Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 31). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Much of weighted polynomial approximation originated with the famous Bernstein qualitative approximation problem of 1910/11. The classical Bernstein approximation problem seeks conditions on the weight functions \V such that the set of functions {W(x)Xn};;"=l is fundamental in the class of suitably weighted continuous functions on R, vanishing at infinity. Many people worked on the problem for at least 40 years. Here we present a short survey of techniques and methods used to prove Markov and Bernstein inequalities as they underlie much of weighted polynomial approximation. Thereafter, we survey classical techniques used to prove Jackson theorems in the unweighted setting. But first we start, by reviewing some elementary facts about orthogonal polynomials and the corresponding weight function on the real line. Finally we look at one of the processes (If approximation, the Lagrange interpolation and present the most recent results concerning mean convergence of Lagrange interpolation for Freud and Erdos weights. / Andrew Chakane 2018

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by Lee Siu-keung. / Parallel title in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 162-164). / Chapter Chapter 1 --- Introduction --- p.5 / Chapter Chapter 2 --- Path Integrals / Chapter 2.1 --- Path´ؤIntegral Approach to Quantum Mechanics --- p.8 / Chapter 2.2 --- Path´ؤIntegral Approach to Statistical Mechanics --- p.14 / Chapter 2.3 --- Variational Principle --- p.18 / Chapter 2.4 --- "Variational Method Proposed by Giachetti and Tognetti, and by Feynman and Kleinert" / Chapter 2.4.1 --- Effective Classical Partition Function --- p.24 / Chapter 2.4.2 --- Particle Distribution Function From Effective Classical Potential --- p.34 / Chapter Chapter 3 --- Systematic Perturbation Corrections to the Variational Approximation Proposed in Section2.4 / Chapter 3.1 --- Formalism / Chapter 3.1.1 --- Free Energy --- p.38 / Chapter 3.1.2 --- Particle Distribution Function --- p.49 / Chapter 3.2 --- Second Order Correction to Free Energy --- p.53 / Chapter 3.3 --- First Order Correction to Particle Distribution Function --- p.60 / Chapter Chapter 4 --- Examples and Results / Chapter 4.1 --- Quartic Anharmonic Oscillator / Chapter 4.1.1 --- "Free Energy, Internal Energy and Specific Heat" --- p.69 / Chapter 4.1.2 --- Particle Distribution Function --- p.87 / Chapter 4.2 --- Symmetric Double-well Potential / Chapter 4.2.1 --- "Free Energy, Internal Energy and Specific Heat" --- p.88 / Chapter 4.2.2 --- Particle Distribution Function --- p.106 / Chapter 4.3 --- Quartic-cubic Anharmonic Potential / Chapter 4.3.1 --- Free Energy --- p.108 / Chapter 4.3.2 --- Particle Distribution Function --- p.115 / Chapter Chapter 5 --- Application to the One-dimensional Ginzburg-Landau Model / Chapter 5.1 --- Introduction --- p.120 / Chapter 5.2 --- Exact Partition Function and Free Energy Per Unit Length --- p.123 / Chapter 5.3 --- Zeroth Order Approximation to Free Energy Per Unit Length --- p.126 / Chapter 5.4 --- Exact Specific Heat --- p.133 / Chapter 5.5 --- Zeroth Order Approximation to Specific Heat --- p.139 / Chapter Chapter 6 --- Conclusion --- p.141 / Chapter Appendix I --- Functional Calculus - Differentiation --- p.145 / Chapter Appendix II --- Evaluation of Feynman Propagator Δf(τ) --- p.147 / Chapter Appendix III --- Vanishing of the First Order Correction-βf1 --- p.150 / Chapter Appendix IV --- Numerical Method for the Energy Eigenvalues and Eigenfunctions of the One-dimensional Schroedinger Equation with ax2 + bx4 Potential --- p.153 / Chapter Appendix V --- Numerical Integrations with imaginary Ω --- p.158 / References --- p.162 / Figures --- p.165

Kwok Chun Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [389]-393). / Text in English; abstracts in English and Chinese. / Kwok Chun Ming. / Abstract --- p.i / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Objective and Methodology --- p.3 / Chapter Chapter 2. --- Theory of the Jaynes-Cummings model --- p.5 / Chapter 2.1 --- Formulation of the Jaynes-Cummings model --- p.5 / Chapter 2.1.1 --- Quantization of the Electromagnetic Field --- p.6 / Chapter 2.1.2 --- Quantization of the Matter Field --- p.11 / Chapter 2.1.3 --- The Interaction between the Radiation and the Matter --- p.13 / Chapter 2.1.4 --- Formulation of the One-quantum JCM --- p.15 / Chapter 2.2 --- Energy Eigenstates and Eigenenergy Spectrum --- p.18 / Chapter 2.3 --- Initial States and Observables --- p.20 / Chapter 2.3.1 --- Initial States --- p.20 / Chapter 2.3.2 --- Field Observables --- p.24 / Chapter 2.3.3 --- Atomic Observables --- p.25 / Chapter 2.4 --- Conclusion --- p.27 / Chapter Chapter 3. --- "Generalized SU(1,1) JCM" --- p.28 / Chapter 3.1 --- "Diagonalization of the SU(1,1) JCM" --- p.28 / Chapter 3.2 --- "SU(1,1) Coherent States and Observables" --- p.32 / Chapter 3.2.1 --- "Realizations of the SU(1,1) JCM" --- p.33 / Chapter 3.2.2 --- "SU(1,1) Coherent States" --- p.33 / Chapter 3.2.3 --- Field Observables --- p.35 / Chapter 3.3 --- Conclusion --- p.36 / Chapter Chapter 4. --- "One-mode, Intensity-dependent JCM" --- p.37 / Chapter 4.1 --- "Properties of the One-mode, Intensity-dependent JCM" --- p.37 / Chapter 4.2 --- Squeezing Effect --- p.40 / Chapter 4.2.1 --- Ordinary Amplitude Squeezing --- p.41 / Chapter 4.2.2 --- "SU(1,1) Squeezing" --- p.44 / Chapter 4.2.3 --- SU(2) Squeezing --- p.47 / Chapter 4.3 --- Atomic Inversion --- p.49 / Chapter 4.4 --- Q-function --- p.52 / Chapter 4.4.1 --- Ordinary Q-function --- p.53 / Chapter 4.4.2 --- "SU(1,1) Q-function" --- p.59 / Chapter 4.5 --- Purity Function --- p.65 / Chapter 4.5.1 --- Field Purity Function --- p.65 / Chapter 4.5.2 --- Atomic Purity Function --- p.68 / Chapter 4.6 --- Asymptotic Behavior of Field Squeezing --- p.70 / Chapter 4.7 --- Conclusion --- p.75 / Chapter Chapter 5. --- "One-mode, Two-quantum JCM" --- p.191 / Chapter 5.1 --- "Properties of the One-mode, Two-quantum JCM" --- p.191 / Chapter 5.2 --- Squeezing --- p.196 / Chapter 5.2.1 --- Ordinary Amplitude Squeezing --- p.197 / Chapter 5.2.2 --- "SU(1,1) squeezing" --- p.202 / Chapter 5.2.3 --- SU(2) squeezing --- p.205 / Chapter 5.3 --- Atomic Inversion --- p.206 / Chapter 5.4 --- Q-function --- p.210 / Chapter 5.4.1 --- Ordinary Q-function --- p.210 / Chapter 5.4.2 --- "SU(1,1) Q-function" --- p.215 / Chapter 5.5 --- Purity Function --- p.217 / Chapter 5.5.1 --- Field Purity Function --- p.217 / Chapter 5.5.2 --- Atomic Purity Function --- p.222 / Chapter 5.6 --- Conclusion --- p.225 / Chapter Chapter 6. --- "Two-mode, Two-quantum JCM" --- p.254 / Chapter 6.1 --- "Properties of the Two-mode, Two-quantum JCM" --- p.254 / Chapter 6.2 --- Squeezing --- p.260 / Chapter 6.2.1 --- Ordinary Amplitude Squeezing --- p.260 / Chapter 6.2.2 --- "SU(1,1) Squeezing" --- p.264 / Chapter 6.2.3 --- SU(2) Squeezing --- p.267 / Chapter 6.3 --- Atomic Inversion --- p.269 / Chapter 6.4 --- Q-function --- p.271 / Chapter 6.4.1 --- "SU(1,1) Q-function" --- p.271 / Chapter 6.5 --- Purity Function --- p.273 / Chapter 6.5.1 --- Field Purity Function --- p.273 / Chapter 6.5.2 --- Atomic Purity Function --- p.275 / Chapter 6.6 --- Conclusion --- p.277 / Chapter Chapter 7. --- "Generalized One-mode, Intensity-dependent JCM" --- p.300 / Chapter 7.1 --- "Diagonalization of the Generalizated One-mode, Intensity-dependent JCM" --- p.301 / Chapter 7.2 --- Energy Eigenstates and Eigenenergy Spectrum --- p.307 / Chapter 7.2.1 --- Energy Eigenstates --- p.307 / Chapter 7.2.2 --- Eigenergy Spectrum --- p.309 / Chapter 7.3 --- Conclusion --- p.310 / Chapter Chapter 8. --- Single Trapped and Laser-irradiated JCM --- p.311 / Chapter 8.1 --- Properties of the One-quantum STLI JCM --- p.311 / Chapter 8.2 --- Squeezing Effect --- p.315 / Chapter 8.2.1 --- Ordinary Amplitude Squeezing --- p.315 / Chapter 8.2.2 --- "SU(1,1) Squeezing" --- p.320 / Chapter 8.2.3 --- SU(2) Squeezing --- p.323 / Chapter 8.3 --- Atomic Inversion --- p.326 / Chapter 8.4 --- Q-function --- p.329 / Chapter 8.4.1 --- Ordinary Q-function --- p.329 / Chapter 8.4.2 --- "SU(1,1) Q-function" --- p.332 / Chapter 8.5 --- Purity Function --- p.334 / Chapter 8.5.1 --- Field Purity Function --- p.335 / Chapter 8.5.2 --- Atomic Purity function --- p.338 / Chapter 8.6 --- Non-classical Effects of the Two-quantum STLI JCM --- p.341 / Chapter 8.7 --- Conclusion --- p.342 / Chapter Chapter 9. --- Conclusion --- p.386 / Bibliography --- p.389

