UNT Libraries - 464 Matching Results

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Properties of Power Series Rings

Description: This thesis investigates some of the properties of power series rings. The material is divided into three chapters. In Chapter I, some of the basic concepts of rings which are a prerequisite to an understanding of the definitions and theorems which follow are stated. Simple properties of power series rings are developed in Chapter II. Many properties of a ring R are preserved when we attach the indeterminant x to form the power series ring R[[x]]. Further results of power series rings are exami… more
Date: August 1990
Creator: O'Brien, Rita Marie
Item Type: Refine your search to only Thesis or Dissertation
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Integrability, Measurability, and Summability of Certain Set Functions

Description: The purpose of this paper is to investigate the integrability, measurability, and summability of certain set functions. The paper is divided into four chapters. The first chapter contains basic definitions and preliminary remarks about set functions and absolute continuity. In Chapter i, the integrability of bounded set functions is investigated. The chapter culminates with a theorem that characterizes the transmission of the integrability of a real function of n bounded set functions. In Cha… more
Date: December 1977
Creator: Dawson, Dan Paul
Item Type: Refine your search to only Thesis or Dissertation
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Valuations on Fields

Description: This thesis investigates some properties of valuations on fields. Basic definitions and theorems assumed are stated in Capter I. Chapter II introduces the concept of a valuation on a field. Real valuations and non-Archimedean valuations are presented. Chapter III generalizes non-Archimedean valuations. Examples are described in Chapters I and II. A result is the theorem stating that a real valuation of a field K is non-Archimedean if and only if $(a+b) < max4# (a), (b) for all a and b in K. Ch… more
Date: May 1977
Creator: Walker, Catherine A.
Item Type: Refine your search to only Thesis or Dissertation
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Properties of R-Modules

Description: This thesis investigates some of the properties of R-modules. The material is presented in three chapters. Definitions and theorems which are assumed are stated in Chapter I. Proofs of these theorems may be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1958. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Properties of R-modules are developed in Chapter II. The most important results presented in this chapter include exis… more
Date: August 1989
Creator: Granger, Ginger Thibodeaux
Item Type: Refine your search to only Thesis or Dissertation
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On the Development of Descriptive Set Theory

Description: In the thesis, the author traces the historical development of descriptive set theory from the work of H. Lebesgue to the introduction of projective descriptive set theory. Proofs of most of the major results are given. Topics covered include Corel lattices, universal sets, the operation A, analytic sets, coanalytic sets, and the continuum hypothesis The appendix contains a translation of the famous letters exchanged between R. Baire, E. Borel, J. Hadamard and H. Lebesgue concerning Zermelo's a… more
Date: August 1988
Creator: Schlee, Glen A. (Glen Alan)
Item Type: Refine your search to only Thesis or Dissertation
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Duals and Reflexivity of Certain Banach Spaces

Description: The purpose of this paper is to explore certain properties of Banach spaces. The first chapter begins with basic definitions, includes examples of Banach spaces, and concludes with some properties of continuous linear functionals. In the second chapter, dimension is discussed; then one version of the Hahn-Banach Theorem is presented. The third chapter focuses on dual spaces and includes an example using co, RI, and e'. The role of locally convex spaces is also explored in this chapter. In the f… more
Date: August 1991
Creator: Dahler, Cheryl L. (Cheryl Lewis)
Item Type: Refine your search to only Thesis or Dissertation
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Fundamental Issues in Support Vector Machines

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 … more
Date: May 2014
Creator: McWhorter, Samuel P.
Item Type: Refine your search to only Thesis or Dissertation
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The Eulerian Functions of Cyclic Groups, Dihedral Groups, and P-Groups

Description: In 1935, Philip Hall developed a formula for finding the number of ways of generating the group of symmetries of the icosahedron from a given number of its elements. In doing so, he defined a generalized Eulerian function. This thesis uses Hall's generalized Eulerian function to calculate generalized Eulerian functions for specific groups, namely: cyclic groups, dihedral groups, and p- groups.
Date: August 1992
Creator: Sewell, Cynthia M. (Cynthia Marie)
Item Type: Refine your search to only Thesis or Dissertation
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Dimension Theory

