Thesis (M.S.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 22).

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 85-89).

Thesis (Ph.D.) - University of St Andrews, November 2008.

No description available.

令B{U+209C}表示一個平面布朗運動。我們把C \B[0, 1] 的無界連通分支的邊界稱爲B[0; 1] 的外邊界。在本文中，我們將討論如何計算B[0,1] 的外邊界的Hausdorff 維數。 / 我們將在第二章討論Lawler早期的工作[7]。他定義了一個常數ζ(所謂的不聯通指數） 。利用能量的方法， 他證明了 B[0,1]的外邊界的Hausdorff維數是2(1 - ζ)概率大於零， 然後0-1律可以明這個概率就是1。但是用他的方法我們不能算出ζ的準確值。 / Lawler, Schramm and Werner 在一系列文章[10]，[11] 和[13] 中研究了SLE{U+2096}和excursion 測度。利用SLE6 和excursion 測度的共形不變性，他們可以計算出了布朗運動的相交指數ξ (j; λ )。因此ζ = ξ (2; 0)/2 = 1/3，由此可以知道B[0, 1] 的外邊界的Hausdorff 維數就是4/3。從而可以說完全證明了著名的Mandelbrot 猜想。 / Let B{U+209C} be a Brownian motion on the complex plane. The frontier of B[0; 1] is defined to be the boundary of the unbounded connected component of C\B[0; 1].In this thesis, we will review the calculation of the Hausdorff dimension of the frontier of B[0; 1]. / We first dissuss the earlier work of Lawler [7] in Chapter 2. He defined a constant ζ (so called the dimension of disconnection exponent). By using the energy method, he proved that with positive probability the Hausdorff dimension of the frontier of B[0; 1] is 2(1 -ζ ), then zero-one law show that the probability is one. But we can not calculate the exact value of ζ in this way. / In the series of papers by Lawler, Schramm and Werner [10], [11] and [13], they studied the SLE{U+2096} and excursion measure. By using the conformal invariance of SLE₆ and excursion measure, they can calculate the exact value of the Brownian intersection exponents ξ(j, λ). Consequently, ζ = ξ(2, 0)/2 = 1/3, and the Hausdorff dimension of the frontier of B [0,1] is 4/3 almost surely. This answers the well known conjecture by Mandelbrot positively. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Pengfei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 53-55). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Hausdorff dimension of the frontier of Brownian motion --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Hausdorff dimension of Brownian frontier --- p.13 / Chapter 3 --- Stochastic Loewner Evolution --- p.24 / Chapter 3.1 --- Definitions --- p.24 / Chapter 3.2 --- Continuity and Transience --- p.26 / Chapter 3.3 --- Locality property of SLE₆ --- p.30 / Chapter 3.4 --- Crossing exponent for SLE₆ --- p.32 / Chapter 4 --- Brownian intersection exponents --- p.37 / Chapter 4.1 --- Half-plane exponent --- p.37 / Chapter 4.2 --- Whole-plane exponent --- p.41 / Chapter 4.3 --- Proof of Theorem 4.6 and Theorem 4.7 --- p.44 / Chapter 4.4 --- Proof of Theorem 1.2 --- p.47 / Chapter A --- Excursion measure --- p.48 / Chapter A.1 --- Metric space of curves --- p.48 / Chapter A.2 --- Measures on metric space --- p.49 / Chapter A.3 --- Excursion measure on K --- p.49 / Bibliography --- p.53

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

Thesis (M.A.)--York University, 2008. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 166-167). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR45921

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 60-61). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 60-61). Also available on the Internet.

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Dr. J. R. Jackson; Committee Member: Dr. D. Scott; Committee Member: Dr. D. V. Anderson; Committee Member: Dr. P. Vela; Committee Member: Dr. R. Mersereau. Part of the SMARTech Electronic Thesis and Dissertation Collection.