Thesis (M.Ch.E.)--University of Delaware, 2006. / Principal faculty advisor: Antony N. Beris, Dept. of Chemical Engineering. Includes bibliographical references.

Perturbations of the Laplacian are known as Schrodinger operators. We pose a question about perturbations of eigenfunctions from multiple eigenspaces and answer the question in the case of the two-sphere. This is used to extend a previously known result about nodal sets of spherical harmonics to eigenfunctions of Schrodinger operators on the two-sphere. We also review some of the classical and recent results about nodal sets and domains for eigenfunctions of the Laplacian.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references. Also available in electronic version.

No description available.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 35-36). Also available in electronic version.

Thesis (M.S.)--Brigham Young University. Dept of Electrical and Computer Engineering, 2006. / Includes bibliographical references (p. 59-60).

Thesis (M.S.)--Ohio State University, 1986. / Includes bibliographical references (leaves 39-40). Available online via OhioLINK's ETD Center

No description available.

In the field of antenna design and analysis, often the need arises to numerically extrapolate the far-zone performance of a radiating structure from its known (or assumed known) near-zone electromagnetic field. Mathematical processes developed to accomplish such a task are known in the literature as near-zone to far-zone transformations (NZ-FZTs) as well as near-field far-field (NF-FF) transformations. These processes make use of sampled near-zone field quantities along some virtual surface, viz., the transformation surface, that surrounds the radiating structure of interest. Depending upon the application, samples of the required near-zone field quantities are supplied via analytical, empirical, or computational means. Over the years, a number of NZ-FZT processes have been developed to meet the demands of many applications. In short, their differences include, but are not limited to, the following: (1) the size and shape of the transformation surface, (2) the required near-zone field quantities and how they are sampled, (3) the computational methodology used, and (4) the imbedding of various application-driven features. Each process has its pros and cons depending upon its specific application as well as the type of radiation structure under consideration. In this dissertation we put forth a new and original NZ-FZT process that allows the transformation surface along which the near-zone is sampled to be spheroidal in shape: namely a prolate or oblate spheroid. Naturally, there are benefits gained in doing so. Our approach uses a formulated eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NZ-FZT algorithms for each type of spheroidal transformation surface. The process only requires knowledge of the E-field along the transformation surface and does not need the corresponding H-field. Given is a systematic exposition of the formulation, implementation, and verification of the newly developed NZ-FZT process. Accordingly, computer software is developed to implement both NZ-FZT algorithms. In the validation process, analytical and empirical radiation structures serve as computational benchmarks. Numerical models of both benchmark structures are created by integrating the software with a field solver, viz., a finite-difference time-domain (FDTD) code. Results of these computer models are compared with theoretical and empirical data to provide additional validation. / Ph. D.

No description available.