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Sufficient Conditions for Uniqueness of Positive Solutions and Non Existence of Sign Changing Solutions for Elliptic Dirichlet Problems

Description: In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $… more
Date: August 1995
Creator: Hassanpour, Mehran
Partner: UNT Libraries
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Topics in Fractal Geometry

Description: In this dissertation, we study fractal sets and their properties, especially the open set condition, Hausdorff dimensions and Hausdorff measures for certain fractal constructions.
Date: August 1994
Creator: Wang, JingLing
Partner: UNT Libraries
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Minimality of the Special Linear Groups

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, q… more
Date: December 1997
Creator: Hayes, Diana Margaret
Partner: UNT Libraries
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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
Partner: UNT Libraries
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Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems

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… more
Date: December 1998
Creator: Richardson, Peter A. (Peter Adolph), 1955-
Partner: UNT Libraries
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π-regular Rings

Description: The dissertation focuses on the structure of π-regular (regular) rings.
Date: May 1993
Creator: Badawi, Ayman R.
Partner: UNT Libraries
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Polish Spaces and Analytic Sets

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.
Date: August 1997
Creator: Muller, Kimberly (Kimberly Orisja)
Partner: UNT Libraries
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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-
Partner: UNT Libraries
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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
Partner: UNT Libraries
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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)
Partner: UNT Libraries
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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
Partner: UNT Libraries
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Concerning Integral Approximations of Bounded Finitely Additive Set Functions

Description: The purpose of this paper is to generalize a theorem that characterizes absolute continuity of bounded finitely additive set functions in the form of an integral approximation. We show that his integral exists if the condition of absolute continuity is removed.
Date: August 1992
Creator: Dawson, Dan Paul
Partner: UNT Libraries
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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
Partner: UNT Libraries
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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
Partner: UNT Libraries
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The Computation of Ultrapowers by Supercompactness Measures

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 relat… more
Date: August 1999
Creator: Smith, John C.
Partner: UNT Libraries
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On the Cohomology of the Complement of a Toral Arrangement

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.
Date: August 1999
Creator: Sawyer, Cameron Cunningham
Partner: UNT Libraries
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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.
Partner: UNT Libraries
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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
Partner: UNT Libraries
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A Continuous, Nowhere-Differentiable Function with a Dense Set of Proper Local Extrema

Description: In this paper, we use the following scheme to construct a continuous, nowhere-differentiable function 𝑓 which is the uniform limit of a sequence of sawtooth functions 𝑓ₙ : [0, 1] → [0, 1] with increasingly sharp teeth. Let 𝑋 = [0, 1] x [0, 1] and 𝐹(𝑋) be the Hausdorff metric space determined by 𝑋. We define contraction maps 𝑤₁ , 𝑤₂ , 𝑤₃ on 𝑋. These maps define a contraction map 𝑤 on 𝐹(𝑋) via 𝑤(𝐴) = 𝑤₁(𝐴) ⋃ 𝑤₂(𝐴) ⋃ 𝑤₃(𝐴). The iteration under 𝑤 of the diagonal in 𝑋 defines a sequence of graphs of… more
Date: December 1993
Creator: Huggins, Mark C. (Mark Christopher)
Partner: UNT Libraries
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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)
Partner: UNT Libraries
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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
Partner: UNT Libraries
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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)
Partner: UNT Libraries
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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)
Partner: UNT Libraries
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