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.

Quadratic perturbations of a quadratic reversible Lotka-Volterra System

"Vegeu el resum a l'inici del document del fitxer adjunt."

Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

Hopf bifurcation for degenerate singular points of multiplicity 2n-1 in dimension 3

"Vegeu el resum a l'inici del document del fitxer adjunt."

Classes of measures generated by capacities

"Vegeu el resum a l'inici del document del fitxer adjunt."

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

On the critical periods of perturbed isochronous centers

"Vegeu el resum a l'inici del document del fitxer adjunt."

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Los procesos de gramaticalización de algunos conectores concesivos del castellano medieval

En aquest treball d’investigació es descriuen els trets principals dels processos de gramaticalització. Alhora, s’ha aplicat alguns dels postulats formulats en el marc de la Teoria de la gramaticalització a la formació d'alguns connectors concessius del castellà medieval: aunque, maguer (que) i comoquier (que). Per a l'anàlisi d'aquests fenòmens s'ha decidit recórrer a la Teoria dels prototips (en termes de Hilferty, 1993) i a la Teoria de la Rellevància (en termes de Blakemore, 2002): creiem que aquestes dues postures casen a la perfecció i ens han permès oferir una visió més global dels fets

Derived categories and Grothendieck duality

"Vegeu el resum a l'inici del document del fitxer adjunt."

Cooperative strategies for imperfect CSI scenarios based on distributed Alamouti

Les comunicacions cooperatives estan guanyant un gran interès en les comunicacions modernes degut a que permeten millorar la transmissió dʼinformació entre un emissor i un receptor utilitzant una sèrie de terminals situats entre ells. Aquest projecte és un estudi complet del sistemes cooperatius, analitzant el seu rendiment i comparant lʼús dʼun sol dʼaquests terminals amb lʼús del codi Alamouti, que utilitza dos terminals. Primer hi ha una introducció als sistemes cooperatius i a la teoria de la informació. Després hem estudiat un sistema cooperatiu amb la teoria de la informació com a base, en termes de probabilitat de fallada del sistema, i posteriorment lʼhem adaptat a un sistema cooperatiu real utilitzant una modulació QPSK, estudiant la seva probabilitat dʼerror de paquet. Finalment es proposen diversos protocols que permeten millorar el rendiment del sistema cooperatiu estudiat.

Códigos binarios no lineales en MAGMA

La finalitat d'aquest projecte és aconseguir representar codis binaris no lineals de manera eficient en un ordinador. Per fer-ho, hem desenvolupat funcions per representar un codi binari a partir del super dual. Hem millorat la funció de càlcul del kernel d'un codi binari, implementada en projectes d'anys anteriors. També hem desenvolupat un paquet software per l'intèrpret MAGMA. Aquest paquet ens proveeix d'eines per al tractament de codis binaris no necessàriament lineals.

On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.