Counting polygon dissections in the projective plane

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Brown representability does not come for free

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On the intersection of free subgroups in free products of groups

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A public-key cryptosystem based on second order linear sequences

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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Hopf bifurcation in higher dimensional differential systems via the averaging method

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Rational first integrals in the Darboux theory of integrability in Cn

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Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Derived categories and Grothendieck duality

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Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Estudio exploratorio sobre tareas traductoras: informe de la estancia de investigación

Investigación elaborada a partir de una estancia en el Centre de Formation de Traducteurs-Localiseurs, Terminologue et Rédacteurs (CFTTR) de la Université Rennes 2 Haute Bretagne, Francia, entre los meses de abril y julio del 2006. El proyecto constituye la fase exploratoria de la tesis doctoral desarrollada en el Departament de Traducció i d’Interpretació de la Universitat Autònoma de Barcelona en torno a la organización del trabajo en las empresas proveedoras de servicios de traducción e interpretación. Se ha recabado información y opiniones sobre la identificación de tareas desempeñadas en el ámbito laboral de quatro empresas sobre la traducción e interpretación y las tareas ajenas a la actividad traductora. Los resultados obtenidos permiten identificar una gran variedad de tareas próximas a la actividad traductora pero distintas de ella. El estudio exploratorio efectuado ha contribuido a mejorar el diseño de la investigación empírica prevista para la tesis doctoral: aportó información sobre la importancia del enfoque cualitativo, las hipótesis por contrastar, la definición del colectivo, la delimitación formal de las unidades de análisis, y sobre las principales variables de estudio y su medición.