UNT Theses and Dissertations - 472 Matching Results

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Ádám's Conjecture and Its Generalizations

Description: This paper examines idam's conjuecture and some of its generalizations. In terms of Adam's conjecture, we prove Alspach and Parson's results f or Zpq and ZP2. More generally, we prove Babai's characterization of the CI-property, Palfy's characterization of CI-groups, and Brand's result for Zpr for polynomial isomorphism's. We also prove for the first time a characterization of the CI-property for 1 SG, and prove that Zn is a CI-Pn-group where Pn is the group of permutation polynomials on Z,, an… more
Date: August 1990
Creator: Dobson, Edward T. (Edward Tauscher)
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Explicit Multidimensional Solitary Waves

Description: In this paper we construct explicit examples of solutions to certain nonlinear wave equations. These semilinear equations are the simplest equations known to possess localized solitary waves in more that one spatial dimension. We construct explicit localized standing wave solutions, which generate multidimensional localized traveling solitary waves under the action of velocity boosts. We study the case of two spatial dimensions and a piecewise-linear nonlinearity. We obtain a large subset of th… more
Date: August 1990
Creator: King, Gregory B. (Gregory Blaine)
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Haar Measure on the Cantor Ternary Set

Description: The purpose of this thesis is to examine certain questions concerning the Cantor ternary set. The second chapter deals with proving that the Cantor ternary set is equivalent to the middle thirds set of [0,1], closed, compact, and has Lebesgue measure zero. Further a proof that the Cantor ternary set is a locally compact, Hausdorff topological group is given. The third chapter is concerned with establishing the existence of a Haar integral on certain topological groups. In particular if G is a l… more
Date: August 1990
Creator: Naughton, Gerard P. (Gerard Peter)
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Hyperspaces of Continua

Description: Several properties of Hausdorff continua are considered in this paper. However, the major emphasis is on developing the properties of the hyperspaces 2x and C(X) of a Hausdorff continuum X. Preliminary definitions and notation are introduced in Chapter I. Chapters II and III deal with the topological structure of the hyperspaces and the concept of topological convergence. Properties of 2x and C(X) are investigated in Chapter IV, while Chapters V and VI are devoted to the Hausdorff continuum X. … more
Date: August 1990
Creator: Simmons, Charlotte
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Manifolds, Vector Bundles, and Stiefel-Whitney Classes

Description: The problem of embedding a manifold in Euclidean space is considered. Manifolds are introduced in Chapter I along with other basic definitions and examples. Chapter II contains a proof of the Regular Value Theorem along with the "Easy" Whitney Embedding Theorem. In Chapter III, vector bundles are introduced and some of their properties are discussed. Chapter IV introduces the Stiefel-Whitney classes and the four properties that characterize them. Finally, in Chapter V, the Stiefel-Whitney class… more
Date: August 1990
Creator: Green, Michael Douglas, 1965-
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Properties of Power Series Rings

Description: This thesis investigates some of the properties of power series rings. The material is divided into three chapters. In Chapter I, some of the basic concepts of rings which are a prerequisite to an understanding of the definitions and theorems which follow are stated. Simple properties of power series rings are developed in Chapter II. Many properties of a ring R are preserved when we attach the indeterminant x to form the power series ring R[[x]]. Further results of power series rings are exami… more
Date: August 1990
Creator: O'Brien, Rita Marie
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Weakly Dense Subsets of Homogeneous Complete Boolean Algebras

Description: The primary result from this dissertation is following inequality: d(B) ≤ min(2^< wd(B),sup{λ^c(B): λ < wd(B)}) in ZFC, where B is a homogeneous complete Boolean algebra, d(B) is the density, wd(B) is the weak density, and c(B) is the cellularity of B. Chapter II of this dissertation is a general overview of homogeneous complete Boolean algebras. Assuming the existence of a weakly inaccessible cardinal, we give an example of a homogeneous complete Boolean algebra which does not attain its cellu… more
Date: August 1990
Creator: Bozeman, Alan Kyle
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Homotopies and Deformation Retracts

Description: This paper introduces the background concepts necessary to develop a detailed proof of a theorem by Ralph H. Fox which states that two topological spaces are the same homotopy type if and only if both are deformation retracts of a third space, the mapping cylinder. The concepts of homotopy and deformation are introduced in chapter 2, and retraction and deformation retract are defined in chapter 3. Chapter 4 develops the idea of the mapping cylinder, and the proof is completed. Three special cas… more
Date: December 1990
Creator: Stark, William D. (William David)
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Uniqueness of Positive Solutions for Elliptic Dirichlet Problems

Description: In this paper we consider the question of uniqueness of positive solutions for Dirichlet problems of the form - Δ u(x)= g(λ,u(x)) in B, u(x) = 0 on ϑB, where A is the Laplace operator, B is the unit ball in RˆN, and A>0. We show that if g(λ,u)=uˆ(N+2)/(N-2) + λ, that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(λ,u)=A f(u) with f(0) < 0, f "superlinear" and monotone. We use a number of methods from nonlinear functional … more
Date: December 1990
Creator: Ali, Ismail, 1961-
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Algebraic Number Fields

