Vol. 47 No. 2 (231) (2013)

We prove that the group of automorphisms $Aut(B(m, n))$ of the free Burnside group $B(m, n)$ is complete for every odd exponent $n\geq 1003$ and for any $m > 1$, that is it has a trivial center and any automorphism of $Aut(B(m, n))$ is inner. Thus, the automorphism tower problem for groups $B(m, n)$ is solved and it is showed that it is as short as the automorphism tower of the absolutely free groups. Moreover, we obtain that the group of all inner automorphisms $Inn(B(m, n))$ is the unique normal subgroup in $Aut(B(m, n))$ among all its subgroups, which are isomorphic to free Burnside group $B(s, n)$ of some rank $s$.

In this article we consider first order linear differential operators in the space of $(n-1)$-dimensionally continuous functions with coefficients having some growth near the domain boundary and prove the boundedness of considered operators.

In this work some properties related to von Neumann effect of commutators of elements from complex Banach algebras are discussed, as well as their “convexity”.

In the paper we introduce new Mӧbius-invariant and efficient divisors for $A^p_{\alpha}$ spaces. The method of construction of new divisors is shown.

In the present paper we describe, up to isomorphism, all order 3 unitary hypergroups over group, arising from the dihedreal group $D_9$.

In the present work the optimal stabilization problem of a moving mass center of satellite under influence of integrally small perturbations during finite time intervals has been considered. The optimal stabilization problem of the above motion in classical sense and under integrally small perturbations is assumed and respectively solved. A comparison between the optimal values of performance indices in mentioned cases proves that the energy consumption at stabilization under integrally small perturbations is less than stabilization in classical sense.

In the present paper a numerical algorithm to construct quadratic Bezier curves for data fitting by least squares method is developed. The problem is solved by constructing so-called minimizing sequence of control points.

The reversible adsorption of short ligands on DNA at arbitrary filling has been theoretically investigated, the kinetics of adsorption of ligands on DNA being described in a self-consistent way with the modified structure of an adsorbing center. The case when one adsorbed ligand occupied two adsorption centers on DNA was considered. It was shown that an allowance for the modification of the potential well of the adsorbing center led to the possibility of realizing various regimes of adsorption.

Two-dimensional (2D) polarization pattern is achieved by the interference of two pairs of beams with perpendicular planes of incidence and orthogonal circular polarizations. Imposing a phase shift of π/2 between consecutive beams contains the amplitude modulation of the optical field in the superposition region and, thus, pure 2D polarization patterns are created. The recording of this interference field in a polarization sensitive material creates reconfigurable 2D periodic microstructure with peculiar diffraction properties.

One dynamic property of some polynomials is investigated. The statements about traces of critical points of some polynomials are proved. The equations of curves, on which critical points move, are obtained.