Xie Chunjing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 65-71). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Stability of Shock Waves in Viscous Conservation Laws --- p.10 / Chapter 1.1 --- Cauchy Problem for Scalar Viscous Conservation Laws and Viscous Shock Profiles --- p.10 / Chapter 1.2 --- Stability of Shock Waves by Energy Method --- p.15 / Chapter 1.3 --- Nonlinear Stability of Shock Waves by Spectrum Anal- ysis --- p.20 / Chapter 1.4 --- L1 Stability of Shock Waves in Scalar Viscous Con- servation Laws --- p.26 / Chapter 2 --- Propagation of a Viscous Shock in Bounded Domain and Half Space --- p.35 / Chapter 2.1 --- Slow Motion of a Viscous Shock in Bounded Domain --- p.36 / Chapter 2.1.1 --- Steady Problem and Projection Method --- p.36 / Chapter 2.1.2 --- Projection Method for Time-Dependent Prob- lem --- p.40 / Chapter 2.1.3 --- Super-Sensitivity of Boundary Conditions --- p.43 / Chapter 2.1.4 --- WKB Transformation Method --- p.45 / Chapter 2.2 --- Propagation of a Stationary Shock in Half Space --- p.50 / Chapter 2.2.1 --- Asymptotic Analysis --- p.50 / Chapter 2.2.2 --- Pointwise Estimate --- p.51 / Chapter 3 --- Nonlinear Stability of Viscous Transonic Flow Through a Nozzle --- p.58 / Chapter 3.1 --- Matched Asymptotic Analysis --- p.58 / Bibliography --- p.65

行为学、社会学、心理学和医药学方面，结构方程模型(SEMs) 是研究有关潜在变量最常用的模型。这篇论文的目的是研究基本和高级结构方程模型的贝叶斯诊断，本文研究的结构方程模型包括非线性纺构方程模型、变换结构方程模型、二层结构方程模型和混合结构方程模型。基于对数贝叶斯因子的一阶与二阶局部影响测度是本文进行贝贝叶斯诊断的基础。局部影响测度的计算和模型参数估计是利用了蒙特卡洛(MCMC) 和扩展数据的方法。对比传统的基于极大似然的诊断，本文提出的贝叶斯诊断方法不仅能检测异常点或者影响点，而且可以诊断模型假设和先验设定的敏感性。 这些是通过对数据、模型假设和先验设定进行不同的扰动获得的 本文用大量的模拟实验来说明所提出的贝叶斯诊断方法的作用。 本文基于不同类型的结构方程模型，应用所提出的贝叶斯诊断方法于一些实际数据。 / In the behavioral, social, psychological, and medical sciences, the most widely used models in assessing latent variables are structural equation models (SEMs). This thesis aims to develop Bayesian diagnostic procedures for basic and advanced SEMs such as nonlinear SEMs, transformation SEMs, two-level SEMs, and mixture SEMs. The first- and second-order local inference measures with the objective functions defined based on the logarithm of Bayes factor are proposed to perform the Bayesian diagnostics. Markov chain Monte Carlo (MCMC) methods, along with data augmentation, are developed to compute the local influence measures and to estimate unknown model parameters. Compared with conventional maximum likelihood-based diagnostic procedures, the proposed Bayesian diagnostic approach can not only detect outliers or influential points in the observed data, but also conduct model comparison and sensitivity analysis by perturbing the data, sampling distributions, and the prior distributions of model parameters via a variety of perturbations. The empirical performances of the proposed Bayesian diagnostic procedures are revealed through extensive simulation studies. Several real-life data sets are used to illustrate the application of our proposed methodology in the context of different SEMs. / Detailed summary in vernacular field only. / Chen, Ji. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 130-135). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Structural equation models --- p.1 / Chapter 1.2 --- Bayesian diagnostics --- p.3 / Chapter 1.2.1 --- The first and second order local influence measures --- p.5 / Chapter 1.2.2 --- A simple example --- p.9 / Chapter 2 --- Bayesian diagnostics of nonlinear SEMs --- p.15 / Chapter 2.1 --- Model description --- p.16 / Chapter 2.2 --- Bayesian estimation and local inference of nonlinear SEMs --- p.17 / Chapter 2.3 --- Simulation study --- p.24 / Chapter 2.3.1 --- Simulation study 1 --- p.24 / Chapter 2.3.2 --- Simulation study 2 --- p.25 / Chapter 2.3.3 --- Simulation study 3 --- p.27 / Chapter 2.4 --- Application: A study of kidney disease for type 2 diabetic patients --- p.29 / Chapter 3 --- Bayesian diagnostics of transformation SEMs --- p.40 / Chapter 3.1 --- Model description --- p.41 / Chapter 3.2 --- Bayesian estimation and local inference of the transformation SEMs --- p.44 / Chapter 3.3 --- Simulation study --- p.54 / Chapter 3.3.1 --- Simulation study 1 --- p.54 / Chapter 3.3.2 --- Simulation study 2 --- p.56 / Chapter 3.4 --- Application: A study on the risk factors of osteoporotic fracture in older people --- p.58 / Chapter 4 --- Bayesian diagnostics of two-level SEMs --- p.73 / Chapter 4.1 --- Model description --- p.74 / Chapter 4.2 --- Bayesian estimation and local inference of two-level SEMs --- p.75 / Chapter 4.3 --- Simulation study --- p.88 / Chapter 4.4 --- Application: A study of AIDS data --- p.91 / Chapter 5 --- Bayesian diagnostics of mixture SEMs --- p.106 / Chapter 5.1 --- Model description --- p.107 / Chapter 5.2 --- Bayesian estimation and local inference ofmixture SEMs --- p.108 / Chapter 5.3 --- Simulation study --- p.116 / Chapter 5.3.1 --- Simulation study 1 --- p.116 / Chapter 5.3.2 --- Simulation study 2 --- p.118 / Chapter 6 --- Conclusion --- p.126 / Bibliography --- p.130 / Chapter A --- Proof of Theorem 1.1 and 1.2 --- p.136 / Chapter B --- Full conditional distributions of the nonlinear SEM --- p.138 / Chapter C --- Full conditional distributions of the transformation SEM --- p.141 / Chapter D --- Full conditional distributions of the two-level SEM --- p.144 / Chapter E --- AIDS preventative intervention data --- p.150 / Chapter F --- Permutation sampler in the mixture SEM --- p.152 / Chapter G --- Full conditional distributions of the mixture SEM --- p.153