Description: This thesis investigates various theorems on polynomials over the rationals, algebraic numbers, algebraic integers, and quadratic fields. The material selected in this study is more of a number theoretical aspect than that of an algebraic structural aspect. Therefore, the topics of divisibility, unique factorization, prime numbers, and the roots of certain polynomials have been chosen for primary consideration.
Date: August 1991
Creator: Hartsell, Melanie Lynne
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Duals and Reflexivity of Certain Banach Spaces

Description: The purpose of this paper is to explore certain properties of Banach spaces. The first chapter begins with basic definitions, includes examples of Banach spaces, and concludes with some properties of continuous linear functionals. In the second chapter, dimension is discussed; then one version of the Hahn-Banach Theorem is presented. The third chapter focuses on dual spaces and includes an example using co, RI, and e'. The role of locally convex spaces is also explored in this chapter. In the f… more
Date: August 1991
Creator: Dahler, Cheryl L. (Cheryl Lewis)
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The Use of the Power Method to Find Dominant Eigenvalues of Matrices

Description: This paper is the result of a study of the power method to find dominant eigenvalues of square matrices. It introduces ideas basic to the study and shows the development of the power method for the most well-behaved matrices possible, and it explores exactly which other types of matrices yield to the power method. The paper also discusses a type of matrix typically considered impossible for the power method, along with a modification of the power method which works for this type of matrix. It g… more
Date: July 1992
Creator: Cavender, Terri A.
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Characterizations of Some Combinatorial Geometries

Description: We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a ch… more
Date: August 1992
Creator: Yoon, Young-jin
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Convergence of Conditional Expectation Operators and the Compact Range Property

Description: The interplay between generalizations of Riezs' famous representation theorem and Radon-Nikodým type theorems has a long history. This paper will explore certain aspects of the theory of bounded linear operators on continuous function spaces, Radon-Nikodým type properties, and their connections.
Date: August 1992
Creator: Dawson, C. Bryan (Charles Bryan)
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The Eulerian Functions of Cyclic Groups, Dihedral Groups, and P-Groups

Description: In 1935, Philip Hall developed a formula for finding the number of ways of generating the group of symmetries of the icosahedron from a given number of its elements. In doing so, he defined a generalized Eulerian function. This thesis uses Hall's generalized Eulerian function to calculate generalized Eulerian functions for specific groups, namely: cyclic groups, dihedral groups, and p- groups.
Date: August 1992
Creator: Sewell, Cynthia M. (Cynthia Marie)
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Existence and Multiplicity of Solutions for Semilinear Elliptic Boundary Value Problems

Description: This thesis studies the existence, multiplicity, bifurcation and the stability of the solutions to semilinear elliptic boundary value problems. These problems are motivated both by the mathematical structure and the numerous applications in fluid mechanics chemical reactions, nuclear reactors, Riemannian geometry and elasticity theory. This study considers the problem for different classes of nonlinearities and obtain the existence and multiplicity of positive solutions.
Date: August 1992
Creator: Gadam, Sudhasree
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Overrings of an Integral Domain

Description: This dissertation focuses on the properties of a domain which has the property that each ideal is a finite intersection of a π-ideal, the properties of a domain which have the property that each ideal is a finite product of π-ideal, and the containment relations of the resulting classes of ideals. Chapter 1 states definitions which are needed in later chapters. Chapters 2 and 3 focuses on domains which have the property that each ideal in D is a finite intersection of π-ideals while Chapter 4 f… more
Date: August 1992
Creator: Emerson, Sharon Sue
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Steepest Descent for Partial Differential Equations of Mixed Type

Description: The method of steepest descent is used to solve partial differential equations of mixed type. In the main hypothesis for this paper, H, L, and S are Hilbert spaces, T: H -> L and B: H -> S are functions with locally Lipshitz Fréchet derivatives where T represents a differential equation and B represents a boundary condition. Define ∅(u) = 1/2 II T(u) II^2. Steepest descent is applied to the functional ∅. A new smoothing technique is developed and applied to Tricomi type equations (which are of … more
Date: August 1992
Creator: Kim, Keehwan
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The Torus Does Not Have a Hyperbolic Structure

Description: Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of… more
Date: August 1992
Creator: Butler, Joe R.
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Universal Branched Coverings

Description: In this paper, the study of k-fold branched coverings for which the branch set is a stratified set is considered. First of all, the existence of universal k-fold branched coverings over CW-complexes with stratified branch set is proved using Brown's Representability Theorem. Next, an explicit construction of universal k-fold branched coverings over manifolds is given. Finally, some homotopy and homology groups are computed for some specific examples of Universal k-fold branched coverings.
Date: May 1993
Creator: Tejada, Débora
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Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory

Description: In this dissertation the results of Jerrum and Sinclair on the conductance of Markov chains are used to prove that almost all generalized Steinhaus graphs are rapidly mixing and an algorithm for the uniform generation of 2 - (4k + 1,4,1) cyclic Mendelsohn designs is developed.
Date: August 1993
Creator: Simmons, Dayton C. (Dayton Cooper)
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