Rate 1/2 systematic recursive convolutional codes over integer rings modulo-q are investigated for their performance. The investigation examines the performance in severe fading and additive white Gaussian noise for codes with various constraint lengths. The arithmetic for the codes is modulo-q. where the value of q is within the range of 2 to 16. An exhaustive search is carried out for codes with short constraint lengths. A reduced search is developed for larger constraint lengths which restricts the tap polynomials to irreducible polynomials over Zq. The irreducible polynomials are generated and the ones not found in the literature are presented in tables. The search algorithms are outlined and the results for the codes are tabulated. The performance of selected codes are verified by Monte-Carlo simulation techniques. Several codes have better performance than comparable codes presented in the literature for the Rayleigh fading channel. In sme of cases, the codes found have better performance on the AWGN channel than the best known ring codes. The characteristics of rotationally invariant (RI) ring codes presented in the literature are used in an exhaustive search for codes over Zq which are invariant to phase shifts of 2[pi]/q. Tables of RI codes optimized for the Rayleigh fading channel are presented along with codes which are optimized for the AWGN channel. / Graduate

A dissertation submitted to the University of the Witwatersrand in ful lment of the requirements for candidacy for the degree of Master of Science. Johannesburg, 2016 / Restricted Schur polynomials can be used to describe large N, non-planar limits of N = 4 super Yang-Mills theory. The R-symmetry generators commute with the dilatation operator. For small deformations of 1 2-BPS operators, the matrix elements of these generators have been computed and a set of recursion relations for the matrix elements of the dilatation operator are obtained from this commutation relation. Together with the knowledge that the smallest eigenvalues of the dilatation operator (corresponding to BPS operators) vanish, these recursion relations can be used to determine the matrix elements of the dilatation operator. Studies up to now have computed the matrix elements of the su(2) generators in the displaced corners approximation. Our first novel result is the computation of the exact su(2) generators. We obtain the matrix elements for the su(3) generators in the displaced corners approximation and exactly, for the first time. This is the first step to computing exact matrix elements of the dilatation operator. / TG2016

by Song Li-Min. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 175-178.

by Chunxuan Ye. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 74-[78]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Information Theory --- p.1 / Chapter 1.2 --- Source Coding --- p.2 / Chapter 1.3 --- Fixed Length Codes and Variable Length Codes --- p.4 / Chapter 1.4 --- Prefix Codes --- p.5 / Chapter 1.4.1 --- Kraft Inequality --- p.7 / Chapter 1.4.2 --- Huffman Coding --- p.9 / Chapter 2 --- Existence of Fix-Free Codes --- p.13 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.2 --- Previous Results --- p.14 / Chapter 2.2.1 --- Complete Fix-Free Codes --- p.14 / Chapter 2.2.2 --- Ahlswede's Results --- p.16 / Chapter 2.3 --- Two Properties of Fix-Free Codes --- p.17 / Chapter 2.4 --- A Sufficient Condition --- p.20 / Chapter 2.5 --- Other Sufficient Conditions --- p.33 / Chapter 2.6 --- A Necessary Condition --- p.37 / Chapter 2.7 --- A Necessary and Sufficient Condition --- p.42 / Chapter 3 --- Redundancy of Optimal Fix-Free Codes --- p.44 / Chapter 3.1 --- Introduction --- p.44 / Chapter 3.2 --- An Upper Bound in Terms of q --- p.46 / Chapter 3.3 --- An Upper Bound in Terms of p1 --- p.48 / Chapter 3.4 --- An Upper Bound in Terms of pn --- p.51 / Chapter 4 --- Two Applications of the Probabilistic Method --- p.54 / Chapter 4.1 --- An Alternative Proof for the Kraft Inequality --- p.54 / Chapter 4.2 --- A Characteristic Inequality for ´ب1´ة-ended Codes --- p.59 / Chapter 5 --- Summary and Future Work --- p.69 / Appendix --- p.71 / A Length Assignment for Upper Bounding the Redundancy of Fix-Free Codes --- p.71 / Bibliography --- p.74

