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  Partner: UNT Libraries
 Department: Department of Mathematics
 Collection: UNT Theses and Dissertations
On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers

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.
Contributing Partner: UNT Libraries
Some Generalizations in the Theory of Summable Series

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.
Contributing Partner: UNT Libraries
Some Properties of Dini Derivatives

Some Properties of Dini Derivatives

Date: August 1953
Creator: Pinkerton, Jane W.
Description: The purpose of this paper is to derive certain of the fundamental properties of the Dini derivatives of an arbitrary real function. To this end it will be necessary to investigate the properties of the limits superior and inferior of real functions and to prove the Vitali Covering Theorem as well as a fundamental theorem on the metric density of arbitrary point sets.
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A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions

A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions

Date: August 1954
Creator: Allen, Alfred I.
Description: 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.
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Convergence Preserving Matrices

Convergence Preserving Matrices

Date: August 1961
Creator: Line, Harrell Harvey
Description: This paper is the result of a study of triangular matrices with particular emphasis on those which are convergence preserving transformations.
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Basic Fourier Transforms

Basic Fourier Transforms

Date: January 1962
Creator: Cumbie, James Randolph
Description: The purpose of this paper is to develop some of the more basic Fourier transforms which are the outgrowth of the Fourier theorem. Although often approached from the stand-point of the series, this paper will approach the theorem from the standpoint of the integral.
Contributing Partner: UNT Libraries
Some Properties of the Perron Integral

Some Properties of the Perron Integral

Date: June 1955
Creator: McWhorter, Bobby J.
Description: The purpose of this thesis is to restate the definition of the integral as given by O. Perron, to establish some of the fundamental properties of the Perron integral, and to prove the equivalence between the Perron and Lebesgue integrals in the bounded case.
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The Structure of a Boolean Algebra

The Structure of a Boolean Algebra

Date: August 1965
Creator: Bryant, June Anne
Description: The purpose of this chapter is to develop a form of a "free" Boolean algebra with Σ as a base, by imposing the usual Boolean operations on the set Σ and thus generating new elements freely within explicitly prescribed restrictions.
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The Laplace Transformation

The Laplace Transformation

Date: August 1965
Creator: Floyd, Russell
Description: A set of definitions, theorems and proofs to describe the Laplace transformation.
Contributing Partner: UNT Libraries
The Comparability of Cardinals

The Comparability of Cardinals

Date: May 1964
Creator: Owen, Aubrey P.
Description: The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.
Contributing Partner: UNT Libraries