Thesis (doctoral)--Georg-Augusts-Universität zu Göttingen, 1910. / Cover title. Vita. Includes bibliographical references.

by Yeung Wai Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 92-[96]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Fuzzy Inference and Real Intelligent Mapping --- p.1 / Chapter 1.2 --- Organization of the thesis --- p.5 / Chapter 2 --- Fuzzy Logic inference --- p.7 / Chapter 2.1 --- Fuzzy logic --- p.7 / Chapter 2.1.1 --- Fuzzy sets --- p.7 / Chapter 2.1.2 --- Operations on fuzzy sets --- p.10 / Chapter 2.2 --- Fuzzy Inference --- p.11 / Chapter 3 --- Weaknesses of fuzzy inference --- p.17 / Chapter 3.1 --- Is the use of linguistic fuzzy if-then rules and membership func- tions a good means of representing human expert knowledge? --- p.17 / Chapter 3.2 --- Role of conventional fuzzy inference doubtful if the expert knowl- edge is in the form of sampled input-output data --- p.21 / Chapter 3.3 --- Computational requirements --- p.23 / Chapter 3.4 --- Low transparency --- p.24 / Chapter 3.5 --- Analytical difficulties --- p.25 / Chapter 4 --- Real Intelligent Mapping --- p.27 / Chapter 5 --- Design of Real Intelligent Mapping Systems Using Dirichlet Tessellation --- p.33 / Chapter 5.1 --- Dirichlet tessellation for function approximation --- p.34 / Chapter 5.2 --- Identification of a DT based RIM system by least-squares --- p.42 / Chapter 5.3 --- Examples --- p.48 / Chapter 5.3.1 --- Defining the problem --- p.48 / Chapter 5.3.2 --- Balancing an inverted pendulum --- p.49 / Chapter 5.3.3 --- Balancing an inverted pendulum with cart --- p.53 / Chapter 5.3.4 --- Truck backing-up --- p.56 / Chapter 5.3.5 --- Chaotic time series prediction --- p.60 / Chapter 5.4 --- Interactive CAD platform for RIM systems design --- p.63 / Chapter 6 --- Analysis of Dirichlet tessellation based Real Intelligent Mapping Systems --- p.67 / Chapter 6.1 --- Local Stability Analysis of DT Based RIM Systems --- p.69 / Chapter 6.1.1 --- Balancing an inverted pendulum --- p.71 / Chapter 6.1.2 --- Truck backing-up --- p.73 / Chapter 6.2 --- Global stability analysis of DT based RIM systems --- p.74 / Chapter 6.3 --- Design of a stable DT based RIM system --- p.79 / Chapter 6.4 --- A method for analyzing Second order DT based RIM systems --- p.82 / Chapter 6.5 --- Piecewise-polynomial real domain representation of a class of fuzzy controller and its stability --- p.85 / Chapter 7 --- Conclusion --- p.90 / Bibliography --- p.92

分形分析的主題是研究分形上的Dirichlet形式和Laplacian. 壓縮的自相似群有一個與之關聯的極限空間,此空間通常具備分形結構，因而引發了分形分析和自相似群兩個分支的結合. / 我們回顧了自相似群和它們的極限空間極限空間可以用Schreier 圖來逼近,事實上其可以看成由Schreier圖構造出來的雙曲圖的雙曲邊界.我們探究了迭代單值群. 通過增加專門的條件我們可以得到迭代單值群的極限空間同胚於某個Julia集. / 通過運用[31] 中的想法和[47] 中自相似隨機游動的方法，我們闡明了極限空間上Laplacian和Dirichlet形式的構造步驟我們介紹了加法器， Basilica群以及Hanoi塔群的極限空間(在第三種情況下是Sierpiríski墊片)上的Laplacian 這裡得到的Dirichlet形式是局部且正則的. / 通過採用[53] 的設置, 我們描述了加法器的極限空間上的誘發型Dirichlet形式在構造了加法器的自相似圖上的嚴格可逆隨機游動後，我們可以得到一個非局部的Dirichlet形式. / The major theme of fractal analysis is studying Dirichlet forms and Laplacians on fractals. For a contracting self-similar group there is an associated limit space, which usually exhibits a fractal structure, thereby triggering the combination of fractal analysis and self-similar groups. / We give reviews of self-similar groups and their limit spaces. Limit space can be approximated by Schreier graphs, and it is in fact identied as a hyperbolic boundary of a hyperbolic graph constructed from Schreier graphs. We explore the iterated monodromy groups. By adding technical conditions, we have that the limit space of an iterated monodromy group is homeomorphic to a Julia set. / We show the construction process of Laplacians and Dirichlet forms on limit spaces using the idea of [31] and the method of self-similar random walks from [47]. We present examples of Laplacians of the limit spaces of adding machine, the Basilica group and the Hanoi Tower group (it is Sierpi´nski gasket in this case). In this context these forms are local and regular. / We describe the induced Dirichlet forms on limit space of the adding machine by adopting the settings of [53] . By constructing strictly reversible random walks on self-similarity graph of the adding machine, we can obtain a non-local Dirichlet form. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lin, Dateng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 71-76). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Review of fractal analysis --- p.6 / Chapter 1.2 --- Applications to self-similar groups --- p.7 / Chapter 1.3 --- Boundary theory method --- p.8 / Chapter 1.4 --- Summary of the thesis --- p.9 / Chapter 2 --- Self-similar groups --- p.11 / Chapter 2.1 --- Basic definitions --- p.11 / Chapter 2.2 --- Limit spaces of self-similar groups --- p.18 / Chapter 2.3 --- Schreier graphs approximations --- p.24 / Chapter 2.4 --- Iterated monodromy groups --- p.28 / Chapter 3 --- Construction of Laplacians on limit spaces --- p.35 / Chapter 3.1 --- Dirichlet forms, Laplacians and resistance forms --- p.35 / Chapter 3.2 --- Representations of groups and functions --- p.42 / Chapter 3.3 --- Laplacians on limit spaces --- p.45 / Chapter 4 --- Induced Dirichlet form on limit space of the adding machine --- p.53 / Chapter 4.1 --- Martin boundary and hyperbolic boundary --- p.53 / Chapter 4.2 --- Graph energy and the induced form --- p.62 / Chapter 4.3 --- Induced Dirichlet form of the adding machine --- p.65 / Bibliography --- p.71

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 162-169). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 162-169). Also available on the Internet.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Includes bibliographical references (leaves 202-204) and index. Issued in print and online. Available via ProQuest Digital Dissertations.