## You limited your search to:

**Partner:**UNT Libraries

**Degree Discipline:**Mathematics

**Collection:**UNT Theses and Dissertations

### Properties of Semigroups

**Date:**June 1966

**Creator:**Donnell, William Anthony

**Description:**This paper is an introductory, algebraic study of semigroups.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130682/

### Metric Half-Spaces

**Date:**May 1972

**Creator:**Dooley, Willis L.

**Description:**This paper is a study of some of the basic properties of the metric half-space topology, a topology on a set which is derived from a metric on the set. In the first it is found that in a complete inner product space, the metric half-space topology is the same as one defined in terms of linear functionals on the space. In the second it is proven that in Rn the metric half-space topology is the same as the usual metric topology. In the third theorem it is shown that in a certain sense the nature of the metric halfspace topology generated by a norm on the space determines whether the norm is quadratic, that is to say, whether or not there exists an inner product on the space with the property that |x|^2=(x,x) for all x in the space.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc131510/

### G-domains, G-ideals, and Hilbert Rings

**Date:**August 1972

**Creator:**Draper, Ruben P.

**Description:**The problem with which this investigation is concerned is that of determining the properties of the following: a particular type of integral domain, the G-domain; a type of prime ideal, the G-ideal; and a special type of ring, the Hilbert ring.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc131539/

### On Uniform Convergence

**Date:**1951

**Creator:**Drew, Dan Dale

**Description:**In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc96930/

### Around the Fibonacci Numeration System

**Date:**May 2007

**Creator:**Edson, Marcia Ruth

**Description:**Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc3676/

### Automorphism Groups

**Date:**August 1965

**Creator:**Edwards, Donald Eugene

**Description:**This paper will be concerned mainly with automorphisms of groups. The concept of a group endomorphism will be used at various points in this paper.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130613/

### Sequences of Real Numbers

**Date:**January 1965

**Creator:**Eskew, Mark F.

**Description:**The purpose of this thesis is to examine general properties, convergence, and limit points of sequences of real numbers.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130563/

### Peripherally Continuous Functions, Graph Maps and Connectivity Maps

**Date:**August 1967

**Creator:**Evans, Bret Edgar

**Description:**The purpose of this paper is to investigate some of the more basic properties of peripherally continuous functions, graph maps and connectivity maps.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130839/

### Applications in Fixed Point Theory

**Date:**December 2005

**Creator:**Farmer, Matthew Ray

**Description:**Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc4971/

### Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

**Date:**August 2011

**Creator:**Farmer, Matthew Ray

**Description:**In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapping. It is further shown that this collection under any topology in the aforementioned class of similar topologies is a strong Choquet space. Finally, a collection of category results are developed since strong Choquet spaces are also Baire spaces.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc84202/

### A Genesis for Compact Convex Sets

**Date:**May 1969

**Creator:**Ferguson, Ronald D.

**Description:**This paper was written in response to the following question: what conditions are sufficient to guarantee that if a compact subset A of a topological linear space L^3 is not convex, then for every point x belonging to the complement of A relative to the convex hull of A there exists a line segment yz such that x belongs to yz and y belongs to A and z belongs to A? Restated in the terminology of this paper the question bay be given as follow: what conditions may be imposed upon a compact subset A of L^3 to insure that A is braced?

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc131089/

### 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

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

### The Laplace Transformation

**Date:**August 1965

**Creator:**Floyd, Russell

**Description:**A set of definitions, theorems and proofs to describe the Laplace transformation.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130616/

### The Use of Chebyshev Polynomials in Numerical Analysis

**Date:**December 1975

**Creator:**Forisha, Donnie R.

**Description:**The purpose of this paper is to investigate the nature and practical uses of Chebyshev polynomials. Chapter I gives recognition to mathematicians responsible for studies in this area. Chapter II enumerates several mathematical situations in which the polynomials naturally arise and suggests reasons for the pursuance of their study. Chapter III includes: Chebyshev polynomials as related to "best" polynomial approximation, Chebyshev series, and methods of producing polynomial approximations to continuous functions. Chapter IV discusses the use of Chebyshev polynomials to solve certain differential equations and Chebyshev-Gauss quadrature.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc663496/

### Hochschild Cohomology and Complex Reflection Groups

**Date:**August 2012

**Creator:**Foster-Greenwood, Briana A.

**Description:**A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the semi-direct product of the group with a polynomial ring on the vector space. Each representation of a group defines a different skew group algebra, which may have its own interesting deformations. In this work, we explicitly describe all graded Hecke algebras arising as deformations of the skew group algebra of any finite group acting by the regular representation. We then focus on rank two exceptional complex reflection groups acting by any irreducible representation. We consider in-depth the reflection representation and a nonfaithful rotation representation. Alongside our study of cohomology for the rotation representation, we develop techniques valid for arbitrary finite groups acting by a representation with a central kernel. Additionally, we consider combinatorial questions about reflection length and codimension orderings on complex reflection groups. We give algorithms using character theory to compute ...

