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The Analogues for t-Continuity of Certain Theorems on Ordinary Continuity
This study investigates the relationship between ordinary continuity and t-continuity.
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.
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.
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 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 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.
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 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.
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.
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.
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 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
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 and Applications of Elliptic Integrals
The object of this paper is to present the properties and some of the applications of the Elliptic Integrals.
Some Properties of Certain Generalizations of the Sum of an Infinite Series
This thesis attempts to establish properties of Hölder and Cesàro summable series analogous to those of ordinary convergent series and also to establish properties that are possibly different from those of convergent series.
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 Properties of Transfinite Cardinal and Ordinal Numbers
Explains properties of mathematical sets, algebra of sets, and set order types.
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 Stability of the Solutions of Ordinary Differential Equations
This thesis is a study of stability of the solutions of differential equations.