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by He Xinggang. / "December 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 69-73). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Zheng Xi Yin. / "December 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 117-121). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Li Jian Lin. / "November 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 85-90) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Lai, Chun Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 83-87). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Spectral sets in Rd --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Fundamental domains and convex sets in Rd --- p.15 / Chapter 2.3 --- Finite union of cubes --- p.20 / Chapter 3 --- Spectral theory on discrete groups --- p.27 / Chapter 3.1 --- Finite groups and Zd --- p.28 / Chapter 3.2 --- Rational spectrums and tiling sets --- p.32 / Chapter 3.3 --- Fuglede´ةs Problem in R1 --- p.37 / Chapter 3.4 --- "Failure of Fuglede´ةs Conjecture in Rd, d >3" --- p.42 / Chapter 4 --- Self-similar tiles in R1 --- p.49 / Chapter 4.1 --- Basics of self-similar tiles --- p.49 / Chapter 4.2 --- Self-similar tile digit sets and spectral problem --- p.52 / Chapter 4.3 --- Kenyon criterion --- p.55 / Chapter 5 --- Spectral self-similar measures --- p.66 / Chapter 5.1 --- Spectral self-similar measures --- p.66 / Chapter 5.2 --- One-dimensional self-similar measures --- p.72 / Chapter 5.3 --- General properties of spectral measures --- p.80 / Bibliography --- p.83

Wong, Wing Chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 66-67). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background Study --- p.4 / Chapter 2.1 --- Basic Definitions and Notations --- p.5 / Chapter 2.2 --- Tarjan and Trojanowski's algorithm --- p.6 / Chapter 2.2.1 --- Techniques --- p.6 / Chapter 2.2.2 --- Algorithm --- p.8 / Chapter 2.3 --- "Fomin, Grandoni and Kratsch's Algorithm" --- p.9 / Chapter 2.3.1 --- Techniques --- p.9 / Chapter 2.3.2 --- Algorithm --- p.14 / Chapter 3 --- Improvements --- p.18 / Chapter 3.1 --- Tarjan and Trojanowski´ةs Algorithm --- p.18 / Chapter 3.1.1 --- Correctness and Running Time Analysis --- p.28 / Chapter 3.1.2 --- Improvement --- p.30 / Chapter 3.1.3 --- Using more weights --- p.35 / Chapter 3.2 --- The First Algorithm --- p.37 / Chapter 3.2.1 --- Standard Analysis --- p.37 / Chapter 3.2.2 --- Measure and Conquer --- p.38 / Chapter 3.2.3 --- Using more weights --- p.42 / Chapter 3.3 --- The Second Algorithm --- p.43 / Chapter 3.3.1 --- Running Time Analysis --- p.44 / Chapter 3.3.2 --- Using More Weights --- p.45 / Chapter 3.4 --- The Third Algorithm --- p.46 / Chapter 4 --- Lower Bounds --- p.52 / Chapter 4.1 --- Tarjan and Trojanowski's Algorithm --- p.52 / Chapter 4.2 --- The First Algorithm --- p.55 / Chapter 4.3 --- The Second Algorithm --- p.58 / Chapter 4.4 --- The Third Algorithm --- p.60 / Chapter 5 --- Conclusion --- p.63 / Bibliography --- p.66

This study investigated the distribution of bibliographic records amongst online bibliographic databases. The topic of Fuzzy Set Theory over the period of 1965 to 1993 was chosen to provide the case study for this investigation. From the DIALOG database host, searches were conducted on 114 databases to determine the number of journal article records relating to the topic of Fuzzy Sets. Both the number of records in each database, as well as the overlap of coverage between the databases were calculated. Six counting techniques were developed to allocate records to databases based on different methods for handling records that were duplicated between databases. When duplicate records are included, the top database accounts for 19% of the records; when duplicates are removed, the top database was found to account for 37% of the records. The distribution of records in databases was found to conform to the Bradford-Zipf hyperbolic distribution. Various other analyses were undertaken including: the duplicate records themselves, the total size of the DIALOG database system over time and the density of Fuzzy Set records in databases over time. A secondary aim of this study was to perform an informetric study on the literature of Fuzzy Set Theory itself. Results obtained include an analysis of the growth of the Fuzzy Set literature, an analysis of the journals covering the topic of Fuzzy Sets, an analysis of the terminology used in describing topics related to Fuzzy Sets. Also, the Ulrich's database was used to provide a subject classification of the journals to analyse the diffusion of the topic of Fuzzy Sets into other disciplines. Apart from the discipline of mathematics, the top disciplines into which Fuzzy Sets have diffused were found to be applied physics, systems and computing. The third aim of the thesis was to refine and develop the methodology used to perform large scale informetric studies using data from a variety of online bibliographic databases. Commercially available software was used wherever possible, but where this was not possible or infeasible, custom written programs were developed to perform various steps in the methodology.

A random variable that is defined as the absorption time of an evanescent finite-state continuous-time Markov chain is said to have a phase-type distribution. A phase-type distribution is said to have a representation (α,T ) where α is the initial state probability distribution and T is the infinitesimal generator of the Markov chain. The distribution function of a phase-type distribution can be expressed in terms of this representation. The wider class of matrix-exponential distributions have distribution functions of the same form as phase-type distributions, but their representations do not need to have a simple probabilistic interpretation. This class can be equivalently defined as the class of all distributions that have rational Laplace-Stieltjes transform. There exists a one-to-one correspondence between the Laplace-Stieltjes transform of a matrix- exponential distribution and a representation (β,S) for it where S is a companion matrix. In order to use matrix-exponential distributions to fit data or approximate probability distributions the following question needs to be answered: “Given a rational Laplace-Stieltjes transform, or a pair (β,S) where S is a companion matrix, when do they correspond to a matrix-exponential distribution?” In this thesis we address this problem and demonstrate how its solution can be applied to the abovementioned fitting or approximation problem. / Thesis (Ph.D.)--School of Applied Mathematics, 2003.

The investigation of this paper is introduced by describing an important collection of classes arising from a class which forms the domain of an abstract measure. Characterizations of the different types of classes will be formulated in order to facilitate the construction and the identification of the various classes considered.

Over the past few years, a considerable number of studies have been made on Support Vector Machines (SVMs) in many domains to improve classification or prediction. However, SVMs request high computational time and memory when the datasets are large. Although incremental learning techniques are viewed as one possible solution developed to reduce the computation complexity of the scalability problem, few studies have considered that some examples close to the decision hyperplane other than support vectors (SVs) might contribute to the learning process. Consequently, we propose three novel algorithms, named Mixed Incremental learning (MIL), Half-Mixed Incremental learning (HMIL), and Partition Incremental learning (PIL), by improving Syed¡¦s incremental learning method based on fuzzy set theory. We expect to achieve better accuracy than other methods. In the experiments, the proposed algorithms are investigated on five standard machine learning benchmark datasets to demonstrate the effectiveness of the method. Experimental results show that HIL have superior classification accuracy than the other incremental or active learning algorithms. Especially, for the datasets that might have high accuracy in other research reports, HMIL and PIL could even improve the performance.