Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 103-109).

Thesis (Ph. D.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 73-75). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 140-146). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 225-235). Also available in print.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

No description available.

Thesis (M.A.)--Boston University / The problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as the Dirichlet Problem. In this paper I consider the special eliptic equation of ∇2 J=0 which is Laplace's equation, and I limit myself to the case of two dimensions. Subject to these limitations I discuss five proofs for the existence of a solution to Laplace's equation for arbitrary regions where the boundary values are given. [TRUNCATED]

The current generation of structural equation modeling (SEM) is loosely split in two divergent groups - covariance-based and variance-based structural equation modeling. The relative newness of variance-based SEM has limited the development of techniques that extend its applicability to non-metric data. This study focuses upon the extension of general linear model techniques within the variance-based platform of partial least squares structural equation modeling (PLS-SEM). This modeling procedure receives it name through the iterative PLS‑SEM algorithm's estimates of the coefficients for the partial ordinary least squares regression models in both the measurement model and the overall structural model. This research addresses the following research questions: (1) What are the appropriate measures for data segmentation within PLS‑SEM? (2) What are the appropriate steps for the analysis of rank-ordered path coefficients within PLS‑SEM? and (3) What is an appropriate model selection index for PLS‑SEM? The limited type of data to which PLS-SEM is applicable suggests an opportunity to extend the method for use with different data and as a result a broader number of applications. This study develops and tests several methodologies that are prevalent in the general linear model (GLM). The proposed data segmentation approaches posited and tested through post hoc analysis of structural model. Monte Carlo simulation allows demonstrating the improvement of the proposed model fit indices in comparison to the established indices found within the SEM literature. These posited PLS methods, that are logical transfers of GLM methods, are tested using examples. These tests enable demonstrating the methods and recommending reporting requirements.

In this thesis, we propose and analyze a fast method for computing the solution of the Helmholtz equation in a bounded domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is first split into one--way wave equations which are then solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one--way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one--way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one--way wave equations are solved with GO with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge-Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is just O(ω1/p) for a p-th order Runge-Kutta method. This has been confirmed by numerical experiments.

No description available.