The problem of minimizing the integral quadratic functional on the trajectories of a quasilinear dynamical system with linear terminal constraints is under consideration. Asymptotic approximations to the optimal open-loop and optimal feedback controls for this problem are constructed.

 

Communicated by Corresponding Member Valentine V. Gorokhovik

The hexagonal tiling in application to algorithms with a two-dimensional computational domain is investigated. A formal definition of a parametrized hexagonal tiling is proposed. Necessary and sufficient conditions for a dense coverage of the computational domain by hexagonal tiles are obtained.

Communicated by Corresponding Member Leonid A. Yanovich

The mixed problem for one-dimensional Klein–Gordon–Fock-type equation with curve derivatives in boundary conditions is considered in half-strip. The solution of this problem is reduced to solving the second type Volterra integral equations. Theorems of existence and uniqueness of the solution in the class of the twice continuously differentiable functions were proven for these equations when initial functions are smooth enough. It is proven that fulfillment of the matching conditions on the given functions is necessary and sufficient for the existence of the unique smooth solution when initial functions are smooth enough. The method of characteristics is used for the problem analysis.

This method is reduced to the splitting the original area of the definition to the subdomains. The solution of the subproblem can be constructed in each subdomain with the help of the initial and boundary conditions. Then obtained solutions are glued in common points, and received glued conditions are the matching conditions. This approach can be used in constructing as analytical solution, in case when solution of the integral equation can be found in explicit way, so for approximate solution. Moreover, approximate solutions can be constructed in numerical and analytical form. When numeric solution is constructed, then matching conditions are essential and they need to be considered while developing numerical methods.

We present experimental results showing that the migration ability of interstitial carbon atom (С_i) in silicon depends noticeably on its charge state. The experimental results were obtained from the analysis of deep level transient spectra in n⁺–p diodes subjected to irradiation with 4–6 MeV electrons or α-particles at T < 273 k and subsequent heat-treatments in the temperature range 280–330 k under reverse bias and without it. It has been found that in the positive charge state the С_i migration energy is 0.88 ± 0.02 eV, while in the neutral charge state it is lowered down to 0.73–0.74 eV.

Oxide-nitride-oxide-silicon (SiO₂/SiN_0.9/SiO₂/Si) structures have been fabricated by chemical vapor deposition. The elemental composition and light emission properties of “SiO₂/SiN_0.9/SiO₂/Si” structures have been studied using Rutherford backscattering spectroscopy (RBS), photo- and electroluminescence (Pl, El). The RBS measurements has shown the presence of an intermediate silicon oxynitride layers at the SiO₂–SiN_0.9 interfaces.

It has been shown that the photoluminescence of the SiO₂/SiN_0.9/SiO₂/Si structure is due to the emission of a SiN_0.9 layer, and the electroluminescence is attributed to the emission of silicon oxide and oxynitride layers. A broad intense band with a maximum at 1.9 eV dominates the Pl spectrum. This band attributed to the radiative recombination of excited carriers between the band tail states of the SiN0.9 layer. The origin of the less intense Pl band at 2.8 eV is associated with the presence  of nitrogen defects in the silicon nitride.

El was excited in the electrolyte-dielectric-semiconductor system. The electric field strength in the SiO₂ layers reached 7–8 MV/cm and exceeded this parameter in nitride layer nearly four times. The electrons accelerating in electric field of 7–8 MV/cm could heat up to energies more than 5 eV. It is sufficient for the excitation of luminescence centres in the silicon oxide and oxynitride layers. The SiO₂/SiN_0.9/SiO₂/Si composition El bands with quantum energies of 1.9 and 2.3 eV are related to the presence of silanol groups (Si–OH) and three-coordinated silicon atoms (≡Si•) in the silicon oxide layers. The El band with an energy of 2.7 eV is attributed to the radiative relaxation of silylene (O₂=Si:) centers in the silicon oxynitride regions. It is observed the least reduction of this band intensity under the influence of strong electric fields after a charge flow  of 1–3 C/cm².

The structure, magnetic and magnetotransport properties of perovskite Sr_0.9Y_0.1CoO_2.63 are studied. It is shown that the sample is structurally two-phase. The main phase has a tetragonal-distorted unit cell and is described by the spatial group I4/mmm. The broadening of the reflexes with indexes corresponding to a doubling of the parameter from the unit cell indicates that there is no strict translational symmetry along the с-axis. The presence of a broadened superstructural reflex observed at small angles on X-ray diffraction patterns at temperatures below 400 K is due to the monoclinic phase, whose content is much smaller than the tetragonal phase. Spontaneous magnetization appears during the formation of the monoclinic phase. The magnetic structure is predominantly an antiferromagnetic G-type structure with magnetic moments of 1.5µ_B in the layers of CoO₆ octahedra and 2µ_B in the anion-deficient CoO_4+γ layers. The electrical conductivity of Sr_0.9Y_0.1CoO_2.63 has a semiconductor in character. The magnetoresistance reaches 57 % in a field of 14 T at a temperature of 5 K and decreases strongly with increasing temperature.

The fluorescent dyes 4,4′-(1E,1′Е)-2,2′-(2-aminopyrimidin-4,6-diyl) bis(ethene-2,l-diyl) bis(N,N-dimethylphenylamine) (АРМ) and 4′-(1E,1′Е)-2,2′-(2-aminopyrimidin-4,6-diyl) bis(ethene-2,l-diyl) bis(N,N-diethylphenylamine) (APE) were incorporated into glutaraldehyde-crosslinked polyvinyl alcohol microspheres containing magnetite. Fluorescence spectra of the obtained microspheres depend on pH of the medium. A technique for pH measurement within the range of 4–9 based on calculation of the green/red ratio of the fragments of color microimages of the microspheres was developed. only negligible loss of the fluorochromes from the microspheres occured during the storage time of 180 days. Thus the microspheres may be used as local pH indicators, e. g. for phagocytosis studies.

The formation of a conjugated bond system in the heat treatment of polyvinyl alcohol films with the addition of hydrochloric acid as an acid catalyst for thermal dehydration in the range of 80-150 °C has been studied on the base of electronic spectra. It is established that the fine structure in the absorption spectra in the 282-443 nm region is associated with electronic transitions in polyconjugated chains with the number of carbon atoms from 8 to 18, with the exception of the bands at 310 and 342 nm; only one peak at 361 nm of four lines in the wide band at 352-380 nm is associated with optical transitions in the polyconjugated chain containing 12 carbon atoms. It is shown that the long-wave boundary of the spectrum is due to electronic transitions in polyconjugated chains of the largest sizes; the maximum size of such chains can be determined by comparing the dependence of the Tauc band gap and the energy of the optical transitions as an inverse function of the number of carbon atoms in the conjugate chain. Since the typical sizes of such poly-conjugation chains are hundreds of carbon atoms (about 300 atoms in films heated at 100 °C), these chains can be considered as trans-polyacetylene nanoclusters incorporated into a polyvinyl alcohol matrix.

Molecular dynamics simulations for the structural complexes of potential HIV-1 inhibitors with the viral envelope gp120 protein were carried out. Free energies of the formation of these supramolecular structures and contributions of individual amino-acid residues of gp120 to the enthalpy binding were calculated. The residues of gp120 critical for interactions with the ligands were identified. Based on the data obtained, five compounds promising for synthesis and testing for antiviral activity were selected. It is suggested that these compounds may be successfully used in the design of novel, potent and broad anti-HIV drugs.

It has been experimentally established that the processes of adaptation of organism under the influence of parasites occur in stages: the stage of anxiety, equilibration and oppression. The are accompanied by a change in behavioral and functional reactions, as well as hematological and biochemical changes in the blood of laboratory animals. At the same time, changes in these parameters were observed in acute and chronic course of the invasive process. The results of the research are the basis for the development and application of drugs-adaptogens, which allow reducing the recovery time of the body against the background of anthelmintic therapy.

Communicated by Academician Mikhail E. Nikiforov

According to the results of the analysis of the complete nucleotide sequence of B. amyloliquefaciens subsp. plantarum BIM B-439D, it is established that the genome of the strain is unique and is represented by a single ring chromosome with a size of 3978134 base pair containing 46.5 % G/C-pairs. The key genetic loci determining synthesis of antimicro-bic metabolites are defined: lipopeptides (surfactin, fengycin, bacillomycin D), dipeptide (bacilysin), siderophor (bacillibac-tin), polyketide antibiotics (difficidin and oxydifficidin, bacillaene and macrolactin), bacteriocin (amylocyclicin) and peptide/ polyketide (putative - tyrocidin), restriction-modification systems and mobile genetic elements (IS-elements and prophages) are characterized. The identified features in the organization and localization of individual genetic determinants (for example, intact prophage of 37558 bp) can be used as reliable molecular genetic markers for fast identification of the strain when it is used commercially. The complete nucleotide sequence of the genome can serve as the basis for a detailed functional analysis of the practically significant properties of the microorganisms of the Bacillus group.

One of the recent perspective trends of molecular biotechnology is cell-free synthesis of protein. The procedure of cell-free synthesis of protein is based on in vitro reconstruction of all stages of a biosynthesis of protein in a whole cell, including a transcription, an aminoacylation of tRNA and translation of mRNA by ribosomes. Procreation of the transcription stage requires participation of specific RNA polymerase which initiates process of mRNA synthesis from the particular sites of recognition. Often the DNA-dependent RNA polymerase of a bacteriophage of T7 (T7 RNA polymerase) is for this purpose applied. For improvement of qualitative characteristics of the T7 RNA polymerase in the real work the new strain of Escherichia coli producing this enzyme fused with the DNA-affine Sso7d domain of a thermophilic bacterium Sulfolobus solfataricus is created. The producing ability of the received recombinant strain concerning synthesized chimera protein reaches 625 un/l of cultural liquid, and the specific activity of the purified enzyme preparation was 80 un/ μg of protein. The received enzyme is intended for use as tools at synthesis of proteins in cell-free system.

