UNT Theses and Dissertations - 464 Matching Results
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- The Dyadic Operator Approach to a Study in Conics, with some Extensions to Higher Dimensions
- The discovery of a new truth in the older fields of mathematics is a rare event. Here an investigator may hope at best to secure greater elegance in method or notation, or to extend known results by some process of generalization. It is our purpose to make a study of conic sections in the spirit of the above remark, using the symbolism developed by Josiah Williard Gibbs.
- The Elementary Transcendental Functions of a Complex Variable as Defined by Integration
- The object of this paper is to define the elementary transcendental functions of a complex variable by means of integrals, and to discuss their properties.
- Lebesgue Linear Measure
- This paper discusses the concept of a general definition of measure, and shows that the Lebesgue measure satisfies the requirements set forth for the ideal definition.
- Number Theoretic Analogies for Certain Theorems and Processes in the Theory of Equations
- The aim of this paper is to exhibit analogs in Number Theory of certain well known theorems and methods of the Theory of Equations.
- Some Properties of Transfinite Cardinal and Ordinal Numbers
- Explains properties of mathematical sets, algebra of sets, and set order types.
- The Analogues for t-Continuity of Certain Theorems on Ordinary Continuity
- This study investigates the relationship between ordinary continuity and t-continuity.
- Some Fundamental Properties of Gamma and Beta Functions
- This paper consists of a discussion of the properties and applications of certain improper integrals, namely the gamma function and the beta function. There are also specific examples of application of these functions in certain fields of applied science.
- Some Properties of Certain Generalizations of the Sum of an Infinite Series
- This thesis attempts to establish properties of Hölder and Cesà ro summable series analogous to those of ordinary convergent series and also to establish properties that are possibly different from those of convergent series.
- The Cantor Ternary Set and Certain of its Generalizations and Applications
- This thesis covers the Cantor Ternary Set and generalizations of the Cantor Set, and gives a complete existential theory for three set properties: denumerability, exhaustibility, and zero measure.
- Some Properties and Applications of Elliptic Integrals
- The object of this paper is to present the properties and some of the applications of the Elliptic Integrals.
- The History of the Calculus
- The purpose of this essay is to trace the development of the concepts of the calculus from their first known appearance, through the formal invention of the method of the calculus in the second half of the seventeenth century, to our own day.
- Some Effects of the War Upon the Mathematics Curriculum and the Motivating Forces at Work as Reflected in the Dallas City Schools
- "To discuss the effect all this war activity has had upon the Dallas Schools and to voice a protest against those who seek to discredit mathematics and at the same time to contribute a readable thesis upon the subject is largely the purpose of this study." --leaf 2
- The Exponential Functions
- The purpose of this paper is to clarify the problems of exponents by introducing notation not customarily used and by demonstrating certain theorems in regard to the properties of the exponential functions.
- A Comparison of Velocities Computed by Two-Dimensional Potential Theory and Velocities Measured in the Vicinity of an Airfoil
- 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.
- Conditions under which Certain Inequalities Become Equalities
- The object of this paper is to consider necessary and sufficient conditions in order for certain important inequalities, which are frequently used in analysis, to reduce to equalities.
- Continuation of Real Functions Defined by Power Series
- This thesis looks at power series, particularly in the areas of: radius of convergence, properties of functions represented by power series, algebra of power series, and Taylor's Theorem and continuation by means of power series.
- A Generalization of Newton's Method
- It is our purpose here to investigate the method of solving equations for real roots by Newton's Method and to indicate a generalization arising from this method.
- Some Properties of Negligible Sets
- In the study of sets of points certain sets are found to be negligible, especially when applied to the theory of functions. The purpose of this paper is to discuss three of these "negligible" types, namely, exhaustible sets, denumerable sets, and sets of Lebesgue measure zero. We will present a complete existential theory in q-space for the three set properties mentioned above, followed by a more restricted discussion in the linear continuum by use of interval properties.
- Some Variation Properties of Real-Valued Functions
- The purpose of this paper is two-fold; we shall first establish a complete existential theory of functions of one real variable with respect to continuity, uniform continuity, absolute continuity, bounded variation, and Lipschitz condition, and second we shall study set-functions in a similar manner, except that the properties to be considered will be continuity, absolute continuity, bounded variation, and additivity.
- The Buckling of a Uniformly Compressed Plate with Intermediate Supports
- This problem has been selected from the mathematical theory of elasticity. We consider a rectangular plate of thickness h, length a, and width b. The plate is subjected to compressive forces. These forces act in the neutral plane and give the plate a tendency to buckle. However, this problem differs from other plate problems in that it is assumed that there are two intermediate supports located on the edges of the plate parallel to the compressive forces.
- A Development of the Real Number System by Means of Nests of Rational Intervals
- The system of rational numbers can be extended to the real number system by several methods. In this paper, we shall extend the rational number system by means of rational nests of intervals, and develop the elementary properties of the real numbers obtained by this extension.
- The Investigation of Some Properties of the Gamma Function
- The purpose of this paper is to prove the existence of the Gamma function and to give some other properties of the function.
- The Stability of the Solutions of Ordinary Differential Equations
- This thesis is a study of stability of the solutions of differential equations.
- 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.
- 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.
- 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.
- Planar Lebesgue Measure
- This thesis attempts to prove the Lebesgue measure is a concrete realization of measure.
- 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.
- 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.
- The Analytical Development of the Trigonometric Functions
- This thesis is a study of the analytical development of the trigonometric 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.
- Means and Mean Value Theorems
- This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.
- 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.
- 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.
- 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.
- 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 Development of the Exponential and Logarithmic Functions
- This thesis discusses a development of the exponential and logarithmic functions.
- A Theorem on the Convergence of a Continued Fraction
- This thesis discusses a theorem on the convergence of a continued fraction.
- 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.
- 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.
- Fundamental Properties of Fourier Series
- This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier 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.
- 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.
- 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.
- 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.
- 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.
- Abstract Measure
- This study of abstract measure covers classes of sets, measures and outer measures, extension of measures, and planer measure.