Thesis (Ph. D.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 139-143).

Thesis (M.S.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains vi, 47 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 41-45).

Thesis (M.S.)--Ohio University, November, 2005. / Title from PDF t.p. Includes bibliographical references (p. 54-55)

For an inequality system, an error bound is an estimation for the distance from any point to the solution set of the inequality. The Ekeland variational principle (EVP) is an important tool in the study of error bounds. We prove that EVP is equivalent to an error bound result and present several sufficient conditions for an inequality system to have error bounds. In a metric space, a condition is similar to that of Takahashi. In a Banach space we express conditions in terms of an abstract subdifferential and the lower Dini derivative. We then discuss error bounds with exponents by a relation between the lower Dini derivatives of a function and its power function. For an l.s.c. convex function on a reflexive Banach space these conditions turn out to be equivalent. Furthermore a global error bound closely relates to the metric regularity. / Graduate

No description available.

D.Phil. / none / Prof. W.F. Harris

The goal of this study was to use a nonlinear approach to create a program to teach positive and negative reinforcement and punishment. A specific interest was to determine whether the program and its testing allowed for specific recommendations for future iterations of the program. The tests and program developed for this study were completed by 18 participants. Pre-test and post-test data showed that participants learned the most about positive contingencies, nonexample items, and ambiguous contingencies. Participants learned the least about negative contingencies. The data also revealed where additions to the instructional program were needed to produce better outcomes in future versions of the program.

by Lai Siu Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 50-52.

Zhang Yuanxiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 38-39). / Abstracts in English and Chinese.

The overall theme of this thesis work concerns the problem of handling measurement error and sources of variation in functional data models. The first part introduces a wavelet-based sparse principal component analysis approach for characterizing the variability of multilevel functional data that are characterized by spatial heterogeneity and local features. The total covariance of the data can be decomposed into three hierarchical levels: between subjects, between sessions and measurement error. Sparse principal component analysis in the wavelet domain allows for reducing dimension and deriving main directions of random effects that may vary for each hierarchical level. The method is illustrated by application to data from a study of human vision. The second part considers the problem of scalar-on-function regression when the functional regressors are observed with measurement error. We develop a simulation-extrapolation method for scalar-on-function regression, which first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We introduce three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. The third part discusses several extensions of the simulation-extrapolation method developed in the second part. Some of the extensions are illustrated by application to diffusion tensor imaging data.