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Descriptions and Computation of Ultrapowers in L(R)
The results from this dissertation are an exact computation of ultrapowers by measures on cardinals $\aleph\sb{n},\ n\in w$, in $L(\IR$), and a proof that ordinals in $L(\IR$) below $\delta\sbsp{5}{1}$ represented by descriptions and the identity function with respect to sequences of measures are cardinals. An introduction to the subject with the basic definitions and well known facts is presented in chapter I. In chapter II, we define a class of measures on the $\aleph\sb{n},\ n\in\omega$, in $L(\IR$) and derive a formula for an exact computation of the ultrapowers of cardinals by these measures. In chapter III, we give the definitions of descriptions and the lowering operator. Then we prove that ordinals represented by descriptions and the identity function are cardinals. This result combined with the fact that every cardinal $<\delta\sbsp{5}{1}$ in $L(\IR$) is represented by a description (J1), gives a characterization of cardinals in $L(\IR$) below $\delta\sbsp{5}{1}. Concrete examples of formal computations are shown in chapter IV.
Date:
August 1995
Creator:
Khafizov, Farid T.
System:
The UNT Digital Library
A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions
The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.
Date:
August 1954
Creator:
Allen, Alfred I.
System:
The UNT Digital Library
A Development of the Real Number System
The purpose of this paper is to construct the real number system. The foundation upon which the real number system will be constructed will be the system of counting numbers.
Date:
August 1961
Creator:
Matthews, Ronald Louis
System:
The UNT Digital Library
Dimension Theory
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 covering dimension and theorems discussing the equivalence of the different dimension functions in certain topological settings. Arguments pertaining to the dimension o f Jn are also contained in Chapter IV.
Date:
August 1986
Creator:
Frere, Scot M. (Scot Martin)
System:
The UNT Digital Library
Direct Sums of Rings
This paper consists of a study of the direct sum U of two rings S and T. Such a direct sum is defined as the set of all ordered pairs (s1, t1), where s1 is an arbitrary element in S and t1 is an arbitrary element in T.
Date:
August 1966
Creator:
Hughes, Dolin F.
System:
The UNT Digital Library
Divisibility in Abelian Groups
This thesis describes properties of Abelian groups, and develops a study of the properties of divisibility in Abelian groups.
Date:
August 1966
Creator:
Huie, Douglas Lee
System:
The UNT Digital Library
Duals and Reflexivity of Certain Banach Spaces
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 fourth chapter, several more theorems concerning dual spaces and related topologies are presented. The final chapter focuses on reflexive spaces. In the main theorem, the relation between compactness and reflexivity is examined. The paper concludes with an example of a non-reflexive space.
Date:
August 1991
Creator:
Dahler, Cheryl L. (Cheryl Lewis)
System:
The UNT Digital Library
Duals and Weak Completeness in Certain Sequence Spaces
In this paper the weak completeness of certain sequence spaces is examined. In particular, we show that each of the sequence spaces c0 and 9, 1 < p < c, is a Banach space. A Riesz representation for the dual space of each of these sequence spaces is given. A Riesz representation theorem for Hilbert space is also proven. In the third chapter we conclude that any reflexive space is weakly (sequentially) complete. We give 01 as an example of a non-reflexive space that is weakly complete. Two examples, c0 and YJ, are given of spaces that fail to be weakly complete.
Date:
August 1980
Creator:
Leavelle, Tommy L. (Tommy Lee)
System:
The UNT Digital Library
Equivalence Classes of Subquotients of Pseudodifferential Operator Modules on the Line
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.
Date:
August 2012
Creator:
Larsen, Jeannette M.
System:
The UNT Digital Library
Euclidean N-space
This study of the Euclidean N-space looks at some definitions and their characteristics, some comparisons, boundedness and compactness, and transformations and mappings.
Date:
August 1962
Creator:
Horner, Donald R.
System:
The UNT Digital Library
The Eulerian Functions of Cyclic Groups, Dihedral Groups, and P-Groups
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)
System:
The UNT Digital Library
Examples and Applications of Infinite Iterated Function Systems
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.
Date:
August 2000
Creator:
Hanus, Pawel Grzegorz
System:
The UNT Digital Library
Existence and Multiplicity of Solutions for Semilinear Elliptic Boundary Value Problems
This thesis studies the existence, multiplicity, bifurcation and the stability of the solutions to semilinear elliptic boundary value problems. These problems are motivated both by the mathematical structure and the numerous applications in fluid mechanics chemical reactions, nuclear reactors, Riemannian geometry and elasticity theory. This study considers the problem for different classes of nonlinearities and obtain the existence and multiplicity of positive solutions.
