The problem of covering the vertex set of a simple graph with a minimum number of complete bipartite subgraphs is studied. It is well known that this problem is NP-complete even for bipartite graphs. This article gives a polynomial time algorithm for solving the considered graph problem when the graph is bipartite permutation or bipartite distance-hereditary.

This article deals with an optimal control problem for a group of dynamically decoupled linear systems subject to unknown disturbances and coupling constraints. A distributed control scheme is proposed, guaranteeing the robust constraints satisfaction, the recursive feasibility of local optimal control problems solved in real-time by the agents and the suboptimality of the distributed control.

The article deals with linear operators A with a spectral radius equal  1 in Hilbert and Banach spaces, for which the successive approximations x_n+1= Ax_n + f with an arbitrarily initial approximation x₀ converge to one of the solutions of the equation x = Ax + f (under the condition that these solutions exist).

In this article, we consider an analog of the Luzin theorem on the correction for Sobolev-type spaces on ultrametric spaces with a doubling condition. The correcting function belongs to the Hölder class and approximates a given function in the metrics of the initial space. Dimensions of exceptional sets are evaluated in terms of capacities and Hausdorff volumes. This result was previously obtained for the special case of the p-adic vector space.

We consider the first-order matrix difference equation with variable noncommutative coefficients. In the algebra of matrix hypersequences, this equation corresponds to the first-order matrix algebraic differential equation with a regular singular point. It is proved that there exists a supstitution, which can reduce the equation under consideration to the Cauchy-type equation. This substitution can be found explicitly as the solution of some infinite system of matrix algebraic equations. The general solution of the equation is obtained in the algebra of matrix sequences.

The paper deals with extremal properties of diagonal Hermite-Pad’e approximants of type I for exponential system {e^λpz}^k_p=0with arbitrary λ₀, λ₁, …, λ_k. Proved theorems complement known results of P. P. Borwein, F. Wielonsky.

On the basis of the method of separation of variables, the complete set of exact solutions of the Dirac equation in the non-static coordinates of the de Sitter space is constructed. In the separation of variables, the formalism of the Wigner D-functions is used. The square and the third projection of the total angular momentum, as well as the space reflection operators are diagonalized on the solutions. Equations for the radial variable lead to a discrete spectrum of the separation constant. The asymptotic properties of the solutions for radial ant time variables are investigated.

The asymptotic of the solution of the discrete Wheeler-DeWitt equation is found in the vicinity of small scale factors. It is shown that this problem is equivalent to the solution of the stationary Schrödinger equation in the (super-) space of negative constant curvature. The minimum positive eigenvalue, with which a continuous spectrum begins, is found.

The selectivity of plasmonic substrates - plasmonic silver films and plasmonic gold crystals - is developed as selective enhancement of different secondary emission types (Raman or fluorescence) with the use of the same chromophores, excitation conditions, but different sizes of metallic grains at the plasmonic substrate surface. It is conditioned by a different contribution of absorption and scattering cross sections to the extinction cross section for small and large nanoparticles.

The novel stabilizing ligand, 5-mercaptotetrazole-1-acetic acid, has been applied for a simple synthesis of noble metal nanoparticles in the aqueous medium. This method is based on the reduction of metal salts in water in the presence of available 5-mercaptotetrazole-1-acetic acid. The interaction of the nanoparticle surface with the ligand has been investigated. According to quantum chemical calculations, the most stable structure has been realized when the capping ligand binds with the surface of nanoparticles through both sulphur and nitrogen N4 atoms. Free carboxyl groups provide good redissolvation in water.
Obtained particles are attractive as precursors for catalysts, as well as biologically active systems with antibacterial and fungicidal properties.

The methods for synthesis of biocidal systems on the basis of the products formed by the reaction of polyphosphoric acids and polyhexamethyleneguanidine have been developed. The high antibacterial activity of these hybrid products is shown.

Based on the analysis of the structural complex between neutralizing antibody VRC01 and the HIV-1 gp120 protein, the virtual screening of chemical compounds able to mimic pharmacophore properties of the immunoglobulin antigen-binding site was carried out. Using the molecular modeling, the complexes of these compounds with gp120 were built and the evaluation of their potential inhibitory activity was performed followed by the calculation of free energy of formation of supramolecular structures. As a result, top-six compounds, which specifically and effectively interact with amino acid residues of gp120 critical for its binding to the primary receptor CD4 of target cell, were selected. In the light of the findings obtained, the identified compounds are considered as promising basic structures for the design of novel anti-HIV drugs with broad viral neutralization.

The research of hydrocarbonic substitutes at quaternary ammonium salt nitrogen atom length influence and the kind of plasticizer on tetraftoroborate electrodes analytical characteristics has been carried out. The functions of electrodes have theoretical gradients. The detection limits change from 5.0 · 10^–6 to 1.3 · 10^–6 mol/l. It is shown that the reason of potentiometric selectivity coefficient decrease is the increase of the steric difficulty of the QAS exchange center.

