Thesis (MSc (Physics))--University of Stellenbosch, 2006. / The aim of this thesis is the semi-classical implementation of Wegner’s flow equations and comparison with the well-established Wentzel-Kramers-Brillouin method. We do this by converting operators, in particular the Hamiltonian, into scalar functions, while an isomorphism with the operator product is maintained by the introduction of the Moyal product. A flow equation in terms of these scalar functions is set up and then approximated by expanding it to first order in ~. We apply this method to two potentials, namely the quartic anharmonic oscillator and the symmetric double-well potential. Results obtained via the flow equations are then compared with those obtained from the WKB method.

A thesis submitted to the Faculty of Science University of the Witwatersrand Johannesburg in fulfillment of the requirements for the Master of Science Johannesburg 1997

A well-known long standing problem in combinatorics and statistical mechanics is to find the generating function for self-avoiding walks (SAW) on a two-dimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger, Mireille Bousquet-Mlou, Thomas Prellberg, Neal Madras, Gordon Slade, Agnes Dit- tel, E.J. Janse van Rensburg, Harry Kesten, Stuart G. Whittington, Lincoln Chayes, Iwan Jensen, Arthur T. Benjamin, and many others. More than three hundred papers and a few volumes of books were published in this area. A SAW is interesting for simulations because its properties cannot be calculated analytically. Calculating the number of self-avoiding walks is a common computational problem. A recently proposed model called prudent self-avoiding walks (PSAW) was first introduced to the mathematics community in an unpublished manuscript of Pra, who called them exterior walks. A prudent walk is a connected path on square lattice such that, at each step, the extension of that step along its current trajectory will never intersect any previously occupied vertex. A lattice path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. We will discuss some enumerative problems in self-avoiding walks, lattice paths and walks with several step vectors. Many open problems are posted. / by Shanzhen Gao. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

Nous montrons la validité du formalisme multifractal pour les mesures aléatoires faiblement Gibbs portées par l’ attracteur associé à une dynamique aléatoire C¹ codée par un sous-shift de type fini aléatoire, et expansive en moyenne. Nous établissons également des loi de type 0-∞ pour les mesures de Hausdorff et de packing généralisées des ensembles de niveau de la dimension locale, et calculons les dimensions de Hausdorff et de packing des ensembles de points en lesquels la dimension inférieure locale et la dimension supérieure locale sont prescrites. Lorsque l’attracteur est un ensemble de Cantor de mesure de Lebesgue nulle, nous montrons la validité du formalisme multifractal pour les mesures discrètes obtenues comme inverses de ces mesures faiblement Gibbs. / We establish the validity of the multifractal formalism for random weak Gibbs measures supported on the attractor associated with a C¹ random dynamics coded by a random subshift of finite type, and expanding in the mean. We also prove a 0-∞ law for the generalized Hausdorff and packing measures of the level sets of the local dimension, and we compute the Hausdorff and packing dimensions of the sets of points at which the lower and upper local dimensions are prescribed. In the case that the attractor is a Cantor set of zero Lebesgue measure, we prove the validity of the multifractal formalism for the discrete measures obtained as inverse of these weak Gibbs measures.

by Jones Chui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 62-[66]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Fundamentals of Artificial Neural Networks --- p.2 / Chapter 1.1.1 --- Processing Unit --- p.2 / Chapter 1.1.2 --- Topology --- p.3 / Chapter 1.1.3 --- Learning Rules --- p.4 / Chapter 1.2 --- Overview of Various Neural Network Models --- p.6 / Chapter 1.3 --- Introduction to the Radial Basis Function Networks (RBFs) --- p.8 / Chapter 1.3.1 --- Historical Development --- p.9 / Chapter 1.3.2 --- Some Intrinsic Problems --- p.9 / Chapter 1.4 --- Objective of the Thesis --- p.10 / Chapter 2 --- Low-dimensional Gaussian RBF networks (LowD RBFs) --- p.13 / Chapter 2.1 --- Architecture of LowD RBF Networks --- p.13 / Chapter 2.1.1 --- Network Structure --- p.13 / Chapter 2.1.2 --- Learning Rules --- p.17 / Chapter 2.2 --- Construction of LowD RBF Networks --- p.19 / Chapter 2.2.1 --- Growing Heuristic --- p.19 / Chapter 2.2.2 --- Pruning Heuristic --- p.27 / Chapter 2.2.3 --- Summary --- p.31 / Chapter 3 --- Application examples --- p.34 / Chapter 3.1 --- Chaotic Time Series Prediction --- p.35 / Chapter 3.1.1 --- Performance Comparison --- p.39 / Chapter 3.1.2 --- Sensitivity Analysis of MSE THRESHOLDS --- p.41 / Chapter 3.1.3 --- Effects of Increased Embedding Dimension --- p.41 / Chapter 3.1.4 --- Comparison with Tree-Structured Network --- p.46 / Chapter 3.1.5 --- Overfitting Problem --- p.46 / Chapter 3.2 --- Nonlinear prediction of speech signal --- p.49 / Chapter 3.2.1 --- Comparison with Linear Predictive Coding (LPC) --- p.54 / Chapter 3.2.2 --- Performance Test in Noisy Conditions --- p.55 / Chapter 3.2.3 --- Iterated Prediction of Speech --- p.59 / Chapter 4 --- Conclusion --- p.60 / Chapter 4.1 --- Discussions --- p.60 / Chapter 4.2 --- Limitations and Suggestions for Further Research --- p.61 / Bibliography --- p.62

Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 34.

