Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Car ownership and access to jobs in Spain

This study analyses the impact that job accessibility in public transport has on car ownership. An ordered probit explaining the number of cars per household is estimated as a function of head of household characteristics, household characteristics and job accessibility. The data used in the analysis come from the Microcensus of year 2001 of the Spanish Institute of Statistics for the areas of Barcelona and Madrid. Our results show a significant effect of accessibility on car ownership. Additionally, we carried out simulation exercises in which the expected number of vehicles decreases as accessibility improves. For instance, in the case of households living outside the central city, an improvement of accessibility up to the average level of the central city would offset the effect of the number of working adults on the expected number of vehicles.

Economic development and changes in car ownership patterns

The contributions of this paper are twofold: On the one hand, the paper analyses the factors determining the growth in car ownership in Spain over the last two decades, and, on the other, the paper provides empirical evidence for a controversial methodological issue. From a methodological point of view, the paper compares the two alternative decision mechanisms used for modelling car ownership: ordered-response versus unordered-response mechanisms. A discrete choice model is estimated at three points in time: 1980, 1990 and 2000. The study concludes that on the basis of forecasting performance, the multinomial logit model and the ordered probit model are almost undistinguishable. As for the empirical results, it can be emphasised that income elasticity is not constant and declines as car ownership increases. Besides, households living in rural areas are less sensitive than those living in urban areas. Car ownership is also sensitive to the quality of public transport for those living in the largest cities. The results also confirmed the existence of a generation effect, which will vanish around the year 2020, a weak life-cycle effect, and a positive effect of employment on the number of cars per household. Finally, the change in the estimated coefficients over time reflects an increase in mobility needs and, consequently, an increase in car ownership.

Diseño de inversores de impedancias de microondas compactos basados en metamateriales: aplicación a divisores de potencia

Recientemente ha surgido un nuevo campo de investigación en el área del electromagnetismo aplicado y de la ingeniería de microondas, basado en el control de las propiedades electromagnéticas de estructuras artificiales, conocidas como metamateriales. El objetivo principal de este proyecto es el estudio y control del comportamiento de estas estructuras artificiales, y su posterior aplicación para la síntesis de dispositivos compactos de microondas. En el primer capítulo se hace una introducción a los metamateriales en la que se exponen sus principales propiedades electromagnéticas, para finalmente presentar las líneas de transmisión zurdas que se suelen utilizar en el diseño de metamateriales. En el segundo capítulo se realiza un estudio de las propiedades y del funcionamiento de una celda metamaterial. Finalmente en el tercer capítulo se exponen diferentes dispositivos diseñados mediante la utilización de este tipo de celdas.

Simulations of parasitic and intrinsic capacitances related to Multiple-Gate-Field-Effect Transistor architectures

Report for the scientific sojourn carried out at the Université Catholique de Louvain, Belgium, from March until June 2007. In the first part, the impact of important geometrical parameters such as source and drain thickness, fin spacing, spacer width, etc. on the parasitic fringing capacitance component of multiple-gate field-effect transistors (MuGFET) is deeply analyzed using finite element simulations. Several architectures such as single gate, FinFETs (double gate), triple-gate represented by Pi-gate MOSFETs are simulated and compared in terms of channel and fringing capacitances for the same occupied die area. Simulations highlight the great impact of diminishing the spacing between fins for MuGFETs and the trade-off between the reduction of parasitic source and drain resistances and the increase of fringing capacitances when Selective Epitaxial Growth (SEG) technology is introduced. The impact of these technological solutions on the transistor cut-off frequencies is also discussed. The second part deals with the study of the effect of the volume inversion (VI) on the capacitances of undoped Double-Gate (DG) MOSFETs. For that purpose, we present simulation results for the capacitances of undoped DG MOSFETs using an explicit and analytical compact model. It monstrates that the transition from volume inversion regime to dual gate behaviour is well simulated. The model shows an accurate dependence on the silicon layer thickness,consistent withtwo dimensional numerical simulations, for both thin and thick silicon films. Whereas the current drive and transconductance are enhanced in volume inversion regime, our results show thatintrinsic capacitances present higher values as well, which may limit the high speed (delay time) behaviour of DG MOSFETs under volume inversion regime.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Diseño de un juego para pantalla LCD gráfica y controlado por el microprocesador HCS12

En una época como la actual, en la que se hace necesario disponer de equipos con grandes características y recursos para poder disfrutar de los últimos lanzamientos en juegos, no dejan de producirse equipos de bajo coste basados en microcontroladores que pueden entretener al mismo nivel que los más caros. Este proyecto reúne el diseño de la configuración, interconexión y programación de código necesarios para ejecutar un juego sencillo. Para ello se ha utilizado una pantalla LCD táctil y un microcontrolador HCS12.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Control biològic del Rhynchophorus ferrugineus a partir de diferents soques de nematodes entomopatògens i la seva problemàtica a Catalunya

En el present treball s’ha avaluat el potencial dels nemàtodes entomopatògens per a controlar la plaga de R. ferrugineus. Per fer-ho, s’ha determinat la susceptibilitat d’aquesta a 4 espècies diferents de nemàtodes: Steinernema carpocasae (soca B14, IDEBIO, BIOVERD), Steinernema feltiae (soca D114), Steinernema sp. (D122) i Heterorhabditis bacteriophora (soca DG46). D’altra banda, s’ha determinat la predació de Steinernema carpocapsae per part de l’àcar Centroupeda almerodai (Acari: Acaridae) per comprovar si aquest pot influir negativament en l’efectivitat de S. carpocapsae com agent de control biològic. S’ha vist que el morrut de les palmeres és molt susceptible als nemàtodes entomopatògens en especial una soca comercial (S. carpocapsae), la qual produeix mortalitats del 91,67%. Hi ha evidències de que l’àcar C. almerodai depreda les formes infectives de S. carpocapsae encara que no és suficient important com perquè es vegi compromès l’efectivitat com a bioinsecticida. L’ús de nemàtodes entomopatògens com a control biològic és una alternativa viable als mètodes químics de eficàcia similar però menys respectuosos amb el medi ambient.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990s

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product e¤ects and time-variant unobserved quality changes, that are assumed to be captured by model age effects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age effects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market.

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.