We show how the singularities are propagated for the (spatially homogeneous) Boltzmann equation (with the usual angular cutoo of Grad) in the context of the small solutions rst introduced by Kaniel and Shinbrot.

The concept of differential-geometric Poisson brackets (DGPB) was introduced in [i] in connection with an investigation of the properties of Poisson brackets of hydrodynamic type [2] and their generalizations. Recall that homogeneous DGPBs of m-th order on a phase space of fields u i @),i = i ..... N,x ~ ~ (in this note we confine attention to the spatially onedimensional case), taking values i...

Consider several independent Poisson point processes on Rd, each with a different colour and perhaps a different intensity, and suppose we are given a set of allowed family types, each of which is a multiset of colours such as red-blue or red-red-green. We study translation-invariant schemes for partitioning the points into families of allowed types. This generalizes the 1-colour and 2-colour m...

Given a classical r-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and modified KP hierachies, the dispersionless Dym hierachy etc.

A model of the precipitation process in reverse micelles has been developed to calculate the size of fine particles obtained therein. While the method shares several features of particle nucleation and growth common to precipitation in large systems, complexities arise in describing the processes of nucleation, due to the extremely small size of a micelle and of particle growth caused by fusion...

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...