On the number of limit cycles bifurcating from a non-global degenerated center

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Distribution center consolidation games

We study the location-inventory model as introduced by Teo et al. (2001) to analyze the impact of consolidation of distribution centers on facility and inventory costs. We extend their result on profitability of consolidation. We associate a cooperative game with each location-inventory situation and prove that this game has a non-empty core for identical and independent demand processes. This illustrates that consolidation does not only lower joint costs (which was shown by Teo et al. (2001)), but it allows for a stable division of the minimal costs as well.

Resum de la tasca realitzada al Center Biomedical Engineering (CBE) del Massachussets Institute of Technology (MIT). Juliol-Agost 2005

Estudi elaborat a partir d’una estada al Center Biomedical Engineering (CBE) del Massachussets Institute of Technology (MIT), durant els mesos de juliol i agost del 2005. S’investiga una metodologia amb l’objectiu d’obtenir biomaterials que puguin actuar de bastida en la interfície os/cartílag, afavorint la diferenciació i creixement cel·lular de cartílag ossificat que pugui actuar d’unió entre l’articulació i l’os. S’experimenta una metodologia per a establir quins són els péptids afavoridors de la formació de teixit ossi utilitzats en materials d’hidroxiapatita. Es conclou que la tecnologia desenvolupada permet disposar d’una plataforma per assajar l’estudi del signaling sobre cèl·lules embrionàries, que permeti desenvolupar materials amb més capacitat diferenciadora.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Mixing invariants of hyperbolic 3-manifolds

Let M be a compact hyperbolic 3-manifold with incompressible boundary. Consider a complete hyperbolic metric on int(M). To each geometrically finite end of int(M) are traditionnaly associated 3 different invariants : the hyperbolic metric associated to the conformal structure at infinity, the hyperbolic metric on the boundary of the convex core and the bending measured lamination of the convex core. In this note we show how invariants of different types can be realised in the different ends.

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

An extension of the Marsden-Ratiu reduction for Poisson manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Parallel spinors on pseudo-riemannian spin(q) manifolds

We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds admitting parallel quaternionic spinors.

Creació d'un media center amb software lliure

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. L’objectiu d’aquest treball de recerca és la creació d’un dispositiu encarregat de centralitzar totes les necessitats multimèdia de casa nostra i distribuir aquest contingut a tots els terminals de la xarxa local d’una manera senzilla i automatitzada. Aquest dispositiu s’ha dissenyat per estar connectat a una televisió d’alta definició, que permetrà la reproducció i l’organització de tot el nostre multimèdia d’una manera còmoda i fàcil. El media center s’encarrega de gestionar la nostra filmoteca, fototeca, biblioteca musical i sèries de TV de manera transparent i automàtica. A més a més, l’usuari pot accedir a tot el multimèdia emmagatzemat al media center des de qualsevol dispositiu de la xarxa local a través de protocols com CIFS o UPnP, en un intent de replicar el cloud computing a escala local. El dispositiu ha estat dissenyat per a suportar tot tipus de formats i subtítols, assegurant la compatibilitat total amb arxius lliures de DRM. El seu disseny minimalista i silenciós el fa perfecte per a substituir el reproductor de DVD de la sala. Tot això sense oblidar el seu baix consum, de l’ordre d’un 75% inferior al d’un PC convencional.

Definició i estudi de viabilitat d'un "support center" funcional en una empresa farmacèutica

Este proyecto comprende dos componentes centrales. Estos son, definir la situación actual sobre el soporte funcional en las aplicaciones y proponer soluciones para una mejora de los servicios. Durante la descripción de la situación actual se han ido encontrando problemas en el soporte, y se proponen soluciones. Se han llegado a proponer 3 modelos distintos de los cuales se ha elegido uno, el cual supone una importante mejora en el servicio.