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Cambridge University Press по журналам "Proceedings of the Glasgow Mathematical Association"

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  • Agarwal R. P. (Cambridge University Press. Cambridge, UK, 1961-01-01)
    MacRobert [2] in 1937 defined the E-function as where the symbol denotes that to the expression following it, a similar expression with α and β interchanged is to be added. For (1) he also gave the integral representation ...
  • Macbeath A. M. (Cambridge University Press. Cambridge, UK, 1959-07-01)
    The aim of this note is to examine the basic ideas underlying Minkowski's theorem on lattice points in a symmetrical convex body and related results of Blichfeldt, and to indicate how these can be generalized. Theorems ...
  • Świerczkowski S. (Cambridge University Press. Cambridge, UK, 1959-07-01)
    The present paper is closely related to a paper with the same title by A. M. Macbeath [3]. We use many notions which are defined there for a measure-space; nevertheless we define them once more because we consider the ...
  • Preston G. B. (Cambridge University Press. Cambridge, UK, 1962-07-01)
    A cardinal number which is too large to be reached by some process is generally said to be inaccessible by that process. Many kinds of inaccessible cardinals have been discussed and for a general survey the book of H. ...
  • Munn W. D. (Cambridge University Press. Cambridge, UK, 1961-01-01)
    By a ‘representation’ we shall mean throughout a representation by n × n matrices with entries from an arbitrary field. Elsewhere [9] the author has introduced the concept of a principal representation of a semigroup S ...
  • Boyd A. V.; Hyslop J. M. (Cambridge University Press. Cambridge, UK, 1952-07-01)
    1. Introduction. Given a series we define , by the relations The series Σan is said to be summable (C, k) to the sum s, if as n→∞, and strongly summable (C, k), k>0, with index p, to the sum s, or summable [C; k, p] to ...
  • Allenby R. B. J. T. (Cambridge University Press. Cambridge, UK, 1966-01-01)
    For any nilpotent group B of class c and any given element h of B generating the subgroup H, Wiegold [1] has shown that if, in addition, [B, H] has exponent pr for some prime p and integer r, then B can be embedded in a ...
  • Rathie C. B. (Cambridge University Press. Cambridge, UK, 1956-02-01)
    The object of this paper is to evaluate a few infinite integrals involving E-functions by applying the Parseval-Goldstein [1] theorem of Operational Calculus; that, if and then when the integrals are convergent.
  • Clark W. Edwin (Cambridge University Press. Cambridge, UK, 1965-07-01)
    Let ℒ V denote the algebra of all linear transformations on an n-dimensional vector space V over a field Φ. A subsemigroup S of the multiplicative semigroup of ℒ V will be said to be an affine semigroup over Φ if S is a ...
  • Carlitz L. (Cambridge University Press. Cambridge, UK, 1957-06-01)
    The formula was stated by Bateman ([2], p. 457); a proof is sketched in [3], p. 144. Here the Laguerre polynomial of degree
  • Tranter C. J. (Cambridge University Press. Cambridge, UK, 1960-09-01)
    This note discusses the determination of the coefficients an in the dual trigonometrical series where p = ± 1 and F(x), G(x) are prescribed functions of X. It is shown that this problem and the corresponding one in which ...
  • Bostock F. A.; Patterson E. M. (Cambridge University Press. Cambridge, UK, 1963-07-01)
    Let A be an associative ring. Given a ∊ A, an element b ∊ A is called a left identity for a if Given a subset S of A, an element b ∊ A is, called a left identity for S if (1) is satisfied for all a ∊ S. An element of A ...
  • Husemoller Dale H. (Cambridge University Press. Cambridge, UK, 1960-01-01)
    Hurwitz's theorem says that the limit of schlicht functions, in the topology of compact convergence, is again a schlicht function or a constant function. We generalize this to mappings between Riemann surfaces and get more ...
  • Tranter C. J. (Cambridge University Press. Cambridge, UK, 1963-07-01)
    In this note I show that where Jdenotes the Bessel function of the first kind of the orders and arguments indicated, n = 0, 1, 2, 3, … and the real parts of both μand v exceed — 1. This is a generalization of Sonine's ...
  • Hunter John (Cambridge University Press. Cambridge, UK, 1956-02-01)
    The main result in this paper, contained in Theorem 1, is a generalisation of the inequality of the arithmetic-geometric means. A result of a similar character has been proved by Siegel (2). The present result gives an ...
  • Northcott D. G. (Cambridge University Press. Cambridge, UK, 1956-02-01)
    The development of the theory of local rings has been greatly stimulated by the importance of the applications to algebraic geometry, but it is none the less true that this stimulus has produced a theory which, on aesthetic ...
  • Zassenhaus Hans J. (Cambridge University Press. Cambridge, UK, 1952-07-01)
    The purpose of this paper is to present a proof of the following theorem of Maclagan-Wedderburn.* Every finite skew-field† is a field. The proof depends on group theory and on the properties of Galois fields. As an ...
  • Ennola Veikko (Cambridge University Press. Cambridge, UK, 1964-07-01)
    Let h (m, n) = αm2 + 2δmn + βn2 be a positive definite quadratic form with determinant αβ–δ2 = 1. It may be put in the shape with y > 0. We write (for s > 1) The function Zn(s) may be analytically continued over the whole ...
  • Ragab F. M. (Cambridge University Press. Cambridge, UK, 1953-12-01)
    The formula to be proved is The formulae required in the proof are the Barnes Integral and Whipple's Formula (1) § 2. Proof of the Formula. From (2) the E-function on the left of (1) is equal to
  • Rankin R. A. (Cambridge University Press. Cambridge, UK, 1953-12-01)
    In some recent work by D. G. Kendall and the author † on the number of points of a lattice which lie in a random circle the mean value of the variance emerged as a constant multiple of the value of the Epstein zeta-function ...