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The purpose of this paper is to examine properties of the ring C(X) of all complex or real-valued continuous functions on an arbitrary topological space X.

This paper examines the relationship between Borel sets and Baire functions.

This paper is primarily concerned with the fundamental properties of a linear algebra of finite order over a field. A discussion of linear sets of finite order over a field is used as an introduction to these properties.

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by Cai, Chun Hing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 109-114). / Abstract also in Chinese. / Acknowledgments --- p.ii / Abstract --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Main Categories in Data Mining --- p.1 / Chapter 1.2 --- Motivation --- p.3 / Chapter 1.3 --- Problem Definition --- p.4 / Chapter 1.4 --- Experimental Setup --- p.5 / Chapter 1.5 --- Outline of the thesis --- p.6 / Chapter 2 --- Literature Survey on Data Mining --- p.8 / Chapter 2.1 --- Statistical Approach --- p.8 / Chapter 2.1.1 --- Statistical Modeling --- p.9 / Chapter 2.1.2 --- Hypothesis testing --- p.10 / Chapter 2.1.3 --- Robustness and Outliers --- p.11 / Chapter 2.1.4 --- Sampling --- p.12 / Chapter 2.1.5 --- Correlation --- p.15 / Chapter 2.1.6 --- Quality Control --- p.16 / Chapter 2.2 --- Artificial Intelligence Approach --- p.18 / Chapter 2.2.1 --- Bayesian Network --- p.19 / Chapter 2.2.2 --- Decision Tree Approach --- p.20 / Chapter 2.2.3 --- Rough Set Approach --- p.21 / Chapter 2.3 --- Database-oriented Approach --- p.23 / Chapter 2.3.1 --- Characteristic and Classification Rules --- p.23 / Chapter 2.3.2 --- Association Rules --- p.24 / Chapter 3 --- Background --- p.27 / Chapter 3.1 --- Iterative Procedure: Apriori Gen --- p.27 / Chapter 3.1.1 --- Binary association rules --- p.27 / Chapter 3.1.2 --- Apriori Gen --- p.29 / Chapter 3.1.3 --- Closure Properties --- p.30 / Chapter 3.2 --- Introduction of Weights --- p.31 / Chapter 3.2.1 --- Motivation --- p.31 / Chapter 3.3 --- Summary --- p.32 / Chapter 4 --- Mining weighted binary association rules --- p.33 / Chapter 4.1 --- Introduction of binary weighted association rules --- p.33 / Chapter 4.2 --- Weighted Binary Association Rules --- p.34 / Chapter 4.2.1 --- Introduction --- p.34 / Chapter 4.2.2 --- Motivation behind weights and counts --- p.36 / Chapter 4.2.3 --- K-support bounds --- p.37 / Chapter 4.2.4 --- Algorithm for Mining Weighted Association Rules --- p.38 / Chapter 4.3 --- Mining Normalized Weighted association rules --- p.43 / Chapter 4.3.1 --- Another approach for normalized weighted case --- p.45 / Chapter 4.3.2 --- Algorithm for Mining Normalized Weighted Association Rules --- p.46 / Chapter 4.4 --- Performance Study --- p.49 / Chapter 4.4.1 --- Performance Evaluation on the Synthetic Database --- p.49 / Chapter 4.4.2 --- Performance Evaluation on the Real Database --- p.58 / Chapter 4.5 --- Discussion --- p.65 / Chapter 4.6 --- Summary --- p.66 / Chapter 5 --- Mining Fuzzy Weighted Association Rules --- p.67 / Chapter 5.1 --- Introduction to the Fuzzy Rules --- p.67 / Chapter 5.2 --- Weighted Fuzzy Association Rules --- p.69 / Chapter 5.2.1 --- Problem Definition --- p.69 / Chapter 5.2.2 --- Introduction of Weights --- p.71 / Chapter 5.2.3 --- K-bound --- p.73 / Chapter 5.2.4 --- Algorithm for Mining Fuzzy Association Rules for Weighted Items --- p.74 / Chapter 5.3 --- Performance Evaluation --- p.77 / Chapter 5.3.1 --- Performance of the algorithm --- p.77 / Chapter 5.3.2 --- Comparison of unweighted and weighted case --- p.79 / Chapter 5.4 --- Note on the implementation details --- p.81 / Chapter 5.5 --- Summary --- p.81 / Chapter 6 --- Mining weighted association rules with sampling --- p.83 / Chapter 6.1 --- Introduction --- p.83 / Chapter 6.2 --- Sampling Procedures --- p.84 / Chapter 6.2.1 --- Sampling technique --- p.84 / Chapter 6.2.2 --- Algorithm for Mining Weighted Association Rules with Sampling --- p.86 / Chapter 6.3 --- Performance Study --- p.88 / Chapter 6.4 --- Discussion --- p.91 / Chapter 6.5 --- Summary --- p.91 / Chapter 7 --- Database Maintenance with Quality Control method --- p.92 / Chapter 7.1 --- Introduction --- p.92 / Chapter 7.1.1 --- Motivation of using the quality control method --- p.93 / Chapter 7.2 --- Quality Control Method --- p.94 / Chapter 7.2.1 --- Motivation of using Mil. Std. 105D --- p.95 / Chapter 7.2.2 --- Military Standard 105D Procedure [12] --- p.95 / Chapter 7.3 --- Mapping the Database Maintenance to the Quality Control --- p.96 / Chapter 7.3.1 --- Algorithm for Database Maintenance --- p.98 / Chapter 7.4 --- Performance Evaluation --- p.102 / Chapter 7.5 --- Discussion --- p.104 / Chapter 7.6 --- Summary --- p.105 / Chapter 8 --- Conclusion and Future Work --- p.106 / Chapter 8.1 --- Summary of the Thesis --- p.106 / Chapter 8.2 --- Conclusions --- p.107 / Chapter 8.3 --- Future Work --- p.108 / Bibliography --- p.108 / Appendix --- p.115 / Chapter A --- Generating a random number --- p.115 / Chapter B --- Hypergeometric distribution --- p.116 / Chapter C --- Quality control tables --- p.117 / Chapter D --- Rules extracted from the database --- p.120

