On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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

Transverse and longitudinal components of the propagating and evanescent waves associated to radially-polarized nonparaxial fields

A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.

Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane

In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.

Analysis and optimization of the satellite-to-plane link of an aeronautical global system

En aquest projecte s’ha analitzat i optimitzat l’enllaç satèl·lit amb avió per a un sistema aeronàutic global. Aquest nou sistema anomenat ANTARES està dissenyat per a comunicar avions amb estacions base mitjançant un satèl·lit. Aquesta és una iniciativa on hi participen institucions oficials en l’aviació com ara l’ECAC i que és desenvolupat en una col·laboració europea d’universitats i empreses. El treball dut a terme en el projecte compren bàsicament tres aspectes. El disseny i anàlisi de la gestió de recursos. La idoneïtat d’utilitzar correcció d’errors en la capa d’enllaç i en cas que sigui necessària dissenyar una opció de codificació preliminar. Finalment, estudiar i analitzar l’efecte de la interferència co-canal en sistemes multifeix. Tots aquests temes són considerats només per al “forward link”. L’estructura que segueix el projecte és primer presentar les característiques globals del sistema, després centrar-se i analitzar els temes mencionats per a poder donar resultats i extreure conclusions.

Exchange-correlation effects on quantum wires with spin-orbit interactions under the influence of in-plane magnetic fields.

Within the noncollinear local spin-density approximation, we have studied the ground state structure of a parabolically confined quantum wire submitted to an in-plane magnetic field, including both Rashba and Dresselhaus spin-orbit interactions. We have explored a wide range of linear electronic densities in the weak (strong) coupling regimes that appear when the ratio of spin-orbit to confining energy is small (large). These results are used to obtain the conductance of the wire. In the strong coupling limit, the interplay between the applied magnetic field¿irrespective of the in-plane direction, the exchange-correlation energy, and the spin-orbit energy-produces anomalous plateaus in the conductance vs linear density plots that are otherwise absent, or washes out plateaus that appear when the exchange-correlation energy is not taken into account.

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Dyrk1A is dynamically expressed on subsets of motor neurons and in the neuromuscular junction: possible role in Down syndrome

Individuals with Down syndrome (DS) present important motor deficits that derive from altered motor development of infants and young children. DYRK1A, a candidate gene for DS abnormalities has been implicated in motor function due to its expression in motor nuclei in the adult brain, and its overexpression in DS mouse models leads to hyperactivity and altered motor learning. However, its precise role in the adult motor system, or its possible involvement in postnatal locomotor development has not yet been clarified. During the postnatal period we observed time-specific expression of Dyrk1A in discrete subsets of brainstem nuclei and spinal cord motor neurons. Interestingly, we describe for the first time the presence of Dyrk1A in the presynaptic terminal of the neuromuscular junctions and its axonal transport from the facial nucleus, suggesting a function for Dyrk1A in these structures. Relevant to DS, Dyrk1A overexpression in transgenic mice (TgDyrk1A) produces motor developmental alterations possibly contributing to DS motor phenotypes and modifies the numbers of motor cholinergic neurons, suggesting that the kinase may have a role in the development of the brainstem and spinal cord motor system.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

On the origin and scope of the second language speech production disadvatage

Los hablantes bilingües tienen un acceso al léxico más lento y menos robusto que los monolingües, incluso cuando hablan en su lengua materna y dominante. Este fenómeno, comúnmente llamado “la desventaja bilingüe” también se observa en hablantes de una segunda lengua en comparación con hablantes de una primera lengua. Una causa que posiblemente contribuya a estas desventajas es el uso de control inhibitorio durante la producción del lenguaje: la inhibición de palabras coactivadas de la lengua actualmente no en uso puede prevenir intrusiones de dicha lengua, pero al mismo tiempo ralentizar la producción del lenguaje. El primer objetivo de los estudios descritos en este informe era testear esta hipótesis mediante diferentes predicciones generadas por teorías de control inhibitorio del lenguaje. Un segundo objetivo era investigar la extensión de la desventaja bilingüe dentro y fuera de la producción de palabras aisladas, así como avanzar en el conocimiento de las variables que la modulan. En lo atingente al primer objetivo, la evidencia obtenida es incompatible con un control inhibitorio global, desafiando la idea de mecanismos específicos en el hablante bilingüe utilizados para la selección léxica. Esto implica que una explicación común para el control de lenguaje y la desventaja bilingüe en el acceso al léxico es poco plausible. En cuanto al segundo objetivo, los resultados muestran que (a) la desventaja bilingüe no tiene un impacto al acceso a la memoria; (b) la desventaja bilingüe extiende a la producción del habla conectada; y (c) similitudes entre lenguas a diferentes niveles de representación así como la frecuencia de uso son factores que modulan la desventaja bilingüe.   

Optical counterpart of galactic plane variable radio sources

We present I-band deep CCD exposures of the fields of galactic plane radio variables. An optical counterpart, based on positional coincidence, has been found for 15 of the 27 observed program objects. The Johnson I magnitude of the sources identified is in the range 18-21.

Analytic behavior of the QED polarizability function at finite temperature

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.