by Lee Kim-hung. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 60.

Wong, Ting Kam Leonard. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 91-97) and index. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Problems of fractal analysis --- p.6 / Chapter 1.2 --- The boundary theory approach --- p.7 / Chapter 1.3 --- Summary of the thesis --- p.9 / Chapter 2 --- Martin boundary --- p.13 / Chapter 2.1 --- Markov chains and discrete potential theory --- p.13 / Chapter 2.2 --- Martin compactification --- p.18 / Chapter 2.3 --- Convergence to boundary and integral representations --- p.20 / Chapter 2.4 --- Dirichlet problem at infinity --- p.25 / Chapter 3 --- Hyperbolic boundary --- p.27 / Chapter 3.1 --- Random walks on infinite graphs --- p.27 / Chapter 3.2 --- Hyperbolic compactification --- p.31 / Chapter 3.3 --- Ancona's theorem --- p.33 / Chapter 3.4 --- Self-similar sets as hyperbolic boundaries --- p.34 / Chapter 3.5 --- Hyperbolic compactification of augmented rooted trees --- p.44 / Chapter 4 --- Simple random walk on Sierpinski graphs --- p.47 / Chapter 4.1 --- Hcuristic argument for d = 1 --- p.48 / Chapter 4.2 --- Symmetries and group invariance --- p.51 / Chapter 4.3 --- Reflection principle --- p.54 / Chapter 4.4 --- Self-similar identity and hitting distribution --- p.60 / Chapter 4.5 --- Remarks and Open Questions --- p.64 / Chapter 5 --- Induced Dirichlet forms on self-similar sets --- p.66 / Chapter 5.1 --- Basics of Dirichlet forms --- p.67 / Chapter 5.2 --- Motivation: the classical Douglas integral --- p.68 / Chapter 5.3 --- Graph energy and the induced forms --- p.69 / Chapter 5.4 --- Induced Dirichlet forms on self-similar sets --- p.74 / Chapter 5.5 --- A uniform tail estimate via coupling --- p.83 / Chapter 5.6 --- Remarks and open questions --- p.89 / Index of selected terms --- p.98

Tsang, Chi Shing Sidney. / "October 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 58-59). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- The main results --- p.6 / Chapter 1.2 --- Structure of the thesis --- p.8 / Chapter 2 --- The Upper Lyapunov Exponent --- p.10 / Chapter 2.1 --- Notation --- p.10 / Chapter 2.2 --- The upper Lyapunov exponent --- p.11 / Chapter 2.3 --- Cocycles --- p.12 / Chapter 2.4 --- The Theorem of Furstenberg and Kesten --- p.14 / Chapter 3 --- Contraction Properties --- p.19 / Chapter 3.1 --- Two basic lemmas --- p.20 / Chapter 3.2 --- Contracting sets --- p.25 / Chapter 3.3 --- Strong irreducibility --- p.29 / Chapter 3.4 --- A key property --- p.30 / Chapter 3.5 --- Contracting action on P(Rd) and converges in direction --- p.36 / Chapter 3.6 --- Lyapunov exponents --- p.39 / Chapter 3.7 --- Comparison of the top Lyapunov exponents and Fursten- berg's theorem --- p.43 / Chapter 4 --- Analytic Dependence of Lyapunov Exponents on The Probabilities --- p.48 / Chapter 4.1 --- Continuity and analyticity properties for i.i.d. products --- p.49 / Chapter 4.2 --- The proof of the main result --- p.50 / Chapter 5 --- The Expression of The Upper Lyapunov Exponent in Complex Functions --- p.54 / Chapter 5.1 --- The set-up --- p.54 / Chapter 5.2 --- The main result --- p.56 / Bibliography --- p.58

Cette thèse traite des problèmes associés à la théorie de grossissement de filtration. Elle est divisée en deux parties.La première partie est consacrée aux temps aléatoires. On étudie les propriétés des différentes classes de temps aléatoires du point de vue du grossissement de la filtration.La deuxième partie concerne l'étude de la stabilité de condition d'arbitrage sur le grossissement de la filtration. On se concentre sur la condition no unbounded profit with bounded risk. Dans un premier temps, on étudie l'absence d'arbitrage dans le cas de grossissement progressif avec un temps aléatoire. Puis on regarde le grossissement initial avec une variable aléatoire qui vérifie l'hypothèse de Jacod. / This thesis treats the problems settled in elargement of filtration theory. It consists of two parts.The first part is devoted to random times. We study the properties of different classes of random times from enlargement of filtration point of view.The second part concerns the study of the stability of the non-arbitrage condition under anlargement of filtration. We are mainly interested in no bounded profit with bounded risk condition. We study absence of arbitrage in the case progressive enlargement up to random time. Then we look at the case of initial enlargement with random variable satisfying Jacod's hypothesis.

Randomised algorithms are an effective method of attacking computationally intractable problems. A simple and fast randomised algorithm may produce results to an accuracy sufficient for many purposes, especially in the average case. In this thesis we consider average case analyses of heuristics for certain NP-hard graph optimisation problems. In particular, we consider algorithms that find dominating sets of random regular directed graphs. As well as providing an average case analysis, our results also determine new upper bounds on domination numbers of random regular directed graphs. The algorithms for random regular directed graphs considered in this thesis are known as prioritised algorithms. Each prioritised algorithm determines a discrete random process. This discrete process may be continuously approximated using differential equations. Under certain conditions, the solutions to these differential equations describe the behaviour of the prioritised algorithm. Applying such an analysis to prioritised algorithms directly is difficult. However, we are able to use prioritised algorithms to define new algorithms, called deprioritised algorithms, that can be analysed in this fashion. Defining a deprioritised algorithm based on a given prioritised algorithm, and then analysing the deprioritised algorithm, is called the deprioritised approach. The initial theory describing the deprioritised approach was developed by Wormald and has been successfully applied in many cases. However not all algorithms are covered by Wormald??s theory: for example, algorithms for random regular directed graphs. The main contribution of this thesis is the extension of the deprioritised approach to a larger class of prioritised algorithms. We demonstrate the new theory by applying it to two algorithms which find dominating sets of random regular directed graphs.