Wang Jin. / "September 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 93-105). / 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.

Leung, Cheung Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 85-86). / Abstracts in English and Chinese. / Introduction --- p.6 / Chapter 1 --- Preliminaries --- p.7 / Chapter 1.1 --- Locally compact groups and unitary representations --- p.7 / Chapter 1.2 --- Positive definite functions --- p.10 / Chapter 1.3 --- Affine isometric actions of groups --- p.23 / Chapter 1.4 --- Ultraproducts --- p.29 / Chapter 2 --- Amenability --- p.33 / Chapter 2.1 --- Reiter's property --- p.33 / Chapter 2.2 --- Fφlner's property --- p.41 / Chapter 3 --- Kazhdan's Property (T) --- p.43 / Chapter 3.1 --- Definition and basic properties --- p.43 / Chapter 3.2 --- Property (FH) --- p.51 / Chapter 3.3 --- Spectral criterion for Property (T) --- p.56 / Chapter 3.4 --- Property (T) for SL3(Z) --- p.60 / Chapter 3.5 --- Expanders --- p.72 / Approximation Properties of Groups --- p.5 / Chapter 4 --- Haagerup Property --- p.74 / Chapter 4.1 --- Equivalent formulations of Haagerup Property --- p.74 / Chapter 4.2 --- Trees and wall structures --- p.82 / Bibliography --- p.85

by Maurice F. Aburdene, Ram-Nandan P. Singh. / Bibliography: leaf 9. / "February, 1979." / Partial support by NASA Ames Research Center under Grant NGL-22-009-124

Thesis (Ph. D.)--State University of New York at Buffalo, 1998. / "April 1998." Includes bibliographical references (leaves 144-153). Also available in print.