We give a topological proof that a free inverse monoid on one or more generators is neither of type left-FP_2 nor right-FP_2. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
In 2002 Meersseman-Verjovsky [2] constructed a smooth, codimension-one, foliation on 5-sphere by complex surfaces with two compact leaves. The aim of this note is to improve their construction in order to give a smooth foliation on 5-sphere by complex surfaces with only one compact leaf.
This Note is answering an old questioning about the Fenyes-Nelson stochastic mechanics. Feynman's interpretation of the Heisenberg uncertainty principle allows to deduce the Brownian fluctuations, which are associated to this mechanics, from an infinitesimal time-discretisation stemming from non-standard analysis. It is therefore no more necessary to combine those fluctuations with a background field, which has never been well understood. Let us add that an extended english abstract is giving most of the details.
In this Note we propose a new method of proving the existence of solutions to −divA(x,∇u)∋f, when A(x,∇u) has x-dependent maximal monotone graph. The idea is based on the theory of Young measures and on the method of compensated compactness. Alternative approaches were proposed elsewhere. However, our method allows us to obtain also the strong convergence of approximate solutions. To cite this article: P. Gwiazda, A. Zatorska-Goldstein, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
The Lagrange--Galerkin method is the coupling of a finite element method for space discretisation with the method of characteristics for the discretisation of the material derivative in some parabolic problems. We propose a new scheme of second-order accuracy in time, which in contrast with previous methods does not require a correction term. Numerical examples, including Burgers equation, illustrate the convergence rate and low computational cost of the method.
