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  Partner: UNT Libraries
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
Exhaustivity, continuity, and strong additivity in topological Riesz spaces.

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

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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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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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T-Functions

T-Functions

Date: June 1960
Creator: Barlow, John Rice
Description: The main purpose of this paper is to make a detailed study of a certain class T of complex functions. The functions of the class T have a special mapping property and are meromorphic in every region. As an application of this study, certain elementary functions are defined and studied in terms of a special T-function.
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The Fundamental Group of Certain Toplogical Spaces

The Fundamental Group of Certain Toplogical Spaces

Date: December 1971
Creator: Hopkins, Billy L.
Description: The problem confronted in this thesis is that of determining direct calculations of the fundamental group of certain topological spaces.
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Fundamental Issues in Support Vector Machines

Fundamental Issues in Support Vector Machines

Date: May 2014
Creator: McWhorter, Samuel P.
Description: This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful function here called E and dened as follows: Let V be a complex inner product space. Let N be a function that maps a vector from V to its norm. Let p be a real number between 0 and 2 inclusive and for any in V , let ( be N() raised to the p-th power. Finally, let a be a positive real number. Then E() is exp(()). Although the result is not new (other proofs are known but involve deep properties of stochastic processes) this proof is accessible to advanced undergraduates with a decent grasp of linear algebra. Its ...
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