Evolutes of plane curves and null curves in Minkowski 33-space

We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski $3$-space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the corresponding plane curves. This leads to an alternative description of all plane curves which are Laguerre congruent to a given one

Ground state for the relativistic one electron atom

We study the Dirac-Maxwell system coupled with an external potential of Coulomb type. We use the Foldy--Wouthuysen (unitary) transformation of the Dirac operator and its realization as an elliptic problem in the 4-dim half space $\mathbb{R}^4_{+}$ with Neumann boundary condition. Using this approach we study the existence of a "ground state" solution

Atletas en movimiento: enfoque teórico a las migraciones de trabajo deportivo

No desporto contemporâneo é comum encontrar atletas a representar equipas de nacionalidades que não a sua, sendo que em algumas modalidades os jogadores estrangeiros se encontram em maioria em relação aos nacionais. Por outro lado é também comum constatar a presença de atletas que, em virtude de mudança de nacionalidade, representam outros países que não o seu. Estas situações resultam de migrações de trabalho desportivo, em que os atletas à semelhança de outros trabalhadores atravessam fronteiras de países, impelidos por forças sociais, políticas e económicas que os transcendem. As abordagens teóricas feitas a este fenómeno, apesar de recentes, permitem uma compreensão ampla das dinâmicas e complexidades. Este texto propõe-se problematizar as migrações de trabalho desportivo no âmbito das migrações gerais, revisitando as elaborações teóricas que interpretaram esta mobilidade de atletas.In contemporary sport it is common to find athletes representing teams of nationalities other than their own, and in some sports foreign players are majority compared to national players. On the other hand, it is also common to note the presence of athletes who, due to the change of nationality, represent other countries than their country of birth. These situations result from the migration of workers of sport, in which athletes, like other workers, cross country borders driven by social, political and economic forces that transcend them. The theoretical approaches to this phenomenon, although recent, allow a broad understanding of dynamics and complexities. This text proposes to problematize the migrations of workers of sport in the scope of the general migrations, revisiting theoretical elaborations that interpreted this mobility of athletes.En el deporte contemporáneo es común encontrar atletas a representar equipos de nacionalidades que no la suya, siendo que en algunas modalidades los jugadores extranjeros se encuentran en su mayoría en relación a los nacionales. Por otro lado es también común constatar la presencia de atletas que, en virtud de cambio de nacionalidad, representan otros países que no el suyo. Estas situaciones resultan de migraciones de trabajo deportivo, en que los atletas a semejanza de otros trabajadores atravesan fronteras de países, impulsados por fuerzas sociales, políticas y económicas que los trascienden. Los enfoques teóricos hechos a este fenómeno, a pesar de los recientes, permiten una comprensión amplia de las dinámicas y complejidades. Este texto se propone problematizar las migraciones de trabajo deportivo en el marco de las migraciones generales, revisitando las elaboraciones teóricas que interpretaron esta movilidad de atletas

Rate of convergence of attractors for semilinear singularly perturbed problems: scalar parabolic equations with localized large diffusion

In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems reaction-diffusion type when the diffusion coefficient becomes large in a subregion which is interior to the domain. We obtain, under suitable assumptions, that the family of attractors behaves continuously and we exhibit the rate of convergence. An accurate description of localized large diffusion is necessary

Ground states for pseudo-relativistic Hartree equations of critical type

We study the existence of ground state solutions for a class of non-linear pseudo-relativistic Schr\"odinger equations with critical two-body interactions. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such a problem using variational methods after transforming the problem to an elliptic equation with a nonlinear Neumann boundary conditions

Urbanization processes along the Mediterranean coast of Alicante province.

The rate of land consumption in the coastal area of Alicante has been over the last decades, one of the highest among all Spanish Mediterranean provinces. This new territorial tendency has involved important changes in the use of land and has led to a new spatial and functional reality. The objective of this paper is to address two specific concerns related to the identification and characterization of these recent artificial surfaces, focusing on the assessment of quantitative details (land consumption surface, density, population, etc.) and qualitative features (morphologies, landscape impact, etc.). The methodological approach is based on graphic and statistical analysis. On the one hand, starting by first identifying artificial areas by comparing satellite imagery (source: the European project Corine Land Cover – 1990, 2000 and 2006). It is possible then, to study in detail the new developments thanks to the aerial photographs (1993, 2002 and 2008). On the other hand, the variety of statistical databases –local, regional and state statistics such as census, registers and other government studies- make possible to quantify and qualify the details of these new urban areas. Thus, the foreseen results are related to the characterization and definition of new urban patterns along the coast of Alicante, taking in account that the identification of the new patterns of urban and territorial occupancy is an important clue in order to establish future planning in both local and regional level.