It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detail. Mathematics Subject Classification (2000). 53D17, 37J15, 58A30.

In this paper, we characterize the class of distributions on an homogeneous Lie group N that can be extended via Poisson integration to a solvable one-dimensional extension S of N. To do so, we introducte the S -convolution on N and show that the set of distributions that are S -convolvable with Poisson kernels is precisely the set of suitably weighted derivatives of L-functions. Moreover, we s...

Kernels of a so-called α-scale space ( 12 < α < 1) have the undesirable property that there is no closed-form representation in the spatial domain, despite their simple closedform expression in the Fourier domain. This obstructs a spatial convolution or recursive implementation. For this reason an approximation of the 2D α-kernel in the spatial domain is presented using the well known Gaussian ...

Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small sc...

We prove that the Bergman kernel function associated to a finitely connected planar domain can be expressed as a rational combination of two independent Ahlfors maps associated to the domain plus the derivative of one of the maps. Similar results are shown to hold for the Szegő and Poisson kernels and other objects of potential theory. These results generalize routinely to the case of a relativ...

This paper deals with the numerical analysis of the focalization of a beam of particles. In particular, this model can be useful to check whether or not the cut-off Boltzmann equation leads to some kind of smoothing effect as for the Fokker-Planck-Landau equation.

The goal of this paper is to define a procedure for bounding the error in a conforming finite element method. The new point is that this upper bound is fully explicit and can be computed locally. Numerical tests prove the efficiency of the method. It is presented here for the case of the Poisson equation and a first order finite element approximation.

In a recent paper [1], a systematic construction of integrable Hamiltonians with coalgebra symmetry has been proposed. Such procedure can be applied to any Poisson coalgebra (A,∆) with generators Xi, i = 1, . . . , l and Casimir element C(X1, . . . , Xl) as follows. Let us consider the N -th coproduct ∆(Xi) of the generators and the m-th order (2 ≤ m ≤ N) coproducts ∆(m)(C) of the Casimir opera...

In this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra’s system. We found in two simplest cases the complete sets of the integrals of motion using Nambu–Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures.

We present an overview of existing methods to generate pseudorandom numbers from a nonhomogeneous Poisson process. We start with various definitions of the nonhomogeneous Poisson process, present theoretical results (sometimes with a proof) that form the basis of existing generation algorithms, and provide algorithm listings. Whenever available, we also provide links to sources containing compu...