Definable sets of Berkovich curves

In this article, we functorially associate definable sets to $k$-analytic curves, and definable maps to analytic morphisms between them, for a large class of $k$-analytic curves. Given a $k$-analytic curve $X$, our association allows us to have definable versions of several usual notions of Berkovich analytic geometry such as the branch emanating from a point and the residue curve at a point of type 2. We also characterize the definable subsets of the definable counterpart of $X$ and show that they satisfy a bijective relation with the radial subsets of $X$. As an application, we recover (and slightly extend) results of Temkin concerning the radiality of the set of points with a given prescribed multiplicity with respect to a morphism of $k$-analytic curves. In the case of the analytification of an algebraic curve, our construction can also be seen as an explicit version of Hrushovski and Loeser's theorem on iso-definability of curves. However, our approach can also be applied to strictly $k$-affinoid curves and arbitrary morphisms between them, which are currently not in the scope of their setting.Comment: 53 pages, 1 figure. v2: Section 7.2 on weakly stable fields added and other minor changes. Final version. To appear in Journal of the Institute of Mathematics of Jussie

Integration and Cell Decomposition in PP-minimal Structures

We show that the class of $\mathcal{L}$-constructible functions is closed under integration for any $P$-minimal expansion of a $p$-adic field $(K,\mathcal{L})$. This generalizes results previously known for semi-algebraic and sub-analytic structures. As part of the proof, we obtain a weak version of cell decomposition and function preparation for $P$-minimal structures, a result which is independent of the existence of Skolem functions. %The result is obtained from weak versions of cell decomposition and function preparation which we prove for general $P$-minimal structures. A direct corollary is that Denef's results on the rationality of Poincar\'e series hold in any $P$-minimal expansion of a $p$-adic field $(K,\mathcal{L})$.Comment: 22 page

An example of a PP-minimal structure without definable Skolem functions

We show there are intermediate $P$-minimal structures between the semi-algebraic and sub-analytic languages which do not have definable Skolem functions. As a consequence, by a result of Mourgues, this shows there are $P$-minimal structures which do not admit classical cell decomposition.Comment: 9 pages, (added missing grant acknowledgement

Estilos de aprendizaje como apertura a una enseñanza/aprendizaje asertiva de la segunda lengua

La educación del nuevo siglo ha venido brindando instrumentos y estrategias para obtener un proceso de enseñanza/aprendizaje más pertinente. La experiencia y el trabajo personal meha mostrado que los procesos que se desarrollan en distintos planteles educativos en la enseñanza de la lengua extrajera son evaluados y dirigidos bajo marcos de referencia de otros países en los cuales el inglés es su idioma nativo, pero en donde queda la descripción de las personas que están siendo formadas en este saber y su contexto social. Los estudiantes son seres totalmente distintos, ya que a pesar de compartir una misma nacionalidad el estilo de vida, de aprendizaje, la forma de hacer determinadas cosasson diferentes de acuerdo a su estilo de vida y formación de infancia. Así mismocada docente tiene un estilo propio de enseñar y/o enseñan de la misma manera a todos los grupos sin identificar las características del aprendizaje de cada uno de ellos

Influencias del nuevo aeropuerto el dorado en las aerolíneas

Este trabajo se centra en el análisis de los servicios que presta el aeropuerto El Dorado a las aerolíneas y en el efecto que ha tenido la entrada en la Opain S.A. a través del contrato suscrito con la Aerocivil. Se identifican los aspectos relevantes que ha tenido esta concesión, como se compone y que marco legal corresponde a este tipo de contrato. De acuerdo a esto se identifican las barreras impone Opain a los mercados que el aeropuerto puede tener de acuerdo a los servicios que estos prestan como explotador y administrador del espacio dado en concesión, de esta forma se analiza que posición tienen las aerolíneas, clientes y pasajeros con respecto a las actividades comerciales que realiza en concesionario Opain en el Aeropuerto Internacional El Dorado.This work focuses on the analysis of the services provided by the El Dorado airport to airlines and the effect it has had input in Opain S.A through contract with the Aerocivil. Relevant aspects that have had this award, as composed and legal framework applicable to this type of contract are identified. Accordingly barriers imposed Opain identify markets that the airport may have according to the services they provide as operator and manager of the concession given space, in that way analyzes that position have airlines, customers and passengers with respect to commercial activities carried on Opain dealer at the El Dorado International Airport