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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 114-117. / by Hans Kleppe. / Ph.D.

In this thesis, we explore the restrictions imposed on the genus of a smooth curve $X$ which possesses at least three independent gonal morphisms to $\Pp^1$. We will prove a sharp lower bound on the dimension of global sections given by the sum of the divisors for the gonal morphisms. This inequality will provide an upper bound on the genus of a curve with the described properties. By considering the birational image of $X$ in $\Pp^1 \times \Pp^1 \times \Pp^1$ under the product of three pairwise independent morphisms, we observe that the boundary case for the previously mentioned inequality is closely related to the case where the image of $X$ is contained in a type 1-1-1 surface. Motivated by this phenomenon, we examine the constraints on the arithmetic genus of an irreducible curve in $\Pp^1 \times \Pp^1 \times \Pp^1$ whose natural projections are pairwise independent and all have degree 7.

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It is well-known that del Pezzo surfaces of degree 9 -- n. are in one-to-one correspondence to flat En bundles over elliptic curves which are anti-canonical curves of such surfaces. In my thesis, we study a broader class of rational surfaces which are called ADE surfaces. We construct Lie algebra bundles of any type on these surfaces, and extend the above correspondence to flat G bundles over elliptic curves, where G is a simple, compact and simply-connected Lie group of any type. Concretely, we establish a natural identification between the following two very different moduli spaces for a Lie group G of any type: the moduli space of rational surfaces with G-configurations and the moduli space of flat G-bundles over a fixed elliptic curve. / Zhang, Jiajin. / "July 2007." / Adviser: Leung Nai Chung Conan. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 77-79). / 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.

Leung, Wai Sing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-62). / Abstracts in English and Chinese. / Chapter 0.1 --- Introduction --- p.6 / Chapter 1 --- Sphere Theorems --- p.8 / Chapter 1.1 --- Rauch-Berger-Klingenberg Sphere Theorem --- p.8 / Chapter 1.2 --- Maximal Diameter Theorem --- p.15 / Chapter 1.3 --- Minimal Diameter Theorem --- p.17 / Chapter 2 --- A Differentiable Sphere Theorem --- p.27 / Chapter 2.1 --- Definitions --- p.27 / Chapter 2.2 --- Preliminary results not related to curvature --- p.28 / Chapter 2.3 --- Preliminary result related to the curvature --- p.33 / Chapter 2.4 --- Differentiable Sphere Theorem --- p.35 / Chapter 3 --- The fundamental equations of Riemannian submer- sions --- p.43 / Chapter 3.1 --- Definitions --- p.43 / Chapter 3.2 --- The fundamental tensors T and A --- p.44 / Chapter 3.3 --- Covariant derivatives of T and A --- p.47 / Chapter 3.4 --- Fundamental equations and O'Neill's formulas --- p.49 / Chapter 4 --- A study on exotic spheres --- p.52 / Chapter 4.1 --- Construction of Milnor sphere --- p.52 / Chapter 4.2 --- Construction of GM-sphere (Σ7) --- p.53 / Chapter 4.3 --- The curvature of Σ7 --- p.54 / Chapter 4.4 --- Some recent results and open questions --- p.59 / Bibliography --- p.61

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, 1917. / "Private edition, distributed by the University of Chicago Libraries." Includes bibliographical references. Also available on the Internet.

This research focuses on the application of guided waves techniques to nondestructively characterize the structural integrity of bonded engineering components. Computational methods are used to examine the properties of multi-layered, adhesive bonded plates. This study quantifies the effect of the adhesive bond parameters (Young's modulus, Poisson's ration and bond thickness) on the dispersion curves. A commercial finite element (FE) code (ABAQUS/Explicit) is used for the numerical model while the global matrix method and the waveguide FE method are used to benchmark the resulting dispersion relationships in the form of a frequency-wavenumber or slowness-frequency relation. The postprocessing of FE data includes the two-dimensional Fourier transform (2D-FFT) and the short-time Fourier transform (STFT). Note that the 2D-FFT and STFT operate on multiple or just one transient output signals of the FE results respectively, while the waveguide FE method uses mass-, damping- and stiffness-matrices to generate the dispersion relations. In the dispersion relations, a set of bond parameter sensitive and FE-visible points is selected. The frequency locations of these points represent the solution criteria for the inversion procedure based on the global matrix method. The capabilities of the inversion process depend on the number of transient output signals from an FE simulation for the forward problem.

Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 147-156).

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2008. / Includes bibliographical references (p. 45-46).