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Optimal control, everywhere dense torus winding, and Wolstenholme primes. (English. Russian original) Zbl 1403.49019

Mosc. Univ. Math. Bull. 73, No. 4, 162-163 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 4, 60-62 (2018).
Summary: An optimal control problem is constructed so that its control runs over an everywhere dense winding of a \(k\)-dimensional torus for arbitrary natural \(k\leq 249 998 919\) given in advance. The construction is based on Galois theory and the Wolstenholme primes distribution.

MSC:

49K99 Optimality conditions
11R32 Galois theory
11B75 Other combinatorial number theory

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References:

[1] Kiselev, D. D.; Lokutsievskii, L. V.; Zelikin, M. I., Optimal control and Galois theory,”, Matem. Sbornik, 204, 83, (2013) · doi:10.4213/sm8211
[2] McIntosh, R. J.; Roettger, E. L., A search for Fibonacci-wieferich and Wolstenholme primes,”, Math. Comput, 76, 2087, (2007) · Zbl 1139.11003 · doi:10.1090/S0025-5718-07-01955-2
[3] Kiselev, D. D.; A, M. (ed.); S, P. (ed.), Applications of Galois theory to optimal control,”, 50-56, (2017), Yekaterinburg
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