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On Groups of Positive Type

Description: We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.
Date: August 1995
Creator: Moore, Monty L.
Partner: UNT Libraries
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The Continuous Wavelet Transform and the Wave Front Set

Description: In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.
Date: December 1993
Creator: Navarro, Jaime
Partner: UNT Libraries
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Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices

Description: The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Σ) and operator theory for the classical … more
Date: August 1999
Creator: Huff, Cheryl Rae
Partner: UNT Libraries
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Existence of a Sign-Changing Solution to a Superlinear Dirichlet Problem

Description: We study the existence, multiplicity, and nodal structure of solutions to a superlinear elliptic boundary value problem. Under specific hypotheses on the superlinearity, we show that there exist at least three nontrivial solutions. A pair of solutions are of one sign (positive and negative respectively), and the third solution changes sign exactly once. Our technique is variational, i.e., we study the critical points of the associated action functional to find solutions. First, we define a codi… more
Date: August 1995
Creator: Neuberger, John M. (John Michael)
Partner: UNT Libraries
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Steepest Sescent on a Uniformly Convex Space

Description: This paper contains four main ideas. First, it shows global existence for the steepest descent in the uniformly convex setting. Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces. Thirdly, it shows an isomorphism between the dual space of H^{1,p}[0,1] and the space H^{1,q}[0,1] where p > 2 and {1/p} + {1/q} = 1. Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H^{1,p}[0,1] to L_{p}[1,0] where p … more
Date: August 1995
Creator: Zahran, Mohamad M.
Partner: UNT Libraries
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A Topological Uniqueness Result for the Special Linear Groups

Description: The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Date: August 1997
Creator: Opalecky, Robert Vincent
Partner: UNT Libraries
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A Numerical Method for Solving Singular Differential Equations Utilizing Steepest Descent in Weighted Sobolev Spaces

Description: We develop a numerical method for solving singular differential equations and demonstrate the method on a variety of singular problems including first order ordinary differential equations, second order ordinary differential equations which have variational principles, and one partial differential equation.
Date: August 1995
Creator: Mahavier, William Ted
Partner: UNT Libraries
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Tensor Products of Banach Spaces

Description: Tensor products of Banach Spaces are studied. An introduction to tensor products is given. Some results concerning the reciprocal Dunford-Pettis Property due to Emmanuele are presented. Pelczyriski's property (V) and (V)-sets are studied. It will be shown that if X and Y are Banach spaces with property (V) and every integral operator from X into Y* is compact, then the (V)-subsets of (X⊗F)* are weak* sequentially compact. This in turn will be used to prove some stronger convergence results for … more
Date: August 1996
Creator: Ochoa, James Philip
Partner: UNT Libraries
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Continuous, Nowhere-Differentiable Functions with no Finite or Infinite One-Sided Derivative Anywhere

Description: In this paper, we study continuous functions with no finite or infinite one-sided derivative anywhere. In 1925, A. S. Beskovitch published an example of such a function. Since then we call them Beskovitch functions. This construction is presented in chapter 2, The example was simple enough to clear the doubts about the existence of Besicovitch functions. In 1932, S. Saks showed that the set of Besicovitch functions is only a meager set in C[0,1]. Thus the Baire category method for showing the e… more
Date: December 1994
Creator: Lee, Jae S. (Jae Seung)
Partner: UNT Libraries
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Primitive Substitutive Numbers are Closed under Rational Multiplication

Description: Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is … more
Date: August 1998
Creator: Ketkar, Pallavi S. (Pallavi Subhash)
Partner: UNT Libraries
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Using Steepest Descent to Find Energy-Minimizing Maps Satisfying Nonlinear Constraints

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) h… more
Date: August 1994
Creator: Garza, Javier, 1965-
Partner: UNT Libraries
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Cycles and Cliques in Steinhaus Graphs

Description: In this dissertation several results in Steinhaus graphs are investigated. First under some further conditions imposed on the induced cycles in steinhaus graphs, the order of induced cycles in Steinhaus graphs is at most [(n+3)/2]. Next the results of maximum clique size in Steinhaus graphs are used to enumerate the Steinhaus graphs having maximal cliques. Finally the concept of jumbled graphs and Posa's Lemma are used to show that almost all Steinhaus graphs are Hamiltonian.
Date: December 1994
Creator: Lim, Daekeun
Partner: UNT Libraries
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Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation

Description: We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is … more
Date: August 1998
Creator: Debrecht, Johanna M.
Partner: UNT Libraries
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Property (H*) and Differentiability in Banach Spaces

Description: A continuous convex function on an open interval of the real line is differentiable everywhere except on a countable subset of its domain. There has been interest in the problem of characterizing those Banach spaces where the continuous functions exhibit similar differentiability properties. In this paper we show that if a Banach space E has property (H*) and B_E• is weak* sequentially compact, then E is an Asplund space. In the case where the space is weakly compactly generated, it is shown th… more
Date: August 1993
Creator: Obeid, Ossama A.
Partner: UNT Libraries
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Descriptions and Computation of Ultrapowers in L(R)

Description: The results from this dissertation are an exact computation of ultrapowers by measures on cardinals $\aleph\sb{n},\ n\in w$, in $L(\IR$), and a proof that ordinals in $L(\IR$) below $\delta\sbsp{5}{1}$ represented by descriptions and the identity function with respect to sequences of measures are cardinals. An introduction to the subject with the basic definitions and well known facts is presented in chapter I. In chapter II, we define a class of measures on the $\aleph\sb{n},\ n\in\omega$, in … more
Date: August 1995
Creator: Khafizov, Farid T.
Partner: UNT Libraries
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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)
Partner: UNT Libraries
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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
Partner: UNT Libraries
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Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Description: We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
Date: August 1995
Creator: Thompson, Jeremy R. (Jeremy Ray)
Partner: UNT Libraries
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Intuition versus Formalization: Some Implications of Incompleteness on Mathematical Thought

Description: This paper describes the tension between intuition about number theory and attempts to formalize it. I will first examine the root of the dilemma, Godel's First Incompleteness Theorem, which demonstrates that in any reasonable formalization of number theory, there will be independent statements. After proving the theorem, I consider some of its consequences on intuition, focusing on Freiling's "Dart Experiment" which is based on our usual notion of the real numbers as a line. This experiment gi… more
Date: August 1994
Creator: Lindman, Phillip A. (Phillip Anthony)
Partner: UNT Libraries
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A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence

Description: We investigate a class of minimal sequences on a finite alphabet Ak = {1,2,...,k} having (k - 1)n + 1 distinct subwords of length n. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of binary Sturmian sequences. We describe two simple combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences (one of which is new even in the Sturmian case). Arnoux-Rauzy sequences arising from fixed points of primitive morphisms are characterized by… more
Date: August 1998
Creator: Risley, Rebecca N.
Partner: UNT Libraries
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Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data

Description: In this study, we consider the generalized function solutions to nonlinear wave equation with distribution initial data. J. F. Colombeau shows that the initial value problem u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 then inspect the generalized function representatives for the initial value problem solution to see if the … more
Date: August 1996
Creator: Kim, Jongchul
Partner: UNT Libraries
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