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Dimension of graphs of Weierstrass-like functions.

Chan, Ying Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 66-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Weierstrass function --- p.7 / Chapter 1.2 --- Rademacher series --- p.10 / Chapter 2 --- Preliminaries --- p.12 / Chapter 2.1 --- Hausdorff dimension and box dimension .. --- p.12 / Chapter 2.2 --- Properties of Hausdorff dimension and box dimension --- p.15 / Chapter 2.3 --- Basic techniques in computing dimensions . --- p.16 / Chapter 2.4 --- Graphs of functions --- p.18 / Chapter 3 --- Weierstrass Function --- p.20 / Chapter 3.1 --- Weierstrass-like functions and their box dimension --- p.20 / Chapter 3.2 --- Hausdorff dimension of Weierstrass-like graphs --- p.23 / Chapter 3.3 --- Weierstrass function with a random phase angle --- p.31 / Chapter 4 --- Rademacher series --- p.37 / Chapter 4.1 --- Basic properties --- p.38 / Chapter 4.2 --- Box dimension for Rademacher series with generalization --- p.39 / Chapter 4.3 --- Some remainders on the infinite Bernoulli convolution --- p.46 / Chapter 5 --- Rademacher series with Pisot reciprocal as parameter --- p.48 / Chapter 5.1 --- Pisot number --- p.48 / Chapter 5.2 --- Hausdorff dimension --- p.49 / Chapter 5.3 --- Matrix representation --- p.54 / Chapter 5.3.1 --- Set-up --- p.54 / Chapter 5.3.2 --- Case of golden ratio --- p.61

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327403
Date January 2011
ContributorsChan, Ying Ying., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 69 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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