A deterministic change to a time-varying queueing model is described as either changing the number of entities, the queue capacity, or the number of servers in the system at selected times. We use a surrogate distribution for N(t), the number of entities in the system at time t, to approximate deterministic changes to the Ph(t)/Ph(t)/1/c and the Ph(t)/M(t)/s/c queueing models. We develop a solution technique to minimize the number of state probabilities to be approximated. / Master of Science

Ce travail est la synthèse de travaux de recherches en mathématiques, dont les thèmes sont empruntés à la géométrie algébrique, la combinatoire analytique et les probabilités. La première partie concerne les variétés algébriques complexes de dimension trois. On y présente un calcul de la cohomologie singulière de variétés toriques lisses non complètes, ainsi que la construction d'un modèle toroïdal des singularités-quotient, dont le calcul nécessite l'étude combinatoire fine de l'action des groupes finis de matrices unitaires sur le plan projectif. La deuxième partie développe une adaptation "hybride" de la méthode de Darboux et de l'analyse des singularités pour le développement asymptotique des coefficients d'une série entière dans certains cas de frontière naturelle d'analyticité. De nombreux exemples issus de l'analyse combinatoire sont ainsi traités, dont celui de l'analyse d'algorithmes de factorisation de polynômes sur les corps finis qui sont utilisés en calcul formel et pour les codes correcteurs d'erreurs. La troisième partie résout une conjecture sur les arbres $m$-aires de recherche qui sont une structure fondamentale de l'algorithmiques des ensembles de données. Le modèle considéré est un modèle d'urnes qui se généralise en la notion de processus aléatoires de Pòlya dont le comportement asymptotique général est étudié. Dans la quatrième partie, on construit un arbre aléatoire associé à la \emph{Chaos Game Representation} utilisée en bio-mathématique et en bio-informatique du génôme. Les asymptotiques de la hauteur et de la profondeur d'insertion de ces arbres y sont établies.

A questão desta pesquisa é investigar a Resolução de Problemas aplicada à situações-problema da OBMEP (Olimpíada Brasileira das Escolas Públicas) em sala de aula, na tentativa de despertar no aluno o gosto pela Matemática, colaborando para o ensino-aprendizagem, construção do espírito crítico e tomada de decisões quanto cidadão. Nos apoiamos em Polya (2006), Dante (1991), Onuchic e Allevato (2004), Mendes (2009), Pozo et al. (1998), Baldin et al. (2012) e documentos oficiais (BRASIL. Secretaria de Educação Fundamental (1997), BRASIL. Secretaria de Educação Fundamental (1998), BRASIL. Secretaria de Educação Média e Tecnológica (1999) e SÃO PAULO (Estado). Secretaria da Educação (2011)). Apresentamos a Resolução de Problemas e as etapas propostas por George Polya (2006) em seu livro, A arte de resolver problemas. Nossa investigação constitui uma pesquisa-ação qualitativa (Lüdke e André (2001), André (2008) e Bogdan e Biklen (1994)), na medida que desenvolvemos uma atividade no 8o ano do Ensino Fundamental - Anos Finais da rede pública estadual paulista, utilizando uma questão do Banco de Questões da OBMEP, com 21 alunos, de 13 a 14 anos, procurando nos aproximar das indicações de Polya (2006), Dante (1991) e Baldin et al. (2012), quanto à Resolução de Problemas. As análises nos indicam que ao optar por desenvolver conteúdos com situações-problema, sendo esses desafiadores, utilizando problemas auxiliares e materiais manipulativos, os alunos mostraram-se participativos e interessados, facilitando sua aprendizagem e encorajando-os a ser curiosos, assumindo um papel ativo na aprendizagem. / The question of this research is to investigate the Problem Solving applied to the OBMEP situation-problem in classroom. The aim is to awaken in students a taste for Mathematics, collaborating for the teaching-learning, the ability to think critically and improve your decisionmaking skills as a citizen. We found support for our objective in Polya (2006), Dante (1991), Onuchic e Allevato (2004), Mendes (2009), Pozo et al. (1998), Baldin et al. (2012) and official documents (BRASIL. Secretaria de Educação Fundamental (1997), BRASIL. Secretaria de Educação Fundamental (1998), BRASIL. Secretaria de Educação Média e Tecnológica (1999) e SÃO PAULO (Estado). Secretaria da Educação (2011)). We present the Problem Solving e as etapas described by George Polya in How to Solve It (1945). Our research is a action research studies combining qualitative (Lüdke e André (2001), André (2008) e Bogdan e Biklen (1994)), since we developed an activity in the 8th grade (elementary school) - Final Years public schools in the State of São Paulo. We using a question from the OBMEP Bank of Questions, with 21 Students, aged from 13 to 14 years old, trying to get closer to the Problem Solving presented in Polya (2006), Dante (1991) e Baldin et al. (2012). The analisys provide convincing evidence that develop learning contents using a combination of manipulative materials and auxiliary problems can provide an extremely useful addition to Mathematics teaching-learning. In addition, based on the analisys, we also noted a increasing students participation and interest, then, facilitating learning and encourage then to be curious, seek new answers and take an active role in learning.

Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.

The purpose of this study was to improve problem solving attitudes and abilities in students of mathematics through the exploration of John Mason’s general problem solving strategy and the use of problem solving groups, and to document and understand this improvement process. The types of problems and tasks assigned to students as well as assessment practices were also examined. A Design-Experiment Research approach was used with thirty grade 9 students participating throughout the year-long study. A teacher-researcher journal, student problem-solving journals, and surveys were used. The study showed that using a general problem solving strategy with groups of students working together to solve problems can improve problem solving attitudes and abilities. Students made significant improvements during initial engagement of problems, in specializing and generalizing, and in communication. Almost all students expressed a more positive attitude toward problem solving and their problem solving abilities. The study demonstrates how focusing on initial stages of the problem solving process like the understanding of the problem in a group context can reach multiple learning objectives and positively impact later stages of problem solving. In addition, recommendations for classroom teachers are provided concerning the roles within the groups, the nature of beneficial problem types and student tasks, and concerning the role of the teacher as researcher of his or her own teaching practice.

<p>Two-sample comparison is a fundamental problem in statistics. Given two samples of data, the interest lies in understanding whether the two samples were generated by the same distribution or not. Traditional two-sample comparison methods are not suitable for modern data where the underlying distributions are multivariate and highly multi-modal, and the differences across the distributions are often locally concentrated. The focus of this thesis is to develop novel statistical methodology for two-sample comparison which is effective in such scenarios. Tools from the nonparametric Bayesian literature are used to flexibly describe the distributions. Additionally, the two-sample comparison problem is decomposed into a collection of local tests on individual parameters describing the distributions. This strategy not only yields high statistical power, but also allows one to identify the nature of the distributional difference. In many real-world applications, detecting the nature of the difference is as important as the existence of the difference itself. Generalizations to multi-sample comparison and more complex statistical problems, such as multi-way analysis of variance, are also discussed.</p> / Dissertation

In a Bayesian framework, prior distributions on a space of nonparametric continuous distributions may be defined using Polya trees. This dissertation addresses statistical problems for which the Polya tree idea can be utilized to provide efficient and practical methodological solutions. One problem considered is the estimation of risks, odds ratios, or other similar measures that are derived by specifying a threshold for an observed continuous variable. It has been previously shown that fitting a linear model to the continuous outcome under the assumption of a logistic error distribution leads to more efficient odds ratio estimates. We will show that deviations from the assumption of logistic error can result in great bias in odds ratio estimates. A one-step approximation to the Savage-Dickey ratio will be presented as a Bayesian test for distributional assumptions in the traditional logistic regression model. The approximation utilizes least-squares estimates in the place of a full Bayesian Markov Chain simulation, and the equivalence of inferences based on the two implementations will be shown. A framework for flexible, semiparametric estimation of risks in the case that the assumption of logistic error is rejected will be proposed. A second application deals with regression scenarios in which residuals are correlated and their distribution evolves over an ordinal covariate such as time. In the context of prediction, such complex error distributions need to be modeled carefully and flexibly. The proposed model introduces dependent, but separate Polya tree priors for each time point, thus pooling information across time points to model gradual changes in distributional shapes. Theoretical properties of the proposed model will be outlined, and its potential predictive advantages in simulated scenarios and real data will be demonstrated.

The purpose of this study was to improve problem solving attitudes and abilities in students of mathematics through the exploration of John Mason’s general problem solving strategy and the use of problem solving groups, and to document and understand this improvement process. The types of problems and tasks assigned to students as well as assessment practices were also examined. A Design-Experiment Research approach was used with thirty grade 9 students participating throughout the year-long study. A teacher-researcher journal, student problem-solving journals, and surveys were used. The study showed that using a general problem solving strategy with groups of students working together to solve problems can improve problem solving attitudes and abilities. Students made significant improvements during initial engagement of problems, in specializing and generalizing, and in communication. Almost all students expressed a more positive attitude toward problem solving and their problem solving abilities. The study demonstrates how focusing on initial stages of the problem solving process like the understanding of the problem in a group context can reach multiple learning objectives and positively impact later stages of problem solving. In addition, recommendations for classroom teachers are provided concerning the roles within the groups, the nature of beneficial problem types and student tasks, and concerning the role of the teacher as researcher of his or her own teaching practice.

