Journal•ISSN: 0008-414X
Canadian Journal of Mathematics
Cambridge University Press
About: Canadian Journal of Mathematics is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Group (mathematics) & Bounded function. It has an ISSN identifier of 0008-414X. Over the lifetime, 5524 publications have been published receiving 123004 citations. The journal is also known as: Journal canadien de mathématiques.
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TL;DR: In this paper, the problem of finding a maximal flow from one given city to another is formulated as follows: "Consider a rail network connecting two cities by way of a number of intermediate cities, where each link has a number assigned to it representing its capacity".
Abstract: Introduction. The problem discussed in this paper was formulated by T. Harris as follows: “Consider a rail network connecting two cities by way of a number of intermediate cities, where each link of the network has a number assigned to it representing its capacity. Assuming a steady state condition, find a maximal flow from one given city to the other.”
2,731 citations
TL;DR: A graph G is a set of elements called vertices and a finite set of edges called edges such that each edge meets exactly two vertices, called the end-points of the edge as mentioned in this paper.
Abstract: A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An edge is said to join its end-points.
1,917 citations
TL;DR: The equations of dynamics were put into a general form by Lagrange, who expressed them in terms of a set of generalized coordinates and velocities as discussed by the authors, and an alternative general form was later given by Hamilton, in the form of coordinates and momenta.
Abstract: 1. Introduction. The equations of dynamics were put into a general form
by Lagrange, who expressed them in terms of a set of generalized coordinates
and velocities. An alternative general form was later given by Hamilton, in
terms of coordinates and momenta. Let us consider the relative merits of the
two forms.
1,725 citations
TL;DR: In this paper, a finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of unitary transformations.
Abstract: Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of unitary transformations (5, p. 257). Such a group may be thought of as a group of congruent transformations, keeping the origin fixed, in a unitary space Un of n dimensions, in which the points are specified by complex vectors with n components, and the distance between two points is the norm of the difference between their corresponding vectors.
1,295 citations
TL;DR: In this paper, a polynomial χ(G, x, y) in two variables x and y, which can be regarded as generalizing both θ(G and n) and ϕ(G n) is studied.
Abstract: Two polynomials θ(G, n) and ϕ(G, n) connected with the colourings of a graph G or of associated maps are discussed. A result believed to be new is proved for the lesser-known polynomial ϕ(G, n). Attention is called to some unsolved problems concerning ϕ(G, n) which are natural generalizations of the Four Colour Problem from planar graphs to general graphs. A polynomial χ(G, x, y) in two variables x and y, which can be regarded as generalizing both θ(G, n) and ϕ(G, n) is studied. For a connected graph χ(G, x, y) is defined in terms of the “spanning” trees of G (which include every vertex) and in terms of a fixed enumeration of the edges.
1,050 citations