Given an odd prime p, we give an explicit factorization over the ring of formal power series with integer coefficients for certain reducible polynomials whose constant term is of the form p with w > 1. Our formulas are given in terms of partial Bell polynomials and rely on the inversion formula of Lagrange. Résumé. Donné un nombre premier impair p, nous donnons une factorisation explicite sur l...

We introduce an alternative way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the 1N accuracy, where N is the genome length. For a smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics and discontinuous dynamics. T...

We consider the extensions of classical r-matrix for κ-deformed Poincaré algebra which satisfy modified Yang-Baxter equation. Two examples introducing additional deformation parameter (dimension-full 1 κ or dimensionless ξ) are presented. We describe the corresponding quantization (two-parameter κ-Poincaré quantum Hopf algebras) in explicite form as obtained by twisting of standard κ-deformed f...

We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicite formulas for two equivalen...

This paper unifies problems and results related to (embedding) universal and homomorphism universal structures. On the one side we give a new combinatorial proof of the existence of universal objects for homomorphism defined classes of structures (thus reproving a result of [6]) and on the other side this leads to the new proof of the existence of dual objects (established by [32]). Our explici...

Abstract. We study the relaxation dynamics of a quantum Ising chain initially prepared in a product of canonical states corresponding each to an equilibrium state of part of the chain at a given temperature. We focus our attention on the transverse magnetization for which a general expression is given. Explicite results are given for the completely factorized initial state, corresponding to a s...

The main research approaches in Computational Fluid Dynamics (CFD) are grid-based (Euler) or based on particle motion (Lagrange). For interactive fluid simulation, techniques have been developed to use the Graphics Processing Unit (GPU) to speed up the computation using an Eulerian approach. This paper describes an approach for setting up a Lagrangian particle based fluid simulation on the GPU....

Résumé. Le domaine de l’extraction de connaissances à partir de texte nécessite des méthodes permettant de détecter et de manipuler l’incertitude. En effet, de nombreux textes contiennent des informations dont la véracité peut être remise en cause. Il convient alors de gérer de manière efficace ces informations afin de représenter les connaissances de manière explicite. Une première démarche co...

RÉSUMÉ. Ce papier porte sur la modélisation de séries temporelles ou de régression à l’aide de réseaux de neurones. En nous appuyant sur des résultats récents sur l’estimation des moindres carrés pour les séries temporelles non linéaires, nous proposons une méthodologie complète et explicite pour l’estimation des paramètres (processus d’apprentissage) et pour le choix du modèle (sélection d’arc...