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Volume 3 - 01 January 1960

Contents

Page 2 of 4

Book Reviews

Book Reviews: Comptes Rendus Critiques

Research Article

  • On a Problem of L. Moser

  • Irwin Guttman
  • Published online by Cambridge University Press:
    20 November 2018, pp. 35-39
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  • In [l], Moser derives a recurrence relation and studies the limiting behaviour of the Expectations En of the following game. “A real number is drawn at random from [0,1]. We may either keep the number selected, or reject it and draw again. We can then either keep the second number chosen or reject it, and draw again, and so on. Suppose we have at most n choices. What stopping rule gives the largest En and how can we estimate En?”

Book Reviews

Book Reviews: Comptes Rendus Critiques

Book Reviews

Notes on Numerical Analysis II

  • Interpolation and Curve Fitting by Sectionally Linear Functions

  • Hans Schwerdtfeger
  • Published online by Cambridge University Press:
    20 November 2018, pp. 41-57
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  • Functions employed for interpolation and curve fitting are for the most part polynomials with numerical coefficients. Indeed these are functions whose values for numerically given arguments can be computed directly without resorting to non-algebraic designs. It is known, however, that there are cases where polynomial interpolation does not yield an adequate approximation to a given function (cf. [4], p. 34).

Other

  • Solutions

  • Published online by Cambridge University Press:
    01 April 2019, pp. 189-190
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Research Article

  • Elementary Proofs of the Extremal Properties of the Eigenvalues of the Sturm-Liouville Equation

  • Paul R. Beesack
  • Published online by Cambridge University Press:
    20 November 2018, pp. 59-77
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  • If the Sturm-Liouville eigenvalue problem

    1

    is first approached from the standpoint of differential equations theory - as opposed, say, to the calculus of variations, or the theory of integral equations - the extremal properties of the eigenvalues seem to be generally regarded as lying beyond the scope of the theory. Thus, neither in the standard work of Bocher [l], nor in the recent work of Coddington and Levinson [2] is any mention made of this topic. Collatz [3, 166-8] gives an elementary proof of the minimum property of the least positive eigenvalue of (1.1), and a brief indication of how this argument can be extended to the higher eigenvalues. The purpose of this paper is to consolidate this elementary approach, and to extend it to cover the singular cases where either the interval is infinite, or one or more of the coefficients are singular at the end-points.

Book Reviews

  • Reflections of a Mathematician, by L. J. Mordell. Canadian Mathematical Congress, 1959. vii + 50 pages, $1.00.

  • H.S.M. Coxeter
  • Published online by Cambridge University Press:
    01 April 2019, pp. 84-86
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Reports Informations

  • A Colloquium on Graph Theory

  • W. T. Tutte
  • Published online by Cambridge University Press:
    01 April 2019, pp. 102-103
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Book Reviews: Comptes Rendus Critiques

  • Mathematical Programming and Electrical Networks , by Jack B. Dennis. Wiley, New York, 1959. 186 pages. $4.50.

  • H. Kaufman
  • Published online by Cambridge University Press:
    01 April 2019, pp. 193-194
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Other

  • Solutions

  • Published online by Cambridge University Press:
    01 April 2019, p. 79
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  • Problems for Solution

  • Published online by Cambridge University Press:
    01 April 2019, p. 189
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  • Problems for Solution

  • Published online by Cambridge University Press:
    01 April 2019, p. 78
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Book Reviews

Research Article

  • Sequence and Series Transformations

  • M. S. Macphail
  • Published online by Cambridge University Press:
    20 November 2018, pp. 80-83
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  • The summability methods

    where bnk=ank+an,k+1+ …,are regarded as the sequenceto-sequence and series-to-sequence forms of the same method, and if sk=uo + … + uk, we speak of the series or the sequence {sk} indifferently, as summable A or B.

Book Reviews

Other

  • Abstract of Thesis

  • Published online by Cambridge University Press:
    01 April 2019, p. 216
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Books Received

  • Also Received

  • Published online by Cambridge University Press:
    01 April 2019, p. 97
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Page 2 of 4