Showing papers in "American Journal of Mathematics in 1941"
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TL;DR: In this paper, the Dirichlet problem for the hyperbolic differential equation (HDE) has been studied in the context of potential equations, where the problem of determining a solution u of (1) from given values on a closed curve C has a completely different character from that of the corresponding problem for an elliptic equation.
Abstract: This paper deals with the Dirichlet problem for the hyperbolic differential equation
$${U_{xy}} = 0$$
(1)
i. e. with the problem of determining a solution u of (1) from given values on a closed curve C.1 Simple examples show that the Dirichlet problem for a hyperbolic equation has a completely different character from that of the corresponding problem for an elliptic equation such as the potential equation
$${U_{xx}} + {U_{yy}} = 0$$
(2)
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TL;DR: In this article, the authors derived a classification of representations of finite groups with special reference to groups which satisfy the following two conditions: 1) every element is equivalent to its reciprocal, i.e., all classes are ambivalent; 2) the Kronecker product of any two irreducible representations of the group contains no representation more than once.
Abstract: The purpose of this paper is the derivation of a classification of the representations of finite groups with special reference to groups which satisfy the following two conditions:
a.
Every element is equivalent to its reciprocal, i. e., all classes are ambivalent.
b.
The Kronecker (or “direct”) product of any two irreducible representations of the group contains no representation more than once.