Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Demand and revenue implications of an integrated public transport policy: the case of Madrid

One of the most popular options for promoting public transport use is the provision of an integrated and high quality public transport system. This was the strategy adopted by the regional government in Madrid in 1986 and since then public transport patronage has increased by more than 50%. This paper has two objectives. The first is to identify the factors underlying the significant increase in the demand for public transport in Madrid. To do this we estimate an aggregate demand function for bus and underground trips, which allows us to obtain the demand elasticities with respect to the main attributes of public transport services and also to calculate the long-term impact of changes in those explanatory variables on patronage. The second objective is to evaluate the impact on revenue derived from the introduction of the travel card scheme, and to discuss the consequences on revenue of changes in the relative fare levels of different types of ticket without substantially affecting patronage. This latter issue is addressed by estimating a matrix of own and cross-price elasticities for different ticket types.

Lower bounds for the number of limit cycles of trigonometric Abel equations

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

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Infraestructures de Transport i Localització Industrial. Evidència Empírica per a Catalunya

El propòsit d'aquest treball és analitzar fins a quin punt la millora en l'accessibilitat dels municipis a la xarxa viària d'alta capacitat ha tingut efectes positius en la creació d'establiments industrials. En concret, estudiem les decisions de localització d'establiments industrials a escala local per a 19 sectors manufacturers amb una desagregació de 2 dígits. Aquest treball incorpora variables de gran rellevància (com ara una mesura d'accessibilitat mesurada en temps de desplaçament i els efectes de les inversions viàries) i utilitza tècniques d'anàlisi espacial. Pel que fa a les entrades d'establiments industrials, les dades han estat obtingudes del Registre d'Establiments Industrials de Catalunya (REIC). Els resultats mostren una incidència positiva de les millores en la xarxa viària sobre les decisions de localització de les empreses.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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

Transport of methotrexate by the in vitro isolated rabbit proximal tubule.

The tubular transport of [3H]methotrexate was studied in isolated nonperfused and perfused superficial proximal tubular segments of rabbit kidneys. Reabsorption represented only 5% of perfused methotrexate, and appeared to be mostly of passive nature inasmuch as it was not modified by reducing the temperature or by ouabain. Cellular accumulation in nonperfused segments and secretion in perfused tubules were highest in the S2 segment and lower in the S3 and S1 segments. Secretion against a bath-to-lumen concentration gradient was observed only in S2 segments (with a maximum methotrexate secretory rate of 478 +/- 48 fmol/mm.min and an apparent Km of transport of 363 +/- 32 microM), and was inhibited by probenecid and folate. The low capacity for methotrexate secretion may be explained by a low capacity of transport across the basolateral membrane of the proximal cell as methotrexate was accumulated only to a low extent in nonperfused tubules (tissue water to medium concentration ratio of 8.2 +/- 1 in S2 segments). During secretion a small amount of methotrexate was metabolized; the nature of the metabolite(s) remains to be defined.

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.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Tourism and urban transport: holding demand pressure under supply constraints

Scholars and local planners are increasingly interested in tourism contribution to economic and social development. To this regard, several European cities lead the world rankings on tourist arrivals, and their governments have promoted tourism activity. Mobility is an essential service for tourists visiting large cities, since it is a crucial factor for their comfort. In addition, it facilitates the spread of benefits across the city. The aim of this study is to determine whether city planners respond to this additional urban transport demand pressure by extending supply services. We use an international database of European cities. Our results confirm that tourism intensity is a demand enhancing factor on urban transport. Contrarily, cities do not seem to address this pressure by increasing service supply. This suggests that tourism exerts a positive externality on public transport since it provides additional funding for these services, but it imposes as well external costs on resident users because of congestion given supply constraints.