Law Chi Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 86-91). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Contents --- p.v / List of Figures --- p.viii / List of Tables --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.4 / Chapter 1.2 --- Thesis Organization --- p.7 / Chapter 2 --- Literature Review --- p.9 / Chapter 2.1 --- Logical Time --- p.9 / Chapter 2.1.1 --- Event Model --- p.9 / Chapter 2.1.2 --- Lamport's Logical Clock --- p.10 / Chapter 2.1.3 --- Mattern's Vector Time --- p.14 / Chapter 2.2 --- Snapshot Algorithms --- p.18 / Chapter 2.2.1 --- Preliminaries --- p.19 / Chapter 2.2.2 --- Chandy-Lamport --- p.22 / Chapter 2.2.3 --- Lai-Yang and Mattern --- p.24 / Chapter 2.2.4 --- Sato --- p.25 / Chapter 3 --- Ad-hoc Network System --- p.29 / Chapter 3.1 --- Event Model --- p.30 / Chapter 3.2 --- Snapshot Problem --- p.32 / Chapter 4 --- Time Approximation in Distributed Systems --- p.37 / Chapter 4.1 --- Definitions --- p.38 / Chapter 4.1.1 --- Preliminary --- p.38 / Chapter 4.1.2 --- Event Ordering --- p.39 / Chapter 4.1.3 --- Clock --- p.40 / Chapter 4.1.4 --- Time Approximation Levels --- p.41 / Chapter 4.1.5 --- Offline Algorithm --- p.41 / Chapter 4.2 --- Time Approximation in Static Network Systems --- p.42 / Chapter 4.2.1 --- Stable Snapshot --- p.43 / Chapter 4.2.2 --- Snapshot --- p.50 / Chapter 4.2.3 --- Latest Snapshot --- p.52 / Chapter 4.2.4 --- Time Approximation Levels --- p.54 / Chapter 4.3 --- Time Approximation in Ad-hoc Network Systems --- p.54 / Chapter 4.3.1 --- Snapshot --- p.56 / Chapter 4.3.2 --- Latest Snapshot --- p.61 / Chapter 4.3.3 --- Time Approximation Levels --- p.61 / Chapter 4.3.4 --- Bi-vector Clock --- p.63 / Chapter 4.3.5 --- Strong Snapshot Problem --- p.67 / Chapter 5 --- Snapshot Algorithm for Ad-hoc Network Systems --- p.69 / Chapter 5.1 --- Algorithm --- p.70 / Chapter 5.1.1 --- Notations --- p.70 / Chapter 5.1.2 --- Rules of Maintaining Si and Ti in Pi --- p.72 / Chapter 5.1.3 --- The Properties --- p.73 / Chapter 5.1.4 --- Algorithm --- p.78 / Chapter 5.2 --- Enhancements --- p.82 / Chapter 5.2.1 --- Reduction of Stored States and Exchanged Logs --- p.82 / Chapter 5.2.2 --- LCC Synchronization --- p.82 / Chapter 6 --- Conclusion --- p.84 / Bibliography --- p.86 / Publications --- p.91

Tao Suyi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 51-53). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.2 / Chapter 1.1.1 --- Mobile Phone Applications --- p.3 / Chapter 1.1.2 --- Location Methods --- p.4 / Chapter 1.1.3 --- Location Algorithms --- p.9 / Chapter 1.2 --- AoA Localization --- p.10 / Chapter 1.3 --- The NLOS Problem --- p.11 / Chapter 2 --- AoA Localization --- p.13 / Chapter 2.1 --- Conventional Approach to AoA Localization --- p.14 / Chapter 2.2 --- Least Squares Approach to AoA Localization --- p.16 / Chapter 2.2.1 --- Ordinary Least Squares Approach (OLS) by Pages-Zamora --- p.16 / Chapter 2.2.2 --- The Weighted Least Squares Approach (WLS) --- p.18 / Chapter 2.3 --- Approximate Maximum Likelihood Method (AML) for AoA Localization --- p.19 / Chapter 2.4 --- Simulations --- p.21 / Chapter 3 --- Analysis and Mitigation of NLoS Effects --- p.26 / Chapter 3.1 --- The Non-Line-of-Sight (NLoS) Effects --- p.26 / Chapter 3.2 --- NLoS Mitigation in AoA Localization --- p.27 / Chapter 3.2.1 --- A Selective Model to Suppress NLOS Errors --- p.27 / Chapter 3.2.2 --- Dimension Determination and LOS Identification --- p.29 / Chapter 3.3 --- Simulations --- p.34 / Chapter 3.3.1 --- Experiment 1 --- p.34 / Chapter 3.3.2 --- Experiment 2 --- p.38 / Chapter 4 --- Conclusions and Suggestions for Future Work --- p.42 / Chapter 4.1 --- Conclusions --- p.42 / Chapter 4.2 --- Suggestions for future work --- p.44 / Chapter A --- Derivation of the Cramer Rao Lower Bound (CRLB) for AoA Localization --- p.45 / Chapter A.1 --- CRLB for all LoS --- p.45 / Chapter A.2 --- CRLB for both LoS and NLoS --- p.46 / Chapter B --- Derivation of the Error Covariance for OLS and WLS Estima- tors --- p.48 / Chapter B.1 --- Error Covariance for OLS Estimator --- p.49 / Chapter B.2 --- Error Covariance for WLS Estimator --- p.50 / Bibliography --- p.51

