The existence and uniqueness of the Lipschitz continuous traveling wave of Godunov’s scheme for scalar conservation laws are proved. The structure of the traveling waves is studied. The approximation error of Godunov’s scheme on single shock solutions is shown to be O(1)∆x.

The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vopěnka scheme is relatively consistent with the existence of a ∆2definable class containing no regular cardinals. In such a model, there can be no Σ2-reflecting cardin...

In this paper, we study the bandwidth allocation problem for an ATM multiplexer loaded with heterogeneous low-motion VBR video sources. We propose a cell scheduling scheme which balances cell loss among different sources so that they experience nearly the same cell loss rate. To estimate the bandwidth required by a VBR video source, we characterize its traffic by four parameters: peak rate, mea...

The lattice Boltzmann space/time discretisation, as usually derived from integration along characteristics, is shown to correspond to a Strang splitting between decoupled streaming and collision steps. Strang splitting offers a second-order accurate approximation to evolution under the combination of two non-commuting operators, here identified with the streaming and collision terms in the disc...

In this paper we describe automatic information nuggetization and its application to text comparison. More specifically, we take a close look at how machine-generated nuggets can be used to create evaluation material. A semiautomatic annotation scheme is designed to produce gold-standard data with exceptionally high inter-human agreement.