The usage of clinical and instrumental methods only may be not sufficient for early diagnosis of autoimmune rheumatic diseases, as well as for their course prediction. The progress of modern rheumatology is largely conditioned by the investigation of molecular-genetic nature of diseases and the identification of biomarkers that can significantly improve diagnostics and therapeutic approach. The present study aimed to evaluate the effect of -174G/C IL-6 gene polymorphism on the risk of developing rheumatoid arthritis (RA) in children and adults in Republic of Belarus. It was established that the CC genotype frequency (p = 0.01, OR = 2.19; 95 % CI [1.31-3.67]) as well as the С allele frequency (p = 0.03; OR = 1.44; 95 % CI [1.04-2.00]) was significantly higher among patients with juvenile idiopathic arthritis (JIA) in the entire group and especially in girls (p = 0.04, OR = 2.55; 95 % CI [1.22-5.36]) in comparison with the controls. In addition, there is a tendency to higher frequency of the С allele in adult patients with RA (p = 0.07), reaching statistical significance in the case of RF-negative arthritis (p = 0.03, OR = 3.04; 95 % CI [1.15-8.06]). The minor С allele (p = 0.03, OR = 2.04; 95 % CI [1.09-3.82]) and homozygous CC genotype (p = 0.02, OR = 3.34; 95 % CI [1.38-8.07]) are also associated with seronegative polyarthritis in children. Thus, the presence of this allele in the tested locus increases the likelihood of developing certain rheumatoid arthritis subtypes in adults and children and can be used to reveal individuals with genetic predisposition.

Today, the possibility of amplifying the signal of Raman scattering is intensively studied in order to realize a simple and reliable tool for monitoring of ultra-small concentrations of chemical and biological substances. Plasmon-active nanostructures can serve as the basic element of substrates for signal amplifying, and the degree of amplification is determined by nanostructures size and shape. The formation of nanostructures with a predetermined morphology requires the development of new approaches. In this concern, the paper considers a complex approach of plasmon-active silver nanostructures with a wide range of shapes and sizes formation in the pores of ion-track Sio₂ templates on silicon. The peculiarities of SiO₂ templates creation are considered and the etching rates, uniquely determining the parameters of the pores as a function of the etching time, are established. The features of the silver nanostructures formation in the pores of the SiO₂ template are described for various pore sizes and synthesis regimes (time and solution temperature). The possibility of formation of nanostructures with different shapes as well as evolution of their morphology with variation of synthesis parameters is shown. on the example of dendrites, having a high potential for practical application for amplification of the Raman scattering signal, the possibility of recording Raman spectra was demonstrated using the model analyzer Nile Blue at the concentration of 10^-6 M/l. The results indicate that plasmon-active silver nanostructures in the pores of ion-track Si0₂ template on silicon can be used as basic element of biosensors to studying ultra-low doses of chemical and biological substances.

Communicated by Corresponding Member Valery M. Fedosyuk

The concept of creation of the common Old Russian state of the eastern Slavs is dominant in belorussian historical science. According to the concept Kiev united described in chronicles tribal unions in one territorial and political structure and had been the center of the state. Centers of the tribal unions being part of the state ruled over individual regions, and during the period of its fragmentation (XII-ХШ centuries), the appanage principalities - the lands.

A new concept of formation and development of early state formations of the eastern Slavs is based on the new facts. Three main territorial and political centers of the tribe period, Kiev, Novgorod and Polotsk became the local base of statehood of the eastern Slavs. Polotsk was the center of the early state formation “the Polotsk land” that had its own territory and ruling  dynasty. The Polotsk land covered the territory of modern North and Central Belarus. The aims of external and internal policy of this formation were strengthening its political and economic prestige, preservation of integrity during X – first half of XIII centuries.

Lands of South and West Belarus during above mentioned period on different terms and at different times had been part of early state formation “Kievan Rus”.

Communicated by Corresponding Member Aleksandr A. Kovalenia

The effect of mononitrogen fertilizer system on biochemical status of high fertility Luvisol sandy loam soil was studied during five years in the field experiment. Data interpretation of enzyme diagnostics was done based on the resulting estimation criteria, which is a biochemical coefficient including four key enzymatic parameters and representing the ratio of average speeds of humification and mineralization activities in С and N cycles. Five-year application of mono nitrogen fertilizer system resulted in progressive increase of organic substances mineralization, which enhanced with nitrogen dose rising. It is ecologically advisable to fertilize the soil with the complete mineral fertilizer with the minimal doses of phosphorus and potassium. Thus, humification and mineralization processes are balanced and organic matter is saved.