883 resultados para group theory


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This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

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Semiconductor nanowhiskers (NWs) made of III-V compounds exhibit great potential for technological applications. Controlling the growth conditions, such as temperature and diameter, it is possible to alternate between zinc-blende (ZB) and wurtzite (WZ) crystalline phases, giving origin to the so called polytypism. This effect has great influence in the electronic and optical properties of the system, generating new forms of confinement to the carriers. A theoretical model capable to accurately describe electronic and optical properties in these polytypical nanostructures can be used to study and develop new kinds of nanodevices. In this study, we present the development of a wurtzite/zinc-blende polytypical model to calculate the electronic band structure of nanowhiskers based on group theory concepts and the k.p method. Although the interest is in polytypical superlattices, the proposed model was applied to a single quantum well of InP to study the physics of the wurtzite/zinc-blende polytypism. By the analysis of our results, some trends can be predicted: spatial carriers' separation, predominance of perpendicular polarization (xy plane) in the luminescence spectra, and interband transition blueshifts with strain. Also, a possible range of values for the wurtzite InP spontaneous polarization is suggested. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767511]

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VIBRATIONAL ANALYSIS OF COORDINATION COMPOUNDS OF NICKEL (II): AN APPROACH TO THE TEACHING OF POINT GROUPS. This paper presents an IR and Raman experiment executed during the teaching of the course "Chemical Bonds" for undergraduated students of Science and Technology and Chemistry at the Federal University of ABC, in order to facilitate and encourage the teaching and learning of group theory. Some key aspects of this theory are also outlined. We believe that student learning was more significant with the introduction of this experiment, because there was an increase in the discussions level and in the performance during evaluations. This work also proposes a multidisciplinary approach to include the use of quantum chemistry tools.

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This paper presents an IR and Raman experiment executed during the teaching of the course "Chemical Bonds" for undergraduated students of Science and Technology and Chemistry at the Federal University of ABC, in order to facilitate and encourage the teaching and learning of group theory. Some key aspects of this theory are also outlined. We believe that student learning was more significant with the introduction of this experiment, because there was an increase in the discussions level and in the performance during evaluations. This work also proposes a multidisciplinary approach to include the use of quantum chemistry tools.

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Interactive theorem provers (ITP for short) are tools whose final aim is to certify proofs written by human beings. To reach that objective they have to fill the gap between the high level language used by humans for communicating and reasoning about mathematics and the lower level language that a machine is able to “understand” and process. The user perceives this gap in terms of missing features or inefficiencies. The developer tries to accommodate the user requests without increasing the already high complexity of these applications. We believe that satisfactory solutions can only come from a strong synergy between users and developers. We devoted most part of our PHD designing and developing the Matita interactive theorem prover. The software was born in the computer science department of the University of Bologna as the result of composing together all the technologies developed by the HELM team (to which we belong) for the MoWGLI project. The MoWGLI project aimed at giving accessibility through the web to the libraries of formalised mathematics of various interactive theorem provers, taking Coq as the main test case. The motivations for giving life to a new ITP are: • study the architecture of these tools, with the aim of understanding the source of their complexity • exploit such a knowledge to experiment new solutions that, for backward compatibility reasons, would be hard (if not impossible) to test on a widely used system like Coq. Matita is based on the Curry-Howard isomorphism, adopting the Calculus of Inductive Constructions (CIC) as its logical foundation. Proof objects are thus, at some extent, compatible with the ones produced with the Coq ITP, that is itself able to import and process the ones generated using Matita. Although the systems have a lot in common, they share no code at all, and even most of the algorithmic solutions are different. The thesis is composed of two parts where we respectively describe our experience as a user and a developer of interactive provers. In particular, the first part is based on two different formalisation experiences: • our internship in the Mathematical Components team (INRIA), that is formalising the finite group theory required to attack the Feit Thompson Theorem. To tackle this result, giving an effective classification of finite groups of odd order, the team adopts the SSReflect Coq extension, developed by Georges Gonthier for the proof of the four colours theorem. • our collaboration at the D.A.M.A. Project, whose goal is the formalisation of abstract measure theory in Matita leading to a constructive proof of Lebesgue’s Dominated Convergence Theorem. The most notable issues we faced, analysed in this part of the thesis, are the following: the difficulties arising when using “black box” automation in large formalisations; the impossibility for a user (especially a newcomer) to master the context of a library of already formalised results; the uncomfortable big step execution of proof commands historically adopted in ITPs; the difficult encoding of mathematical structures with a notion of inheritance in a type theory without subtyping like CIC. In the second part of the manuscript many of these issues will be analysed with the looking glasses of an ITP developer, describing the solutions we adopted in the implementation of Matita to solve these problems: integrated searching facilities to assist the user in handling large libraries of formalised results; a small step execution semantic for proof commands; a flexible implementation of coercive subtyping allowing multiple inheritance with shared substructures; automatic tactics, integrated with the searching facilities, that generates proof commands (and not only proof objects, usually kept hidden to the user) one of which specifically designed to be user driven.

