For the functions defined on normed vector spaces, we introduce a new notion of the LC -convexity that generalizes the classical notion of convex functions. A function is called to be LC -convex if it can be represented as the upper envelope of some subset of Lipschitz concave functions. It is proved that the function is LC -convex if and only if it is lower semicontinuous and, in addition, it is bounded from below by a Lipschitz function. As a generalization of a global subdifferential of a classically convex function, we introduce the set of LC -minorants supported to a function at a given point and the set of LC -support points of a function that are then used to derive a criterion for global minimum points and a necessary condition for global maximum points of nonsmooth functions. An important result of the article is to prove that for a LC -
convex function, the set of LC -support points is dense in its effective domain. This result extends the well-known Brondsted– Rockafellar theorem on the existence of the sub-differential for classically convex lower semicontinuous functions to a wider class of lower semicontinuous functions and goes back to the one of the most important results of the classical convex analysis – the Bishop–Phelps theorem on the density of support points in the boundary of a closed convex set.

A linear control system with an almost periodic matrix of coefficients and the control in the form of feedback linear in phase variables is considered. It is assumed that the feedback coefficient is almost periodic and its frequency module, i. e. the smallest additive group of real numbers, including all the Fourier exponents of this coefficient, is contained in the frequency module of the coefficient matrix. The system under consideration is studied in the case of a zero average value of the matrix of coefficients. For the described class of systems, the control problem of the spectrum of irregular oscillations (asynchronous spectrum) with a target set of frequencies is solved. This task is as follows: to construct such a control from an admissible set so that the system closed by this control has almost periodic solutions, the set of Fourier exponents (frequency spectrum) that are contained in a predetermined subset; the intersection of the solution frequency modules and the coefficient matrix is trivial. The necessary and sufficient conditions for solvability of the control problem of the asynchronous spectrum are obtained.

The article formulates the principles of constructing threshold cryptographic schemes for secret sharing based on a modular coding and a linear masking function with an additive variational component of pseudo-random type. The main attention is paid to the correctness problem of schemes of the considered class within the limits of the accepted model. The congruent condition in the module of the secret-original ring of the masking function values in full and partial modular number systems is obtained. On the basis of the above-said, the method of correct implementation of the threshold principle of secret information sharing is developed. The proposed approach to solving the problem under study is demonstrated by specific numerical examples.

The conditions of converting the reflection coefficients of plane TM or TE for a film-substrate dissipative structure are determined. As a result, the possibilities to maximize the measurement sensitivity by the THz spectroscopy method of the protein concentration in an aqueous solution are established, and the analytical solution to the inverse optical problem of determining the complex permittivity and thickness of a weakly absorbing film located on a weakly absorbing substrate is obtained.

A new technique for implementing external (particle-to-wall) and particle-to-particle radiative heat transfer in discrete elements method (DEM) simulations is proposed. It is based on the idea that an expected view factor value depends on relevant local bed parameters (distance between particles, particle radius ratio, and local bed porosity). Calculation of average view factors via the formula requires considerably less computational effort than direct in situ integration, when this happens a reasonable average value and an overall accuracy comparable to direct calculation are provided. Both mono- and polydisperse mixtures of spherical opaque particles were considered. It was shown that using nondimensional parameters, a simple general dependence for an external radiative heat flux may be introduced. Exponential and linear fits were proposed for estimating the particle-particle radiative heat flux. The generalization of the obtained formulas for various bed porosities is proposed. The distribution of cumulative transferred heat flux across the particles up to a certain distance was found, and the recommendations regarding the choice of that parameter to achieve a desired accuracy were formulated. Also, the method to account for the particle emissivity was proposed on the basis of the empirical dependence between emissivity and radiative heat flux in porous materials. The proposed method satisfies all the requirements to become a standard implementation of radiative heat transfer calculation in DEM.

The article discusses the issues of modifying the photoluminescence intensity of quantum dipole emitters (molecules, quantum dots (nanocryslalls)) located near metal spherical nanoparticles with a dielectric shell. It is shown that by specifying the optimal configuration of a nanoparticle with a shell and the position of the emitter, it is possible to create the conditions, under which an increase in the photoluminescence intensity can be greater than in the case of the same nanoparticle without a shell.

