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Volume 10 - April 1967

Contents

Page 5 of 11

Research Article

  • On Some Limit Theorems Involving the Empirical Distribution Function

  • Miklós Csörgo
  • Published online by Cambridge University Press:
    20 November 2018, pp. 739-741
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  • Let X1 …, Xn be mutually independent random variables with a common continuous distribution function F (t). Let Fn(t) be the corresponding empirical distribution function, that is

    Fn(t) = (number of Xi ≤ t, 1 ≤ i ≤ n)/n.

    Using a theorem of Manija [4], we proved among others the following statement in [1].

Book Reviews: Comptes Rendus Critiques

  • The open mapping and closed graph theorems in topological vector spaces, by T. Husain. (Oxford math, monographs).

  • J. Dieudonné
  • Published online by Cambridge University Press:
    01 April 2019, pp. 311-312
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  • Elements of Abstract Algebra, by Richard A. Dean. Wiley and Sons, New York, N.Y., 1966. xiv + 324 pages. $7.95.

  • John D. Dixon
  • Published online by Cambridge University Press:
    01 April 2019, pp. 141-142
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Research Article

  • Necessity of Alteration

  • C. Dunham
  • Published online by Cambridge University Press:
    20 November 2018, pp. 743-744
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  • In this note we point out a not easily fillable gap in the proof of a major result in Chebyshev approximations on an interval [α, β]. Tornheim developed a theory for approximation by families unisolvent of degree n (n-parameter families), which was extended by Rice to families unisolvent of variable degree.

Book Reviews: Comptes Rendus Critiques

  • Cours de mathématiques supérieures, Tome I, Algèbre et géométrie, par A. Doneddu. Dunod, Paris, 1965, xv + 583 pages.

  • R. Brossard
  • Published online by Cambridge University Press:
    01 April 2019, pp. 472-473
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Other

  • Abstracts of Theses

  • Published online by Cambridge University Press:
    01 April 2019, pp. 631-634
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Book Reviews: Comptes Rendus Critiques

  • Number-systems, A Modern Introduction, by Mervin L. Keedy. Addison-Wesley, 1965. ix + 226 pages. $6.50.

  • H.A. Thurston
  • Published online by Cambridge University Press:
    01 April 2019, p. 154
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  • A Course in Algol Programming, by G. F. Schaefler. MacMillan, Toronto, 1966. ix + 201 pages.

  • C. Froese
  • Published online by Cambridge University Press:
    01 April 2019, pp. 629-630
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Research Article

  • Concerning the Minimum Function of a Stochastic Matrix

  • Richard Sinkhorn
  • Published online by Cambridge University Press:
    20 November 2018, pp. 745-748
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  • A square matrix is said to be stochastic if its elements are non-negative and if each of its row sums is equal to one. Thus λ = 1 is always an eigenvalue of a stochastic matrix.

Book Reviews: Comptes Rendus Critiques

  • Scales and Weights, by Bruno Kisch. McGill University Press, 295 pages + 98 plates. $15.00.

  • Charles Fox
  • Published online by Cambridge University Press:
    01 April 2019, pp. 484-485
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Research Article

  • Footnote to a Formula of Gioia and Subbarao

  • S. L. Segal
  • Published online by Cambridge University Press:
    20 November 2018, pp. 749-750
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  • Recently Gioia and Subbarao [2] studied essentially the following problem: If g(n) is an arithmetic function, and , then what is the behaviour of H(a, n) defined for each fixed integer a ≥ 2 by

    1

    By using Vaidyanathaswamy′s formula [e.g., 1], they obtain an explicit formula for H(a, n) in case g(n) is positive and completely multiplicative (Formula 2.2 of [2]). However, Vaidyanathaswamy′s formula is unnecessary to the proof of this result, which indeed follows more simply without its use, by exploiting a simple idea used earlier by Subbarao [3] (referred to also in the course of [2]).

Book Reviews: Comptes Rendus Critiques

  • Multidimensional Gaussian Distributions, by K. S. Miller. John Wiley and Sons, 1965. vii + 129 pages. $9.50.

  • Irwin Guttman
  • Published online by Cambridge University Press:
    01 April 2019, p. 323
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Other

  • Problems For Solution

  • Published online by Cambridge University Press:
    01 April 2019, pp. 121-122
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Book Reviews: Comptes Rendus Critiques

Page 5 of 11