General Mathematics Seminar
This seminar is organized by St.Petersburg Division of Steklov Institute of Mathematics (POMI) of Russian Academy of Sciences.
The next session of the seminar.
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The next (175th) session will be held on Monday, February 20, in the room no. 311 at 13.00.
|Speaker:||D. D. Kiselev (Russian Foreign Trade Academy, Moscow)|
|Title:||An application of Galois theory to the optimal control.|
Define the Zelikin-Lokutsievskiy polynomial fn(x) with integer coefficients of degree n - 1 as follows
We show the irreducibility of f(q-1)/2(x) over Q for any prime q > 3. We calculate the Galois group of the polynomial fn(x), when the numbers p = n - 1, q = 2n + 1, r = 2n + 7 are prime and 889 is not a square modulo r. We also show under irreducibility hypothesis of the polynomial fp+1(x) over Q for almost all primes p that there exists an infinite sequence of natural n, for which An - 1 is embeddable into GalQ(fn(x)).
An example: for any natural k < 808 there exists an optimal control problem, the optimal control of which throws a dense winding of the k-dimensional torus in finite time.
|Our address:||St.Petersburg Division of|
|Steklov Institute of Mathematics,|
|27, Fontanka, St.Petersburg.|
|Page of St.Petersburg Department of Steklov Institute of Mathematics (POMI).|
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