Approximate formulas for evaluation of mathematical expectation of functionals of solution of the linear stochastic Ito equations in the Hilbert space are obtained. The approach is based on using the functional quadrature formulas.

A new mathematical model of discrete time series is proposed. It is called homogenous vector Markov chain of the order s with partial connections. The conditional probability distribution for this model is determined only by a few components of previous vector states. Probabilistic properties of the model are given: ergodicity conditions and conditions under which the stationary probability distribution is uniform. Consistent statistical estimators for model parameters are constructed.

The mixed problem with the integral condition for the wave equation is considered in the one-dimension case. Existence and uniqueness of the classical solution is proved under certain smoothness and consistency conditions. For numerical solution of a given problem the simple second-type Voltaire integral equations should be solved.

In this article we present the local classification of three-dimensional reductive homogeneous spaces allowing a normal connection. We consider the case, when the Lie group of transformations is unsolvable and the stabilizer is usolvable too. We describe all invariant affine connections together with their curvature and torsion tensors, canonical connections and natural torsion-free connections. We study the holonomy algebras of homogeneous spaces, and sind when the invariant connection is normal.

Multiple enhancement of electroluminescence efficacy and acceleration of modulation of LED light sources are shown to be possible using plasmonic effects. The model is used which accounts for an intrinsic quantum yield of a semiconductor, the modification of probabilities of radiative and non-radiative quantum transitions near metal nanoparticles, and the radiation scattering contribution to the modification of light-matter interactions near metal nanoparticles.

The smooth barrier of finite height and variable shape is constructed by means of joining the central inverted parabolic potential and two side parabolic potentials. The problem of tunneling through this barrier is solved exactly. The dependence of the transmission coefficient on energy is presented. The real and imaginary components of wave functions are shown.

The possibility of band gap engineering by means of impurities or vacancies is investigated in two-dimensional dichalcogenide crystals of MoS2, MoSe2, WS2 and WSe2. Oxygen impurity atoms are considered to substitute chalcogen atoms or to adsorb at the surface of the crystal. The atom substitution leads to a slight increase in the energy band gap, while the adsorption of oxygen atoms at the surface decreases the gap relative to the unalloyed material. A vacancy in the position of the chalcogen atom leads to the change in the band dispersion and the appearance of additional energy levels.

Liposomal streptokinase (a mixture of free (66.3  %) and entrapped (23.7  %) drug) with a diameter of ~60 nm was prepared. The analysis of the D-dimers formation kinetics in the dog’s blood plasma showed that the liposomal streptokinase had
a prolonged effect up to 180 minutes.

The sorption activity of tetrazole-based polymers prepared from commercial copolymer of acrylonitrile, methyl acrylate and 2-acrylamido-2-methylpropanesulfonic acid was studied in relation to Сu2+, Co2+, Ni2+ and Pb2+ in diluted aqueous solutions. It was found that the sorption capacity grew with increasing the tetrazolation ratio and the specific surface area of polymer. The possibility of selective sorption of Cu2+ in the presence of Co2+ was shown. The recovery of the sorbent after ion exchange sorption was achieved by treating with dilute hydrochloric acid.

The study of the features of the protein-protein interaction of cytochrome P450 (CYP3A4 and CYP2B4) and phospholipase A2 (PLA2) using circular dichroism spectroscopy was carried out.
The divergent effects were found in the change of the CD-spectrum of the mixture of snake venom PLA2–CYP2B4 (ratio 1  : 4 mole/mole) and the mixture of porcine pancreatic PLA2-human CYP3A4 (ratio 1  : 20 mole/mole), as compared to the CD-spectra of the individual protein, respectively, which evidences direct protein-protein interactions of PLA2 and CYP.
The resultant CD-spectrum in the first case is characterized by a 2.5-fold increase in the molar ellipticity protein mixture in relation to the molar ellipticity of cytochrome P450, and the second – by a significant reduction of this index, which reflects the significant changes in the conformation of the interaction of these biopolymers.

