The asymptotic distributions of the number of vertices of given degree in random graph K n,p are given. By using the method of Poisson convergence, Poisson and normal distributions are obtained.

We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras of the Drinfeld doubles of Hopf algebras when the Rmatrices act properly. When this construction is applied to quantum groups, we get examples of quantum groupoids, which are semi-classical limits o...

We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability α ∈ (0, 1) or they undergo an elastic collision with probability 1− α. For such a model, the number of particles, the linear momentum and...

We study by means of numerical simulations the velocity reversal model, a onedimensional mechanical model of heat transport introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, which does not conserve momentum, exhibits nevertheless an anomalous Fourier’s law similar to the ones previously observed in momentum-conserving models. This disagrees with what can...

The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We illustrate in detail the case of the Toda lattice both in Flaschka and natural coordinates.

We provide a simple method for obtain boundary asymptotics of the Poisson kernel on a domain in R . 0 Introduction Let Ω ⊆ R be a connected open set—called a domain. It is a matter of considerable interest to estimate the size of the Poisson kernel PΩ(x, t) = P (x, t) of Ω. Here, and throughout this paper, x ∈ Ω and t ∈ ∂Ω. In case Ω has a large group of symmetries, then it is often possible to...

In this paper lattice-Boltzmann equation method is used to simulate non-Darcy flow in porous media. 2-D in-line and staggered arrangements of uniform cylinders have been considered. The results of a comprehensive computational evaluation are reported: the range of validity of Darcy-Forchheimer equation is investigated and correlations for macroscopic transport properties are presented (i. e., f...

It is well known that Poisson binomial distribution can be approximated by Poisson distribution. In this paper, we give a nonuniform bound of this approximation by using Stein-Chen method.

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.