You limited your search to:

  Partner: UNT Libraries
 Department: Department of Mathematics
 Collection: UNT Theses and Dissertations
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
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.
Contributing Partner: UNT Libraries
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.
Contributing Partner: UNT Libraries
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.
Contributing Partner: UNT Libraries
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.
Contributing Partner: UNT Libraries
A Topological Uniqueness Result for the Special Linear Groups

A Topological Uniqueness Result for the Special Linear Groups

Date: August 1997
Creator: Opalecky, Robert Vincent
Description: The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Contributing Partner: UNT Libraries
Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation

Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation

Date: August 1998
Creator: Debrecht, Johanna M.
Description: We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is convex if and only if the curvature does not change sign, and we prove the Isoperimetric Inequality, which gives a bound on the area of a closed curve with fixed length. Finally, we study the deformation of plane curves developed by M. Gage and R. S. Hamilton. We observe that convex curves under deformation remain convex, and simple curves remain simple.
Contributing Partner: UNT Libraries
Primitive Substitutive Numbers are Closed under Rational Multiplication

Primitive Substitutive Numbers are Closed under Rational Multiplication

Date: August 1998
Creator: Ketkar, Pallavi S. (Pallavi Subhash)
Description: Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution then in an attempt to generalize Lehr's result we show that the set M(r) is closed under multiplication by rational numbers. We also show that M(r) is not closed under addition.
Contributing Partner: UNT Libraries
A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence

A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence

Date: August 1998
Creator: Risley, Rebecca N.
Description: We investigate a class of minimal sequences on a finite alphabet Ak = {1,2,...,k} having (k - 1)n + 1 distinct subwords of length n. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of binary Sturmian sequences. We describe two simple combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences (one of which is new even in the Sturmian case). Arnoux-Rauzy sequences arising from fixed points of primitive morphisms are characterized by an underlying periodic structure. We show that every Arnoux-Rauzy sequence contains arbitrarily large subwords of the form V^2+ε and, in the Sturmian case, arbitrarily large subwords of the form V^3+ε. Finally, we prove that an irrational number whose base b-digit expansion is an Arnoux-Rauzy sequence is transcendental.
Contributing Partner: UNT Libraries
Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices

Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices

Date: August 1999
Creator: Huff, Cheryl Rae
Description: The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Σ) and operator theory for the classical continuous function spaces C(K). Numerous authors have worked extensively on extending and generalizing the theorems of the preceding authors. Specifically, we mention Bilyeu and Lewis as well as Brooks and Drewnowski, whose efforts molded the direction and focus of this paper. This paper is a study of the techniques used by Bell, Bilyeu, and Lewis in their paper on uniform exhaustivity and Banach lattices to present a Banach lattice version of two important and powerful results in measure theory by Brooks and Drewnowski. In showing that the notions of exhaustivity and continuity take on familiar forms in certain Banach lattices of measures they show that these important measure theory results follow as corollaries of the generalized Banach lattice versions. This work uses their template to generalize results established by Bator, Bilyeu, and ...
Contributing Partner: UNT Libraries