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Abstract: In this paper, we define in the framework of noncommutative differential forms the notion of cup i-product introduced by Steenrod in [N.E. Steenrod, Product of cocycles and extensions of mappings, Ann. Math. 48 (2) (1947)]. This cup i-product permits to define an operator who will be a generalisation of the operator b defined in Hochschild and cyclic homology. With the operator we define in an explicitly way the Steenrod and Thomas–Pontrjagin squares. [Copyright &y& Elsevier]

Abstract: We introduce a notion of ‘nondegenerate integrable contact system’ for 3-contact manifolds. In the case of compact manifolds, we construct characteristic invariants for such a system. This is the contact analogue of the work done by A. Toulet (1996) for Hamiltonian systems with one degree of freedom, and we use these results. The invariants pointed out indicate that, generally, we arrive at systems which are not contactisations of Toulet models. To cite this article: M. Balde et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: We consider general Schrödinger operators on domains of Riemannian manifolds with possibly exponential volume growth. We prove sharp large time Gaussian upper bounds. These bounds are then used to prove new estimates for the corresponding semigroups. Applications to semi-linear parabolic equations are given. [Copyright &y& Elsevier]

Abstract: The purpose of this Note is to prove an extension result for positive currents satisfying one of the following conditions: either or one of the currents dT or is of locally finite mass, across of a non-Levi-flat submanifold of class . We prove in the first part that a positive current of dimension p defined in the complement of the zero set of a strictly k-convex function of class () and such that dT is of locally finite mass, is itself of locally finite mass. We recover a result of S. Giret in the case of a Cauchy–Riemann subvariety. To cite this article: K. Dabbek, F. Elkhadhra, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]