Thesis (Ph. D.)--University of Hawaii at Manoa, 1998. / Includes bibliographical references (leaves 116-119). Also available by subscription via the World Wide Web.

Thesis--M. Phil., University of Hong Kong, 1985.

Thesis (M. Phil.)--University of Hong Kong, 1986.

Thesis (M.A.) in Mathematics--University of Maine, 2001. / Includes vita. Includes bibliographical references (leaves 66-67).

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

In this thesis I will defend analyticity. Quine has criticized analyticity. To answer Quine’s challenge, P. Boghossian distinguishes metaphysical analyticity and epistemological analyticity. He argues that epistemological analyticity exists while metaphysical analyticity does not. But, T. Williamson further rejects epistemological analyticity. In this thesis, I will defend both metaphysical analyticity and epistemological analyticity. In chapter I, I will generally define and discuss four conceptions of analyticity. I will show that there are different readings of each conception of analyticity. In chapter II, I will criticize K. Glüer, Hofmann & Horvath, and G. Russell’s arguments. They attempt to defend metaphysical analyticity. I will show that their arguments fail. To answer Quine’s challenge and to salve analyticity, Boghossian resorts to implicit definition and Glock suggests a normative view of analyticity. In chapter III, I will argue that their efforts fail. In chapter IV, I will defend metaphysical analyticity in a new perspective. The new perspective holds that metaphysical analyticity is true in virtue of concepts rather than meanings. I will argue that, analytic propositions are about the logical relations of realities. And these logical relations are the projections of our conceptual systems. So, the truth of analytic statements is completely determined by concepts they contain. And then, in chapter V, I will explain how concepts could completely determine the truth of analytic statements. Basing on some theories of concepts, I will show that the truth of analytic statements could be explained by means of the structure of concepts. In chapter VI, I will defend epistemological analyticity. T. Williamson has rejected epistemological analyticity. I will argue that Williamson’s argument fails. I will show that his definitions of analyticity are improper. / published_or_final_version / Philosophy / Doctoral / Doctor of Philosophy

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This work discusses isogeometric analysis as a promising alternative to standard finite element analysis. Isogeometric analysis has emerged from the idea that the act of modeling a geometry exactly at the coarsest levels of discretization greatly simplifies the refinement process by obviating the need for a link to an external representation of that geometry. The NURBS based implementation of the method is described in detail with particular emphasis given to the numerous refinement possibilities, including the use of functions of higher-continuity and a new technique for local refinement. Examples are shown that highlight each of the major features of the technology: geometric flexibility, functions of high continuity, and local refinement. New numerical approaches are introduced for modeling the fine scales within the variational multiscale method. First, a general framework is presented for seeking solutions to differential equations in a way that approximates optimality in certain norms. More importantly, it makes possible for the first time the approximation of the fine-scale Green's functions arising in the formulation, leading to a better understanding of machinery of the variational multiscale method and opening new avenues for research in the field. Second, a simplified version of the approach, dubbed the "parameter-free variational multiscale method," is proposed that constitutes an efficient stabilized method, grounded in the variational multiscale framework, that is free of the ad hoc stabilization parameter selection that has plagued classical stabilized methods. Examples demonstrate the efficacy of the method for both linear and nonlinear equations. / text

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