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 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
Hyperbolic Monge-Ampère Equation

Hyperbolic Monge-Ampère Equation

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Date: August 2006
Creator: Howard, Tamani M.
Description: In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prove some results on the Sobolev gradients that mainly arise from general nonlinear differential equations.
Contributing Partner: UNT Libraries
Hyperspace Topologies

Hyperspace Topologies

Date: August 2001
Creator: Freeman, Jeannette Broad
Description: In this paper we study properties of metric spaces. We consider the collection of all nonempty closed subsets, Cl(X), of a metric space (X,d) and topologies on C.(X) induced by d. In particular, we investigate the Hausdorff topology and the Wijsman topology. Necessary and sufficient conditions are given for when a particular pseudo-metric is a metric in the Wijsman topology. The metric properties of the two topologies are compared and contrasted to show which also hold in the respective topologies. We then look at the metric space R-n, and build two residual sets. One residual set is the collection of uncountable, closed subsets of R-n and the other residual set is the collection of closed subsets of R-n having n-dimensional Lebesgue measure zero. We conclude with the intersection of these two sets being a residual set representing the collection of uncountable, closed subsets of R-n having n-dimensional Lebesgue measure zero.
Contributing Partner: UNT Libraries
Ideals and Boolean Rings: Some Properties

Ideals and Boolean Rings: Some Properties

Date: May 1968
Creator: Hu, Grace Min-Ying Chin
Description: The purpose of this thesis is to investigate certain properties of rings, ideals, and a special type of ring called a Boolean ring.
Contributing Partner: UNT Libraries
Ideals in Quadratic Number Fields

Ideals in Quadratic Number Fields

Date: May 1971
Creator: Hamilton, James C.
Description: The purpose of this thesis is to investigate the properties of ideals in quadratic number fields, A field F is said to be an algebraic number field if F is a finite extension of R, the field of rational numbers. A field F is said to be a quadratic number field if F is an extension of degree 2 over R. The set 1 of integers of R will be called the rational integers.
Contributing Partner: UNT Libraries
Ideals in Semigroups

Ideals in Semigroups

Date: January 1965
Creator: Rodgers, Samuel A.
Description: This thesis investigates ideals in semigroups.
Contributing Partner: UNT Libraries
Improper Integrals

Improper Integrals

Date: 1957
Creator: Hildebrand, Shelby K.
Description: In this paper a definitions shall be given for different types of improper integrals and several theorems concerning them shall be proved.
Contributing Partner: UNT Libraries
Inequalities and Set Function Integrals

Inequalities and Set Function Integrals

Date: December 1971
Creator: Milligan, Kenneth Wayne
Description: This thesis investigates some inequalities and some relationships between function properties and integral properties.
Contributing Partner: UNT Libraries
Infinite Matrices

Infinite Matrices

Date: August 1957
Creator: Smallwood, James D.
Description: This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.
Contributing Partner: UNT Libraries
Infinite Planar Graphs

Infinite Planar Graphs

Date: May 2000
Creator: Aurand, Eric William
Description: How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.
Contributing Partner: UNT Libraries
Integrals Defined on a Field of Sets

Integrals Defined on a Field of Sets

Date: August 1968
Creator: Troute, Grady W.
Description: The purpose of this paper is to define an integral for real-valued functions which are defined on a field of sets and to demonstrate several properties of such an integral.
Contributing Partner: UNT Libraries