http://hdl.handle.net/2117/3919 Sat, 25 May 2013 22:08:12 GMT 2013-05-25T22:08:12Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2117/19168 Title: Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations Authors: Juher Barrot, David; Mañosa Fernández, Víctor Abstract: We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks Description: Preprint version of the paper Mon, 13 May 2013 08:19:06 GMT http://hdl.handle.net/2117/19168 2013-05-13T08:19:06Z Juher Barrot, David; Mañosa Fernández, Víctor no SIS epidemics, Complex networks, Spectral properties, Connectivity matrix, Disease-free equilibrium. We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks http://hdl.handle.net/2117/19152 Title: Los niveles de determinación como herramienta para analizar tareas de modelización matemática Authors: Gómez Urgellés, Joan Vicenç Abstract: Este trabajo se enmarca en las nuevas necesidades y expectativas de la educación matemática en el sistema educativo español: "preparar al alumno para su incorporación a estudios superiores y para su inserción laboral, y formado para el ejercicio de sus derechos y obligaciones en la vida como ciudadanas y ciudadanos" Thu, 09 May 2013 14:08:10 GMT http://hdl.handle.net/2117/19152 2013-05-09T14:08:10Z Gómez Urgellés, Joan Vicenç no Este trabajo se enmarca en las nuevas necesidades y expectativas de la educación matemática en el sistema educativo español: "preparar al alumno para su incorporación a estudios superiores y para su inserción laboral, y formado para el ejercicio de sus derechos y obligaciones en la vida como ciudadanas y ciudadanos" http://hdl.handle.net/2117/19118 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. Tue, 07 May 2013 11:19:15 GMT http://hdl.handle.net/2117/19118 2013-05-07T11:19:15Z Ferrer Biosca, Alberto; Miranda Galcerán, Eva no 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. http://hdl.handle.net/2117/18907 Title: Intoxicació tecnològica: De l'adicció a la seducció Authors: Gómez Urgellés, Joan Vicenç Fri, 19 Apr 2013 17:59:28 GMT http://hdl.handle.net/2117/18907 2013-04-19T17:59:28Z Gómez Urgellés, Joan Vicenç no http://hdl.handle.net/2117/18885 Title: Modelling in spanish secondary education: description of a practical experience Authors: Gómez Urgellés, Joan Vicenç Abstract: The objective of this work is to present preliminary results of a study about the situation of modelling in Spanish secondary education and a proposal of action. Within the framework of anthropological theory we will show, through the analysis of the official syllabus, that modelling is knowledge to be taught. Despite this, after an analysis of official texts, we have observed that didactic formation of secondary teachers is very poor. Through an experience, developed and implemented in classroom by one of the authors, we will show a different way to work modelling tasks in secondary education. Thu, 18 Apr 2013 18:33:18 GMT http://hdl.handle.net/2117/18885 2013-04-18T18:33:18Z Gómez Urgellés, Joan Vicenç no The objective of this work is to present preliminary results of a study about the situation of modelling in Spanish secondary education and a proposal of action. Within the framework of anthropological theory we will show, through the analysis of the official syllabus, that modelling is knowledge to be taught. Despite this, after an analysis of official texts, we have observed that didactic formation of secondary teachers is very poor. Through an experience, developed and implemented in classroom by one of the authors, we will show a different way to work modelling tasks in secondary education. http://hdl.handle.net/2117/18166 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 Mon, 11 Mar 2013 10:51:41 GMT http://hdl.handle.net/2117/18166 2013-03-11T10:51:41Z García Planas, María Isabel; Mediano Valiente, Begoña no 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 http://hdl.handle.net/2117/17931 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. Fri, 22 Feb 2013 11:46:17 GMT http://hdl.handle.net/2117/17931 2013-02-22T11:46:17Z Banica, Valeria; González Nogueras, María del Mar; Sáez, Mariel no 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. http://hdl.handle.net/2117/17870 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 Tue, 19 Feb 2013 10:46:30 GMT http://hdl.handle.net/2117/17870 2013-02-19T10:46:30Z Compta Creus, Albert; Ferrer Llop, Josep no endomorphism, invariant subspaces, uniparametric control system, bimodal control system 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 http://hdl.handle.net/2117/17869 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. Tue, 19 Feb 2013 10:37:39 GMT http://hdl.handle.net/2117/17869 2013-02-19T10:37:39Z Compta Creus, Albert; Ferrer Llop, Josep; Peña Carrera, Marta no Conditioned invariant subspaces, Miniversal deformation, Stratified manifold, Vertical pairs of matrices 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. http://hdl.handle.net/2117/17529 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. Tue, 29 Jan 2013 13:31:50 GMT http://hdl.handle.net/2117/17529 2013-01-29T13:31:50Z Miranda Galcerán, Eva; Solha, Romero no 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. http://hdl.handle.net/2117/17327 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. Mon, 14 Jan 2013 11:51:05 GMT http://hdl.handle.net/2117/17327 2013-01-14T11:51:05Z Miranda Galcerán, Eva; Presas, Francisco no 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. http://hdl.handle.net/2117/17206 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. Tue, 08 Jan 2013 11:05:46 GMT http://hdl.handle.net/2117/17206 2013-01-08T11:05:46Z González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick no 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. http://hdl.handle.net/2117/17084 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. Mon, 10 Dec 2012 11:45:28 GMT http://hdl.handle.net/2117/17084 2012-12-10T11:45:28Z Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; Pacha Andújar, Juan Ramón no transverse homoclinic orbits, hyperbolic equilibria, Hamilton{Jacobi equation, Riccati equations, splitting of separatrices, Melnikov integr 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. http://hdl.handle.net/2117/16881 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 Mon, 12 Nov 2012 09:52:21 GMT http://hdl.handle.net/2117/16881 2012-11-12T09:52:21Z Álvarez Montaner, Josep no 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 http://hdl.handle.net/2117/16859 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. Wed, 07 Nov 2012 15:50:06 GMT http://hdl.handle.net/2117/16859 2012-11-07T15:50:06Z Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Neumann, Frank no 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.