Équations de type de Boltzmann,spatialement homogènes

Summary We study the construction of a nonhomogeneous ⁿ -valued Markov process, whose laws at fixed times evolve according to a Boltzmann type equation (spatially homogeneous). We then consider the problem of the asymptotic propagation of chaos for a system of a large number of interacting particles.     

Groupes résolubles de difféomorphismes de l’intervalle,du cercle et de la droite

We give a complete classification (from the algebraic and dynamical points of view) of solvable groups of orientation preserving C²-diffeomorphisms of the interval, the circle and the real line. We also give some complementary results in the real-analytic case.     

Classes caracteristiques de Γ(G,H)-structures et finitude de leur evaluation

LetG be a Lie group andH a closed subgroup ofG. We denote by (G,H) the groupoïd of germs of left translations ofG over the homogeneous spaceG/H.LetV be a compact manifold andx the universal characteristic class of dimensionk which belongs to the vector spaceH _cont ^k ((G, H)).The evaluation ofx over all the (G, H)-structures overV determines a subsetA _{(G, H)} (x, V) of the vector spaceH ^k (V;).We show that in some cases this set is finite.     

Sur le 2-groupe de classes d'idéaux de ℚ(√d,i)

Let ℕ,i=√−1,k=ℚ(√d,i) andC ₂ the 2-part of the class group ofk. Our goal is to determine alld such thatC ₂⋍ℤ/2ℤ×ℤ/2ℤ. Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC ₂ la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC ₂⋍ℤ/2ℤ×ℤ/2ℤ.      

Moments, continuité, et analyse multifractale des martingales de Mandelbrot

Here, a Mandelbrot measure is a statistically self-similar measure μ on the boundary of a c-ary tree, obtained by multiplying random weights indexed by the nodes of the tree. We take a particular interest in the random variable Y = ‖μ‖: we study the existence of finite moments of negative orders for Y, conditionally to Y > 0, and the continuity properties of Y with respect to the weights. Our results on moments make possible to study, with probability one, the existence of a local Hölder exponent for μ, almost everywhere with respect to another Mandelbrot measure, as well as to perform the multifractal analysis of μ, under hypotheses that are weaker than those usually assumed.     

Propriétés de l'EMV de rupture de processus de Poisson

This Note concerns the estimation of the parameter of the intensity of an inhomogeneous spatial Poisson process by the maximum likelihood method. We consider an intensity admitting a discontinuity along a closed curve depending of an unknown parameter. The established results show the consistency, the convergence in law and the convergence of the moments of the maximum likelihood estimator.     

Cohomologie des groupes linéaires,K-théorie de Milnor et groupes de Witt

We construct some remarkable classes in the cohomology of linear groups.     

Evaluación probabilista de la capacidad,fragilidad y daño sísmico de edificios de hormigón armado

Currently, many structures existing in seismic areas are highly vulnerable because they have been built without the use of seismic design codes or by using outdated codes. Often, methods for assessing the vulnerability of the structures do not take into account that their seismic behavior is dynamic and highly nonlinear and, moreover, that the structural characteristics and action have large uncertainties. This article aims to assess the vulnerability of structures taking into account that the mechanical properties of materials and the seismic action are random variables, by using advanced techniques based on the Monte Carlo method and on the nonlinear stochastic dynamics. The results obtained with these techniques are compared with those corresponding to a standard vulnerability assessment, based on deterministic models, in order to highlight the differences between both approaches. The main conclusion of this work is the need to address the vulnerability assessment problem from a probabilistic perspective which, combined with advanced nonlinear static and dynamic structural analysis techniques, provides a powerful tool giving information impossible to be captured by means of deterministic models. Finally, detailed results obtained for a building with waffle slabs, which is a structural typology widely used in Spain, are included and discussed.     

Constructibilité de de Rham p-adique

We use the theory of special modules to define the category of de Rham p-adic complexes on a smooth scheme over a perfect field and we prove a constructibility criterion implying the first finiteness properties.     

Conductivité électrique de la neige,au courant continu

Sans résumé     

Une variante de la méthode de majoration de Cauchy

Sans résumé Conférence faite au Congrès des mathématiciens scandinaves à Copenhague en ao?t 1964. 10-652932