Building sustainable customer relationships through effective service recovery is a worthwhile goal for all airline companies in an era of intense competition. Developing service recovery strategies that can strengthen customer loyalty in the event of service failure has become a major challenge for the airline business, but yet has received little attention from academics. To address the dearth in the literature, this study sets out to investigate how customers' perceptions of perceived justice of service recovery and those factors external to the recovery encounter, including service failure attributions and company reputation, impact their loyalty recovery in the airline context. This study uses a quantitative method based on a surrey approach. A selfadministered questionnaire was purposively distributed among airline customers at Suvarnabhumi International Airport in Bangkok, Thailand. The study was tested using data collected from 480 travellers who had previously experienced a full service airline's flight delay in the past 12 months and was analysed with Partial Least Squares Structural Equation Modeling (PLS-SEM). First, the results of this research confirm the robustness of the Expectation Disconfirmation Paradigm (EDP) for understanding customer perceived justice of service recovery in an exchange relationship context by emphasising significant positive effects of all dimensions of justice in restoring positive customer relationships. Second, the findings clarify the interrelationships between postrecovery customer trust, customer's overall company satisfaction and customer loyalty by highlighting the important role of which trust plays in recovering customer loyalty. Third, The results further demonstrate how customer perceived justice of service recovery is contingent upon service failure attributions and company reputation. Lastly, the research provides airline managers with useful guidelines on developing cost-effective service recovery strategies focusing on maximising customer loyalty in different service failure situations.