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El objetivo fundamental del PFC desarrollado es el diseño y construcción de una aplicación web, que sirva de soporte a la gestión académica de asignaturas, basadas en un tipo de evaluación mixto, parte teórica y parte práctica, cada una formada por varías notas correspondientes a las diferentes pruebas realizadas, cada una de las cuales posee una ponderación. Permitiendo a los profesores de las asignaturas gestionar alumnos, profesores, grupos de teoría, grupos de prácticas, notas, fórmulas de ponderación, histórico y generar fichero con formato moodle. Además pueden realizar consultas, generar listados, consultar datos estadísticos tanto del curso académico actual, como de un curso académico previo almacenado en el histórico. La base de datos empleada es de tipo relacional y se ha utilizado el sistema gestor de bases de datos (DBMS) MySQLWorkbench 5.2 CE, impuesto por el cliente. Para la implementación de la aplicación se ha usado los lenguajes Java, JavaScript y HTML; por tratarse todos ellos de lenguajes de libre distribución. ABSTRACT The main objective of PFC developed is the design and construction of a web application that serves as support to academic subjects management, based on a type of mixed evaluation, theoretical and practical part, each consisting of several notes to different tests, each of which has a weighting. Allowing subject teachers manage students, teachers, group theory, practice groups, notes, weighting formulas, historical and generate Moodle file format. They can perform queries, generate lists, consult statistics of the current academic year or a previous academic year stored in the history. The database used is relational and has been used MySQLWorkbench CE 5.2 database management system (DBMS), imposed by the client. To implement the application has used the Java, HTML and JavaScript languages; because it is all free distribution languages.

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La diversidad cultural se refleja en las aulas. Es una de las variables que tiene influencia crucial en el clima en el centro. Esta investigación tiene como objetivos analizar la complejidad de la Educación Intercultural, ofrecer fundamentos teóricos para abordar la problemática de la incorporación de alumnos extranjeros al sistema educativo, y plantear modelos alternativos de integración para optimizar la gestión de la interculturalidad. La metodología empleada se basa en el diseño descriptivo. Utilizamos técnicas cuantitativas y cualitativas. Empleamos, como instrumento de investigación, un cuestionario, elaborado por el Grupo Interdisciplinario de Teoría de la Educación, de la Universidad de Alicante. Los resultados de la aplicación del cuestionario, a 3.820 profesores, muestran la existencia de conductas, en el aula, vinculadas con el racismo y la xenofobia. En este trabajo, planteamos la defensa del modelo holístico de Educación Intercultural y observamos los principios y cuestiones clave que hay que considerar para una intervención eficaz.

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Available on demand as hard copy or computer file from Cornell University Library.

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Includes bibliography.

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Available on demand as hard copy or computer file from Cornell University Library.

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Available on demand as hard copy or computer file from Cornell University Library.

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Habilitationsschrift--Universität Leipzig.

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Thesis--Rijksuniversiteit te Groningen.

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Available on demand as hard copy or computer file from Cornell University Library.

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Available on demand as hard copy or computer file from Cornell University Library.