DSpace Collection:

Random test examples with known minimum for convex semi-infinite programming problems

Tue, 07 May 2013 11:19:15 GMT

Title: Random test examples with known minimum for convex semi-infinite programming problems Authors: Ferrer Biosca, Alberto; Miranda Galcerán, Eva Abstract: A signi cant research activity has occurred in the area of convex semi- in nite optimization in the recent years. Many new theoretical, algorithm and computational contribution has been obtained . Despite these numerous con- tributions, there still exits a lack of representative convex semi-in nite test problems. Test problems are of major importance for researchers interested in the algorithmic development. This article is motivated by the scarcity of con- vex semi-in nite test problems and describes a procedure for generating convex semi-in nite families of test problems with optimal solution and optimal value known.

Stability of a pipeline hydraulic fluid with one end fixed

Mon, 11 Mar 2013 10:51:41 GMT

Title: Stability of a pipeline hydraulic fluid with one end fixed Authors: García Planas, María Isabel; Mediano Valiente, Begoña Abstract: The dynamics and stability of pipes conveying fluid has been studied thoroughly in the last decades. In this paper we study the stability in the Liapunov sense, of a clamped-pinned pipe conveying fluid at a low speed. After describing the motion of the system by partial differential equations we solve equations using finite element method testing solutions by means of ANSYS, we analyze the characteristic equation and its eigenvalues in order to obtain the stability conditions

Some constructions for the fractional Laplacian on noncompact manifolds

Fri, 22 Feb 2013 11:46:17 GMT

Title: Some constructions for the fractional Laplacian on noncompact manifolds Authors: Banica, Valeria; González Nogueras, María del Mar; Sáez, Mariel Abstract: We give a de nition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Ca arelli-Silvestre. While this de nition in the compact case is straightforward, in the noncompact setting one needs to have a precise control of the behavior of the metric at in nity and geometry plays a crucial role. First we give explicit calculations in the hyperbolic space, including a formula for the kernel and a trace Sobolev inequality. Then we consider more general noncompact manifolds, where the problem reduces to obtain suitable upper bounds for the heat kernel.

Classi fication of monogenic invariant subspaces and uniparametric linear control systems

Tue, 19 Feb 2013 10:46:30 GMT

Title: Classi fication of monogenic invariant subspaces and uniparametric linear control systems Authors: Compta Creus, Albert; Ferrer Llop, Josep Abstract: The classification of the invariant subspaces of an endomorphism has been an open problem for a long time, and it is a ”wild” problem in the general case. Here we obtain a full classification for the monogenic ones. Some applications are derived: in particular, canonical forms for uniparametric linear control systems, non necessarily controllable, with regard to linear changes of state variables

Miniversal deformations of observable marked matrices

Tue, 19 Feb 2013 10:37:39 GMT

Title: Miniversal deformations of observable marked matrices Authors: Compta Creus, Albert; Ferrer Llop, Josep; Peña Carrera, Marta Abstract: Given the set of vertical pairs of matrices M¿ Mm,n(C)×Mn(C) keeping the subspace Cd×{0} ¿ Cn invariant, we compute miniversal deformations of a given pair when it is observable and the subspace Cd × {0} is marked. Moreover, we obtain the dimension of the orbit, characterize the structurally stable vertical pairs and study the effect of each deformation parameter.

On a Poincaré lemma for singular foliations and geometric quantization

Tue, 29 Jan 2013 13:31:50 GMT

Title: On a Poincaré lemma for singular foliations and geometric quantization Authors: Miranda Galcerán, Eva; Solha, Romero Abstract: In this paper we prove a Poincar e lemma for forms tangent to a foliation with nondegenerate singularities given by an integrable system on a symplectic manifold. As a consequence, the Kostant complex in Geometric Quantization is a ne resolution of the sheaf of at sections when the polarization is spanned by the Hamiltonian vector elds of the rst integrals of this integrable system.

Geometric Quantization of real polarizations via sheaves

Mon, 14 Jan 2013 11:51:05 GMT

Title: Geometric Quantization of real polarizations via sheaves Authors: Miranda Galcerán, Eva; Presas, Francisco Abstract: In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology. The starting point is the definition of representation spaces due to Kostant. We check that the associated sheaf cohomology apparatus satisfies Mayer-Vietoris and K\"unneth formulae. As a consequence, new proofs of classical results for fibrations are obtained. In the general case of Lagrangian foliations, we compute Geometric Quantization with respect to almost any generic regular Lagrangian foliation on a 2-torus.

Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties

Tue, 08 Jan 2013 11:05:46 GMT

Title: Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties Authors: González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick Abstract: where (¿ Hn) corresponds to the fractional Laplacian on hyperbolic space for 2 (0; 1) and f is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections in the following sense; a so-called layer solution is a smooth solution of the previous equation converging to 1 at any point of the two hemispheres S @1Hn and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane :We prove that under additional conditions on the nonlinearity uniqueness holds up to isometry. Then we provide several symmetry results and qualitative properties of the layer solutions. Finally, we consider the multilayer case, at least when is close to one.

Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation

Mon, 10 Dec 2012 11:45:28 GMT

Title: Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation Authors: Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; Pacha Andújar, Juan Ramón Abstract: The key point of our approach is to write the invariant manifolds in terms of generating functions, which are solutions of the Hamilton-Jacobi equation. In some examples, we show that it is enough to analyse the phase portrait of the Riccati equation without solving it explicitly. Finally, we consider an analogous problem in a perturbative situation. If the invariant manifolds of the unperturbed loop coincide, we have a problem of splitting of separatrices. In this case, the Riccati equation is replaced by a Mel0nikov potential defined as an integral, providing a condition for the existence of a perturbed loop and its transversality. This is also illustrated with a concrete example.

Three lectures on local cohomology modules supported on monomial ideals

Mon, 12 Nov 2012 09:52:21 GMT

Title: Three lectures on local cohomology modules supported on monomial ideals Authors: Álvarez Montaner, Josep Abstract: These notes are an extended version of a set of lectures given at ”MONICA: MONomial Ideals, Computations and Applications”, at the CIEM, Castro Urdiales (Cantabria, Spain) in July 2011. The goal of these lectures is to give an overview of some results that have been developed in recent years about the structure of local cohomology modules supported on a monomial ideal. We will highlight the interplay of multi-graded commutative algebra, combinatorics and D-modules theory that allow us to give different points of view to this subject. We will try to preserve the informal character of the lectures, so very few complete proofs are included

Thomason cohomology of categories

Wed, 07 Nov 2012 15:50:06 GMT

Title: Thomason cohomology of categories Authors: Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Neumann, Frank Abstract: We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more classical theories. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.

GROUPOIDS AND FAÀ DI BRUNO FORMULAE FOR GREEN FUNCTIONS IN BIALGEBRAS OF TREES

Wed, 07 Nov 2012 15:41:56 GMT

Title: GROUPOIDS AND FAÀ DI BRUNO FORMULAE FOR GREEN FUNCTIONS IN BIALGEBRAS OF TREES Authors: Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Kock, Joachim Abstract: We prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. For suitable choices of P, the result implies also formulae for Green functions in bialgebras of graphs

Central cohomology operations and K-theory

Wed, 07 Nov 2012 15:18:08 GMT

Title: Central cohomology operations and K-theory Authors: Gálvez Carrillo, Maria Immaculada; Whitehouse, Sarah Abstract: For stable degree zero operations, and also for additive unstable operations of bidegree (0,0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory

Coupling symmetries with Poisson structures

Mon, 05 Nov 2012 15:16:38 GMT

Title: Coupling symmetries with Poisson structures Authors: Laurent-Gengoux, Camille; Miranda Galcerán, Eva Abstract: In this paper we study normal forms problems for integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The equivariant normal forms are obtained at the local level. The existence of Weinstein’s splitting theorem for the integrable system is also studied giving some examples in which such a splitting cannot split. This splitting allows to decompose the integrable system locally as a product of an integrable system on the symplectic leaf and a symplectic leaf on the transversal. The problem of splitting for integrable systems with additional symmetries is also considered

Symplectic and Poisson geometry on b-manifolds

Thu, 04 Oct 2012 11:51:14 GMT

Title: Symplectic and Poisson geometry on b-manifolds Authors: Guillemin, Victor; Miranda Galcerán, Eva; Pissarra Pires, Ana Rita Abstract: Let M2n be a Poisson manifold with Poisson bivector field . We say thatM is b-Poisson if the map n : M ! 2n(TM) intersects the zero section transversally on a codimension one submanifold Z M. This paper will be a systematic investigation of such Poisson manifolds. In particular, we will study in detail the structure of (M, ) in the neighbourhood of Z and using symplectic techniques define topological invariants which determine the structure up to isomorphism. We also investigate a variant of de Rham theory for these manifolds and its connection with Poisson cohomology