Description: This paper contains a discussion of topological dimension theory. Original proofs of theorems, as well as a presentation of theorems and proofs selected from Ryszard Engelking's Dimension Theory are contained within the body of this endeavor. Preliminary notation is introduced in Chapter I. Chapter II consists of the definition of and theorems relating to the small inductive dimension function Ind. Large inductive dimension is investigated in Chapter III. Chapter IV comprises the definition of … more
Date: August 1986
Creator: Frere, Scot M. (Scot Martin)
Item Type: Refine your search to only Thesis or Dissertation
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Weak and Norm Convergence of Sequences in Banach Spaces

Description: We study weak convergence of sequences in Banach spaces. In particular, we compare the notions of weak and norm convergence. Although these modes of convergence usually differ, we show that in ℓ¹ they coincide. We then show a theorem of Rosenthal's which states that if {𝓍ₙ} is a bounded sequence in a Banach space, then {𝓍ₙ} has a subsequence {𝓍'ₙ} satisfying one of the following two mutually exclusive alternatives; (i) {𝓍'ₙ} is weakly Cauchy, or (ii) {𝓍'ₙ} is equivalent to the unit vector basis… more
Date: December 1993
Creator: Hymel, Arthur J. (Arthur Joseph)
Item Type: Refine your search to only Thesis or Dissertation
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The Global Structure of Iterated Function Systems

Description: I study sets of attractors and non-attractors of finite iterated function systems. I provide examples of compact sets which are attractors of iterated function systems as well as compact sets which are not attractors of any iterated function system. I show that the set of all attractors is a dense Fs set and the space of all non-attractors is a dense Gd set it the space of all non-empty compact subsets of a space X. I also investigate the small trans-finite inductive dimension of the space of… more
Date: May 2009
Creator: Snyder, Jason Edward
Item Type: Refine your search to only Thesis or Dissertation
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Urysohn ultrametric spaces and isometry groups.

Description: In this dissertation we study a special sub-collection of Polish metric spaces: complete separable ultrametric spaces. Polish metric spaces have been studied for quite a long while, and a lot of results have been obtained. Motivated by some of earlier research, we work on the following two main parts in this dissertation. In the first part, we show the existence of Urysohn Polish R-ultrametric spaces, for an arbitrary countable set R of non-negative numbers, including 0. Then we give point-by-p… more
Date: May 2009
Creator: Shao, Chuang
Item Type: Refine your search to only Thesis or Dissertation
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Contributions to Descriptive Set Theory

Description: In this dissertation we study closure properties of pointclasses, scales on sets of reals and the models L[T2n], which are very natural canonical inner models of ZFC. We first characterize projective-like hierarchies by their associated ordinals. This solves a conjecture of Steel and a conjecture of Kechris, Solovay, and Steel. The solution to the first conjecture allows us in particular to reprove a strong partition property result on the ordinal of a Steel pointclass and derive a new boundedn… more
Date: August 2015
Creator: Atmai, Rachid
Item Type: Refine your search to only Thesis or Dissertation
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Continuous Combinatorics of a Lattice Graph in the Cantor Space

Description: We present a novel theorem of Borel Combinatorics that sheds light on the types of continuous functions that can be defined on the Cantor space. We specifically consider the part X=F(2ᴳ) from the Cantor space, where the group G is the additive group of integer pairs ℤ². That is, X is the set of aperiodic {0,1} labelings of the two-dimensional infinite lattice graph. We give X the Bernoulli shift action, and this action induces a graph on X in which each connected component is again a two-dimen… more
Date: May 2016
Creator: Krohne, Edward
Item Type: Refine your search to only Thesis or Dissertation
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The Relative Complexity of Various Classification Problems among Compact Metric Spaces