Herein, the environmentally friendly synthesis of the earlier unknown phospholipid analog of kinetin riboside was carried out using phospholipase D of Streptomyces netropsis. Kinetin riboside and soybean lecithin served as substrates. A maximum degree of nucleoside conversion to 5′-phosphatidyl derivative of kinetin riboside at 37°С to 6 h exceeds 95%. The structure of target product was confirmed by UV and ¹Н NMR spectroscopy.

P
olysulfone hollow fiber ultrafiltration membranes cast from the polysulfone solution in dimethylacetamide containing PEG 400 as porophore and hydrophilized with additives of polyvinylpyrrolidon K-90 have been tested after long term storage. The specific influence of the dilute solutions of PEG with M = 6000–20000 on the membrane permeability has been found. The short term treatment by PEG dilute solutions has restored the pore structure and the membrane permeability following the capillary contraction. It is assumed that the detected effect is caused by the wedge action of PEG due to its interaction with polyvinylpyrrolidone in the membrane matrix.

Aseries of purine modified nucleosides with 2′,3′-difluoro-β-D-arabinofuranosyl moiety have been synthesized starting from derivative of 2′,3′-dideoxy-2′,3′-difluoro-D-arabinofuranose via anionic glycosylation reaction of salts of purine hetero­cyclic bases by α-bromide as the universal sugar precursor.2,6-Disubstituted purine 2′,3′-difluoro-D-arabinofuranosyl nucle­osides and guanine nucleoside analogue were prepared by chemical transformations of protected arabinosides of 2,6-dichloro­purine or 2-amino-6-chloropurine as key intermediates for constructing diverse nucleoside analogues of this class.

The methods for identifying M-virus resistance genes of potato were developed.Gene Gm of extreme PVM resistance is rare and available for the present only in breeding material.On the contrary, hypersensitivity gene Rm is quite widely repre­sented in Belarusian and foreign potato cultivars providing their resistance to this pathogen.Potato cultivars and hybrids, se­lected for the availability of markers GP250₅₁₀, GP283₃₂₀, UBC822₁₀₇₉ to gene Rm and marker SC878₈₈₅ to gene Gm, are the valuable donors of resistance to this virus and are recommended for use in breeding.

Uncommon diploid interspecific hybrids are formed along with triploid ones during hybridization between allotetraploid potato species S. acaule, S. stoloniferum, S. polytrichon, and S. tuberosum diploid clones. A comparative RAP AP D-analysis of triploid and diploid hybrids has shown that the representability ratio of S. tuberosum specific for the loci in the hybrids corresponded to 1 : 1. It testifies that the diploid interspecific hybrids obviously obtained the same quantity of genetic material of cultivated potatoes as triploid ones. The representability of RAP AP D-loci specific for wild parental species was proportional to the number of wild species genomes in hybrids (2 – in triploid hybrids and 1 – in diploid hybrids). Hence, the production of diploid hybrids between allotetraploid wild potato species and S. tuberosum diploid clones is probably associated with the loss of one of the genomes of wild species. A hypothesis on the formation of diploid interspecific hybrids as a result of fertilization of atypical monoploid egg cells of allotetraploid potato species with the pollen of S. tuberosum diploid clones was suggested.

The study of the influence of the genome composition of triticale lines with genetic material Aegilops diploid species on the biochemical composition of grain was made. The high content of protein and starch in the grain was detected in triticale lines, in which genomes aegilops foreign material is present either as an entire chromosome, or a translocation. The increase in the content of protein and essential amino acids is observed for the line carrying the 2R(2U) chromosome substitution. Thus, the triticale genome reorganization, which has occurred as a result of introgressive hybridization of hexaploid triticale and genome-substituted forms of wheat, contributes to the creation of new economically valuable forms with a high content of protein, essential amino acids, and starch in the grain.

A traditional hydrocarbon raw material includes oil deposits explored in 80 oil fields in the territory of Belarus. The paths of undiscovered reserves utilization are presented on the basis of the analysis of the resource hydrocarbon potential taking into account its exploration up to 53%. Promising objects are validated with minimal oil reserves to introduce them into prospect drilling with an assurance of their development efficiency.

The method of calculation of a mirror-lens objective with Manzhen’s mirror is presented. Parameters of a catoptric composition with lens compensators are established. It is noted that the design possibilities are expanded by new computer methods. The design parameters of the mirror-lens high-aperture anastigmat are calculated.

In this article, the author presented the results of using the methods of natural sciences (analysis data of the chemical composition of articles) for the study of the manufacture of products made of non-ferrous metals in medieval Polotsk. Based on 166 analyses of 149 products (whole amount of collected products is 1294), the peculiarities of raw material that was used by handicraftsmen for producing different categories of artifacts are discovered. The chemical analysis of non-ferrous metals enables one to trace the main directions of delivery of articles and raw material for their production in the territory of the town (North-West Russia and the Baltic region) and to distinguish the peculiarities of manufacturing articles made of non-ferrous metals in Polotsk during two chronological periods: XI–XIII centuries and and XIV–XII centuries.