In the given work the transcriptomes of different organs and tissues of western poplar, eucalyptus, soybean and common bean were studied. The expression level of cellulose synthase genes was notably different in the studied plant species and in different types of tissues and organs within plants. For common bean and eucalyptus transcriptome the domination of certain cellulose synthase genes was typical. These prevailing genes made up more than 50  % of the total expression pull of cellulose synthases. On the contrary, cellulose synthase expression pulls of western poplar and soybean were distributed between multiple genes. The different expression strategies of CesA-genes may reflect the phylogenetic process that occurred in the genomes studied.

The dependence of action of an inhibitory dose of N-phosphonomethylglycine mixed with epibrassinolide over a wide concentration range, on the root growth of flax (Linum usitatissimum L.) and barley (Hordeum vulgare L.) seedlings is studied. Specific and varietal specificity of growth responses to the incrustation of seeds by such mixtures is identified. The epibrassinolide concentration range, in which its interaction with N-phosphonomethylglycine is most expressed, is detected. It is characterized by the intensification (in spring barley seedlings) or the weakening (in flax seedlings) of the inhibitory effect of glyphosate on the root system.

The composition of leaf volatiles and the antimicrobial activity of essential oils of the representatives of the family Lauraceae Juss. cultured in the hothouse against Bacilus polymyxa (Prazmowski) Mace, Bacillus megaterium de Bary, Staphylococcus saprophyticus Shaw et al, Pseudomonas fluorescens Migula, Pseudomonas putida Trevisan, Escherichia coli Castellani, and Chalmers bacterial strains are studied. It is shown that terpenoids camphor and its fractions are the common components in the composition of volatile compounds of the leaves of the representatives of the family Lauraceae Juss. and its percentage is species-specific. The antimicrobial activity of essential oils determines the dominant components in addition to camphor and its fractions, as compounds having a strong toxic effect against pathogenic bacteria and fungi such as sesquiterpene alpha-cubebene (2.30  %) of Cinnamomum tamala leaves and eugenol (6.22  %) in Laurus azorica leaves.

One of the most important problems of a long monitoring of the patients operated for thyroid carcinoma and receiving suppressive therapy with levothyroxine is the prevention of the adverse effects of treatment on the cardiovascular system. The purpose of the work is to identify the features of formation of symptoms and signs of cardiovascular diseases, as well as heart rhythm abnormalities in young patients receiving suppressive therapy with levothyroxine depending on their body mass index (BMI). Changes in the heart rate variability in patients with tachycardia and high blood pressure are studied. It is shown that patients with normal and overweight have alternative tendencies in the changes of heart rate and the formation of cardiovascular diseases.

Wound healing and cosmetic results of 54 reconstructions of the external nose were evaluated. The clinical methods, the cytological examination of wound samples, the ultrasound examination of the neonose, the wound evaluation scale, and the visual analogue scale were used. We compared the results after the reconstruction with the use of autologous tissue (n  = 30) and plastic material, including an allogenic cartilage graft (n  = 24). No significant differences in wound healing, local complication rates, wound evaluation scores, and visual analogue scores were observed. The ultrasound examination of neonose didn’t detect significant resorption of allogenic cartilage.

The formation and segmentation of the Pripyat–Dnieper–Donetsk aulacogen took place during the Hercynian tectogenesis, when the sinrift Pripyat and Dnieper troughs and the postrift inverted Donetsk folded structure and Carpinsky mountain ridge were formed. The special features of these inverted and noninverted structures are due to their tectonic position, differentiated vertical and horizontal movements of the Earth’s crust blocks along the aulacogen strike, the contribution of transverse fault-shifts to the developmental automism of the longitudinal segments, and their correlation with the old basement structural elements.

The structure and properties of steels subjected to thermochemical heat treatment in multi-carbide forming media are studied. As a result, two types of composite structures are formed. Regularities in the formation of diffusion multi-carbide coatings are established. New models of complex diffusion saturation of steel by transition metals is proposed on the basis of thermodynamics and kinetics.

The influence of Brownian diffusion on the distribution of nanoparticles in an evaporating or growing micron droplet is considered. It is shown that there are possibilities for emerging a spatially non-uniform state of the nanoparticles in the droplet.