Chan Hoi-Yeung = 網絡與競爭系統的物理 : 個體為本模型中的網絡效應 / 陳凱揚. / Thesis submitted in: September 2005. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 191-197). / Text in English; abstracts in English and Chinese. / Chan Hoi-Yeung = Wang luo yu jing zheng xi tong de wu li : ge ti wei ben mo xing zhong de wang luo xiao ying / Chen Kaiyang. / Abstract --- p.i / Acknowledgments --- p.v / Contents --- p.vii / Chapter 1 --- Overview --- p.1 / Chapter I --- Networks --- p.3 / Chapter 2 --- Networks in nature --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Terminology of the networks studies --- p.6 / Chapter 2.2.1 --- Nodes --- p.6 / Chapter 2.2.2 --- Links --- p.6 / Chapter 2.2.3 --- Adjacency matrix --- p.9 / Chapter 2.2.4 --- Connectivity --- p.10 / Chapter 2.2.5 --- Clustering coefficient --- p.11 / Chapter 2.2.6 --- Shortest path --- p.11 / Chapter 2.2.7 --- Connectivity correlation --- p.12 / Chapter 2.3 --- Topology in the real-world networks --- p.13 / Chapter 2.3.1 --- The Internet --- p.13 / Chapter 2.3.2 --- The WWW --- p.15 / Chapter 2.3.3 --- Collaboration networks --- p.15 / Chapter 2.3.4 --- Food webs --- p.16 / Chapter 2.3.5 --- Power grids --- p.17 / Chapter 2.4 --- Discussion --- p.17 / Chapter 3 --- Review on Network Models --- p.19 / Chapter 3.1 --- Introduction --- p.19 / Chapter 3.2 --- Graph Theory --- p.20 / Chapter 3.2.1 --- Classical random graph --- p.20 / Chapter 3.3 --- Evolving networks --- p.23 / Chapter 3.3.1 --- Random growing network --- p.23 / Chapter 3.3.2 --- Fitness growing network --- p.25 / Chapter 3.3.3 --- Barabasi-Albert model --- p.27 / Chapter 3.3.4 --- Fitness model --- p.31 / Chapter 3.4 --- Lattice --- p.33 / Chapter 3.4.1 --- Regular hypercubic lattices (Periodic) --- p.33 / Chapter 3.4.2 --- Regular hypercubic lattices (Free boundary conditions) . --- p.35 / Chapter 3.5 --- Discussion --- p.35 / Chapter 4 --- Network Properties --- p.38 / Chapter 4.1 --- More derivations on existing models --- p.38 / Chapter 4.1.1 --- Classical random graphs --- p.38 / Chapter 4.1.2 --- Barabasi-Albert model --- p.40 / Chapter 4.1.3 --- Fitness Model --- p.42 / Chapter 4.1.4 --- Regular hypercubic lattices (Periodic) --- p.45 / Chapter 4.2 --- New model --- p.48 / Chapter 4.2.1 --- Fitness-BA hybrid model --- p.48 / Chapter 4.3 --- Link removal --- p.55 / Chapter 4.3.1 --- Introduction --- p.55 / Chapter 4.3.2 --- Formalism in connectivity --- p.55 / Chapter 4.3.3 --- Pruned BA Model --- p.56 / Chapter 4.4 --- Link addition --- p.58 / Chapter 4.4.1 --- Introduction --- p.58 / Chapter 4.4.2 --- Regular hypercubic lattices (Periodic) --- p.58 / Chapter 4.5 --- Discussion --- p.60 / Chapter II --- Games --- p.62 / Chapter 5 --- Review on Agent-based models of competing population --- p.63 / Chapter 5.1 --- Introduction --- p.63 / Chapter 5.2 --- The El Farol Bar attendance problem --- p.65 / Chapter 5.2.1 --- Model --- p.65 / Chapter 5.2.2 --- Strategies --- p.66 / Chapter 5.2.3 --- Discussion --- p.66 / Chapter 5.3 --- Minority game --- p.67 / Chapter 5.3.1 --- Model --- p.67 / Chapter 5.3.2 --- Strategies --- p.68 / Chapter 5.3.3 --- Attendance --- p.69 / Chapter 5.3.4 --- History and quasi-Eulerian state --- p.69 / Chapter 5.3.5 --- Success rate and Hamming distance --- p.71 / Chapter 5.3.6 --- Volatility --- p.73 / Chapter 5.3.7 --- Crowd-anticrowd theory --- p.75 / Chapter 5.3.8 --- Discussion --- p.76 / Chapter 6 --- B-A-R model : Dynamics --- p.78 / Chapter 6.1 --- Model --- p.78 / Chapter 6.2 --- Results: Plateaux and periodicity --- p.81 / Chapter 6.3 --- A microscopic view: Agents' decisions and strategy performance --- p.86 / Chapter 6.4 --- A macroscopic view: Bit-string patterns --- p.92 / Chapter 6.4.1 --- The history space --- p.92 / Chapter 6.4.2 --- Bit-string statistics of different states --- p.94 / Chapter 6.5 --- The (max = 1 states --- p.97 / Chapter 6.5.1 --- Values of wm3iX --- p.97 / Chapter 6.5.2 --- "Strategy ranking evolvement: ni, (w)" --- p.101 / Chapter 6.5.3 --- Substates . --- p.105 / Chapter 7 --- B-A-R model : Formalism --- p.108 / Chapter 7.1 --- Resource level at transitions of Cmax = 0 state --- p.108 / Chapter 7.2 --- Resource levels at transitions of Cmax 二 1 states --- p.109 / Chapter 7.2.1 --- Method --- p.109 / Chapter 7.2.2 --- Lmin for upper substate --- p.110 / Chapter 7.2.3 --- Lmin for lower substate --- p.113 / Chapter 7.3 --- Discussion --- p.116 / Chapter 8 --- B-A-R model : Statistics --- p.121 / Chapter 8.1 --- Problem --- p.121 / Chapter 8.2 --- Bit-string statistics --- p.122 / Chapter 8.2.1 --- Allowed transitions --- p.122 / Chapter 8.2.2 --- Grouping the history space --- p.122 / Chapter 8.2.3 --- "Grouping the states, Cmax" --- p.127 / Chapter 8.2.4 --- "Labelling each state, /(C)" --- p.129 / Chapter 8.3 --- Discussion --- p.130 / Chapter III --- Networked games --- p.131 / Chapter 9 --- Networked minority game --- p.132 / Chapter 9.1 --- Model --- p.132 / Chapter 9.2 --- Preliminary results: Agents' success rates --- p.133 / Chapter 9.3 --- Ranking the strategies --- p.135 / Chapter 9.3.1 --- Ranking pattern --- p.136 / Chapter 9.3.2 --- Fraction of strategies in each rank --- p.140 / Chapter 9.4 --- Number of agents using a best strategy belonging to rank r --- p.141 / Chapter 9.4.1 --- Unconnected population --- p.141 / Chapter 9.4.2 --- Networked population . --- p.142 / Chapter 9.5 --- Application: Mean success rate --- p.143 / Chapter 9.6 --- Mean success rate of agents with degree k --- p.147 / Chapter 9.7 --- Application in other networks --- p.149 / Chapter 9.8 --- Discussion --- p.151 / Chapter 10 --- Interacting agents: Networked B-A-R model --- p.154 / Chapter 10.1 --- Model --- p.154 / Chapter 10.2 --- The quasi-Eulerian state (wmax = 1/2 state) --- p.155 / Chapter 10.3 --- The emergent states --- p.159 / Chapter 10.3.1 --- General results --- p.159 / Chapter 10.3.2 --- The Cmax = 0 state --- p.160 / Chapter 10.3.3 --- The Cmax = 1 state --- p.161 / Chapter 10.4 --- Discussion --- p.162 / Chapter IV --- Conclusion --- p.164 / Chapter 11 --- Conclusion --- p.165 / Chapter V --- Appendices --- p.172 / Chapter A --- List of symbols --- p.173 / Chapter A.1 --- Networks --- p.173 / Chapter A.2 --- Games --- p.174 / Chapter A.3 --- Networked games --- p.176 / Chapter B --- Distance distribution in classical random graphs --- p.177 / Chapter B.1 --- Method --- p.177 / Chapter B.2 --- Distance distribution --- p.177 / Chapter B.3 --- Behaviour at small L --- p.178 / Chapter B.4 --- Behaviour at large L --- p.179 / Chapter C --- Co-ordination number in infinite hypercubic lattice --- p.181 / Chapter C.1 --- Method --- p.181 / Chapter C.1.1 --- ID lattice --- p.181 / Chapter C.1.2 --- 2D square lattice --- p.182 / Chapter C.1.3 --- Higher dimension hypercubic lattices --- p.183 / Chapter C.2 --- Coefficients --- p.185 / Chapter D --- Connectivity distribution in fitness-BA hybrid model --- p.187 / Chapter D.1 --- Mean field approach --- p.187 / Chapter D.2 --- Connectivity distribution --- p.188 / Chapter D.3 --- Power-law exponent --- p.190 / Bibliography --- p.191

