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Ï€-regular Rings
The dissertation focuses on the structure of π-regular (regular) rings.
Date:
May 1993
Creator:
Badawi, Ayman R.
System:
The UNT Digital Library
Valuations and Valuation Rings
This paper is an investigation of several basic properties of ordered Abelian groups, valuations, the relationship between valuation rings, valuations, and their value groups and valuation rings. The proofs to all theorems stated without proof can be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1858. In Chapter I several basic theorems which are used in later proofs are stated without proof, and we prove several theorems on the structure of ordered Abelian groups, and the basic relationships between these groups, valuations, and their valuation rings in a field. In Chapter II we deal with valuation rings, and relate the structure of valuation rings to the structure of their value groups.
Date:
August 1975
Creator:
Badt, Sig H.
System:
The UNT Digital Library
Complemented Subspaces of Bounded Linear Operators
For many years mathematicians have been interested in the problem of whether an operator ideal is complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. Let L(X, Y ) be a Banach space of all bounded linear operator between Banach spaces X and Y , K(X, Y ) be the space of all compact operators, and W(X, Y ) be the space of all weakly compact operators. We denote space all operator ideals by O.
Date:
August 2003
Creator:
Bahreini Esfahani, Manijeh
System:
The UNT Digital Library
Level Curves of the Angle Function of a Positive Definite Symmetric Matrix
Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.
Date:
December 2009
Creator:
Bajracharya, Neeraj
System:
The UNT Digital Library
Near-Rings
The primary objective of this work is to discuss some of the elementary properties of near-rings as they are related to rings. This study is divided into three subdivisions: (1) Basic Properties and Concepts of Near-Rings; (2) The Ideal Structure of Near-Rings; and (3) Homomorphism and Isomorphism of Near-Rings.
Date:
May 1972
Creator:
Baker, Edmond L.
System:
The UNT Digital Library
Completely Simple Semigroups
The purpose of this thesis is to explore some of the characteristics of 0-simple semigroups and completely 0-simple semigroups.
Date:
August 1968
Creator:
Barker, Bruce W.
System:
The UNT Digital Library
T-Functions
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.
Date:
June 1960
Creator:
Barlow, John Rice
System:
The UNT Digital Library
Product and Function Spaces
In this paper the Cartesian product topology for an arbitrary family of topological spaces and some of its basic properties are defined. The space is investigated to determine which of the separation properties of the component spaces are invariant.
Date:
August 1971
Creator:
Barrett, Lewis Elder
System:
The UNT Digital Library
Properties of Order Relations and Certain Partly Ordered Systems
The purpose of this paper is to present a study of partly ordered sets. It includes a rigorous development of relations based on the notion of a relation as a set, lattices, and theorems concerning the lattice of subgroups of a group.
Date:
June 1961
Creator:
Barros, David Nicholas
System:
The UNT Digital Library
Mycielski-Regular Measures
Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence are called Mycielski-regular. We show that the self-similar measure generated by a finite family of contracting similitudes and which up to a constant is the Hausdorff measure in its dimension on an invariant set C is Mycielski-regular.
Date:
August 2011
Creator:
Bass, Jeremiah Joseph
System:
The UNT Digital Library
A Set of Axioms for a Topological Space
Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.
Date:
August 1960
Creator:
Batcha, Joseph Patrick
System:
The UNT Digital Library
The Development of the Natural Numbers by Means of the Peano Postulates
This thesis covers the development of the natural numbers by means of the peano postulates.
Date:
1951
Creator:
Baugh, Orvil Lee
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
On Sets and Functions in a Metric Space
The purpose of this thesis is to study some of the properties of metric spaces. An effort is made to show that many of the properties of a metric space are generalized properties of R, the set of real numbers, or Euclidean n--space, and are specific cases of the properties of a general topological space.
Date:
December 1971
Creator:
Beeman, Anne L.
System:
The UNT Digital Library
Lebesgue Linear Measure
This paper discusses the concept of a general definition of measure, and shows that the Lebesgue measure satisfies the requirements set forth for the ideal definition.
Date:
1940
Creator:
Beeman, William Edwin
System:
The UNT Digital Library
Compactness and Equivalent Notions
One of the classic theorems concerning the real numbers states that every open cover of a closed and bounded subset of the real line contains a finite subcover. Compactness is an abstraction of that notion, and there are several ideas concerning it which are equivalent and many which are similar. The purpose of this paper is to synthesize the more important of these ideas. This synthesis is accomplished by demonstrating either situations in which two ordinarily different conditions are equivalent or combinations of two or more properties which will guarantee a third.
Date:
August 1967
Creator:
Bell, Wayne Charles
System:
The UNT Digital Library
Restricting Invariants and Arrangements of Finite Complex Reflection Groups
Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Röhrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X is in the lattice of the reflection arrangement of G. The main result characterizes when the restriction mapping is surjective in terms of the exponents of G and C and their reflection arrangements.
Date:
August 2015
Creator:
Berardinelli, Angela
System:
The UNT Digital Library
Dimensions in Random Constructions.
We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
Date:
May 2002
Creator:
Berlinkov, Artemi
System:
The UNT Digital Library
Some Theorems and Product Spaces
This thesis is a study of some axioms and theorems, and product spaces.
Date:
1957
Creator:
Bethel, Edward Lee
System:
The UNT Digital Library
Metric Spaces
This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.
Date:
1957
Creator:
Bilyeu, Russell Gene
System:
The UNT Digital Library
Algebraic Integers
The primary purpose of this thesis is to give a substantial generalization of the set of integers Z, where particular emphasis is given to number theoretic questions such as that of unique factorization. The origin of the thesis came from a study of a special case of generalized integers called the Gaussian Integers, namely the set of all complex numbers in the form n + mi, for m,n in Z. The main generalization involves what are called algebraic integers.
Date:
August 1969
Creator:
Black, Alvin M.
System:
The UNT Digital Library
Means and Mean Value Theorems
This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.
Date:
1951
Creator:
Blummer, Raymond O.
System:
The UNT Digital Library
Random Sampling
The purpose of this study is to show the use of random sampling in solving certain mathematical problems. The origin of random numbers to be used in sampling is discussed and methods of sampling from known distributions are then given together with an indication that the sampling procedures are unbiased.
Date:
January 1957
Creator:
Booker, Aaron Hicks
System:
The UNT Digital Library
The Riemann-Complete Integral
The problem with which this paper is concerned is that of defining the Riemann-Complete Integral and comparing it with the Riemann and the Lebesgue Integrals.
Date:
May 1972
Creator:
Boyd, Eddie
System:
The UNT Digital Library