Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (p. 114).

Thesis (Ph. D.)--University of Nevada, Reno, 2008. / "December, 2008." Includes bibliographical references. Online version available on the World Wide Web.

Thesis (M.F.A.)--Rochester Institute of Technology, 1991. / Typescript. Includes bibliographical references (24-25).

Thesis (M.A.)--The University of North Carolina at Greensboro, 2009. / Directed by Paul Duvall; submitted to Dept. of Mathematics and Statistics. Title from PDF t.p. (viewed Jun. 7, 2010). Includes bibliographical references (p. 37-38).

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, June 2002. / Includes bibliographical references (p. 123-132) Also available on the Internet.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Includes bibliographical references (leaves 80-85). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 87-91). Also available on the Internet.

Orientador: Alice Kimie Miwa Libardi / Coorientador: Tatiana Miguel Rodrigues de Souza / Banca: Elíris Cristina Rizziolli / Banca: Edivaldo Lopes dos Santos / Resumo: Intuitivamente, um ponto tem dimensão 0, uma reta tem dimensão 1, um plano tem dimensão 2 e um cubo tem dimensão 3. Porém, na geometria fractal encontramos objetos matemáticos que possuem dimensão fracionária. Esses objetos são denominados fractais cujo nome vem do verbo "frangere", em latim, que significa quebrar, fragmentar. Neste trabalho faremos um estudo sobre o conceito de dimensão, definindo dimensão topológica e dimensão de Hausdorff. O objetivo deste trabalho é, além de apresentar as definições de dimensão, também apresentar algumas aplicações da dimensão de Hausdorff na geometria fractal / Abstract: We know, intuitively, that the dimension of a dot is 0, the dimension of a line is 1, the dimension of a square is 2 and the dimension of a cube is 3. However, in the fractal geometry we have objects with a fractional dimension. This objects are called fractals whose name comes from the verb frangere, in Latin, that means breaking, fragmenting. In this work we will study about the concept of dimension, de ning topological dimension and Hausdor dimension. The purpose of this work, besides presenting the de nitions of dimension, is to show an application of the Hausdor dimension on the fractal geometry / Mestre

With life expectancy on the rise, age-related ailments are a significant strain on the welfare of individuals and the economy. Progress is being made towards combating the leading cause of unavoidable blindness, age-related macular degeneration (AMD). AMD affects ten million Americans and costs the world economy $343 billion annually. Retinal implants promise to restore sight by replacing the eye's damaged photoreceptors with electronic photodiodes. Clinical trials succeed at restoring some vision, but are limited by the stimulating electrodes. We study the electrode-neuron interface with a focus on the geometrical dependence of the electrode. The functionality of neurons is intimately connected to their branching and curving shape, described by fractal geometry. We examine the morphology of neurons using fractal analysis. The results inform our electrode designs, which are fabricated using top-down lithographic and bottom-up self-assembly techniques. A novel technique for fabricating a fractal electrode is presented. Heating and cooling a film of poly(methyl methacrylate) on a SiO2 substrate causes fractal structures to form on the surface. The geometry of the structures is temperature dependent, producing crystalline branches at lower temperatures and diffusion-limited aggregates at higher temperatures. Subsequent deposition of antimony nanoclusters shows preferred diffusion to the fractal surface features. The dependence of a photodiode's performance on its top contact geometry is explored using modified nodal analysis. The results reinforce the need to balance a low mean semiconductor-metal separation distance with an adequate contact width for low resistance, all while maximizing light input. Future designs will benefit from the spatial voltage maps produced by the simulation. The electric field emanating from an electrode is also dependent on the geometry of the electrode. The Faraday cage effect is exploited to achieve similar electric field responses to traditional electrode shapes. A preliminary study of neural adhesion to SU-8 fractal electrodes is promising. The neuron grows along the electrode even at 90° turns. The role the fractal geometry plays in neuron and electrode functionality is shown to be significant. Continued study of, and experimentation with, new electrode designs is sure to produce exciting possibilities in the future. This dissertation includes previously unpublished co-authored material.

Made available in DSpace on 2014-06-11T19:25:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-10-31Bitstream added on 2014-06-13T19:12:21Z : No. of bitstreams: 1 cressonifilho_l_me_rcla.pdf: 1066090 bytes, checksum: 8e2400d1325663e46120c47cecd0a935 (MD5) / A importância da água para os seres humanos é indiscutível. Com a organização da sociedade humana em grupos cada vez maiores, não só a água, mas todo o processo de captação, tratamento e distribuição dela, torna-se cada vez mais uma preocupação importante. Redes de distribuição de água são estruturas que aparentemente apresentam características fractais e o que este trabalho propôs foi a análise dessas em algumas cidades, observando-se os valores de consumo lidos nos hidrômetros, em busca de algumas características que possam indicar a existência de fractais que descrevem essas redes. Notou-se que as distribuições estatísticas dos consumos de água obedecem à distribuição gaussiana com máximo em torno de 18 m3 para pontos de baixo consumo (residências, por exemplo) e à lei de potência para pontos de consumo médio e elevado (residências de alto padrão, comércio e indústria). Observou-se que o expoente da lei de potência (alfa) varia com o número de habitantes, obedecendo a lei de escala. Foi proposto como uma possível explicação para estas características o mecanismo de realimentação positiva. / The importance of water to human beings is unquestionable. With human society forming ever larger groups, water, as well as the processes of capturing, treating and distributing water are increasingly important concerns. Water distribution networks are structures that apparently show fractal characteristics. This work is an analysis of water distribution networks in different cities. The analysis utilized water consumption readings from hydrometers to search for characteristics that describe the networks. This study determined that the statistical distribution of water consumption follows a Gaussian distribution for low values of consumption (residential users) and Power law for large values (high-level residences, commerce and industry). It also determined that the exponent (α ) of the Power Law varies with the number of citizens, obeying to a scale law. The Positive Feedback Mechanism is proposed as a possible explanation for these characteristics.