The tetrahexahedric angular Calogero model

The spherical reduction of the rational Calogero model (of type A n−1 and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the (n−2)-sphere subject to a very particular potential. We present a detailed analysis of the simplest non-separable case, n=4, whose potential is singular at the edges of a spherical tetrahexahedron. A complete set of independent conserved charges and of Hamiltonian intertwiners is constructed, and their algebra is elucidated. They arise from the ring of polynomials in Dunkl-deformed angular momenta, by classifying the subspaces invariant and antiinvariant under all Weyl reflections, respectively.

Generalized cluster states based on finite groups

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.

Estudo de modelos simplificados com interações de longo alcance no ensemble microcanônico

Tese (doutorado)Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2015.

Census of quadrangle groups inclusions

In a classical result of 1972 Singerman classifies the inclusions between triangle groups. We extend the classification to a broader family of triangle and quadrangle groups forming a particular subfamily of Fuchsian groups. With two exceptions, each inclusion determines a finite bipartite map (hypermap) on a 2-dimensional spherical orbifold that encodes the complete information and gives a graphical visualisation of the inclusion. A complete description of all the inclusions is contained in the attached tables.

Matemáticas previas al cálculo

El presente texto nace de la preocupación y necesidad de entregar a los estudiantes de todas las disciplinas, que tengan en su plan de estudios la formación matemática, elementos previos que le permiten afrontar con relativo éxito y motivación, los cursos del Cálculo Infinitesimal. Esta publicación exhibe una exposición clara, sencilla, ordenada y encadenada de eventos matemáticos que van desde las ecuaciones; el concepto de función como herramienta básica de construcción del cálculo, hasta concluir en la parte correspondiente a la trigonometría, presente ésta en todas las disciplinas que requieran de las matemáticas, mínimo como un elemento de formación y ayuda en la presentación de modelos matemáticos de interés. Todos los capítulos incluyen, y esa es una de las fortalezas del texto, ejercicios de aplicación que tienen que ver con la formación de estudiantes iniciando estudios de ingeniería y áreas económicas; por esto los estudiantes aprenden a aplicar, los conceptos proporcionados por el texto, a problemas prácticos con información real del medio que tienen que ver, fundamentalmente, con temas propios de las disciplinas de las áreas antes mencionadas.

Using the Higgs to Probe Naturalness

The extreme sensitivity of the mass of the Higgs boson to quantum corrections from high mass states, makes it 'unnaturally' light in the standard model. This 'hierarchy problem' can be solved by symmetries, which predict new particles related, by the symmetry, to standard model fields. The Large Hadron Collider (LHC) can potentially discover these new particles, thereby finding the solution to the hierarchy problem. However, the dynamics of the Higgs boson is also sensitive to this new physics. We show that in many scenarios the Higgs can be a complementary and powerful probe of the hierarchy problem at the LHC and future colliders. If the top quark partners carry the color charge of the strong nuclear force, the production of Higgs pairs is affected. This effect is tightly correlated with single Higgs production, implying that only modest enhancements in di-Higgs production occur when the top partners are heavy. However, if the top partners are light, we show that di-Higgs production is a useful complementary probe to single Higgs production. We verify this result in the context of a simplified supersymmetric model. If the top partners do not carry color charge, their direct production is greatly reduced. Nevertheless, we show that such scenarios can be revealed through Higgs dynamics. We find that many color neutral frameworks leave observable traces in Higgs couplings, which, in some cases, may be the only way to probe these theories at the LHC. Some realizations of the color neutral framework also lead to exotic decays of the Higgs with displaced vertices. We show that these decays are so striking that the projected sensitivity for these searches, at hadron colliders, is comparable to that of searches for colored top partners. Taken together, these three case studies show the efficacy of the Higgs as a probe of naturalness.

Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Pseudospectral methods and numerical continuation for the analysis os structured population models.

191 p.

Estereotipo, prejuicio y discriminación hacia la mujer en el contexto laboral

Con el propósito de identificar las regularidades en los estereotipos, los prejuicios y las formas de discriminación, asociados a la mujer en el contexto laboral latinoamericano, se analizaron treinta estudios empíricos, publicados en revistas adscritas a las bases Redalyc y Psicodoc correspondientes al período de 2005 a 2015. Para el análisis se diseñó una matriz con las siguientes categorías: Título, autores, año, país, variables, objetivos, tipo de investigación, instrumento y resultados. La información se sometió a un análisis descriptivo y se concluyó que pese a que se ha generado una cultura de inclusión de la mujer en las organizaciones, persisten los prejuicios, estereotipos y conductas discriminatorias.

Introdução à Matemática - Álgebra, Análise e Otimização

Este livro destina-se às/aos estudantes das várias disciplinas de introdução à matemática nos cursos superiores que incluem algum conteúdo matemático, mas sem prosseguirem para uma formação aprofundada nesta disciplina. Aprender é difícil. No caso particular da matemática essa dificuldade está principalmente na sua natureza estritamente abstrata, embora seja aumentada por um conjunto de factores materiais e culturais (que incluem a infame pergunta/desculpa "mas afinal, para que é que isto serve?" e más práticas como "deixar as matemáticas para o fim do curso"). Com este livro pretendemos ajudar a reduzir as dificuldades materiais e, portanto, contingentes mas desnecessárias que assombram a aprendizagem da Matemática. A nossa experiência como professores (em conjunto, mais de sessenta anos) precisamente para estes estudantes, nestes cursos, produziu uma atitude pragmática para este tipo específico de ensino: o conteúdo deve ser comunicado claramente, rigorosamente e em pequenas doses concretizadas abundantemente com exemplos e exercícios. Ao longo dos anos, conforme fomos refinando esta abordagem, também fomos observando os seus efeitos: os nossos estudantes aprendem melhor a matéria, de forma mais aprofundada e com melhores resultados. É esse pragmatismo que orienta o conteúdo da "Introdução à Matemática": a apresentação dos conceitos teóricos é sucinta, rigorosa, está claramente identificada, acompanhada por exemplos e complementada por inúmeros exercícios. Cada parte do livro corresponde a uma das grandes áreas da matemática normalmente presentes no ensino superior: a álgebra linear, a análise infinitesimal e a otimização.