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Linear Algebras (open access)

Linear Algebras

This paper is primarily concerned with the fundamental properties of a linear algebra of finite order over a field. A discussion of linear sets of finite order over a field is used as an introduction to these properties.
Date: August 1961
Creator: Smith, Nickie Lee
System: The UNT Digital Library
Some Theorems from Plane Lobachevskian Geometry (open access)

Some Theorems from Plane Lobachevskian Geometry

This paper will investigate the geometry that results when Euclid's fifth postulate is replaced by the Lobachevskian assumption. The investigations will be limited to the plane.
Date: June 1961
Creator: Walker, Henry L.
System: The UNT Digital Library
Abstract Vector Spaces and Certain Related Systems (open access)

Abstract Vector Spaces and Certain Related Systems

The purpose of this paper is to make a detailed study of vector spaces and a certain vector-like system.
Date: August 1961
Creator: Goddard, Alton Ray
System: The UNT Digital Library
On Envelopes and Extraneous Loci of Differential Equations of Order One and Higher Degree (open access)

On Envelopes and Extraneous Loci of Differential Equations of Order One and Higher Degree

The purpose of this paper is to examine the properties of the envelope and the extraneous loci associated with the solution curves of ordinary differential equations of the first order and degree greater than one.
Date: August 1961
Creator: Lane, Hal Burns
System: The UNT Digital Library
Convergence Preserving Matrices (open access)

Convergence Preserving Matrices

This paper is the result of a study of triangular matrices with particular emphasis on those which are convergence preserving transformations.
Date: August 1961
Creator: Line, Harrell Harvey
System: The UNT Digital Library
A Development of the Real Number System (open access)

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
The Wave Equation in One Dimension (open access)

The Wave Equation in One Dimension

It is intended that this paper present an acceptable proof of the existence of a solution for the wave equation.
Date: January 1961
Creator: Carlson, Kenneth Emil
System: The UNT Digital Library
Properties of Order Relations and Certain Partly Ordered Systems (open access)

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
Theory of Congruences (open access)

Theory of Congruences

This thesis presents a series of theorems along with proofs to establish a theory of congruences.
Date: June 1961
Creator: Green, Harold Rugby
System: The UNT Digital Library
The Runge-Kutta Method (open access)

The Runge-Kutta Method

This paper investigates the Runge-Kutta method of numerically integrating ordinary differential equations. An existence theorem is given insuring a solution to the differential equation, then the theorem is modified to yield an analytic solution. The derivation of the method itself is followed by an analysis of the inherent error.
Date: June 1961
Creator: Powell, Don Ross
System: The UNT Digital Library