In this paper, it is shown that the linearized Boltzmann-Enskog collision operator cannot be dissipative in the L2-space setting contrarily to the linearized Boltzmann operator. Some estimates useful for the spectral theory are given. The Enskog equation is a modification of the Boltzmann kinetic equation, in which each particle is considered as a hard sphere with nonzero diameter a > 0 (and th...

We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by I. Vaisman. We show that these connections play an important role in the study of global properties of Poisson manifolds and we use them to define Poisson holonomy and new invariants of Poisson manifolds.

The paper provides a survey of known results on geometric aspects related to Nambu-Poisson brackets.

Article history: Received 11 September 2013 Received in revised form 3 May 2014 Accepted 3 July 2014 Available online 16 July 2014

We propose an original approximation method, which is based on the Stein’s method and the zero bias transformation, to calculate CDO tranches in the general factor framework. We establish first-order correction terms for the Gaussian and the Poisson approximations respectively and we estimate the approximation errors. The application to the CDOs pricing consists of combining the two approximati...

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...

Using a Poisson bracket representation, in 3D, of the Lie algebra sl(2), we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras of the “kinetic energy”, related to the quadratic Casimir function. We then consider the potentials which can be added, whilst remaining integrable, leading to families ...

The covariant Boltzmann equation for a relativistic gas mixture is used to formulate a theory of relativistic irreversible thermodynamics. The modified moment method is applied to derive various evolution equations for macroscopic variables from the covariant Boltzmann equation. The method rigorously yields the entropy differential which is not an exact differential if

We apply Hardy-Littlewood’s Tauberian theorem to obtain an estimate on the harmonic expansion of a complex measure on the unit sphere, using a monotonicity property for positive harmonic functions. Let Bn = {x ∈ Rn : |x| < 1}, n ≥ 2 be the unit ball in Rn and Sn−1 = ∂Bn be the unit sphere. From a monotonicity property, we obtain a precise asymptotic for the spherical harmonic expansion of a com...

The classical theory of transport processes is based on the Boltzmann transport equation. The equation can be derived simply by defining a distribution function and inspecting its time derivative. From this equation, many important results can be derived. In addition to some of the textbook results from the Boltzmann transport equation, it is still being used in many contemporary research proje...