Pong Ting Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 79-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Notations --- p.7 / Chapter 2.3 --- On properties of Normal Cones --- p.9 / Chapter 2.4 --- Polar Calculus --- p.13 / Chapter 2.5 --- Notions of Relative Interior --- p.17 / Chapter 2.6 --- Properties of Minkowski functional --- p.18 / Chapter 2.7 --- Properties of Epigraphs --- p.19 / Chapter 3 --- The Strong Conical Hull Intersection Property (Strong CHIP): Definition and Some Properties --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Definition of the strong CHIP --- p.24 / Chapter 3.3 --- Relationship between the strong CHIP and projections onto sets --- p.26 / Chapter 3.4 --- Relationship between the strong CHIP and the Basic Constraint Qualifications (BCQ) --- p.35 / Chapter 3.5 --- The strong CHIP of extremal subsets --- p.42 / Chapter 4 --- Sufficient Conditions for the Strong CHIP --- p.46 / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- ̐ưجI̐ưجis finite --- p.47 / Chapter 4.2.1 --- Interior point conditions --- p.47 / Chapter 4.2.2 --- Boundedly linear regularity --- p.52 / Chapter 4.2.3 --- Epi-sum --- p.54 / Chapter 4.3 --- ̐ưجI̐ưجis infinite --- p.56 / Chapter 4.3.1 --- A Sum Rule --- p.57 / Chapter 4.3.2 --- The C-Extended Minkowski Functional --- p.58 / Chapter 4.3.3 --- Relative Interior Point Conditions --- p.62 / Chapter 4.3.4 --- Bounded Linear Regularity --- p.68 / Chapter 5 --- "The SECQ, Linear Regularity and the Strong CHIP for Infinite System of Closed Convex Sets in Normed Linear Spaces" --- p.69 / Chapter 5.1 --- Introduction --- p.69 / Chapter 5.2 --- The strong CHIP and the SECQ --- p.71 / Chapter 5.3 --- Linear regularity and the SECQ --- p.73 / Chapter 5.4 --- Interior-point conditions and the SECQ --- p.76 / Bibliography --- p.79

Lee Shuk Yee. / "October 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 87-92) / 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.