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3 results

  • Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

  • Simon Macourt, Ilya D. Shkredov, Igor E. Shparlinski
  • Journal:
    Canadian Journal of Mathematics / Volume 70 / Issue 6 / 01 December 2018
    Published online by Cambridge University Press:
    20 November 2018, pp. 1319-1338
    Print publication:
    01 December 2018
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  • We prove a new bound on collinear triples in subgroups of prime finite fields and use it to give some new bounds on exponential sums with trinomials.

  • The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X5 + aX + b

  • Blair K. Spearman, Kenneth S. Williams
  • Journal:
    Canadian Mathematical Bulletin / Volume 45 / Issue 1 / 01 March 2002
    Published online by Cambridge University Press:
    20 November 2018, pp. 138-153
    Print publication:
    01 March 2002
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  • Let ${{X}^{5}}\,+\,aX\,+\,b\,\in \,Z\left[ X \right]$ have Galois group ${{D}_{5}}$. Let $\theta $ be a root of ${{X}^{5}}\,+\,aX\,+\,b$. An explicit formula is given for the discriminant of $Q\left( \theta \right)$.

  • Probability of maintaining or attaining a structure in one step

  • G. Abdallaoui
  • Journal:
    Journal of Applied Probability / Volume 24 / Issue 4 / December 1987
    Published online by Cambridge University Press:
    14 July 2016, pp. 1006-1011
    Print publication:
    December 1987

  • Our concern is with a particular problem which arises in connection with a discrete-time Markov chain model for a graded manpower system. In this model, the members of an organisation are classified into distinct classes. As time passes, they move from one class to another, or to the outside world, in a random way governed by fixed transition probabilities. In this paper, the emphasis is placed on evaluating exact values of the probabilities of attaining and maintaining a structure.