Geometrical and electronic parameters of the microstates of the molecular models of polyacrylamide and co-polymers of acrylamide-acrylic acid in aqueous solutions of sodium and potassium chlorides were computed by the non-empirical SCF MO LCAO method with the use of the basis MINI Huzinaga. The models contained four monomeric units of the polymer, including two metal carboxylate groups, 80 water molecules and two pairs of ions Na+ and Cl– or K+ and Cl–. It follows from the calculation results that there is a principal difference in the hydration of Na+ and K+: the Na+‧‧‧О2– bond is shorter than the sum of the radii of the interacting ions, while the k+‧‧‧O2– bond is equal or longer. This indicates that in the first case, the bonds are partially covalent, while in the second one they are pure electrostatic. All elements of the molecular models in the both cases are combined by the intermolecular bonds forming a spatial net. The polymer molecules have a flexible chain with oxygen containing functional groups that are built into the structure of the salt solutions without distorting it. We assume that this is the main reason for the good solubility of the studied polymers in the aqueous salt solutions.

The distribution of pesticides of different classes (amides, anilinopyrimidines, benzene derivatives, benzoylphenylureas, benzenesulfonates, hydrazides, dinitroanilines, carbamates, pyretroids, pyrimidines, tetrazines, triazoles, pheny lureas, organophosphorus compounds, esters of carboxylic acids) was studied at 20 ± 1 °C in the extraction systems of hexane–water, hexane–acetonitrile, hexane– acetonitrile and water mixture that are most often used in analytical chemistry of pesticides. The distribution constants P of pesticides and the increments of logarithms of the distribution constants If of their functional groups between the hydrocarbon and polar phases are calculated. Two main methods for evaluative prediction of lg P of pesticides are proposed and approved – substitutive method based on the calculation of lg P by replacing the substituents in the base molecule and the method of absolute addition of increments. The possibilities of the both methods are illustrated. The reasons for the deviations of the experimental values from the calculated ones are discussed. The influence of the nature and composition of the polar phase on the magnitudes of the observed deviations is estimated. In particular, they decrease dramatically with an increase in the acetonitrile content in the polar phase. Averaged values of correction to the calculated values of lg P are introduced. In most cases, they allow predicting lg P of pesticides with a deviation of not more than 0.5–1.0 from the calculated one.

On the example of synthesis of 4-acetylamino-3-fluoroalkyl(aryl)-4,5,6,7-tetrahydro-1,2-benzisoxazoles, the effective approach to a synthesis of novel 4-acylamino-4,5,6,7-tetrahydro-1,2-benzisoxazoles is proposed. 3-Fluoroalkyl(aryl)- 6,7-dihydro-1,2-benzisoxazol-4-ones were reduced by a sodium borohydride in isopropanol to obtain 3-fluoroalkyl(aryl)- 4,5,6,7-tetrahydro-1,2-benzisoxazol-4-ols that in the conditions of the Ritter reaction (acetonitrile, acetic acid, sulfuric acid) gave target 4-acylamino derivatives with 80–94 % yields.

Anthocyanins are high-value plant antioxidants; they also determine biotic and abiotic stress resistance. The aim of our research was to study the allelic polymorphism of Antocyanin 1 orthologs in the vegetable Solanaceae crops of C. annuum and S. melongena. The search revealed the following closest genes in C. annuum: Myb113-like1 TF and Myb113like2 transcription factors and Myb1 in S. melongena. Exon amplicons of those genes were obtained and then sequenced in the pepper and eggplant samples with contrasting anthocyanin fruit coloration. Primers to the identified polymorphisms were developed and their correlation with the anthocyanin accumulation in fruits was studied. A close correlation was found between a minimum accumulation or the complete absence of anthocyanin synthesis in fruits with a single nucleotide deletion (Myb113-like1), and in the pepper samples, 2 SNP (Myb113-like2) was detected using the CAPS marker Myb 113-AccI. In the eggplant samples, the deletions of 6 and 26 bp were detected using the SCAR marker MybMel and the CAPS marker MybmelPst1. The disturbance of anthocyanin synthesis in pepper forms with 1Indel in Myb113-like1 TF was determined by a shift in the reading frame and SNPs in Myb113-like2 TF lead to amino acid substitutions: Lys → Arg and Thr → Lys. In the eggplant, a deletion of 6 bp leads to the loss of ala and arg in the protein; a deletion of 26 bp causes disorder during the mRNA maturation. The developed markers allow identifying the Myb-like TF alleles under study, resulting in anthocyanin synthesis disturbance in fruits. C. annuum and S. melongena samples with different alleles were selected for a further study and new varieties in agriculture. 