Date:
August 1992
Creator:
Gadam, Sudhasree
System:
The UNT Digital Library
Existence of a Sign-Changing Solution to a Superlinear Dirichlet Problem
We study the existence, multiplicity, and nodal structure of solutions to a superlinear elliptic boundary value problem. Under specific hypotheses on the superlinearity, we show that there exist at least three nontrivial solutions. A pair of solutions are of one sign (positive and negative respectively), and the third solution changes sign exactly once. Our technique is variational, i.e., we study the critical points of the associated action functional to find solutions. First, we define a codimension 1 submanifold of a Sobolev space . This submanifold contains all weak solutions to our problem, and in our case, weak solutions are also classical solutions. We find nontrivial solutions which are local minimizers of our action functional restricted to various subsets of this submanifold. Additionally, if nondegenerate, the one-sign solutions are of Morse index 1 and the sign-changing solution has Morse index 2. We also establish that the action level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. Our results extend and complement the findings of Z. Q. Wang ([W]). We include a small sample of earlier works in the general area of superlinear elliptic boundary value problems.
Date:
August 1995
Creator:
Neuberger, John M. (John Michael)
System:
The UNT Digital Library
Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains
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.
Date:
August 1998
Creator:
Finan, Marcel Basil
System:
The UNT Digital Library
Explicit Multidimensional Solitary Waves
In this paper we construct explicit examples of solutions to certain nonlinear wave equations. These semilinear equations are the simplest equations known to possess localized solitary waves in more that one spatial dimension. We construct explicit localized standing wave solutions, which generate multidimensional localized traveling solitary waves under the action of velocity boosts. We study the case of two spatial dimensions and a piecewise-linear nonlinearity. We obtain a large subset of the infinite family of standing waves, and we exhibit several interesting features of the family. Our solutions include solitary waves that carry nonzero angular momenta in their rest frames. The spatial profiles of these solutions also furnish examples of symmetry breaking for nonlinear elliptic equations.
Date:
August 1990
Creator:
King, Gregory B. (Gregory Blaine)
System:
The UNT Digital Library
Extensions of Modules
This thesis discusses groups, modules, the module of homomorphisms, and extension of modules.
Date:
August 1967
Creator:
Chen, Paulina Tsui-Chu
System:
The UNT Digital Library
Field Extensions and Galois Theory
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.
Date:
August 1967
Creator:
Votaw, Charles I.
System:
The UNT Digital Library
Finite Difference Methods for Approximating Solutions to the Heat Equation
This paper is concerned with finite difference methods for approximating solutions to the partial differential heat equation. The first chapel gives some introductory background into the physical problem, then motivates three finite difference methods. Chapters II through IV provide statements and proofs for the theorems used in the methods of Chapter I. The final Chapter, V, provides conclusions and an indication of future work. An appendix includes the computer codes written by the author with numerical results.
Date:
August 1982
Creator:
Neuberger, Barbara O. (Barbara Osher)
System:
The UNT Digital Library
Finite Dimensional Vector Space
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.
Date:
August 1960
Creator:
Power, Billy Joe
System:
The UNT Digital Library
Finite Element Solutions to Nonlinear Partial Differential Equations
This paper develops a numerical algorithm that produces finite element solutions for a broad class of partial differential equations. The method is based on steepest descent methods in the Sobolev space H¹(Ω). Although the method may be applied in more general settings, we consider only differential equations that may be written as a first order quasi-linear system. The method is developed in a Hilbert space setting where strong convergence is established for part of the iteration. We also prove convergence for an inner iteration in the finite element setting. The method is demonstrated on Burger's equation and the Navier-Stokes equations as applied to the square cavity flow problem. Numerical evidence suggests that the accuracy of the method is second order,. A documented listing of the FORTRAN code for the Navier-Stokes equations is included.
Date:
August 1981
Creator:
Beasley, Craig J. (Craig Jackson)
System:
The UNT Digital Library
Fourier Transforms of Functions on a Finite Abelian Group
This paper presents a theory of Fourier transforms of complex-valued functions on a finite abelian group and investigates two applications of this theory. Chapter I is an introduction with remarks on notation. Basic theory, including Pontrvagin duality and the Poisson Summation formula, is the subject of Chapter II. In Chapter III the Fourier transform is viewed as an intertwining operator for certain unitary group representations. The solution of the eigenvalue problem of the Fourier transform of functions on the group Z/n of integers module n leads to a proof of the quadratic reciprocity law in Chapter IV. Chapter V addresses the, use of the Fourier transform in computing.
Date:
August 1982
Creator:
Currey, Bradley Norton
System:
The UNT Digital Library
Fundamental Properties of Fourier Series
This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.
Date:
August 1954
Creator:
Hubbard, Geogre U.
System:
The UNT Digital Library
Fundamental Properties of the Contingent
This thesis explores the fundamental properties of the contingent.
Date:
August 1960
Creator:
Haggard, Paul W.
System:
The UNT Digital Library