Dimension pure globale des anneaux commutatifs

For every (n,m) ? IN^?× IN ^?, verifying l We study direct systems of rings and give a bound for the pure - global - dimension of their limits, not depending on the ring cardinality. Using this result and a theorem of C0UCH0T we give examples of pure -heriditary group- rings (ie. of pure -global - dimension one) of large cardinality.

Finaly we prove - using a result of VASC0NCEL0S and a theorem of JENSEN - that some countably products of noetherian rings are coherent rings and that their pure - global - dimension is exactly two.     

Structure globale des extensions regulieres galoisiennes

A natural characterization of known types of inverse transversal leads to the introduction of several new types, which we characterize in a similar natural way. Relations between the various types produce a general classification. We also determine for which types of inverse transversal considered the congruence extension property holds.     

Independance lineaire des valeurs des solutions transcendantes de certaines equations fonctionnelles

Sans résumé     

Problemes aux limites pour l'equation de boltzmann: existence globale de solutions

This work is concerned by the initial and boundary value problem for the Boltzmann equation. Existence in the large and asymptotic behaviour results are proved for small data and general reemission laws. The colisional kernel satisfies the cut—off angular hypothesesand, the intermolecular potential is such that 7/3 <s≤∞ for the Dirichlet case and 7/3 <s≤5for the general case

Mot—clés: Equation de Boltzmann— Problèmes aux limites intérieurs et extérieurs — Gaz raréfiés —Condition aux limites de Dirichlet— Conditions aux limites non lináeaires— Existence globale de petites solutions     

Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions

We prove global existence of solutions to the continuous nonhomogeneous Smoluchowski equation for coagulation rates satisfying a more general structure condition than the Galkin–Tupchiev monotony hypothesis considered in (Ph. Laurençot, S. Mischler, Arch. Rational Mech. Anal. 162 (1) (2002) 45–99). The Smoluchowski coagulation rate fulfils this condition as well as some rates which vanish on the diagonal. Under the condition of positivity of the coagulation rate outside of the diagonal we prove that solutions tend to 0 in the large time asymptotic. These results depend on a new estimate from below for the dissipation rate of the L^p-norm, p>1. To cite this article: S. Mischler, M. Rodriguez Ricard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Sur les natures des processus solutions de certaines equations stochastiques aux differences

A study of the natures of the processes that are solutions of some finite difference stochastic equations, the right‐hand member of which is a stationary process, is given in the paper. Since the principal application of the present work concerns ARIMA models with or without seasonal variation, these processes are named G‐ARIMA. First, a criterion for a G‐ARIMA process to be stationary is established and some properties of a special class of stationary G‐ARIMA processes are studied. Then, we deduce some conditions for a finite difference stochastic equation to uniquely possess non‐stationary solutions. These have the particular property that their backward shift‐operator may be either a linear or a non‐linear operator, depending on the initial conditions of the solutions. So criteria are established for a non‐stationary G‐ARIMA process to have a bounded linear backward shift operator. Finally, some further properties of the G‐ARIMA processes are given, by comparing them with the broad class of V‐bounded processes. This comparison shows that a non‐stationary process cannot be at the same time G‐ARIMA and V‐bounded.     

Sul metodo delle approssimazioni successive: Convergenza globale e plus-convergenza globale

With reference to the notions of global convergence and plus-global convergence introduced in [4], we prove that, for a dendriteX with a finite number of end points and a continuous mapF ofX into itself, the successive approximations method relative to pair (X, F) converges globally if and only ifF has no periodic points; furthermore, we show that ifF has no periodic points and the set of fixed points ofF is totally disconnected then the successive approximations method relative to the pair (X, F) plus-converge globally. Some auxiliary propositions have been proved in more general topological areas. One of them refers to a compact metric space (Γ,d′), to a continuous map ? of Γ into itself and to a sequence \((x_n )_{n \in IN} \) of points of Γ such that the sequence \((d^1 (x_{n + 1} ,\varphi (x_n )))_{n \in IN} \) converges to zero, and concerns the set of the cluster points of the sequence \((x_n )_{n \in IN} \) . In the end the global convergence and plus-global convergence in any metric space are characterized.     

Solution of Boolean equations

We reconstruct and refine the Boole-Jevons-Schroeder-Poretskii method of solving the inverse problems of logic, which through a misunderstanding is nowadays forgotten. We study characteristic examples of the application of the method with a suitable interpretation of the solutions that result. We give a brief presentation of the algebra of boolean expressions and the princples of its constructive implementation on a computer, making it possible in particular to automate the solution of systems of boolean equations. Translated fromMetody Matematicheskogo Modelirovaniya, 1998, pp. 59–68.     

Solution of fifth-degree equations

In this paper we establish a relationship between two approaches to the solution of algebraic fifth-degree equations, namely, the Hermite-Kronecker method (based on the modular elliptic equation) and the Mellin method (based on hypergeometric series).     

Solution of nonlinear evolution equations

Nonlinear evolution equations are solved by decomposition.     

Solution of axisymmetric Maxwell equations

In this article, we study the static and time‐dependent Maxwell equations in axisymmetric geometry. Using the mathematical tools introduced in (Math. Meth. Appl. Sci. 2002; 25 : 49), we investigate the decoupled problems induced in a meridian half‐plane, and the splitting of the solution in a regular part and a singular part, the former being in the Sobolev space H¹ component‐wise. It is proven that the singular parts are related to singularities of Laplace‐like or wave‐like operators. We infer from these characterizations: (i) the finite dimension of the space of singular fields; (ii) global space and space–time regularity results for the electromagnetic field. This paper is the continuation of (Modél. Math. Anal. Numér. 1998; 32 : 359, Math. Meth. Appl. Sci. 2002; 25 : 49). Copyright © 2003 John Wiley & Sons, Ltd.     

Solution of multivariable fuzzy equations

A method for the solution of multivariable fuzzy equations and inequalities is proposed. The proposed method is an extension of Sanchez' technique for a single fuzzy equation. A numerical example is given.