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...

Stochastic point sets are considered that display a diffraction spectrum of mixed type, with special emphasis on explicitly computable cases together with a unified approach of reasonable generality. Several pairs of autocorrelation and diffraction measures are discussed which show a duality structure that may be viewed as analogues of the Poisson summation formula for lattice Dirac combs.

The main purpose of this note is to present a new approach to Poisson Approximations. Some bounds in Poisson Approximations in term of classical Le Cam’s inequalities for various row-wise triangular arrays of independent Poisson-binomial distributed random variables are established via probability distances based on Trotter-Renyi operators. Some analogous results related to random sums in Poiss...

We derive the ‘exact’ Newtonian limit of general relativity with a positive cosmological constant Λ. We point out that in contrast to the case with Λ ≤ 0, the presence of a positive Λ in Einsteins’s equations enforces, via the condition |Φ| 1, on the potential Φ, a range Rmax(Λ) r Rmin(Λ), within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, Mmax(Λ). As a...

We present an abstract method for deriving decay estimates on the resolvents and semigroups of non-symmetric operators in Banach spaces in terms of estimates in another smaller reference Banach space. This applies to a class of operators writing as a regularizing part, plus a dissipative part. The core of the method is a high-order quantitative factorization argument on the resolvents and semig...

The mu-basis of a planar rational curve is a polynomial ideal basis comprised of two polynomials that greatly facilitates computing the implicit equation of the curve. This paper defines a mu-basis for a rational ruled surface, and presents a simple algorithm for computing the mu-basis. The mu-basis consists of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z and degre...