8,406 research outputs found
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
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 , 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
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