Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (M.A.S.)--Memorial University of Newfoundland, 2003. / Bibliography: leaves 68-70. Also available online.

There are many problems that lead to analysis of dynamical systems with phase variables of two types, slow and fast ones. Such systems are called slow-fast systems. The dynamics of such systems is usually described by means of different versions of perturbation theory. Many questions about accuracy of this description are still open. The difficulties are related to presence of resonances. The goal of the proposed thesis is to establish some estimates of the accuracy of the perturbation theory for slow-fast systems in the presence of resonances. We consider slow-fast Hamiltonian systems and study an accuracy of one of the methods of perturbation theory: the averaging method. In this thesis, we start with the case of slow-fast Hamiltonian systems with two degrees of freedom. One degree of freedom corresponds to fast variables, and the other degree of freedom corresponds to slow variables. Action variable of fast sub-system is an adiabatic invariant of the problem. Let this adiabatic invariant have limiting values along trajectories as time tends to plus and minus infinity. The difference of these two limits for a trajectory is known to be exponentially small in analytic systems. We obtain an exponent in this estimate. To this end, by means of iso-energetic reduction and canonical transformations in complexified phase space, we reduce the problem to the case of one and a half degrees of freedom, where the exponent is known. We then consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, ~ε, perturbing term from the Hamiltonian of a linear oscillatory system. We consider passage through a resonance: the frequency of the latter system slowly changes with time and passes through 0. The speed of this passage is of order of ε. We provide asymptotic formulas that describe effects of passage through a resonance with an improved accuracy O(ε3/2). A numerical verification is also provided. The problem under consideration is a model problem that describes passage through an isolated resonance in multi-frequency quasi-linear Hamiltonian systems. We also discuss a resonant phenomenon of scattering on resonances associated with discretisation arising in a numerical solving of systems with one rotating phase. Numerical integration of ODEs by standard numerical methods reduces continuous time problems to discrete time problems. For arbitrarily small time step of a numerical method, discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of systems with one fast rotating phase leads to a situation of such kind: numerical solution demonstrates phenomenon of scattering on resonances, that is absent in the original system.

Thesis (Ed. D.)--National-Louis University. / Bibliography: leaves 106-120.

Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Thomas, Robin; Committee Co-Chair: Cook, William J.; Committee Member: Dvorak, Zdenek; Committee Member: Parker, Robert G.; Committee Member: Yu, Xingxing.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 114-117). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 114-117). Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisors: James W. Fredrickson and Gautam Ahuja. Vita. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 112-115).

O presente trabalho tem como objetivo investigar as aplicações do método fenomenológico à pesquisa empírica em psicologia. O foco da investigação é o passo reflexivo designado redução fenomenológica, considerado elemento fundamental da identidade analítica na tradição da fenomenologia. O trabalho foi dividido em três estudos. O Estudo I tratou da transposição da fenomenologia pura descrita pelo filósofo Edmund Husserl (1859-1938) para a fenomenologia empírica, com especial atenção para o desenvolvimento conceitual da redução fenomenológica e sua aplicação à psicologia. No Estudo II, foi realizado um levantamento de artigos empíricos que utilizaram o método fenomenológico nos últimos dez anos de publicação. Revelou pluralidade lógica e técnica na aplicação do método entre os artigos publicados no Brasil, e homogeneidade aplicativa entre os relatos de pesquisa publicados em um periódico norte-americano especializado na temática. No Estudo III, a aplicação da redução fenomenológica foi exercitada e discutida no cruzamento entre relatos de percepção corpóreo-motoras, em um contexto de tarefa motora induzida, e respostas a uma Escala de autoconsciência. O cruzamento evidenciou associação entre perfis extraídos do sub-fator autoconsciência privada e autoconsciência geral a padrões de resposta e engajamento na tarefa experimental. A evolução dos três estudos almeja descrever uma tendência histórica ascendente de aproximação entre teoria fenomenológica e prática científica. / The aim of the current work is to investigate the applications of phenomenological method in the psychological empirical research. The investigation locus applies to the reflexive step known as phenomenological reduction, considered fundamental piece of the analytical identity in phenomenology. The work is divided in three studies. The first one debates the transition between pure phenomenology, described by German philosopher Edmund Husserl (1859-1938), to the empirical phenomenology, with special attention to the conceptual development of phenomenological reduction and its application in the framework of psychology. The second study was conducted within a survey on empirical articles that have used phenomenological method, published in psychology journals in the last ten years. It reveals logical and technical plurality on the application of method between the Brazilian articles, and the opposite, coherent application in an specialized North American journal on the theme. On the third study, the application of phenomenological reduction was exercised and discussed in the intersection between the exam of perceptual proprioceptive reports, obtained in an experimental setting of induced motor tasks, and results of self-consciousness scale. The intersection evidenced association between the profiles extracted from factor private self-consciousness and general selfconsciousness to reaction verbal patterns and engagement on experimental task. The evolution of three studies indicate an ascendant tendency of approximation between phenomenological theory and scientific practice.