El Documento nos brinda un panorama amplio de la investigación cualitativa. Inicia con una revisión necesaria del tema del conocimiento, abordado desde su naturaleza epistemológica para poder entender la totalidad concreta de la realidad, y en la terminología del autor, como un todo polisistémico y la interdisciplinariedad. En un segundo plano identifica la dimensión dinámica de la investigación cualitativa, en cuanto trata de identificar la naturaleza profunda de las realidades, su estructura y relaciones que se establecen, para cumplir las dos tareas básicas de toda investigación: recoger datos y categorizarlos e interpretarlos. Hace un tratamiento del marco referencial, los objetivos, las hipótesis y las variables, identificando varios métodos cualitativos, así como los instrumentos y procedimientos.

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description is supplied with the local comparison of the trajectories of the diffusion processes with those of a skew Brownian motion.

We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We propose several necessary conditions and a sufficient one. The hierarchy between these conditions is studied via suitable counterexamples. Equivalence criteria are given in abstract form for general dynamics and algebraic form for systems with constant coefficients or continuous switching. The problem is motivated by the study of lysis phenomena in biological organisms and price prediction on spikedriven commodities.

In this article we extend the exact simulation methods of Beskos et al. in [4] to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case where the solution of the SDE with local time corresponds to a divergence form operator with a discontinuous coefficient at zero. Numerical examples are shown to illustrate the method and the performances are compared with more traditional discretization schemes.

This result was presented by Fernando Alcalde at the conference Foliations 2014, that took place in Madrid, Spain, in September 2014.Corrigendum in "Discrete and continuous dynamical systems vol. 37 n° 8 (2017), 4585-4586 p. DOI: 10.3934/dcds.2017196International audienceWe consider a minimal compact lamination by hyperbolic surfaces. We prove that if it admits a leaf whose holonomy covering is not topologically trivial, then the horocycle flow on its unitary tangent bundle is minimal