# UNT Theses and Dissertations - 49 Matching Results

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- Abstract Measure
- This study of abstract measure covers classes of sets, measures and outer measures, extension of measures, and planer measure.
- The Analytical Development of the Trigonometric Functions
- This thesis is a study of the analytical development of the trigonometric functions.
- Atmospheric Gusts and Their Effect on Aircraft
- This thesis investigates atmospheric gusts and their effect on aircraft.
- Certain Properties of Functions Related to Exhaustibility
- In this thesis, we shall attempt to present a study of certain properties of real functions related to the set property exhaustible.
- Convergence Tests for Infinite Series
- The field of infinite series is so large that any investigation into that field must necessarily be limited to a particular phase. An attempt has been made to develop a number of tests having a wide range of applications. Particular emphasis has been placed on tests for series of positive terms.
- A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions
- 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.
- A Development of the Exponential and Logarithmic Functions
- This thesis discusses a development of the exponential and logarithmic functions.
- 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.
- Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance
- The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.
- Elements of Boolean Algebra Theory
- 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.
- Exhaustibility and Related Set Properties
- The purpose of this paper is to develop certain fundamental properties of exhaustible sets and their complements and to examine various set properties which are generalizations, with respect to exhaustible neglect, or well-known set properties.
- Fundamental Properties of Fourier Series
- This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.
- L'Hospital's Rule
- The purpose of this paper is to present proofs for six cases of L'Hospital's Rule for the evaluation of indeterminate forms. It is also a purpose to reduce to one of these six cases some other indeterminate forms to which L'Hospital's Rule is applicable. In the course of presenting these proofs several theorems and definitions will be used without proof.
- Improper Integrals
- In this paper a definitions shall be given for different types of improper integrals and several theorems concerning them shall be proved.
- Infinite Matrices
- This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.
- Introduction to the Theory of Games
- 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.
- An Investigation of Points About the Circle of Convergence
- This paper will be concerned with the convergence of complex power series.
- The Lebesgue and Equivalent Integrals
- The purpose of this thesis is to present a study of the Lebesgue definite integral, defined in four different ways.
- Linear and Planar Jordan Content
- 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.
- Linear Order
- This paper will be concerned with some fundamental properties of a line. In particular, fundamental ordering properties of a line segment are covered.
- Means and Mean Value Theorems
- This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.
- Mechanization of Aircraft Performance
- 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.
- A Method for Approximating the Distributed Loads of an Airplane by Sets of Point Loads
- This paper gives the derivation of a method for determining the forces to be applied to these points which will simulate the load distributed over all the airplane.
- Metric Spaces
- This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.
- The Moore-Smith Limit
- It is the purpose of this thesis to indicate in more detail how various limits defined in analysis, as well as other concepts not ordinarily defined as limits, may be obtained as special cases of the Moore-Smith limit.
- A Numerical Method for the Calculation of the Inertial Loads on an Airplane
- This paper is an extension of various projects that the writer has been associated with at Chance Vought Aircraft, Incorporated.
- On Continuity of Functions Defined on Unrestricted Point Sets
- This thesis is concerned with an investigation of the generalizations of continuous real functions of a real variable. In particular, the relationship between uniform continuity and ordinary continuity is concerned. The concept of uniform continuity was first introduced by Heine about 1900.
- On Ordered Pairs of Cardinal Numbers
- This thesis is on ordered pairs of cardinal numbers.
- On Uniform Convergence
- 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.
- Orthogonal Functions
- 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.
- Planar Lebesgue Measure
- This thesis attempts to prove the Lebesgue measure is a concrete realization of measure.
- Properties of Commutators
- This paper is a study of the properties of commutators, and deals exclusively with finite groups.
- Quadratic Forms
- 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.
- 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.
- Random Variables of One Dimension
- This thesis examines random variables of one dimension.
- The Riemann Definite Integral of a Bounded Real Function
- The object of this paper is to define, to establish necessary and sufficient conditions for the existence of, and to consider the elementary properties of the Riemann definite integral of a bounded function.
- Semi-continuity and Related Properties
- The elementary notion of a function originated in the work of mathematicians of the seventeenth century, and was somewhat closely connected with investigations in the field of algebra. This paper will be concerned with an investigation of a generalized type of continuity known as semi-continuity.
- Solutions of Algebraic Equations
- It is the object of this paper to present a method for finding the roots of any algebraic equation.
- Some Fundamental Theorems on Infinite Products
- 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.
- Some Generalizations in the Theory of Summable Series
- 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.
- Some Properties of a Lebesgue-Stieltjes Integral
- It is the purpose of this paper to define a Lebesgue integral over a measurable set, the integration being performed with respect to a monotone non-decreasing function as in the Stieltjes integral, and to develop a few of the fundamental properties of such an integral.
- Some Properties of Derivatives
- This paper is concerned with certain properties of derivatives and some characterizations of linear point sets with derivatives. In 1946, Zygmunt Zahorski published a letter on this topic listing a number of theorems without proof, and no proof of these assertions has been published. Some of the theorems presented here are paraphrases of Zahorski's statements, developed in a slightly different order.
- Some Properties of Dini Derivatives
- 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.
- Some Properties of the Perron Integral
- 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.
- Some Results of Two Topological Spaces
- This thesis explores some results of two topological spaces.
- Some Theorems and Product Spaces
- This thesis is a study of some axioms and theorems, and product spaces.
- Stieljes Integral and Related Topics
- 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.
- A Theorem on the Convergence of a Continued Fraction
- This thesis discusses a theorem on the convergence of a continued fraction.
- The Ultraspherical Polynomials
- This study involves the ultraspherical polynomials, the Legendre polynomials, the Tchebichef polynomials of the first kind, and the Tchebichef polynomials of the second kind.