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The Dyadic Operator Approach to a Study in Conics, with some Extensions to Higher Dimensions

Description: 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.
Date: 1940
Creator: Shawn, James Loyd

Lebesgue Linear Measure

Description: 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.
Date: 1940
Creator: Beeman, William Edwin

Some Fundamental Properties of Gamma and Beta Functions

Description: 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.
Date: 1941
Creator: Nolen, Robert L.

The History of the Calculus

Description: 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.
Date: 1945
Creator: Ashburn, Andrew

The Exponential Functions

Description: 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.
Date: 1947
Creator: Sloan, Robert S.

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

Continuation of Real Functions Defined by Power Series

Description: 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.
Date: 1948
Creator: Strickland, Warren, G.

A Generalization of Newton's Method

Description: 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.
Date: 1948
Creator: LeBouf, Billy Ruth

Some Properties of Negligible Sets

Description: 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.
Date: 1948
Creator: Butts, Hubert S.

Some Variation Properties of Real-Valued Functions

Description: 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.
Date: 1948
Creator: Dawson, David Fleming

The Buckling of a Uniformly Compressed Plate with Intermediate Supports

Description: 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.
Date: 1949
Creator: Dean, Thomas S.

A Development of the Real Number System by Means of Nests of Rational Intervals

Description: 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.
Date: 1949
Creator: Williams, Mack Lester

Convergence Tests for Infinite Series

Description: 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.
Date: 1950
Creator: Latimer, Philip W.