A valence bond perturbation method is developed for the purpose of treating the pi electron spectra of molecules related to a parent conjugated hydrocarbon molecule. A spectral perturbation reflects the change in pi electron transition energy of the parent hydrocarbon as a result of heteroatom replacement of one or more carbon atoms or introducing substituents. Such spectral perturbations may be correlated with inductive and mesomeric heteroatom or substituent effects. Preliminary studies involve a comparison of semi-empirical valence bond and molecular orbital methods using similar approximations and integral values in each. Zero order wave functions and energy eigenvalues required for the perturbation analysis are obtained from the semi-empirical valence bond calculation for butadiene. First order perturbation theory is applied to acrolein, gyloxal, acrylonitrile and methyl butadienes to study inductive effects. These molecules are iso-pi-electronic with butadiene. First and second order perturbation theory is applied to chloroprene, bromoprene, iodoprene and 1,4-dichlorobutadiene. Inductive effects as well as mesomeric effects which arise as a result of additional pi electrons contributing to the conjugated system by the halogen substituents are considered. Inductive and mesomeric effects of the halogen on spectral perturbations are separated and identified. Values for empirical parameters required for agreement between calculated and observed spectral perturbations are correlated with relative substituent or heteroatom inductive and mesomeric effects. / Ph. D.

This dissertation concerns the development of a perturbation theory applicable to the algebraic eigenvalue problem. The objective is to express the perturbed eigenvalues and eigenvectors in terms of the unperturbed eigenvalues and eigenvectors and the perturbing matrices, without solving a new eigenvalue problem. If all of the unperturbed eigenvalues are clearly distinct, which is to say that the difference between no two of them is small, this objective can be accomplished. Alternatively, if some of the unperturbed eigenvalues are not clearly distinct, an eigenvalue problem, of the same dimension as the number of not clearly distinct unperturbed eigenvalues, must be solved. It is shown that Rayleigh's quotient is related to the perturbation theory. The use of Rayleigh's quotient is a key ingredient in defining a generalized basis for application of the perturbation theory, which does not depend upon the use of eigenvectors satisfying an eigenvalue problem. This generalized basis is then used to define an iterative eigensolution algorithm. The perturbation theory was initially developed as an efficient means of solving the eigenvalue problem associated with linear gyroscopic systems for which the damping and/or circulatory effects are sufficiently small that they can be regarded as perturbations. The perturbation theory is applied to an example of such a system. One interesting aspect of this example is that for one of the combinations of parameters, it exhibits both divergence and flutter instability, simultaneously. Other numerical examples are given. / Ph. D.

by Yu Zhenli. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 193-202). / 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.

Cheung, Sin Shuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 55-59). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.5 / Chapter 2.1 --- Heuristics by Hoeffding and Janson --- p.5 / Chapter 2.2 --- Facts in Matrix Theory --- p.10 / Chapter 2.3 --- Facts in Probability --- p.11 / Chapter 3 --- General Chance-Constrained LMIs --- p.18 / Chapter 3.1 --- Probability Inequalities --- p.18 / Chapter 3.2 --- Safe Tractable Approximations --- p.22 / Chapter 4 --- Chance-Constrained Quadratically Perturbed LMIs --- p.27 / Chapter 4.1 --- Exact Proper Fractional Covers --- p.27 / Chapter 4.2 --- Bounding the Matrix Moment Generating Functions --- p.32 / Chapter 5 --- Computational Study --- p.39 / Chapter 5.1 --- Update Procedures for Safe Tractable Approximations --- p.39 / Chapter 5.2 --- A Numerical Example and Comparisons --- p.44 / Chapter 6 --- Conclusion --- p.54 / Bibliography --- p.55

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.

<p>This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.</p>

An investigation focusing on methods of estimation of robustness of nominally linear dynamic systems with unstructured uncertainties was performed. The algorithm proposed involves the consideration of an associated system, selection, and subsequent development, of Liapunov function candidate and integration of their derivatives along the solution trajectory. A nominally linear multi-dimensional dynamic system is considered with unstructured, nonlinear, time-varying and bounded perturbations. The examples illustrate the success of the method: better estimates of the bounds, than those which results from traditional approaches were obtained. Robustness of linear, time-invariant systems subject to nonlinear, time-varying perturbations has been a matter of considerable research interest recently. Design of conventional state-feedback controllers requires knowledge of the bounds for disturbances. The knowledge of disturbance bounds is also important in adaptive control and control of nonlinear & uncertain systems. Numerous applications can be found in the fields of automation, aircraft control, manipulator trajectory control, etc. The technique for the determination of robust stability bounds proposed in this paper can be utilized effectively in computerized robust control system design. / Graduation date: 1992

Thesis (M.S.)--Ohio University, November, 2009. / Title from PDF t.p. Includes bibliographical references.

<p>This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.</p>

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