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  Partner: UNT Libraries
 Department: Department of Mathematics
 Decade: 1990-1999
 Collection: UNT Theses and Dissertations
The Computation of Ultrapowers by Supercompactness Measures

The Computation of Ultrapowers by Supercompactness Measures

Date: August 1999
Creator: Smith, John C.
Description: The results from this dissertation are a computation of ultrapowers by supercompactness measures and concepts related to such measures. The second chapter gives an overview of the basic ideas required to carry out the computations. Included are preliminary ideas connected to measures, and the supercompactness measures. Order type results are also considered in this chapter. In chapter III we give an alternate characterization of 2 using the notion of iterated ordinal measures. Basic facts related to this characterization are also considered here. The remaining chapters are devoted to finding bounds fwith arguments taking place both inside and outside the ultrapowers. Conditions related to the upper bound are given in chapter VI.
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Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains

Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains

Date: August 1998
Creator: Finan, Marcel Basil
Description: The aim of this work is the study of the existence and multiplicity of sign changing nonradial solutions to elliptic boundary value problems on annular domains.
Contributing Partner: UNT Libraries
Minimality of the Special Linear Groups

Minimality of the Special Linear Groups

Date: December 1997
Creator: Hayes, Diana Margaret
Description: Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, quotient groups, and subgroups. Minimality of SLn(F) is concluded by appealing to the associated Lie group decomposition as the product of a compact group and an upper triangular group. We also prove the universal minimality of homeomorphism groups of one dimensional manifolds, and we give a new simple proof of the universal minimality of S∞.
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Multifractal Analysis of Parabolic Rational Maps

Multifractal Analysis of Parabolic Rational Maps

Date: August 1998
Creator: Byrne, Jesse William
Description: The investigation of the multifractal spectrum of the equilibrium measure for a parabolic rational map with a Lipschitz continuous potential, φ, which satisfies sup φ < P(φ) x∈J(T) is conducted. More specifically, the multifractal spectrum or spectrum of singularities, f(α) is studied.
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Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems

Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems

Date: December 1998
Creator: Richardson, Peter A. (Peter Adolph), 1955-
Description: In this paper, we prove, for a certain class of open billiard dynamical systems, the existence of a family of smooth probability measures on the leaves of the dynamical system's unstable manifold. These measures describe the conditional asymptotic behavior of forward trajectories of the system. Furthermore, properties of these families are proven which are germane to the PYC programme for these systems. Strong sufficient conditions for the uniqueness of such families are given which depend upon geometric properties of the system's phase space. In particular, these results hold for a fairly nonrestrictive class of triangular configurations of scatterers.
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On Groups of Positive Type

On Groups of Positive Type

Date: August 1995
Creator: Moore, Monty L.
Description: We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.
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On the Cohomology of the Complement of a Toral Arrangement

On the Cohomology of the Complement of a Toral Arrangement

Date: August 1999
Creator: Sawyer, Cameron Cunningham
Description: The dissertation uses a number of mathematical formula including de Rham cohomology with complex coefficients to state and prove extension of Brieskorn's Lemma theorem.
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Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Date: August 1995
Creator: Thompson, Jeremy R. (Jeremy Ray)
Description: We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
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Polish Spaces and Analytic Sets

Polish Spaces and Analytic Sets

Date: August 1997
Creator: Muller, Kimberly (Kimberly Orisja)
Description: A Polish space is a separable topological space that can be metrized by means of a complete metric. A subset A of a Polish space X is analytic if there is a Polish space Z and a continuous function f : Z —> X such that f(Z)= A. After proving that each uncountable Polish space contains a non-Borel analytic subset we conclude that there exists a universally measurable non-Borel set.
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A Presentation of Current Research on Partitions of Lines and Space

A Presentation of Current Research on Partitions of Lines and Space

Date: December 1999
Creator: Nugen, Frederick T.
Description: We present the results from three papers concerning partitions of vector spaces V over the set R of reals and of the set of lines in V.
Contributing Partner: UNT Libraries
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