No description available.

A Identificação de Sistemas é uma das técnicas utilizadas para se obter a representação matemática de um sistema. Diversos métodos podem ser aplicados para se obter um modelo matemático através da identificação de sistemas, entre eles o método de identificação assintótico, também chamado de ASYM (Zhu, 1998). Este trabalho propõe aplicar o método de identificação assintótico em sistemas SISO para a obtenção de modelo de sistemas ditos caixa-preta e avaliar o seu desempenho buscando também o melhor detalhamento do método. Os modelos obtidos foram avaliados de acordo com sua nota calculada através do método ASYM, através da comparação do índice de ajuste fit para autovalidação e validação cruzada e pela variância dos parâmetros dos modelos. O método ASYM é exaustivamente testado para sua avaliação. Entre os testes realizados neste trabalho destacam-se dois experimentos tipo Monte-Carlo com mais de quinhentas identificações e a aplicação do método em uma planta real. Os testes comprovaram a viabilidade da aplicação do método assintótico na identificação de sistemas SISO do tipo caixa-preta com excelente desempenho para estruturas ARMAX. / System Identification is one of the techniques used to obtain the mathematical representation of a system. Several methods can be applied to obtain a mathematical model by the system identification, including the asymptotic method, also called ASYM (Zhu, 1998). This work proposes to apply the ASYM method for SISO systems identification, then obtain models of black-box systems called \"black box\" and evaluate its performance and show details of the method. The models obtained were evaluated according to their grade calculated using the ASYM method, by comparing the fit adjustment index, self-validation and cross validation and the variance of model parameters. The asymptotic method has been extensively tested to be evaluated. Among the tests in this work, two stand out such Monte Carlo experiments with more than five hundred identifications and a real plant identification. The tests proved the feasibility of applying the asymptotic method in the \"black box\" SISO systems identification with excellent performance for ARMAX structures.

Random functions is the central component in many statistical and probabilistic problems. This dissertation presents theoretical analysis and computation for random functions and its applications in statistics. This dissertation consists of two parts. The first part is on the topic of classic continuous random fields. We present asymptotic analysis and computation for three non-linear functionals of random fields. In Chapter 1, we propose an efficient Monte Carlo algorithm for computing P{sup_T f(t)>b} when b is large, and f is a Gaussian random field living on a compact subset T. For each pre-specified relative error ɛ, the proposed algorithm runs in a constant time for an arbitrarily large $b$ and computes the probability with the relative error ɛ. In Chapter 2, we present the asymptotic analysis for the tail probability of ∫_T e^{σf(t)+μ(t)}dt under the asymptotic regime that σ tends to zero. In Chapter 3, we consider partial differential equations (PDE) with random coefficients, and we develop an unbiased Monte Carlo estimator with finite variance for computing expectations of the solution to random PDEs. Moreover, the expected computational cost of generating one such estimator is finite. In this analysis, we employ a quadratic approximation to solve random PDEs and perform precise error analysis of this numerical solver. The second part of this dissertation focuses on topics in statistics. The random functions of interest are likelihood functions, whose maximum plays a key role in statistical inference. We present asymptotic analysis for likelihood based hypothesis tests and sequential analysis. In Chapter 4, we derive an analytical form for the exponential decay rate of error probabilities of the generalized likelihood ratio test for testing two general families of hypotheses. In Chapter 5, we study asymptotic properties of the generalized sequential probability ratio test, the stopping rule of which is the first boundary crossing time of the generalized likelihood ratio statistic. We show that this sequential test is asymptotically optimal in the sense that it achieves asymptotically the shortest expected sample size as the maximal type I and type II error probabilities tend to zero. These results have important theoretical implications in hypothesis testing, model selection, and other areas where maximum likelihood is employed.

Wang Jing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-59). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Formulation of the Problem --- p.10 / Chapter 1.1 --- Reformulated Navier-Stokes Equations --- p.10 / Chapter 1.2 --- Linearized Problems --- p.15 / Chapter 2 --- Construction of the Approximate Solution --- p.19 / Chapter 2.1 --- Two-scale Asymptotic Expansions --- p.19 / Chapter 2.2 --- Determination of Each Inner and Boundary Terms --- p.22 / Chapter 2.3 --- Truncation Terms --- p.31 / Chapter 3 --- Estimates of the Error Term of the Approximate Solution and Main Results --- p.33 / Chapter 3.1 --- Error Equations --- p.33 / Chapter 3.2 --- Energy Estimates --- p.36 / Chapter 3.2.1 --- BasicL2 Estimates --- p.36 / Chapter 3.2.2 --- Tangential Derivatives Estimates --- p.38 / Chapter 3.2.3 --- Normal Derivatives Estimates --- p.49 / Chapter 3.3 --- Pointwise Estimates --- p.52 / Bibliography --- p.55

