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**Partner:**UNT Libraries

**Decade:**1990-1999

**Degree Discipline:**Mathematics

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2201/

### 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.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc278251/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc279280/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc278398/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc278917/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc277804/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2198/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc277898/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc277605/

### 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.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2243/