Dissertations / Theses on the topic 'Functionsof real variables'

We present a utility accrual real-time scheduling algorithm called CIC-VCUA, for tasks whose execution times are functions of their starting times. We model such variable execution times employing variable cost functions (or VCFs). The algorithm considers application activities that are subject to time/utility function time constraints (or TUFs), execution times de- scribed using VCFs, and concurrent, mutually exclusive sharing of non-CPU resources. We consider the multi-criteria scheduling objective of (1) assuring that the maximum interval between any two consecutive, successful completions of jobs of a task must not exceed a specified upper bound, and (2) maximizing the system's total accrued utility, while satis- fying mutual exclusion resource constraints. Since the scheduling problem is intractable, CIC-VCUA statically computes worst-case sojourn times of tasks, selects tasks for execution based on their potential utility density, and completes them at specific times, in polynomial- time. We establish that CIC-VCUA achieves optimal timeliness during under-loads. Further, we identify the conditions under which timeliness assurances hold. Our simulation experi- ments illustrate CIC-VCUA's effectiveness and superiority.
Master of Science

Thesis (Ph. D.)--West Virginia University, 2001.
Title from document title page. Document formatted into pages; contains iv, 60 p. Includes abstract. Includes bibliographical references (p. 64-66).

The study of biological diversity has seen a tremendous growth over the past few decades. Among the commonly used indices capturing both the richness and evenness of a community, the Berger-Parker index, which relates to the maximum proportion of all species, is particularly effective. However, when the number of individuals and species grows without bound this index changes, and it is important to develop statistical tools to measure this change. In this thesis, we introduce two estimators for this maximum: the multinomial maximum and the length of the longest increasing subsequence. In both cases, the limiting distribution of the estimators, as the number of individuals and species simultaneously grows without bound, is obtained. Then, constructing the 95% confidence intervals for the maximum proportion helps improve the comparison of the Berger-Parker index among communities. Finally, we compare the two approaches by examining their associated bias corrected estimators and apply our results to environmental data.

Abstract of thesis submitted in partial fulfilment of the requirements for the Degree of Master of Commerce and Management Dynamics of macroeconomic variables in Fiji : a cointegrated VAR analysis By Shiu Raj Singh The objective of this study is to examine how macroeconomic variables of Fiji inter-relate with aggregate demand and co-determine one another using a vector autoregression (VAR) approach. This study did not use a prior theoretical framework but instead used economic justification for selection of variables. It was found that fiscal policy, which is generally used as a stabilisation tool, did not have a positive effect on real Gross Domestic Product (GDP) growth in the short term. Effects on GDP growth were positive over the long term but not statistically significant. Furthermore, expansionary fiscal policy caused inflationary pressures. Fiji has a fixed exchange rate regime, therefore, it was expected that the focus of monetary policy would be the maintenance of foreign reserves. It was, however, found that monetary expansion in the short term resulted in positive effects on real GDP growth and resulted in inflation. The long term effects of monetary policy on real GDP growth were negative, which are explained by the fixed exchange rate regime, endogenous determination of money supply by the central bank, an unsophisticated financial market and, perhaps, an incomplete transmission of the policy. Both merchandise trade and visitor arrivals growth were found to positively contribute to short term and long term economic growth. Political instability was found not to have significant direct effects on real GDP growth but caused a significant decline in visitor arrivals which then negatively affected economic growth in the short term.

Orientador: Sandra Augusta Santos
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho aborda a otimizacao de um processo de destilacao de uma mistura binaria em uma coluna de pratos, motivado pela destilacao do metanol no processo de produção do biodiesel. Mais especificamente, considera a minimização de uma função custo energetico envolvendo o calor do refervedor e a temperatura fornecida a carga de alimentação sujeita a restrições de equilibrio e canalizações. Esse problema foi formulado baseado no artigo de More A collection of Nonlinear Model Problems. Para a solução foi utilizada a metodologia dos multiplicadores de Lagrange delineada no Teorema de Karush-Kuhn-Tucker para otimização de problemas com restrições mistas. Os softwares Maxima e MatLab foram utilizados para a investigação numerica da solução do problema. Uma explanação do funcionamento da coluna tambem e feita, bem como a apresentação dos principais resultados envolvendo otimização, desde problemas irrestritos ate problemas com varias restrições mistas
Abstract: This work tackles the optimization of a distillation process of a binary mixture in a column with plates, which came from the methanol distillation in the production process of the biodiesel. More specifically, it considers the minimization of a cost objective function that encompass the heat rate supplied to the reboiler and the feed temperature, subject to equilibrium constraints and simple bounds. This problem was formulated based on Mor'e¿s article A collection of Nonlinear Model Problems. The Lagrange multiplier methodology was used for solve it, outlined in the Karush-Kuhn-Tucker Theorem for optimization problems with mixed constraints. The softwares Maxima and MatLab were employed for the numerical investigation of the problem solution. An explanation about the operation of the column is also included, together with the presentation of the main results encompassing optimization, from unconstrained to mixed constrained problems
Mestrado
Otimização
Mestre em Matemática