Thesis (Ph.D)--Stanford University, 1999. / Title from pdf t.p. (viewed April 3, 2002). "August 1999." "Adminitrivia V1/Prg/20000907"--Metadata.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2005. / Includes bibliographical references (p. 82-85).

In manufacturing, measurement systems are used to control processes and inspect parts with the goal of producing high quality product for the customer. Modern Quality Systems require the periodic assessment of key measurement systems to ensure that they are functioning as expected. Estimating the proportion of the process variation due to the measurement system is an important part of these assessments. The measurement system may be simple, for example, with one gauge automatically measuring a single characteristic on every part or complex with multiple characteristics, gauges, operators etc. Traditional assessment plans involve selecting a random sample of parts and then repeatedly measuring each part under a variety of conditions that depend on the complexity of the measurement system. In this thesis, we propose new plans for assessing the measurement system variation based on the concept of leveraging. In a leveraged plan, we select parts (non-randomly) with extreme initial values to measure repeatedly. Depending on the context, parts with initial measurements may be available from regular production or from a specially conducted baseline study. We use the term leveraging because of the re-use of parts with extreme values. The term leverage has been used by the  proponents of the problem solving system initially proposed by Dorian  Shainin. Parts with relatively large and small values of the response  are compared to identify the major causes of the variation. There is no discussion of the theory of leveraging in the literature or its application to measurement system  assessment. In this thesis, we provide motivation for why leveraging  is valuable and apply it to measurement system  assessments. We consider three common contexts in the thesis: Simple measurement systems with one gauge, no operator effects and no external information about the process performance; Measurement systems, as stated above, where we have external information, as would be the case, for example, if the measurement system was used for 100% inspection; Measurement systems with multiple operators. For each of these contexts, we develop new leveraged assessment plans and show that these plans are substantially more efficient than traditional plans in estimating the proportion of the process variation due to the measurement system. In each case, we also provide methodology for planning the leveraged study and for analysing the data generated. We then develop another new application of leveraging in the assessment of a measurement system used for 100% inspection. A common practice is to re-measure all parts with a first  measurement outside of inspection limits. We propose using these repeated measurements to assess the variation in the measurement system. Here the system itself does the leveraging since we have repeated measurements only on relatively large or small parts. We recommend using maximum likelihood estimation but we show that the ANOVA estimator, although  biased, is comparable to the MLE when the measurement system is reliable.  We also provide guidelines on how to schedule such assessments. To outline the thesis, in the first two chapters, we review the contexts described above. For each context, we discuss how to characterize the measurement system performance, the common assessment plans and their analysis. In Chapter 3, we introduce the concept of leveraging and provide motivation for why it is effective. Chapters 4 to 7 contain the bulk of the new results in the thesis. In Chapters 4, 5 and 6, which correspond to the three contexts described above, we provide new leveraged plans, show their superiority to the standard plans and provide a methodology to help design leveraged plans. In Chapter 7, we show how to assess an inspection system using repeated measurements on initially rejected parts. In the final chapter, we discuss other potential applications of leveraging to other measurement system assessment problems and to a problem in genetics.

The aim of the thesis is to study ordering in binary alloys on the basis of first-principles or {\it ab-initio} techniques employing density functional theory (DFT). The ordering phenomena of materials are of crucial importance for technological applications. The results of the thesis are intended to demonstrate the applicability of the first-principles calculations to provide fundamental insight to the true, namely electronic structure, nature of ordering in binary alloys. The main part of the thesis focuses on atomic short- and long-range order phenomena in binary alloys as a function of both temperature and chemical composition in FeCo and NiCr alloys. In particular, the influence of magnetism on atomic ordering in FeCo alloys is investigated using the disordered local moment.A large number of concentration dependent effective cluster interactions, derived without the use of any adjustable parameters, are obtained by the SGPM as it is implemented in the EMTO within the CPA. The SGPM interactions can subsequently be used in thermodynamic Monte-Carlo simulations or mean field approximations to determine the ordering phenomena in binary alloys. First-principles calculations of intrinsic stacking-fault energies (SFE) andanti-phase boundary energies (APBE) in Al$_{3}$Sc and the effects of temperature on SFE and APBE are investigated by using the axial Ising model and supercellapproach. Temperature effects have been taken into consideration byincluding the one-electron thermal excitations in the electronicstructure calculations, and vibrational free energy in the harmonicapproximation as well as by using temperature dependent lattice constants.The latter has been determined within the Debye-Gr{\"u}neisen model,which reproduces well the experimental data. Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties of B2- FeCo alloy are studied using first-principles calculations. The calculated thermal and elastic properties are found to be in good agreement withthe available measured values when the generalized gradientapproximations is used for the exchange correlation potential.The calculated finite temperature elastic constants show thatthe FeCo alloy is mechanically stable in the ordered phase.Meanwhile, a large elastic anisotropy exhibits a moderate dependence ontemperature. / <p>QC 20130927</p>