No description available.

There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

No description available.

In any group G, we may extend the definition of the conjugacy class of an element to the conjugacy class of a k-tuple, for a positive integer k. When k = 2, we are forming the conjugacy classes of ordered pairs, when k = 3, we are forming the conjugacy classes of ordered triples, etc. In this report we explore a generalized question which Professor B. Doug Park has posed (for k = 2). For an arbitrary k, is it true that: (G has finitely many k-conjugacy classes) implies (G is finite)? Supposing to the contrary that there exists an infinite group G which has finitely many k-conjugacy classes for all k = 1, 2, 3, ..., we present some preliminary analysis of the properties that G must have. We then investigate known classes of groups having some of these properties: universal locally finite groups, existentially closed groups, and Engel groups.

In any group G, we may extend the definition of the conjugacy class of an element to the conjugacy class of a k-tuple, for a positive integer k. When k = 2, we are forming the conjugacy classes of ordered pairs, when k = 3, we are forming the conjugacy classes of ordered triples, etc. In this report we explore a generalized question which Professor B. Doug Park has posed (for k = 2). For an arbitrary k, is it true that: (G has finitely many k-conjugacy classes) implies (G is finite)? Supposing to the contrary that there exists an infinite group G which has finitely many k-conjugacy classes for all k = 1, 2, 3, ..., we present some preliminary analysis of the properties that G must have. We then investigate known classes of groups having some of these properties: universal locally finite groups, existentially closed groups, and Engel groups.

Orientador: Reginaldo Palazzo Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-12T13:34:06Z (GMT). No. of bitstreams: 1 Albuquerque_JulioCesarHolandade_M.pdf: 1364323 bytes, checksum: 01181adde228aa4d914d7edabdde4aca (MD5) Previous issue date: 2008 / Resumo: A proposta deste trabalho é apresentar uma abordagem aos processos genéticos e moleculares, utilizando a teoria de comunicações e codificação na modelagem do dogma central da biologia molecular. A partir desta modelagem associamos o código genético a um modulador de um sistema de comunicação. Mais especificamente, tal procedimento consiste em construir uma constelação de sinais a partir dos subgrupos de S3 e S4 baseado no código genético. Considerando este método algébrico de construção de sinais, propomos duas possíveis constelações de sinais para o código genético. A representação do código genético em constelações de sinais correlacionadas deu origem à idéia de "constelação de sinais concatenadas", idéia inovadora na teoria de comunicação e codificação. As constelações de sinais concatenadas possui a propriedade de correção de erros, consistindo de novos conceitos úteis para utilização na teoria da comunicação e codificação. Por outro lado, estas representações do código genético não são únicas pois, até o presente momento, desconhecemos uma álgebra que descreva o código genético juntamente com as suas partições geradas pelos aminoácidos. / Abstract: The purpose of this work is to present an approach to the genetic and molecular processes by use of the communication and coding theory in modelling the central dogma of the molecular biology. From this modelling we associate the genetic code to a modulator in the communication system. More specifically, such a procedure consists is in the construction of a signal constellation by use of the S3 and S4 permutation subgroups based on the code genetic. By considering this algebraic method of signal design, we propose two possible signal constellations to the genetic code. The representation of the genetic code as correlated signal constellations provides the idea idea of "concatenated signal constellation", an innovative idea in communication and coding theory. The concatenated signal constellations have the property of error-correction, a new concept being introduced. On the other hand, these representations of the genetic code are not unique for currently, we do not know an algebraic structure capable of describing the genetic code together with the partitioning generated by the amino acids. / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica