# Наукові вісті

The International Science and Technology journal was founded in 1997.

State registration certificate: KB № 18963-775 ПР of April 25 2012.

ISSN 1810-0546 (Print)

ISSN 2519-8890 (Online)

CODEN: NVNTB7

LCCN: 2016214741

The journal publishes only the new results of fundamental and applied scientific research on the subjects of the journal, which had not been previously published in other scientific publications in Ukraine or abroad.

The editorial board of the journal accepts overview and original research papers on the following topics: electronics, radio engineering and telecommunications; power engineering and energy generating technologies; Information technologies, system analysis and control; science of materials and mechanical engineering; instrument- making and information-measuring equipment; problems of biotechnology; energy saving problems; problems of chemistry and chemical technology; theoretical and applied problems of physics and mathematics.

According to the order of MES of Ukraine from 07.13.2015 no. 747, from 07.10.2015 no. 1021, and from 09.03.2016 no. 241 the journal specializes in the physical and mathematical, technical, chemical and biological sciences.

The periodicity of the journal is 6 times a year (no. 1, 2, 5, 6 – engineering sciences, no. 3 – chemical and biological sciences and technology, no. 4 – physical and mathematical sciences).

Languages: Ukrainian, Russian, English.

Founder: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”.

Mailing address of the editorial office: building 1, room 171-3 and 193-Б, Peremohy Str. 37, Kyiv 03056, Ukraine.

E-mail: n.visti@kpi.ua and n-visti@kpi.ua

Tel.: +38(044)204-91-23; +38(044)204-94-53

The journal is covered by following indexing services:

*Адреса URL:*http://bulletin.kpi.ua/

*Оновлено:*12 годин 57 хв тому

### Boundedness of Lebesgue Constants and Interpolating Faber Bases

**Background.** We investigate the relationship between the boundedness of Lebesgue constants for the Lagrange polynomial interpolation on a compact subset of

\[\mathbb R\]

and the existence of a Faber basis in the space of continuous functions on this compact set.

**Objective.** The aim of the paper is to describe the conditions on the matrix of interpolation nodes under which the interpolation of any continuous function coincides with the decomposition of this function in a series on the Faber basis.

**Methods.** The methods of general theory of Schauder bases and the results which describe the convergence of interpolating Lagrange processes are used.

**Results. **The structure of matrices of interpolation nodes which generate the interpolating Faber bases is described.

**Conclusions.** Every interpolating Faber basis is generated by the interpolating Lagrange process with the interpolating matrix of a special kind and bounded Lebesgue constants.

### Estimation of Accuracy and Reliability of Models of φ-sub-Gaussian Stochastic Processes in Spaces

**Background.** At present, in the theory of stochastic process modeling a problem of assessment of reliability and accuracy of stochastic process model in *C*(*T*) space wasn’t studied for the case of inexplicit decomposition of process in the form of a series with independent terms.

**Objective.** The goal is to study reliability and accuracy in *C*(*T*)** **of models of processes from Subφ(Ω)* *that cannot be decomposed in a series with independent elements explicitly.

**Methods.** Using previous research in the field of modeling of stochastic processes, assumption is considered about possibility of decomposition of a stochastic process in the series with independent elements that can be found using approximations.

**Results.** Impact of approximation error of process decomposition in series with independent elements on reliability and accuracy of modeling of stochastic process in *C*(*T*) is studied.

**Conclusions.** Theorems are proved that allow estimation of reliability and accuracy of a model in *C*(*T*) of a stochastic process from Subφ(Ω)* *in the case when decomposition of this process in a series with independent elements can be found only with some error, for example, using numerical approximations.

### An Efficiency of Strategies in Models of Conflict Redistribution of Resource Space

**Background. **The model of conflict redistribution of resource space (territory) between a pair of opponents in the case of infinite fractal division of space is investigated.

**Objective**. The aim of the paper is to consider the problem of conflict redistribution of resource space, if the opponent presence measures on the space are limited, but not necessarily probabilistic.

**Methods****. **To specify the measures of the occupied territories and to find their limiting values a probabilistic approach was applied.

**Results****. **The existence of limit values of measures of occupied territories with an infinite increase in the division step is established. The possible values are indicated. Using computer simulation graphs are obtained which show the behavior of the measures of the occupied territories with increasing of the division step.

**Conclusions.**It is shown that the limit values of measures of occupied territories depend only on the selected strategies (that is, the way of structured representation of measures that correspond to each of the opponents).

### The Main Properties of q-Functions

**Background.** The new generalization of the function of complex variable (*q*-function) is considered, its main properties are investigated. Such distributions have a special place among the special functions due to their widespread use in many areas of applied mathematics.

**Objective**. The aim of the paper is to study the new generalization of the function of complex variable for application in applied sciences.

**Methods.** To obtain scientific results the general methods of the mathematical analysis, and the theory of special functions have been used.

**Results.** The article deals with new generalization of the function of complex variable – *q*-functions, its main properties are investigated. The theorem on integral representation of *q* = *xk*-analytical functions is proved, its inverse formula is constructed.

**Conclusions.** Considered in the article new generalization of the function of complex variable opens up opportunities for the use of *q*-functions in the theory of special functions, and in the applications of mathematical and physical problems. In the future we plan to use the results to solve the boundary value problems of mathematical physics, in the theory of elasticity, for solving of, the theory of integral equations, etc.

### Surface of Maximums of AR(2) Process Spectral Densities and its Application in Time Series Statistics

**Background.** In the problem on probabilities of large deviations of discrete time and sub-Gaussian AR(2) noise nonlinear regression model parameter least squares estimate a constant is determined that controls the rate of exponential convergence to zero of indicated probabilities.

**Objective.** The aim of the paper is to find the surface of maximums of AR(2) process spectral densities in the domain of its stationarity in explicit form.

**Methods.** The results were obtained on the use of methodology developed in the works by A. Sieders, K. Dzhaparidze (1987), A.V. Ivanov (1997, 2016) and standard Calculus methods.

**Results.** A complex formula that describes a continuous surface of maximums of AR(2) process spectral densities assigned on the stationary triangle of the time series of this type is obtained.

**Conclusions.**The obtained formula of surface of maximums of noise spectral densities gives an opportunity to realize for which values of AR(2) process characteristic polynomial coefficients it is possible to look for greater rate of convergence to zero of the probabilities of large deviations of the considered estimates.

### Consistency of the Least Squares Estimate of Textured Surface Parameters

**Background.** For sinusoidal observation model of textured surface, i.e. model where regression function is a two-parameter harmonic oscillation and noise is a homogeneous isotropic Gaussian random field on the plane with zero mean and covariance function of the special kind, the problem of statistical estimation of sinusoidal model unknown amplitudes and angular frequencies is considered.

**Objective.** The aim of the paper is to study asymptotic behavior of the least squares estimate (LSE) of unknown amplitudes and angular frequencies of textured surface sinusoidal model.

**Methods.** The results were obtained on the application of methodology developed in the papers by A.V. Ivanov et al. (2009, 2015) and monograph by A.V. Ivanov, N.N. Leonenko (1989).

**Results.** Sufficient conditions on random noise covariance function that ensure strong consistency of sinusoidal model parameters LSE are obtained.

**Conclusions.**The obtained results allow extending them on the models where regression function is a sum of several two-parameter harmonic oscillations. Besides LSE consistency property will allow proving asymptotic normality of these estimates in further works.

### A Generalization of Rényi’s Parking Problem

**Background****.**** **A generalization of the A. Rényi’s stochastic parking model is considered. In our model, the probability distribution of the left end of a parked car is a mixture of a uniform distribution and a degenerated one. This allows distinguishing drivers with different skills.

**Objective. **The aim of the paper is an asymptotic study of the mean number of parked cars

\[m_{p}(x) \]

when the length of parking space

\[x\]

increases unboundedly.

**Methods. **A functional-integral equation satisfied by the function

\[m_{p}\]

is derived. This equation admits an explicit solution in terms of the Laplace transform which allows for applying Tauberian theorems to study the required asymptotics.

**Results. **For the above model it is shown, that

\[m_{p}(x)=\lambda_{p}x+o(x)\]

as

\[x\rightarrow\infty.\]

The explicit form of the constant

\[\lambda_{p}\]

is given by

\[\frac{1}{1-p}\int_{0}^{\infty} \mathrm{exp}\left(-2\int_{0}^{S}\frac{e^{\tau}-1}{\tau({e^{\tau}-p})}d\tau\right)ds.\]

A similar asymptotic bound is obtained for a wider class of models in which the uniform component of the mixture of distributions is replaced by a more general one.

