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Conditionally convergent vector series
(University of Missouri--Columbia, 1914)
In this paper we propose to study the behavior of series of complex numbers, or of vectors in two dimensions; and to generalize this study to the case of vectors in n dimensions. The particular properties to be studied are ...
Some new aspects of the Galois theory
(University of Missouri--Columbia, 1913)
Realizing that the Galois theory of algebraic equations as commonly presented seems artificial, abstract, and intricate, we have been led in the following paper to attempt to present in a clear, tangible fashion the general, ...
A collection of graphs to accompany certain topics in the study of function theory of a real variable
(University of Missouri--Columbia, 1913)
In Part I of this paper, I have dealt with only well-known properties of functions - treating them from the graphic standpoint entirely and referring the reader, to the best authorities I could find, for the Algebraic ...
Oscillation of certain sets of orthogonal functions
(University of Missouri--Columbia, 1914)
In the classic memoirs of Sturm and Liouville, two classes of theorems are found concerning sets of orthogonal functions. The first deal with the number of sign-changes in [phi]3, and the second with the number of sign-changes ...
Study of the convergence of series in certain orthogonal functions
(University of Missouri--Columbia, 1914)
In this present paper we will develop some theorems concerning the degree of convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding ...