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Moscow University Mathematics Bulletin

, Volume 73, Issue 4, pp 162–163 | Cite as

Optimal Control, Everywhere Dense Torus Winding, and Wolstenholme Primes

  • D. D. KiselevEmail author
Brief Communications
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Abstract

An optimal control problem is constructed so that its control runs over an everywhere dense winding of a k-dimensional torus for arbitrary natural k ≤ 249 998 919 given in advance. The construction is based on Galois theory and the Wolstenholme primes distribution.

References

  1. 1.
    D. D. Kiselev, L. V. Lokutsievskii, and M. I. Zelikin, “Optimal Control and Galois Theory,” Matem. Sbornik 204 (11), 83 (2013) [Sbornik: Math. 204 (11), 1624 (2013)].MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. J. McIntosh and E. L. Roettger, “A Search for Fibonacci–Wieferich and Wolstenholme Primes,” Math. Comput. 76, 2087 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    D. D. Kiselev, “Applications of Galois Theory to Optimal Control,” in: Proc. 48th Int. Youth School-Conference “Modern Problems in Mathematics and its Applications,” Yekaterinburg, Russia, February 5–11, 2017, ed. by A. Makhnev and S. Pravdin (Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, 2017), pp. 50–56Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Russian Foreign Trade Academy, Chair of Informatics and MathematicsMoscowRussia

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