Gorbunov, É. A. Vorontsova, E. A. Gasnikov, A. V.
Published in
Mathematical Notes

We consider the problem of constructing upper bounds for the expectation of the norm of a vector uniformly distributed on the Euclidean unit sphere.

Prokhorov, Yu. G. Shramov, K. A.
Published in
Mathematical Notes

Lyakhov, L. N. Sanina, E. L.
Published in
Mathematical Notes

The definition of a B-derivative is based on the notion of generalized Poisson shift; this derivative coincides, up to a constant, with the singular Bessel differential operator. We introduce the fractional powers of a B-derivative by analogy with fractional Marchaud and Weyl derivatives. We prove statements on the coincidence of these derivatives ...

Kochurov, A. S. Tikhomirov, V. M.
Published in
Mathematical Notes

The problem of the greatest possible absolute value of the kth derivative of an algebraic polynomial of order n > k with real coefficients at a given point of the complex plane is considered. It is assumed that the polynomial is bounded by 1 on the interval [-1,1]. It is shown that the solution is attained for the polynomial κ · Tσ, where Tσ is one...

Shishkov, A. E. Yevgenieva, Ye. A.
Published in
Mathematical Notes

Singular blow-up regimes are studied for a wide class of second-order quasilinear parabolic equations. Energy methods are used to obtain exact (in a certain sense) estimates of the final profile of the generalized solution near the blow-up time depending on the rate of increase of the global energy of this solution.

Smaoui, K.
Published in
Mathematical Notes

The purpose of this paper is to establish a local uncertainty inequality for arbitrary connected, simply connected nilpotent Lie groups. This allows us to prove a couple of global uncertainty inequalities. In the nilpotent case, this type of result is only obtained for the Heisenberg group.

Mardanov, M. J. Melikov, T. K. Malik, S. T.
Published in
Mathematical Notes

In this paper, by introducing the notion of γ-convex set, we distinguish a wider class of discrete control systems in which the global maximum principle holds. A new type of variation of control for such classes of discrete control systems is proposed and stronger global maximum principle and second-order optimality condition expressed in terms of ...

Runovskii, K. V.
Published in
Mathematical Notes

Norms of images of operators of multiplier type with an arbitrary generator are estimated by using best approximations of periodic functions of one variable by trigonometric polynomials in the scale of the spaces Lp, 1

Zaitov, A. A. Ishmetov, A. Ya.
Published in
Mathematical Notes

A subspace If(X) of the space of idempotent probability measures on a given compact space X is constructed. It is proved that if the initial compact space X is contractible, then If(X) is a contractible compact space as well. It is shown that the shapes of the compact spaces X and If(X) are equal. It is also proved that, given a compact space X, th...

Podoprikhin, D. A. Fomenko, T. N.
Published in
Mathematical Notes

The article develops results of the authors’ previous papers on the topic. The notion of the homotopy of a multivalued mapping of an ordered set is introduced. We study the problem as to whether the existence of a fixed point (or a coincidence point) is preserved under multivalued homotopies of a multivalued mapping (or a pair of multivalued mappin...