The Mammals and birds of Camiguin Island, Philippines, a distinctive center of biodiversity / Lawrence R. Heaney, editor.

n.s. no.106(2006)

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.