Reactive oxygen species (ROS) have a crucial role in human physiological and pathophysiological processes. Prolonged exposure to high ROS concentrations may lead to cardiovascular, neurodegenerative, etc. diseases. In this study, gallocyanine has been proposed to register the ROS production. The gallocyanine spectral properties changes under ROS (•О2ˉ, H2O2) and reactive halogen (HOCl) species are analyzed. It is shown that the dye is oxidized in solution, both under the action of ROS and reactive halogen species. Based on the data obtained, it is possible to suggest that superoxide anion radicals make a major contribution to chemical conversion of the dye in suspensions of activated neutrophils. It is that gallocyanine can be used to assess the functional activity of neutrophils, namely, the NADPH-oxidase, as well as to design and test novel therapeutic agents for diseases associated with developing oxidative stress.

In acute rat experiments (thiopental sodium narcosis), it is established that introducing a 5 % glucose solution into the stomach lowers a frequency of heart rates (HR) and an amplitude of potentials of smooth muscles of the stomach and simultaneously raises doubtfully and shortly the potentials of sooth muscles (PSM) of the colon. Food additives used in the glutamate sodium, benzoate, tartrazine complex do not influence HR, but as before, reduces PSM of the stomach, and in the thick gut precise exciting or brake responses are marked. In the preliminarily developed heart insufficiency conditions, the glucose infusion into the stomach does not change HR. At the same time, the action of glucose, as well as of food additives, still results in reliable reactions of the stomach and the thick gut. Important is the present work information on the ability of glucose and food additives to modulate the heart activity estimated through the indicators of modification of electrocardiogram teeth. As appeared, the infusion of the specified irritants in the stomach of rats in control and heart insufficiency is accompanied by precise enough changes in such indicators as the RST duration, the amplitude and duration of the Т-wave,
i. e. the prognostic attributes of the opportunity of occurrence of heart аrrhythmia, fibrillations.

The reactivity of biological systems to UV-A/B and the photoprotective potential of skin applications of lichen extracts Hypogymnia physodes according to the biochemical parameters of blood and morphometric parameters of the skin were evaluated in vivo in laboratory mice. Ethanol, acetone and hexane–acetone extracts (1 % in dimethylsulfoxide) effectively absorb the UV range inducing the most erythema. On the 4th day after UV-A/Вirradiation, severe brown burns of the back skin, severe erythema and edema, scab formation were observed. In serum, there were significantly changed biochemical parameters – the prooxidant capacity, the level of nitrate/nitrite-ions NOx, advanced oxidation protein products AOPP, glutathioneperoxidase activity GPx increased, the level of SH-groups reduced. Solutions of extracts (5 %) in dimethylsulfoxide at
a different degree exhibited the photoprotective effect: morphologically – in minimizing the burn symptoms of the skin (edema, erythema, scab); biochemically – in the regulation of these parameters at the control level. According to the set of biochemical and morphometric parameters, the most promising photoprotectors were acetone extracts. The prooxidant capacity, GPx, AOРР (in all cases reduced) and NOx showed a non-specificity and rather high sensitivity and are more suitable for estimating inflammatory and oxidative processes. The highest efficiency and the adequacy to the tasks and the specifications are shown by the level of protein SH-groups.

Based on the petrological and geochemical data, the formation conditions of the ultrabasic-basic rocks of the Rusinovsky complex of the crystalline basement of Belarus are determined. It is shown that the rocks of the Rusinovsky complex are divided into two petrochemical series: magnesian and titanium-ferruginous. The peculiarities of the rare-element rock composition indicate the melting and processing of the original composition of magma, and its crust contamination. According to the formation conditions of the rock, the complex is close to island-arc formations.

Fluid capturing by a moving inclined surface is analyzed theoretically. A task for non-Newtonian fluid is stated in general form. The solving of this task enables revealing the basic physical principles and the mechanisms of the fluid withdrawal process over an entire range of withdrawal velocities realized in practice. The case of withdrawal of finite yield stress viscoplastic fluid is considered.