UNT Theses and Dissertations - 464 Matching Results

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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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Hausdorff, Packing and Capacity Dimensions

Description: In this thesis, Hausdorff, packing and capacity dimensions are studied by evaluating sets in the Euclidean space R^. Also the lower entropy dimension is calculated for some Cantor sets. By incorporating technics of Munroe and of Saint Raymond and Tricot, outer measures are created. A Vitali covering theorem for packings is proved. Methods (by Taylor and Tricot, Kahane and Salem, and Schweiger) for determining the Hausdorff and capacity dimensions of sets using probability measures are discussed… more
Date: August 1989
Creator: Spear, Donald W.
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Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions

Description: Hill and Monticino (1998) introduced a constructive method for generating random probability measures with a prescribed mean or distribution on the mean. The method involves sequentially generating an array of barycenters that uniquely defines a probability measure. This work analyzes statistical properties of the measures generated by sequential barycenter array constructions. Specifically, this work addresses how changing the base measures of the construction affects the statististics of m… more
Date: December 2002
Creator: Valdes, LeRoy I.
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Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

Description: In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedr… more
Date: August 1986
Creator: Sutherland, David C. (David Craig)
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The Maximum Size of Combinatorial Geometries Excluding Wheels and Whirls as Minors

Description: We show that the maximum size of a geometry of rank n excluding the (q + 2)-point line, the 3-wheel W_3, and the 3-whirl W^3 as minor is (n - 1)q + 1, and geometries of maximum size are parallel connections of (q + 1)-point lines. We show that the maximum size of a geometry of rank n excluding the 5-point line, the 4-wheel W_4, and the 4-whirl W^4 as minors is 6n - 5, for n ≥ 3. Examples of geometries having rank n and size 6n - 5 include parallel connections of the geometries V_19 and PG(2,3).
Date: August 1989
Creator: Hipp, James W. (James William), 1956-
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Geometric Problems in Measure Theory and Parametrizations

Description: This dissertation explores geometric measure theory; the first part explores a question posed by Paul Erdös -- Is there a number c > 0 such that if E is a Lebesgue measurable subset of the plane with λ²(E) (planar measure)> c, then E contains the vertices of a triangle with area equal to one? -- other related geometric questions that arise from the topic. In the second part, "we parametrize the theorems from general topology characterizing the continuous images and the homeomorphic images of t… more
Date: August 1981
Creator: Ingram, John M. (John Michael)
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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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T-Sets of Normed Linear Spaces

Description: This paper is a study of T-sets of normed linear spaces. Geometrical properties of normed linear spaces are developed in terms of intersection properties shared by a subcollection of T-sets of the space and in terms of special spanning properties shared by each T-set of a subcollection of T-sets of the space. A characterization of the extreme points of the unit ball of the dual of a normed linear space is given in terms of the T-sets of the space. Conditions on the collection of T-sets of a nor… more
Date: December 1976
Creator: McCormick, Robert E.
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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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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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Bounded, Finitely Additive, but Not Absolutely Continuous Set Functions

Description: In leading up to the proof, methods for constructing fields and finitely additive set functions are introduced with an application involving the Tagaki function given as an example. Also, non-absolutely continuous set functions are constructed using Banach limits and maximal filters.
Date: May 1989
Creator: Gurney, David R. (David Robert)
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Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Description: Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction f… more
Date: August 2002
Creator: Arthur, Christopher
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Examples and Applications of Infinite Iterated Function Systems

Description: The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems. We discuss particular examples of infinite iterated function systems derived … more
Date: August 2000
Creator: Hanus, Pawel Grzegorz
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Maximum-Sized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7

Description: Let M be the class of simple matroids which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find all the maximum-sized matroids for each rank.
Date: May 2000
Creator: Mecay, Stefan Terence
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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.
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Infinite Planar Graphs

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 exte… more
Date: May 2000
Creator: Aurand, Eric William
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Maximum Likelihood Estimation of Logistic Sinusoidal Regression Models

Description: We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample perform… more
Date: December 2013
Creator: Weng, Yu
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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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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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