Central configurations of three nested regular polyhedra for the spatial 3n–body problem

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Contenidos de aprendizaje para estudiantes de diseño en podcast

La Universitat Politècnica de Catalunya, a través del Graduado Superior de Diseño, ha realizado una experiencia en donde los contenidos de aprendizaje se han distribuido mediante podcast. Es el primer curso de diseño en esta universidad que distribuye materiales de formación con estas características, persiguiendo el objetivo de proporcionar a los estudiantes un acceso a contenidos educativos mediante un dispositivo móvil. Para evaluar esta experiencia, hemos analizado las respuestas obtenidas de los estudiantes, mediante un cuestionario. Nos encontramos con que dan un valor al Podcast como vehículo de revisión de contenidos, pero se valora más como una alternativa al aprendizaje. Los podcast crecen en cuanto a popularidad, y se han puesto a disposición de los alumnos esta tecnología considerando este reclamo y no la tecnología en sí. Con este artículo, planteamos que el podcasting ofrece a las Universidades nuevas posibilidades educacionales para llegar a más estudiantes y ofrecer otro medio de aprendizaje. Además, no solo se planteo recopilar estadísticas sobre las descargas a través de este experimento, si no también conocer las reflexiones de los estudiantes sobre la tecnología utilizada.

Percepciones de estudiantes sobre el Aprendizaje móvil; la nueva generación de la educación a distancia

Durante años, muchas instituciones y universidades han comenzado a experimentar con los dispositivos móviles en el aprendizaje a través de diferentes proyectos como parte de su metodología de aprendizaje. La experiencia adquirida con el empleo de estrategias y enfoques en la educación a distancia puede facilitar la conceptualización del aprendizaje móvil, así como el desarrollo de aplicaciones para este nuevo medio de aprendizaje. Los dispositivos móviles abren además nuevos caminos para el aprendizaje y una nueva generación para la educación a distancia, y los investigadores conocen estos nuevos caminos para el aprendizaje y oportunidades de llegar a un público más amplio. Este trabajo, muestra los resultados de un grupo de discusión que se llevó a cabo entre 20 estudiantes de licenciatura con el fin de explorar las percepciones, y en general todo aquello que afecta a la interpretación subjetiva de los individuos y su interacción con un fenómeno social como el aprendizaje móvil.

On the Selection of Non-Invasive Methods Based on Speech Analysis Oriented to Automatic Alzheimer Disease Diagnosis

The work presented here is part of a larger study to identify novel technologies and biomarkers for early Alzheimer disease (AD) detection and it focuses on evaluating the suitability of a new approach for early AD diagnosis by non-invasive methods. The purpose is to examine in a pilot study the potential of applying intelligent algorithms to speech features obtained from suspected patients in order to contribute to the improvement of diagnosis of AD and its degree of severity. In this sense, Artificial Neural Networks (ANN) have been used for the automatic classification of the two classes (AD and control subjects). Two human issues have been analyzed for feature selection: Spontaneous Speech and Emotional Response. Not only linear features but also non-linear ones, such as Fractal Dimension, have been explored. The approach is non invasive, low cost and without any side effects. Obtained experimental results were very satisfactory and promising for early diagnosis and classification of AD patients.

On Automatic Diagnosis of Alzheimer's Disease based on Spontaneous Speech Analysis and Emotional Temperature

Alzheimer's disease is the most prevalent form of progressive degenerative dementia; it has a high socio-economic impact in Western countries. Therefore it is one of the most active research areas today. Alzheimer's is sometimes diagnosed by excluding other dementias, and definitive confirmation is only obtained through a post-mortem study of the brain tissue of the patient. The work presented here is part of a larger study that aims to identify novel technologies and biomarkers for early Alzheimer's disease detection, and it focuses on evaluating the suitability of a new approach for early diagnosis of Alzheimer’s disease by non-invasive methods. The purpose is to examine, in a pilot study, the potential of applying Machine Learning algorithms to speech features obtained from suspected Alzheimer sufferers in order help diagnose this disease and determine its degree of severity. Two human capabilities relevant in communication have been analyzed for feature selection: Spontaneous Speech and Emotional Response. The experimental results obtained were very satisfactory and promising for the early diagnosis and classification of Alzheimer’s disease patients.

El consum multipantalla. Estudi sobre l’ús de mitjans tradicionals i nous per part de nens, joves, adults i gent gran a Catalunya

Des de fa una dècada es parla de la convergència digital, que ha propiciat la conjunció de la informàtica amb els mitjans de comunicació i la interconnexió en xarxa. Actualment circulen amb facilitat suports vells i nous cada vegada més flexibles. La conseqüència per als usuaris és que avui disposen d’una varietat àmplia de continguts connectats permanentment en qualsevol lloc i en qualsevol moment, a través de diverses plataformes i amb una convivència rica i complexa. En aquest context, aquest article mostra les conclusions d’un estudi de camp sobre l’ús, el consum i les preferències de suports i de continguts de la comunicació digital per part de grups d’infants, de joves, d’adults i de gent gran a Catalunya.

El periodista polivalente. Transformaciones en el perfil del periodista a partir de la digitalización de los medios audiovisuales catalanes

Este trabajo analiza las transformaciones que ha experimentado la figura del periodista en el actual panorama audiovisual catalán, especialmente en lo referido a la asunción de nuevas tareas y funciones. Tras una introducción en la que se expone el marco teórico y la metodología de trabajo, se describen las transformaciones en los perfiles profesionales y se presentan las principales tendencias observadas en las empresas de radio y televisión, agencias de noticias y medios en línea de Cataluña. El artículo concluye con una serie de reflexiones sobre la polivalencia del periodista.

Comunicación móvil: actores y producción de contenidos en Cataluña

El presente artículo presenta los resultados de una investigación realizada durante el año 2008 donde se describen los actores y contenidos de la comunicación móvil producidos en Cataluña. La comunicación móvil, además de ser uno de los sectores más dinámicos de la economía global, está transformando diferentes aspectos de la vida social, desde las formas de relacionarse hasta los procesos de producción, distribución y analiconsumo cultural. La investigación traza un primer mapa de la situación, propone una serie de categorías de análisis y sienta las bases para futuros estudios más específicos sobre la comunicación móvil en Cataluña.