Thesis (Ph. D. in Mathematics)--Vanderbilt University, May 2007. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 123-128). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 129-133). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 106-111). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 106-111). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 129-133). Also available on the Internet.

The Intrinsic Low-Dimensional Manifold (ILDM) has been adopted as an approximation to the slow manifold representing the long-term evolution of a non-linear chemical system. The computation of the slow manifold simplifies the model without sacrificing accuracy because the trajectories are rapidly attracted to it. The ILDM has been shown to be a highly accurate approximation to the manifold when the curvature of the manifold is not too large. An efficient method of calculating an approximation to the slow manifold which may be equivalent to the ILDM is presented. This method, called Functional Equation Truncation (FET). is based on the assumption that the local curvature of the manifold is negligible, resulting in a locally linearized system. This system takes the form of a set of algebraic equations which can be solved for given values of the independent variables. Two-dimensional and three-dimensional models are used to test this method. The approximations to onedimensional slow manifolds computed by FET are quite close to the corresponding ILDMs and those for two-dimensional ones seem to differ from their ILDM counterparts. / vii, 61 leaves ; 29 cm.

The spin^c-invariants for a compact smooth simply-connected oriented four-manifold, as defined by Pidstrigach and Tyurin, are studied in this thesis. Unlike the Donaldson polynomial invariants, they are defined by cutting down the moduli space M' of '1-instantons', which is the subspace of the moduli space M of anti-self-dual connections parametrizing coupled (spin^c) Dirac operators with non-trivial kernel. Our main goal is to study the relationship between these spin^c-invariants and the Donaldson polynomial invariants. The 'jumping subset' M' defined a cohomology class P of M which is given by the generalised Porteous formula. When the index l of the coupled Dirac operator is 1, the two smooth invariants are the same by definition. When l = 0 (or when M is compact), the spin^c-invariants are expressable as a Donaldson polynomial evaluating the 'Porteous class' P. Our main results concern the first two non-trivial cases l = -1 and -2, when the generalised Porteous formula can not be applied directly. Using cut-and-paste arguments to the moduli space M, we show that for the former case the spin^c-invariants and the contracted Donaldson invariants differ by a correction term. It is the number of points in the immediate lower stratum of the Uhlenbeck compactification times a universal 'linking invariant' on S⁴, which is obtained by computing an example (the K3 surface). The case when l = -2 and dimM = 8 is a parametrized version of the l = -1 situation and the correction term, which involves the same 'linking invariant', is obtained from a suitable obstruction theory.

Thesis (Ph.D.)--Tufts University, 2004. / Adviser: Eric Todd Quinto. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 282-290). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [59]-61).