The estimated norm of the solutions to the linear differential systems from special classes is obtained with the use of special trygonometric sums.

In this article we consider the mixed problem where the derivative of the unknown function of arbitrary order is set as one of the boundary conditions.

This article deals with a linear-quadratic optimal control problem for a group of dynamically coupled systems. It is assumed that each system has its own local controller, and a delay is present in the communication network. A distributed feedback control, which is linear in current and delayed states, is constructed and a sub-optimality estimate for the distributed control is obtained.

The aim of this article is to obtain sufficient conditions for existence of cyclic invariant towers for a wide class of division algebras with unitary involutions. This gives us the opportunity to prove the congruence theorem for special Henselian division algebras.

For functions, which belong to different (continuous, Lipschitz, difference-sublinear, piecewise-linear) subspaces of the space of positively homogeneous functions, we prove the existence and establish the characteristic properties of a two-index family of linear functions which provides simultaneously both minimax and maximin representations of such functions.

The article deals some classes of non self-adjoint operators acting in a Hilbert space X, for which the statement of the M.A. Krasnoselski theorem on the convergence of successive approximations for equations with self-adjoint operators in the critical case is true. For some classes of operators in Hilbert and Banach spaces, we also study invariant subspaces, in which the M.A. Krasnoselski theorem is to be valid.

It is shown that lenses based on the metal – dielectric (MD) structure are energetically more efficient in ultraviolet and violet ranges of wavelengths. Phase characteristics of flat lenses in ultraviolet as well as in visible ranges for the p-polarized light have a concave shape, which is the necessary condition of focusing. For the first time, direct measurement is made of the flat optically thin two-layered MD-structure (Ag/SiO₂ ). It has been found experimentally that for an incident spherical wave with radial polarization (p-polarization), the focusing regime is realized, and with azimuthal polarization (s-polarization) the channeling regime is realized.

The processes of formation and annealing of vacancy–oxygen-related V_n O_m complexes in Czochralski-grown silicon crystals irradiated with fast electrons have been investigated by means of low-temperature IR Fourier spectroscopy. A number of arguments are presented confirming the identification of the vibrational absorption band at 829.3 cm^–1 as arising from the V₂ O₂ defect.

The crystal structure and magnetic properties of Bi_1–x Ca_x Fe_1–x Mn_x O₃ (x ≤ 0.22) have been studied. It was shown that the rhombohedral (R3c) polar phase at x > 0.18 transforms into the nonpolar orthorhombic phase (Pnma). The polar phase is antiferromagnetic and metamagnetic at x < 0.1. The polar and nonpolar phases are weak ferromagnets with remnant magnetization around 0.07 emu/g (x = 0.18 and х = 0.22). Decreasing the temperature leads to the state close to antiferromagnetic. 

For expanding de Sitter space-time, a spin 1 particle is investigated in the non-relativistic Pauli approximation. After separation of the variables in the relativistic Duffin–Kemmer–Petiau equation, the procedure of non-relativistic approach is performed for the system of 10 equations in the variables (t, r). As a result, the problem reduces to three second-order related differential equations. Requirement of diagonalization of the parity operator allows the system to be split into (1 + 2) subsystems. The fourth-order equations obtained are solved with the help of the factorization method, which permits the problem to be reduced to the analysis of second-order equations. In this way, the Pauli equation for a spin 1 particle in the expanding De Sitter universe is solved exactly: three series of states and the relevant rules of quantization of the spectral parameter are obtained.

The mechanism of deposition of a poly-L-lactide film from the active gas phase has been shown to be associated with destructing a macromolecule into large fragments rather than with depolymerizing a poly-L-lactide film to a monomer followed by its polycondensation on substrate. The transformation of the initial polymer powder into a thin film under the great energetic effect is accompanied by decreasing the molecule mass, while the D-isomer content increases from 4 to 12 %. In so doing, not only the phase state of the polymer changes from semi-crystalline to amorphous one, but the poly-L-lactide relaxation state is transformed from glass to rubber one; these changes could promote an accelerated release of different biocide additives from the film.

Tea extracts (TE) and permeate of culture liquid (PCL) of Penicillium adametzii LF F-2044.1 were used in forming of iron-containing nanocomposite PVP-Fe-PEI including polyvinylpyrrolidone (PVP; 24 kDa) and polyethyleneimine (PEI; 1800 Da). Either TE or PCL were added to the reaction mixture or PVP-Fe-PEI was introduced into TE or PCL. PVP-Fe-PEI composite is formed with TE. PCL was associated with Fe³⁺ butdon’t reduce its. Zero-valent iron can be produced in decreasing PCL concentration and increasing NaBH₄ concentration. PVP-Fe-PEI composite was conjugated to periodate-oxidized dextran T20.

Copper(II) chloride and bromide complexes with 4,5-dihlorizotiazol-N-(2-hydroxyethyl)-3-carboxamide (L) with the compositions [CuLHal₂ ]_n , where Hal = Cl^– , Br^– , are synthesized. The X-ray analysis revealed that the ligand is coordinated to the copper(II) atoms tridentate by the nitrogen atom of the heterocycle and two exocyclic oxygen atoms to form polymer chains. The copper bromide complex showed a synergistic effect in the compositions of insecticides Kerber and Vitan. 

A conjugate has been obtained in the reaction of chloramphenicol 3-hemisuccinate with diethylenetriaminepentaacetic acid N¹ -(2-aminoethylamide) Eu³⁺-complexonate. Kinetic and equilibrium parameters of conjugate binding to polyclonal antichloramphenicol antibodies biospecifically immobilized onto microtiter plate wells were determined. It was concluded that the new bioconjugate can be used in a lanthanide immunofluorometric assay of chloramphenicol.

The collection of 54 maize samples of different eco-geographical origin was evaluated for the key polymorphisms of the LcyE and CrtRB1 genes (LcyE 5′TE, LcyE 3′Indel and CrtRB1 3′TE) associated with the provitamin A content in maize grain. Favorable alleles of LcyE were not detected in the studied material. Selected genotypes with favorable allele 1 of СrtRB1 3′TE functional marker (35 % of the samples) are of interest for maize breeding programs aimed at improving the grain quality.

The growth rate of narrow-clawed crayfish in Lake Sominskoe (Belarus) and Lake Sevan (Armenia) is defined as the derivative of the Bertalanffy equation of growth. The average annual growth rate for the age group of 2–7 years was 12.0 ± 2.15 grams in Lake Sominskoe, 10.23 ± 2.62 grams in Lake Sevan. The difference between the average values was not statistically significant.

Triboengineering and strength properties of hybrid composite materials based on copper–copper-plated polytetrafluoroethylene–carbon nanostructure power systems are investigated. It is shown that the introduction of carbon nanostructures and metal-plated polytetrafluoroethylene (PTFE) into a metal powder matrix of composite, when it is formed by the electrocontact sintering method, allows obtaining materials with high-performance characteristics. By the criteria of strength and wear resistance it is established that the optimal content of copper-plated PTFE particles in the investigated composites with powder copper matrix is 5–6 wt. % and of a carbon nanostructured filler – 0.06–0.07 wt. %.

The principles of simulation and analytical modeling of an administrative cycle in organizational structures of management with use of the classical analytical strategy are stated. The offered model gives the chance of receiving a quantitative assessment of an optimality of planning and realization of an administrative cycle. A comparative analysis of linear, functional and network structures of management through the optimality criterion of organizational planning has been made.

The changes of biochemical indices of mineralization and humification of organic substances in high-fertility derno-podzolic sandy-loam soil depending on the application of different fertilizer systems were established using the data on the activity of cellulolytic and amylolytic microbial communities, as well as the results of enzymatic soil diagnostics (hydrolytic and oxidative enzymes). The application of N₉₀₊₃₀P₁₅K₃₀ was shown to provide high and sustainable crop yields under a moderate level of organic substances mineralization in С and N-circles.