Bibliography: p.109-111. / Contract DA36-030-AMC-03200(E).

Steven I. Marcus, Sanjoy K. Mitter, Daniel Ocone. / Bibliography: p. 19-20. / Caption title. "October 2, 1978." / Supported in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-77-C-0101 Air Force Office of Scientific Research Contract AFOSR 77-3281 National Science Foundation Grant ENG 76-11106

Thesis (M.S.)--University of North Carolina at Wilmington, 2003. / Includes bibliographical references (leaf : 44).

Turing patterns have been studied for over 50 years as a pattern forming mechanism. To date the current focus has been on the reaction mechanism, with little to no emphasis on the diffusion terms. This work focuses on combining the simplest reaction mechanism possible and the use of nonlinear cross diffusion to form Turing patterns. We start by using two methods of bifurcation analysis to show that our model can form a Turing instability. A diffusion model (along with some variants) is then presented along with the results of numerical simulations. Various tests on both the numerical methods and the model are done to ensure the accuracy of the results. Finally an additional model that is closed to mass flow is introduced along with preliminary results. / vi, 55 leaves : ill. ; 29 cm.

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Classical mechanics provides a phase space representation of mechanical systems in terms of position and momentum state variables. The Hamiltonian system, a set of partial differential equations, defines a vector field in phase space and uniquely determines the evolutionary process of the system given its initial state.A closed form solution describing system trajectories in phase space is only possible if the system of differential equations defining the Hamiltonian is linear. For nonlinear cases approximate and qualitative methods are required.Generalized phase space methods do not confine state variables to position and momentum, allowing other observables to describe the system. Such a generalization adjusts the description of the system to the required information and provides a method for studying physical systems that are not strictly mechanical.This thesis presents and uses the methods of generalized phase space to compare linear to nonlinear systems.Ball State UniversityMuncie, IN 47306 / Department of Physics and Astronomy

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008. / Committee Chair: Uzer, Turgay; Committee Member: Aral, Mustafa; Committee Member: Flannery, Raymond; Committee Member: Raman, Chandra; Committee Member: Schatz, Michael.