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Let G be a group, Ω a set and K = {g ∈ G | ω * g = ω, Ɐω ∈ Ω} the nucleus of Ω where G acts on the set Ω. We will show that G/K is simple in the case that the group G verifies to be primitive on Ω, as well as that it is equal to its derived subgroup and finally if α ∈ Ω then Gα has a subgroup A that is abelian and normal such that G =< Ag | g ∈ G >, where Gα is the stabilizer of α in G. To finish we will give an application that the alternating group A5 is simple., Sean G un grupo, Ω un conjunto y K = {g ∈ G | ω * g = ω, Ɐω ∈ Ω} el núcleo de Ω donde G actua sobre el conjunto Ω. Mostraremos que G/K es simple en el caso que el grupo G verifique ser primitivo sobre Ω, así como también que sea igual a su subgrupo derivado y por último si α ∈ Ω entonces Gα tiene un subgrupo A que es abeliano y normal tal que G =< Ag | g ∈ G >, donde Gα es el estabilizador de α en G. Para finalizar daremos una aplicación de que el grupo alternante A5 es simple.

This PhD thesis, entitled TRANSITIVITY, no stone left unturned: Introducing flexibility and granularity into the framework for the analysis of courtroom discourse, considers four main areas, to include Critical Discourse Analysis, Corpus Linguistics, Forensic Linguistics (FL) and Systemic Functional Linguistics (SFL). As features of SFL, the two transitivity models put forward to date, i.e. the Sydney model (Halliday, 1985, 1994; Halliday & Matthiessen, 2004, 2014) and the Cardiff model (Fawcett, 1987, 2000; Neale, 2002) are critiqued here and, in turn, a revised transitivity network is proposed. Using the new framework, we analyse a piece of courtroom discourse in which a man finds himself accused and, subsequently, wrongly convicted of raping a minor. Thus, the intention is to determine the language patterns employed by particular individuals involved in the court case (i.e. the lawyers for both sides and the victim) as a means to verify the impact that their questioning and/or testimony may have had on the defendant’s untimely fate. To add to this, a well established SFL theory, namely Appraisal, is also employed here for the analysis of the lawyers’ closing arguments. This is aimed at gaining further insights into the types of evaluation that emerge in their discourse and, thus, uncover the potential bearing this may have had on the outcome of the trial at hand. We hope that this study will serve as a contribution to the current shortage of SFL research within the field of FL., Tesis Univ. Granada. Programa Oficial de Doctorado en: Lenguas, Textos y Contextos, This PhD thesis has been carried out with the support of the Spanish Ministry of Economy and Competitiveness, who provided me with a scholarship (reference number BES-2012-059336) under the auspices of the project “The Construction of Otherness in the Public Domain: A Critical Study of the Case of Ireland” (reference number FFI2011-25453).

A sectional-Anosov flow on a manifold is a C¹ vector field inwardly transverse to the boundary for which the maximal invariant is sectional hyperbolic [10]. We prove that every attractor of every vector field C¹ close to a transitive sectional-Anosov flow with singularities on a compact manifold has a singularity. This extends the three-dimensional result obtained in [9]. Un flujo seccional-Anosov sobre una variedad es un C¹ campo vectorial transversal a la frontera apuntando hacia el interior, para el cual su conjunto maximal invariante es un conjunto seccional hiperbólico [10]. Probamos que todo atractor de todo campo vectorial C¹ próximo a un flujo seccional-Anosov transitivo con singularidades sobre una variedad compacta tiene una singularidad. Este resultado extiende el resultado tres-dimensional obtenido en [9].

En este trabajo se reconstruye la demostración del teorema principal del artículo [Mor07] del profesor Carlos Morales de la Universidad Federal de Rio de Janeiro. Se presentan y se demuestran resultados conocidos sobre conjuntos hiperbólicos y parcialmente hiperbólicos. Además se enuncian y demuestran los resultados que se obtienen a partir de este teorema principal. / Abstract. In this paper we reconstructs the proof of the theorem of the Carlos Morales�s paper [Mor07] professor at the Federal University of Rio de Janeiro. We introduce and prove known results on hyperbolic sets and partially hyperbolic sets. Also set forth and show the results obtained from this main theorem. Maestría

Nosotros conocemos que dos clases homoclínicas diferentes contenidas en un conjunto hiperbólico son disjuntas. Además un conjunto transitivo singular-hiperbólico con orbitas periódicas densas y una única singularidad es transitivo o es unión de dos clases homoclínicas diferentes. De estos resultados se puede preguntar si dos clases homoclínicas diferentes contenidas en un conjunto singular hiperbólico son disjuntas o si la segunda alternativa no puede ocurrir. Aquí se da una respuesta negativa a la pregunta. / Abstract. We know that two different homoclinic classes contained in the hyperbolic set are disjoint. Moreover singular-hyperbolic attracting set whit dense periodic orbits and unique equilibrium is either transitive or the union of two different homoclinic classes. These results motivate the questions of if two different homoclinic classes contained in the same singular-hyperbolic set are disjoint or if second alternative in cannot. Here it give a negative the answer for both questions. Maestría

Estudiamos las soluciones de un sistema no lineal de ecuaciones, conocido como el sistema Lorenz, cuyas soluciones reposan en una región de atracción del espacio de fases y analizamos la evolución en el tiempo, cuando sus parámetros toman los valores: σ=10, b=8/3, y r=24.74, donde los valores propios complejos cruzan el eje imaginario perdiendo su estabilidad, lo que implica que el sistema exhibe una bifurcación tipo Hopf. Dicho sistema inspiró la elaboración de un modelo geométrico, conocido como el atractor geométrico de Lorenz, de donde analizamos su estructura y las propiedades que comparte con el sistema Lorenz, además de reconstruir la demostración del por qué el atractor geométrico de Lorenz, siendo uno de los ejemplos más importantes de conjunto singular hiperbólico, es una clase homoclínica. / Abstract. We study the solutions of a nonlinear system of equations, known as the Lorenz systems, whose solutions lie in a region of attraction in phase space and analyze the evolution in time, when its parameters take the values: σ =10, b=8/3, y r=24.74, where complex eigenvalues cross the imaginary axis losing its stability, which implies that the system exhibits a Hopf bifurcation type. Such a system inspired the development of a geometric model, known as the geometric Lorenz attractor, where we analyze its structure and properties it shares with the Lorenz system, in addition to rebuilding the demonstration of why the geometric Lorenz attractor, one of the most important examples of singular hyperbolic set, is a homoclinic class. Maestría

International audience

12 p. El objetivo del presente trabajo es examinar las propiedades gramaticales y semánticas de dos verbos de percepción, encontrarse y sentirse.