**Conclusions.**As a generalization of the classical A. Rényi’s random parking model, a new parking model is proposed. In this model the uniform distribution of the parking point is replaced by a mixture of a uniform distribution and a degenerated one. In the new model, a counterpart of the Rényi’s theorem on the asymptotic behavior of the mean number of parked cars is deduced.

### Strong Law of Large Numbers for Solutions of Non-Autonomous Stochastic Differential Equations

**Background. **Asymptotic behavior at infinity of non-autonomous stochastic differential equation solutions is studied in the paper.

**Objective.** The aim of the work is to find sufficient conditions for the strong law of large numbers for a random process which is a solution of non-autonomous stochastic differential equation.

**Methods.** Basic results of the theory of stochastic differential equations related to stochastic integrals estimation.

**Results.** Sufficient conditions for almost sure convergence to zero of normalized term related to diffusion of non-autonomous stochastic differential equation are obtained.

**Conclusions**. Results of the paper can be used for further research on the asymptotic behavior of stochastic differential equation solutions, finding the stability condition of stochastic differential equation solution and ergodic type problems also.

### An Alternative Surface Measures Construction in Finite-Dimensional Spaces and its Consistency with the Classical Approach

**Background. **The area formulae are well known for surfaces embedded into a finite-dimensional Euclidean space. However, in the case of an infinite-dimensional Banach manifold, such formulae cannot be used. Thus, a problem of finding an alternative approach to the surface measures construction appears, that, on the one hand, leads to classical results in finite-dimensional case, and on the other hand, can be used for infinite-dimensional Banach manifolds.

**Objective. **The aim of the paper is to get a construction of surface measure induced by the Lebesgue measure and the associated form for a parametrically defined surface embedded into finite-dimensional Euclidean space. Show the consistency of surface area calculation by this construction with an area calculated by using well-known classical formulae.

**Methods. **Basic results of mathematical analyses, measure theory and differential geometry are used.

**Results. **An alternative construction of surface measures induced by the Lebesgue measure on surfaces in finite-dimensional space is obtained. It is shown that such approach is consistent with the classical definition of the surface area.

**Conclusions. **The construction of surface measures suggested for infinite-dimensional spaces is a generalization of the classical approach in finite-dimensional spaces. Therefore further investigation of the described approach seems to be reasonable.

### Magnetic Spin-Wave Properties of Ferromagnetic Nanosystems of Various Shapes. Peculiarities of the Border Conditions Accounting in the Process of the Wavenumber Values Spectrum Finding

**Background.** The paper continues the investigation of linear dipole-exchange spin waves in ferromagnetic nanosystems started by the author in previous papers. The known papers investigating dipole-exchange spin waves obtain their spectral characteristics only for a narrow range of special cases. In the presented paper, an approach that allows expanding substantially this range of cases is described and applied.

**Objective.** The aim of the paper is to develop a method – based on the use of boundary conditions – for obtaining the spectral characteristics of dipole-exchange spin waves in a number of nanosystems’ configurations as well as an application of this method to specific configurations.

**Methods.** A method for obtaining a values’ spectrum of the wavenumbers for dipole-exchange spin waves in ferromagnetic nanosystems of a series of typical configurations is proposed. The method does not require specific assumptions, e.g. the absence of transverse spin excitations or the presence of a high-conductivity metal outside the ferromagnet. The method uses imposition of boundary conditions for the magnetic field and the magnetization on the boundary of the ferromagnetic medium for a linear spin wave in the magnetostatic approximation. This method allows obtaining the above-mentioned spectral characteristics for a wider range of cases compared to the known previous papers.

**Results.** The results of the paper are conditions for the magnetic potential – that imply from the above-mentioned boundary conditions – of a linear spin wave on the boundary of a ferromagnetic nanosystem as well as the spectrum of the wavenumbers’ values of such wave for the investigated nanosystems (in the implicit form). In particular, for a ferromagnetic nanosystem of an arbitrary cross section with a one-dimensional translational symmetry, the conditions specifying this spectrum are found. Such conditions are specified – and an implicit expression for this spectrum is obtained – for the case when such nanosystem is a nanotube with a circular cross section. The analysis of the obtained results is carried out.