Ng Kin Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 186-189). / Ng Kin Man. / Contents --- p.i / List of Figures --- p.ii / Abstract --- p.iv / Acknowledgement --- p.v / 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.6 / Chapter 2.1 --- Formulation of the Problem --- p.6 / Chapter 2.1.1 --- Quantization of the Electromagnetic Field --- p.7 / Chapter 2.1.2 --- Quantization of the Matter Field --- p.11 / Chapter 2.1.3 --- The Interaction between the Radiation and the Matter --- p.12 / Chapter 2.1.4 --- Formulation of the one-photon JCM --- p.14 / Chapter 2.2 --- Eenergy eigenstates and Eigenvalue Spectrum --- p.16 / Chapter 2.3 --- Dynamics of the one-photon JCM --- p.18 / Chapter 2.3.1 --- The time evolution of the system --- p.19 / Chapter 2.3.2 --- Atomic Observables --- p.20 / Chapter 2.3.3 --- Field Observables --- p.23 / Chapter 2.4 --- Asymptotic solution of the JCM --- p.27 / Chapter 2.5 --- Discussion of the role of the RWA in the JCM --- p.29 / Chapter 2.6 --- Conclusion --- p.30 / Chapter Chapter 3. --- Numerical Results for the one-photon JCM --- p.40 / Chapter 3.1 --- Eigenstates and Eigenvalue Spectrum --- p.40 / Chapter 3.2 --- Dynamics of the System --- p.44 / Chapter 3.2.1 --- Atomic Observables --- p.44 / Chapter 3.2.2 --- Field Observables --- p.45 / Chapter 3.3 --- Conclusion --- p.47 / Chapter Chapter 4. --- Generalization of the JCM --- p.60 / Chapter 4.1 --- Multiphoton JCM --- p.60 / Chapter 4.2 --- Intensity-dependent JCM --- p.62 / Chapter 4.3 --- Two-mode two-photon JCM --- p.64 / Chapter 4.4 --- Conclusion --- p.66 / Chapter Chapter 5. --- Multiphoton Jaynes-Cummings model --- p.67 / Chapter 5.1 --- Energy Eigenstates and Eigenvalue Spectrum --- p.67 / Chapter 5.1.1 --- Energy Eigenstates and Eigenvalue Spectrum of the two- photon JCM --- p.71 / Chapter 5.1.2 --- Eigenstates and Eigenvalue Spectrum for the k-photon JCM with k>2 --- p.73 / Chapter 5.2 --- Dynamics of the two-photon JCM --- p.75 / Chapter 5.2.1 --- Atomic Observables --- p.75 / Chapter 5.2.2 --- Field Observables --- p.77 / Chapter 5.3 --- Conclusion --- p.84 / Chapter Chapter 6. --- Intensity-dependent Jaynes-Cummings model --- p.107 / Chapter 6.1 --- Eigenstates and Eigenvalue Spectrum --- p.107 / Chapter 6.1.1 --- Energy Eigenstates and Eigenvalue Spectrum of the one- photon intensity-dependent JCM --- p.110 / Chapter 6.1.2 --- "Energy Eigenstates and Eigenvalue Spectrum for the k-photon intensity-dependent, JCM with k > 1" --- p.113 / Chapter 6.2 --- Dynamics of the one-photon intensity-dependent JCM --- p.115 / Chapter 6.2.1 --- Atomic Observables --- p.115 / Chapter 6.2.2 --- Field Observables --- p.116 / Chapter 6.3 --- Conclusion --- p.123 / Chapter Chapter 7. --- Two-mode Two-photon Jaynes- Cummings model --- p.148 / Chapter 7.1 --- Eigenstates and Eigenvalue Spectrum --- p.148 / Chapter 7.2 --- Dynamics of the System --- p.156 / Chapter 7.2.1 --- Atomic Observables --- p.156 / Chapter 7.2.2 --- Field Observables --- p.160 / Chapter 7.3 --- Conclusion --- p.161 / Chapter Chapter 8. --- Conclusion --- p.183 / Bibliography --- p.186

Analytical performance analysis on Direction-Of-Arrival (DOA) estimation algorithms has attracted much excellent research in recent years, various statistical properties have been revealed. However, in most of these analyses, insights of the performance were masked because of the involvement of singular values and singular vectors which depend on the character of the algorithms and data structures in a complex and nonlinear manner.