UNT Libraries - 23 Matching Results

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Description: 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

Properties of Order Relations and Certain Partly Ordered Systems

Description: 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

Quadratic Forms

Description: This paper shall be mostly concerned with the development and the properties of three quadratic polynomials. The primary interest will by with n-ary quadratic polynomials, called forms.
Date: June 1959
Creator: Cadenhead, Clarence Tandy

Which Came First : The Measure or the Integral?

Description: This thesis provides a development of integration from two different points of view. In Chapter I, a measure and a measurable function are defined. A theory of integration is then developed in Chapter II based on the measure. In Chapter III, the integral is introduced directly without first going through the process of defining a measure, and a measure is developed from the integral. The concluding chapter shows the equivalence of the two integrals under rather general conditions.
Date: June 1966
Creator: Chapman, John Barnes

Compact Topological Spaces

Description: The purpose of this paper is to investigate some properties of compact topological spaces and to relate these concepts to the separation properties.
Date: June 1964
Creator: Conway, Thomas M.

A Comparison of Velocities Computed by Two-Dimensional Potential Theory and Velocities Measured in the Vicinity of an Airfoil

Description: In treating the motion of a fluid mathematically, it is convenient to make some simplifying assumptions. The assumptions which are made will be justifiable if they save long and laborious computations in practical problems, and if the predicted results agree closely enough with experimental results for practical use. In dealing with the flow of air about an airfoil, at subsonic speeds, the fluid will be considered as a homogeneous, incompressible, inviscid fluid.
Date: June 1947
Creator: Copp, George

Properties of Semigroups

Description: This paper is an introductory, algebraic study of semigroups.
Date: June 1966
Creator: Donnell, William Anthony

Some Fundamental Properties of Categories

Description: This paper establishes a basis for abelian categories, then gives the statement and proof of two equivalent definitions of an abelian category, the development of the basic theory of such categories, and the proof of some theorems involving this basic theory.
Date: June 1968
Creator: Gardner, Harold L.

Concerning linear spaces

Description: The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."
Date: June 1965
Creator: Gilbreath, Joe

Theory of Congruences

Description: This thesis presents a series of theorems along with proofs to establish a theory of congruences.
Date: June 1961
Creator: Green, Harold Rugby

Differentiable Functions

Description: The primary purpose of this thesis is to carefully develop and prove some of the fundamental, classical theorems of the differential calculus for functions of two real variables.
Date: June 1966
Creator: McCool, Kenneth B.

Additive Functions

Description: The purpose of this paper is the analysis of functions of real numbers which have a special additive property, namely, f(x+y) = f(x)+f(y).
Date: June 1963
Creator: McNeir, Ridge W.

Convex Sets in the Plane

Description: The purpose of this paper is to investigate some of the properties of convex sets in the plane through synthetic geometry.
Date: June 1970
Creator: McPherson, Janie L.

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.

Some Properties of Hilbert Space

Description: This thesis is a study of fundamental properties of Hilbert space, properties of linear manifold, and realizations of Hilbert space.
Date: June 1960
Creator: Parker, Donald Earl

The Runge-Kutta Method

Description: 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

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

Introduction to the Theory of Games

Description: The purpose of this thesis is to provide a beginning graduate student in mathematics with the general theory underlying competition between rational, intelligent opponents. This competition can be described as a game of opposing strategies; hence, the name game theory.
Date: June 1959
Creator: Taylor, James Lyle

Some Theorems from Plane Lobachevskian Geometry

Description: 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.

Some Properties of the Fibonacci Numbers

Description: This thesis is presented as an introduction to the Fibonacci sequence of integers. It is hoped that this thesis will create in the reader more interest in this type of sequence and especially the Fibonacci sequence. It seems that this particular area of mathematics is often ignored in the classroom or touched upon far too briefly to stimulate curiosity and develop further interest in this field.
Date: June 1967
Creator: Willey, Wm. Riley

A Generalized Study of the Conjugate and Inner-Product Functions

Description: The usual practice in any discussion of an inner-product space is to restrict the field over which the inner-product space is defined to the field of complex numbers. In defining the inner-product function, (x,y), a second function is needed; namely the conjugate function (x,y)* so that (x,y) ± (y,x)*. We will attempt to generalize this concept by investigating the existence of a conjugate function defined on fields other than the field of complex numbers and relate this function to an inner-product function defined on a linear space L over these fields.
Date: June 1967
Creator: Wright, Dorothy P.