Orientador: Sandra Augusta Santos
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho se inicia com um breve resgate histórico da abordagem de Fermat para encontrar máximos e mínimos sem o uso de derivadas. Em termos teóricos, trás uma discussão sobre máximos e mínimos de funções em Rn, com um estudo detalhado sobre a otimizacao sem restrições, destacando a regra de Fermat e a classificacao dos pontos críticos. Trata também da otimização com restrições, por meio dos Teoremas dos Mul-tiplicadores de Lagrange para restrições de igualdade e desigualdade, e para restrições mistas, o Teorema de Karush-Kuhn-Tucker (KKT). Do ponto de vista prático, apresenta uma aplicacao envolvendo uma coluna de destilacao do metanol vinculada 'a produção do biodiesel, com a otimização da proporção de metanol destilado
Abstract: This work begins with a brief historical overview of Fermat¿s method to find maxima and minima without derivatives. In theoretical terms, the elements concerning maximum and minimum of functions of n variables are discussed, together with a detailed study of unconstrained optimization, focusing on the Fermat¿s rule and the classification of critical points. Constrained optimization is also analyzed, by means of the Lagrange Multilplier Theorem for equality constrained problems, and the Karush-Kuhn-Tucker (KKT) Theorem for mixed constrained optimization. In practical terms, an application concerning a distillation column of methanol associated to the biodiesel production is presented, with the optimization of the proportion of methanol in the amount of material that is removed from the top of the column
Mestrado
Otimização
Mestre em Matemática

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Secretaria da Educação do Estado de São Paulo
This research was developed with the goal of verifying the difficulties and the knowledge shown by students related to the transition of the study of functions of one variable to the case of two variables, regarding dependent and independent variables well as the interdependence between them, to the dominion and the graphic, to the relation between the graphic of the dominion of the function and also which manifestations are revealed in the study of the partial derivatives of the first order. In order to do so we developed two questionnaires based upon the Theory of the Registers of Semiotic Representation of Raymond Duval, the questionnaires having been answered by students of the fourth and fifth term of the course of Mathematics of a private university in the greater São Paulo area. The first questionnaire was applied to students of the fourth term and it made possible to verify not only one first analysis of their difficulties, but also how pertinent the questions were, as well as how fitting the wording was. It has been found that some of the questions needed rephrasing, and also that the addition of new questions was necessary, which contributed to the making of a new questionnaire, which was answered by students of the fifth term. This research revealed some difficulties that students show when studying functions of two variables, such as the comprehension of the system of the 3D axis, the lack of clarity when determining and representing the dominium of the function, difficulty when performing the conversion from the representation of the natural language to the algebric language in contextualised situations, the confusion between the graphic representation of the dominion and the function, and the obstacles for the interpretation of the graphic of a function of two variables, difficulties that have negative effect on the study of partial derivatives. The registers of semiotic representation proved themselves an efficient tool for the explanation of the knowledge and the complexity that the study of functions with two variables represent for students
Esta pesquisa foi desenvolvida com o objetivo de verificar as dificuldades e saberes manifestados por estudantes relativos à transição do estudo das funções de uma variável para o caso de duas, no que diz respeito às variáveis dependentes e independentes e à interdependência entre elas, ao domínio e o gráfico, à relação entre o gráfico do domínio e o gráfico da função e, também quais manifestações são reveladas no estudo das derivadas parciais de primeira ordem. Para isso, elaboramos dois questionários fundamentados na Teoria dos Registros de Representação Semiótica de Raymond Duval, os quais foram aplicados a estudantes do quarto e quinto semestre de um curso de Licenciatura em Matemática de uma universidade particular da grande São Paulo. O primeiro questionário foi aplicado a alunos do quarto semestre e possibilitou, além de uma primeira análise das dificuldades, verificar a pertinência das questões, bem como a adequação dos enunciados. Foi constatado que algumas questões necessitavam de uma reestruturação e, também, que era necessário o acréscimo de novas questões, o que contribuiu na elaboração do questionário definitivo, que foi aplicado a estudantes do quinto semestre. Esta pesquisa revelou algumas dificuldades que os alunos apresentam quando estudam as funções de duas variáveis, como: a não compreensão do sistema de eixos 3D, a falta de clareza na determinação e representação do domínio da função, a dificuldade em realizar a conversão do registro da língua natural para o algébrico em situações contextualizadas, a confusão entre o registro gráfico do domínio e da função, e os obstáculos para a interpretação do gráfico de uma função de duas variáveis, dificuldades estas que se refletem negativamente no estudo das derivadas parciais. Os registros de representação semiótica se mostraram uma eficaz ferramenta para a explicitação dos saberes e da complexidade que o estudo de funções de duas variáveis representa para os alunos