Zhang Hedan. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 78-81). / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Convex Scalar Conservation Laws --- p.9 / Chapter 2.1 --- Cauchy Problems and Weak Solutions --- p.9 / Chapter 2.2 --- Rankine-Hugoniot Condition --- p.11 / Chapter 2.3 --- Entropy Condition --- p.13 / Chapter 2.4 --- Uniqueness of Weak Solution --- p.15 / Chapter 2.5 --- Riemann Problems --- p.17 / Chapter 3 --- General Scalar Conservation Laws --- p.21 / Chapter 3.1 --- Entropy-Entropy Flux Pairs --- p.21 / Chapter 3.2 --- Admissibility Conditions --- p.22 / Chapter 3.3 --- Kruzkov Theory --- p.23 / Chapter 4 --- Elementary waves and Riemann Problems for Nonconvex Scalar Conservation Laws --- p.35 / Chapter 4.1 --- Basic Facts --- p.35 / Chapter 4.2 --- Riemann Solutions --- p.36 / Chapter 5 --- Asymptotic Behavior --- p.46 / Chapter 5.1 --- Periodic Asymptotic Behavior --- p.46 / Chapter 5.2 --- Asymptotic Behavior of Convex Conservation Law --- p.49 / Chapter 5.3 --- Asymptotic Behavior of Non-convex case --- p.52 / Chapter 5.3.1 --- L∞ Behavior --- p.53 / Chapter 5.3.2 --- Wave-Interactions and Asymptotic Behavior Toward Shock Waves --- p.55 / Bibliography --- p.78

Wang Hui Ying. / "June 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 67-72). / 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.

This thesis deals with the problem of the asymptotic behavior of solutions to several nonlinear equations from fluid dynamics on both mesoscopic and macroscopic levels, including Boltzmann equation, compressible Navier-Stokes equations and the system of viscous conservation laws with positive definite viscosity matrix. The main purpose is to study the asymptotic behavior of solutions to those equations towards linear and nonlinear waves, such as shock waves, rarefaction waves and contact discontinuities as either the times goes to infinity, or the viscosity and heat conductivity go to zero for the macroscopic equations or the mean free path goes to zero for the mesoscopic equations. Those limit processes are singular. For the system of viscous conservation laws, we show the large time asymptotic nonlinear stability of a superposition of viscous shock waves and viscous contact waves for the system of viscous conservation laws with small initial perturbations, provided that the strengths of these viscous waves are small and of the same order. The results are obtained by elementary weighted energy estimates based on the underlying wave structure and a new estimate on the heat equation. For the Boltzmann equation, the main purpose is to study the asymptotic equivalence for the hard-sphere collision model to its corresponding Euler equations of compressible gas dynamics in the limit of small mean free path. When the fluid flow is a smooth rarefaction (or centered-rarefaction) wave with finite strength, the corresponding Boltzmann solution exists globally in time, and the solution converges to the rarefaction wave uniformly for all time (or away from t = 0) as the mean free path epsilon → 0. A decomposition of a Boltzmann solution into its macroscopic (fluid) part and microscopic (kinetic) part is adopted to rewrite the Boltzmann equation in a form of compressible Navier-Stokes equations with source terms. As a by-product, the same asymptotic equivalence of the full compressible Navier-Stokes equations to its corresponding Euler equations in the limit of small viscosity and heat-conductivity (depending on the viscosity) is also obtained. / Zeng, Huihui. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 70-09, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 102-110). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

He Yiran. / Includes index. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 74-80) and index.. / 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.

Abstract not available

In order to introduce the investigation contemplated in this thesis, let us consider the differential equation d3y d2y dyz3 ____+ z2___(b0 + blzm) + z - (c0 + clzm) dz3 dz2 dz+ (d0 + dlzm + d2z2m) y = 0Here, m is an arbitrary positive integer and the variable z is complex as are the constantsbi,ci (i=0,1) and di (i=0,1,2) with d2≠0. It is also assumed that the difference of no two roots of the indicial equation about z = 0 is congruent to zero modulo m.Ball State UniversityMuncie, IN 47306