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UNT Theses and Dissertations
Infinite Matrices
Date: August 1957
Creator: Smallwood, James D.
Description: This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.
Contributing Partner: UNT Libraries
Permallink:digital.library.unt.edu/ark:/67531/metadc107976/
Some Generalizations in the Theory of Summable Series
Date: August 1950
Creator: Penner, Jimmie G.
Description: It will be our purpose to study a generalized definition of sum of a series and the restrictions which must be placed upon it in order that it shall satisfy the generally accepted requirements of any generalized definition of sum of a series. We shall then proceed to investigate the possibilities of further generalizing this process.
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Permallink:digital.library.unt.edu/ark:/67531/metadc130256/
Linear Spaces
Date: August 1960
Creator: Carroll, Nelva Dain
Description: The purpose of this paper is to present the results of a study of linear spaces with special emphasis of linear transformations, norms, and inner products.
Contributing Partner: UNT Libraries
Permallink:digital.library.unt.edu/ark:/67531/metadc108094/
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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Permallink:digital.library.unt.edu/ark:/67531/metadc149627/
Hochschild Cohomology and Complex Reflection Groups
Date: August 2012
Creator: Foster-Greenwood, Briana A.
Description: A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the semi-direct product of the group with a polynomial ring on the vector space. Each representation of a group defines a different skew group algebra, which may have its own interesting deformations. In this work, we explicitly describe all graded Hecke algebras arising as deformations of the skew group algebra of any finite group acting by the regular representation. We then focus on rank two exceptional complex reflection groups acting by any irreducible representation. We consider in-depth the reflection representation and a nonfaithful rotation representation. Alongside our study of cohomology for the rotation representation, we develop techniques valid for arbitrary finite groups acting by a representation with a central kernel. Additionally, we consider combinatorial questions about reflection length and codimension orderings on complex reflection groups. We give algorithms using character theory to compute ...
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Permallink:digital.library.unt.edu/ark:/67531/metadc149591/
On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers
Date: August 2012
Creator: Xuan, Mingzhi
Description: In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of closed permutation groups of natural numbers with respect to their universal and surjectively universal groups. We characterize two-sided invariant groups, and prove that there is no universal group for countable groups, nor universal group for two-sided invariant groups in permutation groups of natural numbers.
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Permallink:digital.library.unt.edu/ark:/67531/metadc149691/
On Ordered Pairs of Cardinal Numbers
Date: 1957
Creator: Dickinson, John Dean
Description: This thesis is on ordered pairs of cardinal numbers.
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Permallink:digital.library.unt.edu/ark:/67531/metadc107930/
Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance
Date: 1956
Creator: Haynes, Joe Preston
Description: The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.
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Permallink:digital.library.unt.edu/ark:/67531/metadc107908/
Mechanization of Aircraft Performance
Date: 1956
Creator: Cotten, Frances Patterson
Description: The purpose of this paper is to describe the mechanization of the basic equations of motion for the performance and maneuver characteristics of an airplane with some simplifications which render solutions more practicable. The results of a study made to program these equations for calculation by the IBM MODEL 650 digital computer are presented as well as the steps to be taken in using this method of calculation.
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Permallink:digital.library.unt.edu/ark:/67531/metadc107899/
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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Permallink:digital.library.unt.edu/ark:/67531/metadc108077/