Canadian Journal of Mathematics

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The Representation of a Graph by Set Intersections
Canadian Journal of Mathematics - Tập 18 - Trang 106-112 - 1966
P. Erdős, A. W. Goodman, L. Pósa
Geometrically, a graph is a collection of points (or vertices) together with a set of edges (or curves) each of which joins two distinct vertices of the graph, and no two of which have points in common except possibly end points. Two given vertices of the graph may be joined by no edge or one edge, but may not be joined by more than one edge. From an abstract point of view, a graph G is a collecti... hiện toàn bộ
Abstract Quadratic Forms
Canadian Journal of Mathematics - Tập 21 - Trang 1218-1233 - 1969
Irving Kaplansky, R. J. Shaker
We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence relation on unordered n-ples of G. For n = 2:... hiện toàn bộ
Classification of Finite Spaces of Orderings
Canadian Journal of Mathematics - Tập 31 Số 2 - Trang 320-330 - 1979
Murray Marshall
1. Introduction. A space of orderings will refer to what was called a “set of quasi-orderings” in [5]. That is, a space of orderings is a pair (X, G) where G is an elementary 2-group (i.e. x2 = 1 for all x ∈ G) with a distinguished element – 1 ∈ G, and X is a subset of the character group x(G) = Horn (G, {1, –1};) satisfying the following properties:01: X is a closed subset of χ(G).02: σ(−l) = −1 ... hiện toàn bộ
Tensor Algebras, Induced Representations, and the Wold Decomposition
Canadian Journal of Mathematics - Tập 51 Số 4 - Trang 850-880 - 1999
Paul S. Muhly, Baruch Solel
AbstractOur objective in this sequel to [18] is to develop extensions, to representations of tensor algebras overC*-correspondences, of two fundamental facts about isometries on Hilbert space: The Wold decomposition theorem and Beurling’s theorem, and to apply these to the analysis of the invariant subspace structure of certain subalgebras of Cuntz-Krieger algebras.
Comma-Free Codes
Canadian Journal of Mathematics - Tập 10 - Trang 202-209 - 1958
S. W. Golomb, Basil Gordon, L. R. Welch
Let n be a fixed positive integer, and consider an alphabet consisting of the numbers 1, 2, … , n. With this alphabet form all possible k-letter words (a 1 a 2 … a k ), where k is also fixed. There are evidently n k such words in all.... hiện toàn bộ
Bireflectionality in Classical Groups
Canadian Journal of Mathematics - Tập 29 Số 6 - Trang 1157-1162 - 1977
Erich W. Ellers
The motion groups of the real Euclidean plane and of the elliptic plane, the group of projectivities of a line, the projective general linear group PGL2(K), some orthogonal groups O3(K, Q) with char K = 2 (see [8]), are all bireflectional (zweispiegelig). There can be no doubt that bireflectional groups are of prime importance in any theory of groups that are generated by involutions. A brief look... hiện toàn bộ
On Transformation and Oscillation of Linear Differential System
Canadian Journal of Mathematics - Tập 29 Số 2 - Trang 392-399 - 1977
Donald F. St. Mary
In this paper we study second order linear differential systems. We examine the relationship between oscillation of n-dimensional systems and certain associated n-dimensional systems, where m ≧ n. Several theorems are presented which unify and encompass in the linear case a number of results from the literature. In particular, we present a transformation which extends an oscillation theorem due to... hiện toàn bộ
Oscillation Criteria for Matrix Differential Equations
Canadian Journal of Mathematics - Tập 19 - Trang 184-199 - 1967
H. C. Howard
We shall be concerned at first with some properties of the solutions of the matrix differential equation1.1whereis an n × n symmetric matrix whose elements are continuous real-valued functions for 0 < x < ∞, and Y(x) = (yij(x)), Y″(x) = (y″ ij(x)) are n × n matrices. It is clear such equations possess solutions for 0 < x < ∞, since one can reduce them to a first-order system and then apply known e... hiện toàn bộ
An integral Representation of a 10ϕ9 and Continuous Bi-Orthogonal 10ϕ9 Rational Functions
Canadian Journal of Mathematics - Tập 38 Số 3 - Trang 605-618 - 1986
Mizan Rahman
1. Introduction. One of the most remarkable q-extensions of the classical beta integral was recently introduced by Askey and Wilson [1](1.1)where |q| < 1 and the pairwise products of {a, b, c, d} as a multiset do not belong to the set {qj, j = 0, – 1, – 2, …}. The contour C is the unit circle described in the positive direction, but with suitable deformations to separate the sequences of poles con... hiện toàn bộ
On Indefinite Ternary Quadratic Forms
Canadian Journal of Mathematics - Tập 8 - Trang 592-608 - 1956
Barrie Jones, G. L. Watson
1, Introduction. The first systematic study of equivalence of indefinite ternary quadratic forms seems to be that of A. Meyer (10) (see also Bachmann (1)). By methods which are often obscure he showed that the number of classes in a genus is a power of 2, the exact power depending on certain quadratic characters associated with the form.
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