**Conclusions.**The obtained expressions for the spectrum of the values of the investigated spin waves’ wavenumbers can be used for a wider range of cases than the ones obtained in the previous papers dedicated to the investigated configurations of nanosystems. For a nanotube of the circular cross-section with small (compared to the inverse characteristic size of the nanotube cross-section) values of the longitudinal wave number, the dependence of the latter on the transverse wave number is weak, as well as for the big longitudinal to transverse wavenumber component ratio. The obtained dependence is also represented graphically.

### Analytical Models Development of Compact Monopole Vortex Flows

**Background. **Mathematical description of vortex flows as a part of basic fundamental concepts of continuum mechanics, hydro- and gas dynamics, thermal physics, theoretical basics of chemical engineering, geophysics, meteorology.

**Objective. **Replenishment of existing information in traditional scientific, technical and educational publications about vortices and their analytical models by new data for scientists, teachers, post-graduates and students with the purpose of using in further investigations of fluids and gas vortex motion.

**Methods. **Analytical review of existing vortex current models, including monopole compact vortices, on a basis of the latest data from scientific articles and specialized monographs and their comparison with traditional data containing in the known textbooks and educational materials.

**Results. **The lack of modern compact vortices models was revealed in traditional scientific, technical and educational literary sources. They include the compact analogs of the point vortex and Rankine vortex: quasi-point vortex and compact compensated vortex. On basis of these ones and similar to them solutions (circular vortex, vortex with triad constant vorticity zones) the models of compact helical flows and vortices with helical symmetry were elaborated. The solutions of such tasks were analyzed: diffusion of compact vortices (Taylor vortex, Kloosterziel solution), turbulent diffusion of compact vortex, solutions for quasi-compact (laminar and turbulent) vortex-source, vortex-sink and also solution of the problem about compact turbulent vortex generation by rotating cylinder. All considered models are consistent with the energy conservation law and have advantages in their use.

**Conclusions.**The article contains series of the latest analytical models that describe both laminar and turbulent dynamics of monopole vortex flows which have not been reflected in traditional publications up to the present. The further research must be directed to search of analytical models for the coherent vortical structures in flows of viscous fluids, particularly near curved surfaces, where known in hydromechanics “wall law” is disturbed and heat and mass transfer anomalies take place.

### Frequency Dependencies of the Exchange Spin Wave Reflection Coefficient on a One-Dimensional Magnon Crystal with Complex Interfaces

**Background.** This work is devoted to theoretical study of the behavior of spin waves passing through multilayer ferromagnetic with complex interfaces.

**Objective. ****T**he aim of the paper is to calculate the reflection coefficient of multilayer ferromagnetic with complex interfaces as function of spin wave frequency at variable material parameter and constant value of external magnetic field. The formalism of geometric optics allows describing the spin wave refraction process and the reflection coefficient, as well as controlling this process by changing the frequency of the spin wave for given parameters of the medium.

**Methods.**** **To find the reflection coefficient from a multilayer** **ferromagnetic the mathematical apparatus of geometric optics was used**.**** **To describe the dynamics of the magnetization vector the formalism of the spin density order parameter was used allowing for the use of methods of quantum mechanics to calculate the reflection coefficient from a semi-infinite multilayer structure.

**Results.** The spin wave reflection coefficient of semi-infinite multilayer structure of ferromagnetic materials with complex interfaces has been found. The dependency graphs of the reflection coefficient from the frequency of the spin waves at different parameters of magnetic anisotropy inhomogeneity and constant value of the external magnetic field were obtained.

**Conclusions.**It is shown that the frequency dependencies are periodic, points of full transmission and areas, full of reflection. Decreasing exchange parameter value in interface causes the increase of reflectance coefficient. Changing the material parameters we get the necessary intensity value of the reflection coefficient depending on the frequency at a constant value of the external magnetic field.

### The Biosynthesis of Antibiotics as a Taxonomic Marker of Some Species of the Genus Pseudomonas

**Background.** The ability to biosynthesis of antibiotics was established for 20 of 250 species of *Pseudomonas*. The value of the biosynthesis of antibiotics as a taxonomic characteristic for the genus *Pseudomonas* is not studied. This issue will be analyzed using the experimental results.

**Оbjective.** The aim of the paper is to identify the ability of usage of antibiotics synthesized by certain types of bacteria of the genus *Pseudomonas*, as a taxonomic marker.

**Methods.** Methods of thin-layer *chromatography** *(TLC) and LC/MS-analysis were used to determine the synthesis of antibiotics.

**Results.** A unique set of antibiotics was determined for some types of bacteria *Pseudomonas,* which are specific for them only: pyocyanin – *P. aeruginosa*, 2,4-diacetylphloroglucinol – *P. brassicacearum*, 2-hydroxyphenazine-1-carboxylic acid – *P. chlororaphis subsp. aureofaciens*, pyrrolnitrin and 2,4-diacetylphloroglucinol – *P. protegens*, batumin – *P. batumici*.

**Conclusions.** The ability to synthesize certain antibiotic substances may serve as a taxonomic marker and be used to identify certain species of *Pseudomonas*. However, the biosynthesis of antibiotics did not show specificity for several species. This problem requires a deeper study of different types of *Pseudomonas*.

### Biotechnological Approaches for Intensification of Ammonium Removal During Drinking Water Treatment

**Background.** Nitrogen-containing substances are the most common components of groundwater of Ukraine. It was detected, that ammonium may impact on the process of water disinfection, the appearance of nitrite in the distribution system and the problem with the taste and smell of water. The presence of high concentrations of nitrites and nitrates in water can cause methemoglobinemia in children that causes cyanosis and asphyxia. So, there is an urgent demand of developing approaches to intensification of ammonia removing from drinking water.

**Objective.** The aim of these studies is to examine the characteristics of biotechnological processes of nitrogen compounds removing from drinking water in its purification with charge BIOFILTER.

**Methods.** The object of the study was underground water from wells located in the Khmelnitsky region. The initial concentration of ammonia in water was 2.16 mg/dm3, nitrite – 0.48 mg/dm3, nitrate – 4.5 mg/dm3. Investigation of removing of nitrogen-containing substances was conducted on a pilot plant, consisting of aerator, closed contact tank and model filters with charge BIOFILTER. Water was saturated with oxygen in water aerator then came to closed contact tank, where the following parameters were gauged: the concentration of dissolved oxygen, ammonia, nitrites and nitrates. The concentration of dissolved oxygen, ammonia, nitrites and nitrates were controlled in the output water. The pilot plant was set up and worked on the well.

**Results.** It is shown that when the concentration of oxygen decreased from 8.0 to 6.4 mg/dm3, a sharp decrease in nitrate concentrations from 4.5 to 3.9 mg/dm3 was observed. A gradual decrease of nitrates concentrations was observed with increasing doses of consumed oxygen. It was suggested that the nitrification process was passing simultaneously with a process of denitrification as evidenced by a sharp decrease in the concentration of nitrates with a decrease in the oxygen dissolved in water.

**Conclusions.**A decrease in dissolved oxygen concentration violates theoretical ratio of nitrate content in water was experimentally confirmed. The actual content of nitrates in the treated water was less than the theoretical, indicating the passage of denitrification process simultaneously with a process of nitrification. The less concentration of dissolved oxygen in the water at the outlet of the filter, the deeper denitrification is held.

### Isolation of Polyclonal Antibodies to Collagen by Ion Exchange Chromatography on Column with DEAE-Sepharose

**Background.** Development of new methods for isolation and purification of polyclonal antibodies.

**Objective.** Analysis of the efficiency of the ion exchange column with DEAE-Sepharose at isolation of polyclonal antibodies to collagen.

**Methods.** IgG were isolated from precipitated γ-globulin fraction of serum of immunized rabbit by ion exchange chromatography on column with DEAE-Sepharose.

**Results.** It was determined that the IgG output at volume ratio of 4:3 of starting material and the carrier applied to the column is 1.67 times higher than the ratio of 2:3. It is shown that IgG goes out of the column together with the protein that has a molecular weight of about 57–60 kDa. We found that 5.123 mg of IgG with minor impurities of serum proteins is obtained from 30 cm3 of rabbit’s serum.

**Conclusions.**The method of ion exchange chromatography on column with DEAE-Sepharose provides a high yield of IgG with few impurities and can be used as a way of pre-treatment of polyclonal antibodies.

### Effect of a Complex Preparation With Polyguanidine and Microelements on Preservation, Growth and Development of Potatoes

**B****ackground.** Preservation and increase in potato growth.

**O****bjective.** The aim of the paper is to obtain a composition for potatoes processing increasing preservation effectiveness and potato growth.

**M****ethods.** Study of influence of the complex preparation containing polyhexamethyleneguanidine and microelements on preservation, growth and development of potatoes.

**R****esults.** Treatment of potatoes using complex preparation containing polyhexamethyleneguanidine and microelements decreased tubers damage 4.3 times during preservation. Spraying tubers with PGMG and microelements solution before planting caused growth stimulation of potato plants in the early stages of growth and increased potato productivity for 12–23 % depending on the concentration of microelements. The greatest effect was observed in cases where potatoes were treated with PGMG (0.1 %) and microelements in total concentration of 0.4 %. Potato productivity was increased by rising tubers number.

**Conclusion.**Optimal concentration to achieve a positive effect was determined.

### Pecularities of Composite Lacto- and Bifidoprobiotic Biotechnology: Determination of Rational Dose Influence upon Chicken Broilers’ Performance

**Background****. **The EU decision completely stopped the use of promoter antibiotics as fodder therapeutic and prophylactic additives for animals from 01.01.2006. Therefore, probiotic preparations containing adjuvant microorganisms for the intestine of the individual are actively developed and introduced into the practice of livestock. The use of environmentally compatible probiotic preparations has become a priority in poultry farming.

**Objective****. **The aim of the paper is to identify the features and effectiveness of the rational dose and the temporal regime of using the feed lactobiphidoprobiotic in production conditions on the control and experimental groups in 1000 heads of broiler chickens at poultry farming enterprises.

**Methods****. **The main zootechnical indices were studied in accordance with the generally accepted methods, chemical and biochemical analysis was carried out, the coefficient of energy value, the meat-and-bone quality index and the calorific value of the broiler chicken meat of the control and experimental groups were calculated.

**Results****. **Experimental results on the effectiveness of the rational dose of the complex fodder probiotic supplement are presented on the basis of the functional mixture of *Bifidobacterium pullorum*, *Lactobacillus plantarum*, *L. paracasei* *ssp*.*bacteria. Paracasei* and *L. rhamnosus* for broiler chickens.It was found that with the use of a probiotic composite, the live weight of broiler chickens of the experimental group increased by 6.8%, the average daily gain increased by 6.9 %, safety by 3.2%, the productivity index increased by 37.7 units compared to the control. It was found that the content of protein and ash in carcasses and parts thereof as a result of the use of a functional additive increased, and the moisture and fat content, on the contrary, decreased.

**С****onclusions****. **It has been proved that the use of a complex fodder probiotic based on lacto- and bifidobacteria significantly improves the quality of production of broiler chickens under production conditions. The obtained results on a production scale and conditions confirm the effectiveness of the introduction of a complex probiotic for agricultural birds developed on the broiler chickens model, are the basis for further research and implementation in large-scale production, and also open prospects for its use for Galliformes taxon birds, including meat and ornamental breeds.

### Antibacterial Properties of Some Macromycetes

**Background.** The constant emergence of pathogen forms and their new species multi-resistant to existing drugs, and the frequent occurrence of side effects of these drugs cause need to find new antibiotic compounds, especially antibiotics of natural origin (from plants, fungi, mosses). Fungi are promising object of research because of production of various biologically active substances.

**Objective.** The aim of the paper is to analyze the results of research of antibacterial properties of various macromycetes representatives and determine prospects of their practical application.

**Methods.** The analysis and generalisation of information about objects and methods of macromycetes antibacterial activity research.

**Results.** Much attention is paid to Basidiomycetes among macromycetes, especially species of the genus *Agaricus, Ganoderma, Lentinus, Phellinus, Pleurotus, Polyporus, Trametes*. In practice macromycetes are used both as fruiting bodies, biomass and culture liquid and as isolated antibiotic substances. Therefore, edible species of fungi are preferred (*Agaricus* sp., *Pleurotus* sp. and *Lentinus *sp.).

**Conclusions.** Considering the diversification of investigations dedicated to the search for antibacterial properties of fungi, obtained data on antibiotic activity are quite hard to generalize. Studying of antibacterial activity, action mechanisms is especially important and promising research direction of antibacterial compounds found in macromycetes for further implementation of antibiotics and/or components based on culture liquid, mycelium and fruiting bodies of fungi.

### The Effect of Lactic Acid Bacteria and Bifidobacteria on the Number of Natural Killer Cells in Normal Conditions and in Cases of Intravaginal Staphylococcosis in Mice

**Background.** Development of new immunobiotics based on commensal nonpathogenic probiotic bacteria such as lactic acid bacteria and bifidobacteria with antibacterial and immunomodulatory effects is an important area of modern biotechnology.

**О****bjective.** The aim of this study was to determine the effect of *Lactobacillus acidophilus *IMV B-7279*, L. casei* IMV B-7280*, **L.* *delbrueckii* subsp. *bulgaricus* ІМV В-7281, *Bifidobacterium animalis *VKL* *and* B.** **animalis *VKB (individually) or their different compositions on the number of natural killer cells (NKC) in the spleen of BALB/c mice at normal conditions and in the case of the experimental intravaginal staphylococcosis.

**Methods**. The number of NKC in the spleen was studied** **using monoclonal phycoerythrin*-*conjugated antibodies against NKC antigens (MACS, Miltenyi Biotec, Germany).** **Calculations of NKC as well as analysis of the results were performed using flow cytometry method on a FACStar Plus cytofluorometer.

**Results.** It is shown that the number of NKC in the spleen of intact mice did not change under the influence of *L.* *acidophilus* ІМV В-7279,* L. casei* ІМV В-7280,* B.** **animalis *VKL or *B.** **animalis *VKB (individually). But, using *L.* *acidophilus* ІМV В-7279,* L. casei* ІМV В-7280,* L.* *delbrueckii* subsp. *bulgaricus* ІМV В-7281,* B.** **animalis *VKL and *B.** **animalis** *VKB (individually) or their different compositions for colonization of the vagina in the case of intravaginal staphylococcosis associated with increasing of the number of NKC in spleen in different periods of observation. The number of NKC in the spleen of staphylococcus-infected mice completely normalized after treatment with some probiotic compositions. The probiotic bacteria (individually) only partially normalized the number of NKC in the spleen of staphylococcus-infected mice.* *

**Conclusions.**Thus,

*L.*

*acidophilus*ІМV В-7279,

*L. casei*ІМV В-7280,

*L.*

*delbrueckii*subsp.

*bulgaricus*ІМV В-7281

*or*

*B. animalis*VKL (individually) or their various compositions are promising to create highly effective immunobiotics, that are able to increase the innate immunity in cases of infections.

### Risk Assessment of Technology of Preparation Based on Recombinant Human Interleukin-7 and Its Perspective Validation

**Background****.** Quality management is a very important activity of any industrial enterprise, especially when it comes to manufacturing products in health care (drugs, including medical immunobiological preparations, medical devices, cosmetics, dietary supplements, etc.). Risk-oriented thinking enables an organization to identify factors that may cause rejection of its processes and its quality management system for planned results to establish preventive controls to minimize negative impacts and the greatest possible shaft advantage of the opportunities as they arise. The logical continuation of the risk assessment is validation processes. This article is a fragment of the complex scientific and technical work on the development and standardization of biotechnology products based on recombinant human interleukin-7 (rhIL-7).

**Objective.**** **Justification for approaches to risk assessment in the technology for getting preparation based on rhIL-7 in the form of nasal spray and particularly risk assessment of the production process, and perspective validation of developed technologies.

**Methods.** The methodology of risk assessment according to ISO 14971:2009 “Medical devices. Guidelines for risk management” was used. Pharmacopoeial methods were used to control the process and product quality (potentiometric determination of pH, osmolality, sterility). The integrity of the filters was determined by the method according to the manometer producer.

**Results.** The work consistently study approaches to risk assessment in the technology for getting preparation based on rhIL-7 in the form of nasal spray and particularly risk assessment of the production process, and the validation of promising technologies developed. Selection of guidelines on risk assessment was conducted for Guidelines for Good Manufacturing Practices, ISO 9001:2015, ISO 13485:2005, and ISO 14971:2009. The greater acceptability of the use of the past two standards was showed. Technological production scheme is presented and qualitative approach to analyze the identified risks is applied. For the most critical stage of production (preparation of sterile solution) the validation process is conducted.

**Conclusions.**The feasibility of risk assessment in the technology for getting preparation based on rhIL-7 in the form of nasal spray according to ISO 14971:2009 together with the system using risk analysis and critical control points is theoretically justified. It was found that the most critical step in the production is part of the preparation of a sterile solution, which includes the preparation of intermediate filtering and sterilizing drug. The conducted prospective validation of the most critical stages of the technology demonstrated its stability and compliance with established eligibility criteria.