Description: In this thesis, we discuss three main projects which are related to Polish groups and their actions on standard Borel spaces. In the first part, we show that the complexity of the classification problem of continua is Borel bireducible to a universal orbit equivalence relation induce by a Polish group on a standard Borel space. In the second part, we compare the relative complexity of various types of classification problems concerning subspaces of [0,1]^n for all natural number n. In the last … more
Date: May 2016
Creator: Chang, Cheng
Item Type: Refine your search to only Thesis or Dissertation
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Quantum Drinfeld Hecke Algebras

Description: Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring is generated by variables which commute only up to a set of quantum parameters. Certain finite groups may act by graded automorphisms on a quantum polynomial ring and quantum Drinfeld Hecke algebras deform the natural semi-direct product. We classify these algebras for the infinite family of complex… more
Date: August 2016
Creator: Uhl, Christine
Item Type: Refine your search to only Thesis or Dissertation
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Irreducible Modules for Yokonuma-Type Hecke Algebras

Description: Yokonuma-type Hecke algebras are a class of Hecke algebras built from a Type A construction. In this thesis, I construct the irreducible representations for a class of generic Yokonuma-type Hecke algebras which specialize to group algebras of the complex reflection groups and to endomorphism rings of certain permutation characters of finite general linear groups.
Date: August 2016
Creator: Dave, Ojas
Item Type: Refine your search to only Thesis or Dissertation
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Contributions to Descriptive Set Theory

Description: Assume AD+V=L(R). In the first chapter, let W^1_1 denote the club measure on \omega_1. We analyze the embedding j_{W^1_1}\restr HOD from the point of view of inner model theory. We use our analysis to answer a question of Jackson-Ketchersid about codes for ordinals less than \omega_\omega. In the second chapter, we provide an indiscernibles analysis for models of the form L[T_n,x]. We use our analysis to provide new proofs of the strong partition property on \delta^1_{2n+1}
Date: December 2016
Creator: Dance, Cody
Item Type: Refine your search to only Thesis or Dissertation
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Rankin-Cohen Brackets for Hermitian Jacobi Forms and Hermitian Modular Forms

Description: In this thesis, we define differential operators for Hermitian Jacobi forms and Hermitian modular forms over the Gaussian number field Q(i). In particular, we construct Rankin-Cohen brackets for such spaces of Hermitian Jacobi forms and Hermitian modular forms. As an application, we extend Rankin's method to the case of Hermitian Jacobi forms. Finally we compute Fourier series coefficients of Hermitian modular forms, which allow us to give an example of the first Rankin-Cohen bracket of two Her… more
Date: December 2016
Creator: Martin, James D. (James Dudley)
Item Type: Refine your search to only Thesis or Dissertation
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A Decomposition of the Group Algebra of a Hyperoctahedral Group

Description: The descent algebra of a Coxeter group is a subalgebra of the group algebra with interesting representation theoretic properties. For instance, the natural map from the descent algebra of the symmetric group to the character ring is a surjective algebra homomorphism, so the descent algebra implicitly encodes information about the representations of the symmetric group. However, this property does not hold for other Coxeter groups. Moreover, a complete set of primitive idempotents in the descent… more
Date: December 2016
Creator: Tomlin, Drew E
Item Type: Refine your search to only Thesis or Dissertation
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Crystallographic Complex Reflection Groups and the Braid Conjecture

Description: Crystallographic complex reflection groups are generated by reflections about affine hyperplanes in complex space and stabilize a full rank lattice. These analogs of affine Weyl groups have infinite order and were classified by V.L. Popov in 1982. The classical Braid theorem (first established by E. Artin and E. Brieskorn) asserts that the Artin group of a reflection group (finite or affine Weyl) gives the fundamental group of regular orbits. In other words, the fundamental group of the spac… more
Date: August 2017
Creator: Puente, Philip C
Item Type: Refine your search to only Thesis or Dissertation
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A Classification of the Homogeneity of Countable Products of Subsets of Real Numbers

Description: Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And f… more
Date: August 2017
Creator: Allen, Cristian Gerardo
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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.
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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
Item Type: Refine your search to only Thesis or Dissertation
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