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Two Axiomatic Definitions of the Natural Numbers

Description: The purpose of this thesis is to present an axiomatic foundation for the development of the natural numbers from two points of view. It makes no claim at originality other than at the point of organization and presentation of previously developed works.
Date: June 1970
Creator: Rhoads, Lana Sue
Partner: UNT Libraries

Some Properties of Topological Spaces

Description: This thesis presents a development of some useful concepts concerning topological spaces. Most of the theorems given apply to the most general form of topological space.
Date: August 1968
Creator: Smith, Bayard M., Jr.
Partner: UNT Libraries

On Uniform Convergence

Description: In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.
Date: 1951
Creator: Drew, Dan Dale
Partner: UNT Libraries

Some Properties of the Perron Integral

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.
Date: June 1955
Creator: McWhorter, Bobby J.
Partner: UNT Libraries

Metric Spaces

Description: This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.
Date: 1957
Creator: Bilyeu, Russell Gene
Partner: UNT Libraries

Elements of Boolean Algebra Theory

Description: The primary purpose of this paper is to state a set of postulates for Boolean algebra and show the characteristic theorems derivable from them, and to unify in one paper the more important methods of representing Boolean algebra and show their equivalence.
Date: 1957
Creator: Harvill, John Bowman
Partner: UNT Libraries

Some Fundamental Theorems on Infinite Products

Description: Since infinite products are seldom encountered in elementary mathematics, it is the purpose of this paper to familiarize the reader with their concept and properties. In the main, it is the compilation of material found in various references and revised to conform to standard notation.
Date: 1957
Creator: Gonzalez, Genaro B.
Partner: UNT Libraries

Mechanization of Aircraft Performance

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.
Date: 1956
Creator: Cotten, Frances Patterson
Partner: UNT Libraries

Orthogonal Functions

Description: In this study the idea of orthogonality of two lines will be generalized to the idea of orthogonality of two functions. In particular, the orthogonality of two lines may be treated from the standpoint of the orthogonality of two vectors in two-dimensional space.
Date: 1956
Creator: Harrison, Ivan
Partner: UNT Libraries

Abstract Measure

Description: This study of abstract measure covers classes of sets, measures and outer measures, extension of measures, and planer measure.
Date: 1957
Creator: Bridges, Robert Miller
Partner: UNT Libraries

Improper Integrals

Description: In this paper a definitions shall be given for different types of improper integrals and several theorems concerning them shall be proved.
Date: 1957
Creator: Hildebrand, Shelby K.
Partner: UNT Libraries

Linear and Planar Jordan Content

Description: This paper considers the concept of inner and outer content, which was introduced by Camille Jordan and Giuseppe Peano near the end of the nineteenth century.
Date: 1957
Creator: Hodge, James E.
Partner: UNT Libraries

Stieljes Integral and Related Topics

Description: The principal purpose of this paper is to develop the properties of Riemann-Stieljes Integrals. Consequently, a knowledge of the terminology and theory of point sets and functions of real variables shall be assumed.
Date: August 1958
Creator: Willis, Charles L.
Partner: UNT Libraries

Some Amine Derivatives of 1,4-naphthoquinone

Description: It was the aim of this investigation to prepare derivatives of 1,4-naphthoquinone substituted at the 2- and 3- positions with various amino groups. 2,3-Dichloro-1,4-naphthoquinone was selected as the starting material because of the possibility of replacing the chloro groups in direct substitution reactions with amines.
Date: August 1959
Creator: Cunningham, Robert Gipson
Partner: UNT Libraries

Topological Groups

Description: The notion of a topological group follows naturally from a combination of the properties of a group and a topological space. Since a group consists of a set G of elements which may be either finite or infinite and since this is also common to a topological space, a question is opened as to whether or not it is possible to assign a topology to a set of elements which form a group under a certain operation. Now it is possible to assign a topology to any set of elements if no restriction is placed on the topology assigned and hence this study would be of little value from the standpoint of the group itself. If however it is required that the group operation be continuous in the topological space then a very interesting theory is developed.
Date: May 1960
Creator: Carry, Laroy Ray
Partner: UNT Libraries