We consider the system of N (≥ 2) hard balls with masses m1, . . . , mN and radius r in the flat torus TL = R /L · Z of size L, ν ≥ 3. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection (m1, . . . , mN ; L) of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the c...

This paper describes the use of Bernoulli mixture models for extracting boolean rules from data. Bernoulli mixtures identify high data density areas on the corners of a hypercube. One corner represents a conjunction of literals in a boolean clause and the set of all identified corners, of the hypercube, indicates disjuncts of clauses to form a rule. Further class labels can be used to select fe...

By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate Lévy processes. Many properties of these polynomials are stated straightforwardly thanks to this representation, which could be easily implemented in any symbolic manipulation system. A very simple relation between these two families of multivariate po...

In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite-Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained ...

Athermal random fiber networks are usually modeled by representing each fiber as a truss, a Euler-Bernoulli or a Timoshenko beam, and, in the case of cross-linked networks, each cross-link as a pinned, rotating, or welded joint. In this work we study the effect of these various modeling options on the dependence of the overall network stiffness on system parameters. We conclude that Timoshenko ...

We consider initial and boundary value problems modelling the vibrations of a plate with piezoelectric actuator. The simplest model leads to the Bernoulli-Euler plate equation with right hand side given by a distribution concentrated in an interior curve multiplied by a real valued time function representing the voltage applied to the actuator. We prove that, generically with respect to the cur...

The formulation of a bending vibration problem of an elastically restrained Bernoulli–Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli–Euler beam. This hybrid strat...

We show that the Akiyama-Tanigawa algorithm and Chen’s variant for computing Bernoulli numbers can be generalized to Carlitz’s q-Bernoulli numbers. We also put these algorithms in the larger context of generalized Euler-Seidel matrices.