Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure

We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves at the discrete level the formal gradient flow structure, allowing the use of some nonlinear test functions in the analysis. The existence of a solution to and the convergence of the scheme are proved under very general assumptions on the continuous problem (nonlinearities, anisotropy, heterogeneity) and on the mesh. Moreover, we provide numerical evidences of the efficiency and of the robustness of our approach

Topological Invariants of Anosov Representations

We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.Comment: 66 pages, several changes, some consequences adde

On Salem numbers, expansive polynomials and Stieltjes continued fractions

A converse method to the Construction of Salem (1945) of convergent families of Salem numbers is investigated in terms of an association between Salem polynomials and Hurwitz quotients via expansive polynomials of small Mahler measure. This association makes use of Bertin-Boyd's Theorem A (1995) of interlacing of conjugates on the unit circle; in this context, a Salem number $\beta$ is produced and coded by an m-tuple of positive rational numbers characterizing the (SITZ) Stieltjes continued fraction of the corresponding Hurwitz quotient (alternant). The subset of Stieltjes continued fractions over a Salem polynomial having simple roots, not cancelling at $\pm 1$, coming from monic expansive polynomials of constant term equal to their Mahler measure, has a semigroup structure. The sets of corresponding generalized Garsia numbers inherit this semi-group structure.Comment: 35 pages, Journal de Th{\'e}orie des nombres de Bordeaux, Soumissio

The impact of ICT sophistication on geographically distant networks: the case of space physics as seen from France

This paper examines scientific collaboration between French public research teams and distant partners. We first analyse the role and the development of trust and then, the relation between the degree of sophistication of Information and Communication Technologies (ICT) and the constraint of geographical proximity. In that purpose, we present a typology of the different kinds of knowledge and a classification of technologies. A case study in the field of space physics allows us to confront our theoretical elements to real life. We study the evolution of ICT sophistication parallel to collaboration patterns. Finally, we give some recommendations for public funding of virtual networks.collaboratory, knowledge transfer, trust, ICT classification, space physics

Anosov representations and proper actions

We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of reductive groups.Comment: 73 pages, 4 figures; to appear in Geometry & Topolog