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  Partner: UNT Libraries
 Department: Department of Mathematics
 Language: English
 Collection: UNT Theses and Dissertations
Elements of Boolean Algebra Theory

Elements of Boolean Algebra Theory

Date: 1957
Creator: Harvill, John Bowman
Description: The primary purpose of this paper is to state a set of postulates for Boolean algebra and show the characteristic theorems derivable from them, and to unify in one paper the more important methods of representing Boolean algebra and show their equivalence.
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Elliptic Geometry

Elliptic Geometry

Date: January 1966
Creator: Robertson, Barbara McKinzie
Description: This thesis discusses elliptic geometry including the order and incidence properties, projective properties and congruence properties.
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Equivalence Classes of Cauchy Sequences of Rational Numbers

Equivalence Classes of Cauchy Sequences of Rational Numbers

Date: January 1965
Creator: Darnell, Linda Jane
Description: The purpose of this thesis is to define equivalence classes of Cauchy sequences of rational numbers and the operations of taking a sum and a product and then to show that this system is an uncountable, ordered, complete field. In so doing, a mathematical system is obtained which is isomorphic to the real number system.
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Equivalence Classes of Subquotients of Pseudodifferential Operator Modules on the Line

Equivalence Classes of Subquotients of Pseudodifferential Operator Modules on the Line

Date: August 2012
Creator: Larsen, Jeannette M.
Description: Certain subquotients of Vec(R)-modules of pseudodifferential operators from one tensor density module to another are categorized, giving necessary and sufficient conditions under which two such subquotients are equivalent as Vec(R)-representations. These subquotients split under the projective subalgebra, a copy of ????2, when the members of their composition series have distinct Casimir eigenvalues. Results were obtained using the explicit description of the action of Vec(R) with respect to this splitting. In the length five case, the equivalence classes of the subquotients are determined by two invariants. In an appropriate coordinate system, the level curves of one of these invariants are a pencil of conics, and those of the other are a pencil of cubics.
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Euclidean N-space

Euclidean N-space

Date: August 1962
Creator: Horner, Donald R.
Description: This study of the Euclidean N-space looks at some definitions and their characteristics, some comparisons, boundedness and compactness, and transformations and mappings.
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Examples and Applications of Infinite Iterated Function Systems

Examples and Applications of Infinite Iterated Function Systems

Date: August 2000
Creator: Hanus, Pawel Grzegorz
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 from complex continued fraction expansions with restricted entries. Each system is obtained from an infinite number of contractions. We show that under certain conditions the limit sets of such systems possess zero Hausdorff measure and positive finite packing measure. We include an algorithm for an approximation of the Hausdorff dimension of limit sets. One numerical result is presented. In this thesis we also explore the concept of positively recurrent function. We use iterated function systems to construct a natural, wide class of such functions that have strong ergodic properties.
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Exhaustibility and Related Set Properties

Exhaustibility and Related Set Properties

Date: 1950
Creator: Cargal, Buchanan
Description: The purpose of this paper is to develop certain fundamental properties of exhaustible sets and their complements and to examine various set properties which are generalizations, with respect to exhaustible neglect, or well-known set properties.
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Exhaustivity, continuity, and strong additivity in topological Riesz spaces.

Exhaustivity, continuity, and strong additivity in topological Riesz spaces.

Access: Use of this item is restricted to the UNT Community.
Date: May 2004
Creator: Muller, Kimberly O.
Description: In this paper, exhaustivity, continuity, and strong additivity are studied in the setting of topological Riesz spaces. Of particular interest is the link between strong additivity and exhaustive elements of Dedekind s-complete Banach lattices. There is a strong connection between the Diestel-Faires Theorem and the Meyer-Nieberg Lemma in this setting. Also, embedding properties of Banach lattices are linked to the notion of strong additivity. The Meyer-Nieberg Lemma is extended to the setting of topological Riesz spaces and uniform absolute continuity and uniformly exhaustive elements are studied in this setting. Counterexamples are provided to show that the Vitali-Hahn-Saks Theorem and the Brooks-Jewett Theorem cannot be extended to submeasures or to the setting of Banach lattices.
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Existence and Uniqueness Theorems for Nth Order Linear and Nonlinear Integral Equations

Existence and Uniqueness Theorems for Nth Order Linear and Nonlinear Integral Equations

Date: May 1969
Creator: Hurlbert, Gayle Jene Shultz
Description: The purpose of this paper is to study nth order integral equations. The integrals studied in this paper are of the Riemann type.
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Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains

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.
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