ESPINOZA HERRERA S.J. - DOCTORAL THESIS - FUNCTION OF MAGNESIUM IONS IN THE FORMATION OF BIOLOGICALLY-ACTIVE NUCLEIC ACIDS STRUCTURES ____________________________________________________________________ ABSTRACT Interaction of magnesium ions, the divalent ions with the highest concentration inside living cells, with the key biomolecules of nucleic acids was studied with aim to find out structural details of the interaction mechanism and effect of the magnesium ions presence on the nucleic-acid structure and structural transitions. Raman spectroscopy was chosen as the main experimental method, some complementary measurements of UV absorption spectra were also performed. Basic analyses of the spectral series obtained as a function of temperature and/or for various concentrations of Mg2+ ions were done by means of factor analysis. Where possible the factor analysis outputs were used for fits of appropriate thermodynamic equations. For the studies, various nucleic-acid molecular models were employed, in particular complementary RNA homopolynucleotides polyA and polyU, DNA homopolynucleotides polydA and polydT and RNA 14-mer oligonucleotide representing the apical hairpin of the TAR segment of HIV-1 genomic RNA. We have confirmed via Raman spectroscopy that magnesium ions added to a solution of polyA-polyU...

A questão desta pesquisa é investigar a Resolução de Problemas aplicada à situações-problema da OBMEP (Olimpíada Brasileira das Escolas Públicas) em sala de aula, na tentativa de despertar no aluno o gosto pela Matemática, colaborando para o ensino-aprendizagem, construção do espírito crítico e tomada de decisões quanto cidadão. Nos apoiamos em Polya (2006), Dante (1991), Onuchic e Allevato (2004), Mendes (2009), Pozo et al. (1998), Baldin et al. (2012) e documentos oficiais (BRASIL. Secretaria de Educação Fundamental (1997), BRASIL. Secretaria de Educação Fundamental (1998), BRASIL. Secretaria de Educação Média e Tecnológica (1999) e SÃO PAULO (Estado). Secretaria da Educação (2011)). Apresentamos a Resolução de Problemas e as etapas propostas por George Polya (2006) em seu livro, A arte de resolver problemas. Nossa investigação constitui uma pesquisa-ação qualitativa (Lüdke e André (2001), André (2008) e Bogdan e Biklen (1994)), na medida que desenvolvemos uma atividade no 8o ano do Ensino Fundamental - Anos Finais da rede pública estadual paulista, utilizando uma questão do Banco de Questões da OBMEP, com 21 alunos, de 13 a 14 anos, procurando nos aproximar das indicações de Polya (2006), Dante (1991) e Baldin et al. (2012), quanto à Resolução de Problemas. As análises nos indicam que ao optar por desenvolver conteúdos com situações-problema, sendo esses desafiadores, utilizando problemas auxiliares e materiais manipulativos, os alunos mostraram-se participativos e interessados, facilitando sua aprendizagem e encorajando-os a ser curiosos, assumindo um papel ativo na aprendizagem. / The question of this research is to investigate the Problem Solving applied to the OBMEP situation-problem in classroom. The aim is to awaken in students a taste for Mathematics, collaborating for the teaching-learning, the ability to think critically and improve your decisionmaking skills as a citizen. We found support for our objective in Polya (2006), Dante (1991), Onuchic e Allevato (2004), Mendes (2009), Pozo et al. (1998), Baldin et al. (2012) and official documents (BRASIL. Secretaria de Educação Fundamental (1997), BRASIL. Secretaria de Educação Fundamental (1998), BRASIL. Secretaria de Educação Média e Tecnológica (1999) e SÃO PAULO (Estado). Secretaria da Educação (2011)). We present the Problem Solving e as etapas described by George Polya in How to Solve It (1945). Our research is a action research studies combining qualitative (Lüdke e André (2001), André (2008) e Bogdan e Biklen (1994)), since we developed an activity in the 8th grade (elementary school) - Final Years public schools in the State of São Paulo. We using a question from the OBMEP Bank of Questions, with 21 Students, aged from 13 to 14 years old, trying to get closer to the Problem Solving presented in Polya (2006), Dante (1991) e Baldin et al. (2012). The analisys provide convincing evidence that develop learning contents using a combination of manipulative materials and auxiliary problems can provide an extremely useful addition to Mathematics teaching-learning. In addition, based on the analisys, we also noted a increasing students participation and interest, then, facilitating learning and encourage then to be curious, seek new answers and take an active role in learning.