Thesis (MCS)--University of Melbourne, Dept. of Computer Science and Software Engineering, 2010. / Typescript. Includes bibliographical references (leaves 63-67)

Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2006. / Shapiro, Alexander, Committee Member ; Vidakovic, Brani, Committee Member ; Ume, Charles, Committee Member ; Sadegh, Nader, Committee Chair ; Liang, Steven, Committee Member. Vita.

Thesis (doctoral)--Université de Rennes I, 1984. / "Série: 17. No d'ordre: 386. No de série: 57." Includes bibliographical references.

Thesis (doctoral)--Rheinischen Friedrich-Wilhelms-Universität, Bonn, 1980. / Includes bibliographical references (p. 252-258).

Thesis--Bonn. Thesis statement on added t.p. / Includes bibliographical references (p. 53-57).

Thesis (M.S.)--Brigham Young University. Dept. of Computer Science, 2006. / Includes bibliographical references (p. 65-72).

Thesis (Ph. D.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 130-132). Also available on the World Wide Web.

Thesis (M.S.)--Worcester Polytechnic Institute. / Title from title screen. Keywords: genetic programming; approximations; machine learning; artificial intelligence. Includes bibliographical references (p. 92-94).

In this dissertation we are interested in studying two extremal problems in the Bergman space. The topics are divided into three chapters. In Chapter 2, we study Putnam’s inequality in the Bergman space setting. In [32], the authors showed that Putnam’s inequality for the norm of self-commutators can be improved by a factor of 1 for Toeplitz operators with analytic symbol φ acting on the Bergman space A2(Ω). This improved upper bound is sharp when φ(Ω) is a disk. We show that disks are the only domains for which the upper bound is attained. In Chapter 3, we consider the problem of finding the best approximation to z ̄ in the Bergman space A2(Ω). We show that this best approximation is the derivative of the solution to the Dirichlet problem on ∂Ω with data |z|2 and give examples of domains where the best approximation is a polynomial, or a rational function. Finally, in Chapter 4 we study Bergman analytic content, which measures the L2(Ω)-distance between z ̄ and the Bergman space A2(Ω). We compute the Bergman analytic content of simply connected quadrature domains with quadrature formula supported at one point, and we also determine the function f ∈ A2(Ω) that best approximates z ̄. We show that, for simply connected domains, the square of Bergman analytic content is equal to torsional rigidity from classical elasticity theory, while for multiply connected domains these two domain constants are not equivalent in general.

Orientador: Ary Orozimbo Chiacchio / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T03:11:09Z (GMT). No. of bitstreams: 1 Oliveira_CarlosEduardo_M.pdf: 6339093 bytes, checksum: ef1c6e7f77bfce98e679d319c779ec3f (MD5) Previous issue date: 2014 / Resumo: Neste trabalho apresentamos uma proposta de abordagem do conteúdo didático-programático de trigonometria de ensino médio, com apresentação teórica, exercícios e problemas, ambos classificados por nível de dificuldade com o intuito de auxiliar e mensurar a evolução individual de cada aluno no decorrer do curso. Apresentamos também, além do conteúdo supramencionado, a aproximação de funções contínuas por polinômios trigonométricos com o auxílio do Teorema da Aproximação de Weierstrass / Abstract: In this work we present a proposed approach of the educational content of high school trigonometry with theoretical presentation, exercises and problems, both ranked by difficulty level in order to assist and measure the individual progress of each student during the course. We also present, in addition to the above content, the approximation of continuous functions by trigonometric polynomials with the aid of the Weierstrass Approximation Theorem / Mestrado / Matemática em Rede Nacional - PROFMAT / Mestre em Matemática em Rede Nacional - PROFMAT