Quantization of complex Lagrangian submanifolds

Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X.     

Almost sure estimates for the concentration neighborhood of Sinai’s walk

We consider Sinai’s random walk in random environment. We prove that infinitely often (i.o.) the size of the concentration neighborhood of this random walk is bounded almost surely. We also get that i.o. the maximal distance between two favorite sites is bounded almost surely.     

Trois formulations d'un modèle de plasma quasi-neutre avec courant non nul

In this Note, we propose three formulations of a model describing a quasi-neutral plasma with non-vanishing current. In order to study and compare the numerical efficiency of each formulation, two test-problems are implemented in one dimension. The first is a periodic perturbation of a uniform stationary plasma. The second is a case of plasma expansion in vacuum between two electrodes. To cite this article: P. Crispel et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The number of commutative semigroups of order N

An explicit upper bound is given for the number of commutative semigroups withn elements.     

Computing Finite Semigroups, I: The First Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this first part describe the first row of the multiplication table in detail and provide a numerical profile with which it can be compared to other rows.     

An efficient sampling method for stochastic inverse problems

A general framework is developed to treat inverse problems with parameters that are random fields. It involves a sampling method that exploits the sensitivity derivatives of the control variable with respect to the random parameters. As the sensitivity derivatives are computed only at the mean values of the relevant parameters, the related extra cost of the present method is a fraction of the total cost of the Monte Carlo method. The effectiveness of the method is demonstrated on an example problem governed by the Burgers equation with random viscosity. It is specifically shown that this method is two orders of magnitude more efficient compared to the conventional Monte Carlo method. In other words, for a given number of samples, the present method yields two orders of magnitude higher accuracy than its conventional counterpart.     

An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.     

A diffusion approximation result for two parameter processes

Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010