Mathematical concepts have aided the progression of many different fields of study. Math is not only helpful in science and engineering, but also in the humanities and social sciences. Therefore, it seemed quite natural to apply my preliminary work with set intersections to voting theory, and that application has helped to focus my thesis. Rather than studying set intersections in general, I am attempting to study set intersections and what they mean in a voting situation. This can lead to better ways to model preferences and to predict which campaign platforms will be most popular. Because I feel that allowing people to only vote for one candidate results in a loss of too much information, I consider approval voting, where people can vote for as many platforms as they like.

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Quantum game theory is an exciting new topic that combines the physical behaviour of information in quantum mechanical systems with game theory, the mathematical description of conflict and competition situations, to shed new light on the fields of quantum control and quantum information. This thesis presents quantizations of some classic game-theoretic problems, new results in existing quantization schemes for two player, two strategy non-zero sum games, and in quantum versions of Parrondo's games, where the combination of two losing games can result in a winning game. In addition, quantum cellular automata and quantum walks are discussed, with a history-dependent quantum walk being presented. / Thesis (Ph.D.)--School of Electrical and Electronic Engineering , 2005.

This study deals specifically with classical cubic splines. Based on a lemma of John Rice, best approximation in the uniform norm by cubic splines is explored. The purpose of this study is to characterize the best approximation to a given continuous function f(x) by a cubic spline with fixed knots by counting alternating extreme points of its error function E(t). / Graduation date: 1991