Theses (M.A.)--Marshall University, 2006. / Title from document title page. Includes abstract. Document formatted into pages: contains v, 53 pages. Bibliography: p. 52-53.

This research examines an ordered perception rater model, an extension of the equal perception signal detection theory (SDT) latent class rater model. The expectation-maximization algorithm and the Newton-Raphson algorithm are used to estimate parameters. Four simulation studies are conducted to answer three research questions. Simulation studies 1 and 2 fit correct models to the data. Simulation study 1 generates one hundred data sets from the equal perception rater model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the equal perception model. Parameter recovery is excellent for fully-crossed design and reasonable for BIB design, and all rater effects are detected. Simulation study 2 generates one hundred simulated data sets from the ordered perception model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the ordered perception rater model. Although parameter recovery is biased for some parameters in the BIB design, all rater effects are recovered. Simulation studies 3 and 4 fit wrong models to the data. Simulation study 3 fits equal perception models to the fully-crossed and BIB ordered perception data sets generated in simulation study 2. All rater effects are revealed, although rater effects are distorted to some extent in the BIB design. Simulation study 4 fits ordered perception models to the fully-crossed and BIB equal perception data sets generated in study 1. All rater effects are recovered. Using essay scores from a large-scale language test, an empirical study is conducted. Both the equal and the ordered perception models are fitted. Information criteria favor the equal perception model.

The behavior of a fluid with a thin capillary meniscus can be modelled on a one-dimensional domain Ω = [−L, L] by the thin film equation ht = −(hnhxxx)x with boundary conditions hx(±L) = ±α (giving a fixed contact angle) and hxxx(±L) = 0 (prohibiting mass flux). It is desirable to know whether or not such a film experiences rupture; that is, whether there exists some x0, t0 (with t0 possibly ∞) such that h(x0, t0) = 0, corresponding to the appearance of a dry spot. We approach this problem using energy methods, which use the conservation or dissipation of quantities such as mass, surface area, coating energy, and other more abstract quantities to describe the behavior of the fluid. We present a brief analysis of the behavior of some of these energies, as well as a proof that, given certain assumptions, rupture cannot occur in a thin capillary meniscus for n > 4 and, in more restricted cases, for n > 7/2. We also show that rupture must occur for 0 < n < 1/2. We describe the asymptotic behavior of the regions in which rupture occurs. We also describe the numerical implementation of this problem and the advantages and drawbacks of using certain prewritten solvers in MATLAB and new implementations of θ-weighted schemes and the Newton-Raphson method. We propose uses of these numerical methods to make further progress on the problem.

Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaf 53). Also available on the World Wide Web.

Dissertation (Ph.D.)--Worcester Polytechnic Institute. / Keywords: Periodic Solutions, Under-Determined Systems, Continuation, Nonlinear Eigenvalue, Inexact Newton Methods, Newton's Method, Trust Region Methods Includes bibliographical references (p.93-95).

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

One of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the Wang and Yau quasi-local energy has yet to be explored. In this region, the results of this thesis indicate that the Wang and Yau quasi-local energy yields complex values and is essentially equivalent to the previously defined Brown and York quasi-local energy. However, an application of their quasi-local mass is suggested in a dynamical setting, which can potentially give new and meaningful measures. In supporting this thesis, the development of a novel adiabatic isometric mapping algorithm is included. Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical topology into Euclidean 3-space necessary for completing the calculation of quasilocal energy in numerical relativity codes. The innovation of this algorithm is the guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm to provide accuracy of the edge lengths up to a user set tolerance. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007. / "May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.