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The purpose of this investigation was the elaboration and implementation of a virtual environment for a part time distance course for students of the Computer Science and Systems of Information. The students failed in a former discipline that approaches topics of elementary Mathematics. It happened in a particular university in the city of São Paulo. Our focus was on analyzing this environment, the tools and interactions that happened on distance mode, about the content of real function of one variable. The methodology used, design-based research, favored proposing and analyzing the activities about this topic, as well as their reorganization and, the re design of the environment. The Blackboard platform and the used tools were analyzed based on Chaves (2000) criteria, and it seemed efficient as a virtual environment for the learning in our course. However, we leaved some critical and suggestions for future works, mainly about the role of the tools for communication within part time distance courses. The analysis of the students and teacher speeches' was based on the Model of Argumentative Strategy (CASTRO et al, 2004) and allowed to raise some aspects on the understanding of Real Functions of one variable, as they were privileged in the different interactive spaces such as forum, chat, email and daily log. Aspects like the meaning production in Mathematics can be produced due to the authority of a teacher or of another student who is considered good by the classroom peers, or based on everyday language usage or on cultural characteristics. Moreover, we found that besides the students lack of prerequisite elementary mathematics, there is a lack of a culture for on-line courses
Nesta pesquisa objetivamos a elaboração e implementação de um ambiente virtual para um curso semipresencial, para estudantes dos cursos de Bacharelado em Ciência da Computação e Sistemas de Informação de uma instituição particular na cidade de São Paulo, dependentes na disciplina que aborda tópicos de pré-calculo. Nosso foco recaiu na análise do ambiente, da viabilidade das ferramentas e das interações que ocorreram a distância, no que tange o conteúdo de Funções de uma Variável Real. A metodologia utilizada, design research, permitiu propor e analisar as atividades sobre este tópico, incluindo a reestruturação e complementação deste ambiente. A plataforma Blackboard e as ferramentas foram analisadas segundo critérios definidos por Chaves (2000) e se mostraram eficazes como ambiente virtual de aprendizagem atendendo, para nosso curso, os critérios necessários. Entretanto, deixamos algumas críticas e sugestões para trabalhos futuros, principalmente quanto o papel do uso de ferramentas de comunicação em cursos semipresenciais. A análise dos discursos dos alunos e docente baseados no Modelo de Estratégia Argumentativa (CASTRO et al, 2004) permitiu levantar alguns aspectos sobre a compreensão de Funções de uma Variável Real que foram privilegiados nos diferentes espaços interativos como fórum, chat, e-mail e diário de rotina, tais como o fato de que a produção de significados em Matemática pode estar apoiada na autoridade do professor ou alunos bem vistos pela classe, na linguagem cotidiana e no aspecto cultural. Observamos ainda que além da falta de pré-requisitos de matemática básica, ainda há falta de cultura de trabalhos on-line

A thesis submitted to the Faculty of Science, School of Statistics and Actuarial Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, January 25, 2017.
The classical Wishart distribution, was first derived byWishart (1928) as the distribution of the maximum likelihood estimator of the covariance matrix of the multivariate normal distribution. It is a matrix variate generalization of the gamma distribution. In high dimensional settings,Wishart distributions defined within the framework of graphical models are of particular importance. [No abstract provided. Information taken from introduction]
MT2017

Let φ be a self-map of B₂, the unit ball in C². We investigate the equation C_φf=λf where we define C_φf : -f◦φ, with f a function in the Drury Arves on Space. After imposing conditions to keep C_φ bounded and well-behaved, we solve the equation C_φf - λf and determine the spectrum σ(C_φ) in the case where there is no interior fixed point and boundary fixed point without multiplicity. We then investigate the existence of one-parameter semigroups for such maps and discuss some generalizations.

The aim of this thesis is to didactically properly assemble a set of exercises and tests form the field of Mathematical Analysis. Examples will be based on themes: real-valued functions of a real variable and its properties, limits and continuity of a function, derivative of a function and course of a function. Moodle software will be used to randomly generate specific tests in a way that from each set will be generated certain number of exercises. In addition to the test assignments this thesis will include their detailed solutions. This thesis will work as an individual preparation for the exam in mathematical analysis or the exam itself.