Roger Chalkley

Information about group matrices

Abstract Each ordering for the elements of a finite group G of order n defines a corresponding class of group matrices for G . First, this paper proves that the number of distinct classes of group matrices for G equals ( n − 1)!/ m , where m is the number of automorphisms of G . Then, a study is made of a block-diagonal reduction for the group matrices of any particular class.

Basic global relative invariants for homogeneous linear differential equations

Introduction Some problems of historical importance Illustrations for some results in Chapters 1 and 2

A first-order algebraic differential equation

\boldsymbol{L}_n

The differential equation Q=0 in which Q is a quadratic form in y″, y', y having meromorphic coefficients

and

Explicit solutions of an algebraic differential equation

\boldsymbol{I}_{n,\boldsymbol{i}}

A formula giving the known relative invariants for homogeneous linear differential equations

as semi-invariants of the first kind

An IBM-704 Code for a Harmonics Method Applied to Two-Region Spherical Reactors

\boldsymbol{V}_n

New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points

and

Matrices Derived from Finite Abelian Groups

\boldsymbol{J}_{n,\boldsymbol{i}}

Relative invariants for homogeneous linear differential equations

as semi-invariants of the second kind The coefficients of transformed equations Formulas that involve