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  Partner: UNT Libraries
 Resource Type: Thesis or Dissertation
 Degree Discipline: Mathematics
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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The Exponential Functions

The Exponential Functions

Date: 1947
Creator: Sloan, Robert S.
Description: The purpose of this paper is to clarify the problems of exponents by introducing notation not customarily used and by demonstrating certain theorems in regard to the properties of the exponential functions.
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Extensions of Modules

Extensions of Modules

Date: August 1967
Creator: Chen, Paulina Tsui-Chu
Description: This thesis discusses groups, modules, the module of homomorphisms, and extension of modules.
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Field Extensions and Galois Theory

Field Extensions and Galois Theory

Date: August 1967
Creator: Votaw, Charles I.
Description: This paper will be devoted to an exposition of some of the relationships existing between a field and certain of its extension fields. In particular, it will be shown that many fields may be characterized rather simply in terms of their subfields which, in turn, may be directly correlated with the subgroups of a finite group of automorphisms of the given field.
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Finite Dimensional Vector Space

Finite Dimensional Vector Space

Date: August 1960
Creator: Power, Billy Joe
Description: The object of this thesis is to examine properties of an abstract vector space of finite dimension n. The properties of the set of complex numbers are assumed, and the definition of a field and of an abelian group are not stated, although reference to these systems is made.
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