Soit A un anneau intègre de corps des fractions K et soit A[X]sub = {P(X) ∈ K[X] ; P(ℤ) ⊂ A} l'anneau des polynômes à valeurs entières sur A. Lorsque la caractéristique de A est nulle, le A-module A[X]sub est contenu dans le A-module {P(X) ∊ K[X] ; P(Z) ⊂ A] engendré par les polynômes binomiaux Bn(X) – X(X – 1) (X – n + 1)/n′. Nous caractérisons ici les anneaux de Dedekind A pour lesquels ces A-modules sont égaux.

Puis nous étudions la situation plus générale dans laquelle A[X]sub = {P(X) ∈ K[X] ; P(A0) ⊂ A} OÙ A0 désigne un anneau de Dedekind contenu dans A. Ce sont alors des polynômes généralisant les binômes de Fermat FP(X) – (Xq – X)/p qui jouent le rôle central.

Let d be a non-zero derivation on a primitive ring R and ƒ(x1,…, xn) a homogeneous polynomial of degree m. We prove that the condition d(ƒ(r1,…, rn)t) = 0, for all r1,…, rn ∈ R, with t depending on r1,…, rn, forces R to be a finite dimensional central simple algebra and ƒ power-central valued on R. We also obtain bounds on [R : Z(R)] in terms of m.

A Banach space satisfying some physically significant geometric properties is shown to be the predual of a JBW*–triple. If one considers the unit ball of this Banach space as the state space of a physical system, the result shows that the set of observables is equipped with a natural ternary algebraic structure. This provides a spectral theory and other tools for studying the quantum mechanical measuring process

Borovik found a Lie primitive subgroup of E8(ℂ) isomorphic to (Alt5 × Sym6) : 2. In this note, we provide a short proof of existence and his result that the conjugacy class of this subgroup is the only one among those of non-local Lie primitive subgroups of finite dimensional simple complex Lie groups having a socle with more than one simple factor.

The purpose of this paper is to characterize the weight functions for which the Hardy operator , with non-decreasing function ƒ, is bounded between various weighted Lp-spaces for a wide range of indices. Our characterizations complement for the most part those of E. T. Sawyer [11] and V. D. Stepanov [15] for the Hardy operator of non-increasing function.

In this paper we prove an inequality that involves the minimal crossing number and the braid index of links by estimating Murasugi and Przytycki’s index for a planar bipartite graph.

Consider the n-th order (n ≥ 1 ) neutral differential equation where σ1 < σ 2 < ∞ and μ and η are increasing real-valued functions on [Ƭ1, Ƭ2] and [σ1, σ2] respectively. The function μ is assumed to be not constant on [Ƭ1, Ƭ2] and [Ƭ1, Ƭ2] for every Ƭ ∈ (Ƭ1, Ƭ2) similarly, for each σ ∈ (σ1, σ2), it is supposed that r\ is not constant on [σ1 , σ] and [σ, σ2]. Under some mild restrictions on Ƭ1,- and σ1, (ι = 1,2), it is proved that all solutions of (E) are oscillatory if and only if the characteristic equation of (E) has no real roots.

Let be independent Ornstein-Uhlenbeck processes and In this paper the law of iterated logarithm for X(t, n)is considered. The results obtained improve those of Csorgő and Lin(1988) and Schmuland(1987).

On sait que la méthode classique de Schneider (en une variable) permet de minorer des combinaisons linéaires de deux logarithmes de nombres algébriques avec des coefficients algébriques. Nous généralisons cette méthode en plusieurs variables pour minorer des combinaisons linéaires de plusieurs logarithmes.