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc149591/

### 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

**Permallink:**digital.library.unt.edu/ark:/67531/metadc2902/

### Some Fundamental Properties of Categories

**Date:**June 1968

**Creator:**Gardner, Harold L.

**Description:**This paper establishes a basis for abelian categories, then gives the statement and proof of two equivalent definitions of an abelian category, the development of the basic theory of such categories, and the proof of some theorems involving this basic theory.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130942/

### Separation Properties

**Date:**December 1970

**Creator:**Garvin, Billy Ray

**Description:**The problem with which this paper is concerned is that of investigating a class of topological properties commonly called separation properties. A topological space which satisfies only the definition may be very limited in open sets. By use of the separation properties, specific families of open sets can be guaranteed.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc131327/

### Using Steepest Descent to Find Energy-Minimizing Maps Satisfying Nonlinear Constraints

**Date:**August 1994

**Creator:**Garza, Javier, 1965-

**Description:**The method of steepest descent is applied to a nonlinearly constrained optimization problem which arises in the study of liquid crystals. Let Ω denote the region bounded by two coaxial cylinders of height 1 with the outer cylinder having radius 1 and the inner having radius ρ. The problem is to find a mapping, u, from Ω into R^3 which agrees with a given function v on the surfaces of the cylinders and minimizes the energy function over the set of functions in the Sobolev space H^(1,2)(Ω; R^3) having norm 1 almost everywhere. In the variational formulation, the norm 1 condition is emulated by a constraint function B. The direction of descent studied here is given by a projected gradient, called a B-gradient, which involves the projection of a Sobolev gradient onto the tangent space for B. A numerical implementation of the algorithm, the results of which agree with the theoretical results and which is independent of any strong properties of the domain, is described. In chapter 2, the Sobolev space setting and a significant projection in the theory of Sobolev gradients are discussed. The variational formulation is introduced in Chapter 3, where the issues of differentiability and existence of ...

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc278362/

### Dimension spectrum and graph directed Markov systems.

**Access:**Use of this item is restricted to the UNT Community.

**Date:**May 2006

**Creator:**Ghenciu, Eugen Andrei

**Description:**In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary conditions for a finitely primitive conformal GDMS to have full HD spectrum. A GDMS is said to be regular if the Hausdorff dimension of its limit set is also the zero of the topological pressure function. We show that every number in the Hausdorff dimension spectrum is the Hausdorff dimension of a regular subsystem. In the particular case of a conformal iterated function system we show that the Hausdorff dimension spectrum is compact. We introduce several new systems: the nearest integer GDMS, the Gauss-like continued fraction system, and the Renyi-like continued fraction system. We prove that these systems have full HD spectrum. A special attention is given to the backward continued fraction ...

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc5226/

### Spaces of Compact Operators

**Access:**Use of this item is restricted to the UNT Community.

**Date:**May 2004

**Creator:**Ghenciu, Ioana

**Description:**In this dissertation we study the structure of spaces of operators, especially the space of all compact operators between two Banach spaces X and Y. Work by Kalton, Emmanuele, Bator and Lewis on the space of compact and weakly compact operators motivates much of this paper. Let L(X,Y) be the Banach space of all bounded linear operators between Banach spaces X and Y, K(X,Y) be the space of all compact operators, and W(X,Y) be the space of all weakly compact operators. We study problems related to the complementability of different operator ideals (the Banach space of all compact, weakly compact, completely continuous, resp. unconditionally converging) operators in the space of all bounded linear operators. The structure of Dunford-Pettis sets, strong Dunford-Pettis sets, and certain spaces of operators is studied in the context of the injective and projective tensor products of Banach spaces. Bibasic sequences are used to study relative norm compactness of strong Dunford-Pettis sets. Next, we use Dunford-Pettis sets to give sufficient conditions for K(X,Y) to contain c0.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc4463/

### Hamiltonian cycles in subset and subspace graphs.

**Access:**Use of this item is restricted to the UNT Community.

**Date:**December 2004

**Creator:**Ghenciu, Petre Ion

**Description:**In this dissertation we study the Hamiltonicity and the uniform-Hamiltonicity of subset graphs, subspace graphs, and their associated bipartite graphs. In 1995 paper "The Subset-Subspace Analogy," Kung states the subspace version of a conjecture. The study of this problem led to a more general class of graphs. Inspired by Clark and Ismail's work in the 1996 paper "Binomial and Q-Binomial Coefficient Inequalities Related to the Hamiltonicity of the Kneser Graphs and their Q-Analogues," we defined subset graphs, subspace graphs, and their associated bipartite graphs. The main emphasis of this dissertation is to describe those graphs and study their Hamiltonicity. The results on subset graphs are presented in Chapter 3, on subset bipartite graphs in Chapter 4, and on subspace graphs and subspace bipartite graphs in Chapter 5. We conclude the dissertation by suggesting some generalizations of our results concerning the panciclicity of the graphs.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc4662/

### Concerning linear spaces

**Date:**June 1965

**Creator:**Gilbreath, Joe

**Description:**The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130586/

### Topological Transformations

**Date:**August 1960

**Creator:**Gillespie, Arthur Alan

**Description:**This thesis investigates some of the properties of certain transformations. Some properties are considered in general; others, only in the xy-plane.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc108097/