Gap probabilities for the cardinal sine

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length.

Measuring sustained superior performance at the firm level

This paper proposes a two-dimensional Strategic Performance Measure (SPM) to evaluate the achievement of sustained superior performance. This proposal builds primarily on the fact that, under the strategic management perspective, a firm's prevalent objective is the pursuit of sustained superior performance. Three basic conceptual dimensions stem from this objective: relativity, sign dependence, and dynamism. These are the foundations of the SPM, which carries out a separate evaluation of the attained superior performance and of its sustainability over time. In contrast to existing measures of performance, the SPM provides: (i) a dynamic approach by considering the progress or regress in performance over time, and (ii) a cardinal measurement of performance differences and its changes over time. The paper also proposes an axiomatic framework that a measure of strategic performance should comply with to be theoretically and managerially sound. Finally, an empirical illustration of the Spanish banking sector during 1987-1999 is herein provided by discussing some relevant cases.

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

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

The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

Sources of Competitiveness in Tourist Local Systems

At the end of the XIX Century, Marshall described the existence of some concentrations of small and medium enterprises specialised in a specific production activity in certain districts of some industrial English cities. Starting from his contribute, Italian scholars have paid particular attention to this local system of production coined by Marshall under the term industrial district. In other countries, different but related territorial models have played a central role as the milieu or the geographical industrial clusters. Recently, these models have been extended to non-industrial fields like culture, rural activities and tourism. In this text, we explore the extension of these territorial models to the study of tourist activities in Italy, using a framework that can be easily applied to other countries or regions. The paper is divided in five sections. In the first one, we propose a review of the territorial models applied to tourism industry. In the second part, we construct a tourist filiere and we apply a methodology for the identification of local systems through GIS tools. Thus, taxonomy of the Italian Tourist Local Systems is presented. In the third part, we discuss about the sources of competitiveness of these Tourist Local Systems. In the forth section, we test a spatial econometrics model regarding different kinds of Italian Tourist Local Systems (rural systems, arts cities, tourist districts) in order to measure external economies and territorial networks. Finally, conclusions and policy implications are exposed.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

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.

Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

Do creative industries cluster? mapping creative local production systems in Italy

An important debate on the role of creativity and culture as factors of local economic development is distinctly emerging. Despite the emphasis put on the theoretical definition of these concepts, it is necessary to strengthen comparative research for the identification and analysis of the kind of creativity embedded in the territory as well as its determinants. Creative local production systems are identified in Italy and Spain departing from local labour markets as territorial units, and focusing on two different kinds of creative

Estudi neurofisiològic del control executiu de l'atenció en l'esquizofrènia

Report for the scientific sojourn carried out at the Departament de Psicologia de la Universitat de les Illes Balears, Spain, from May until July 2006. Abnormalities in executive functions, including set shifting ability, represent a cardinal feature in schizophrenia. This ability to adapt behavior to changing environmental events or contingencies requires a mechanism for switching attention between learned stimulus-response associations, or task-sets. This project aimed at gaining further knowledge on the brain mechanisms related to the executive control of attention in schizophrenia during the performace of a task switching paradigm. Furthermore, a secondary goal was to further examine the interrelationships between endogenous and exogenous control processes in task set switching.

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.