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Introduction. This paper shows the results of a study of the frequency of maintenance of passenger cars in various operating conditions, and provides recommendations for replacing the engine oil of gasoline engines (category SN classification according to API) according to the actual engine operating time (moto-hours). The service book of passenger cars contains the regulations for car maintenance with a list of operations that must be performed. The oil change intervals specified in the Regulations on Maintenance and Repair of Rolling Stock of motor Transport and the factory instructions do not take into account the specifics of the operation of vehicles. Depending on the road and climatic conditions and the operating mode, the standard maintenance schedule can be adjusted, in particular, the frequency of engine oil changes. The scientific novelty of the work is to determine the intervals of car maintenance for specific operating conditions.Materials and methods. The paper presents an analysis of Russian and foreign car maintenance systems, in particular, the oil change intervals of gasoline engines in European countries, the United States and Japan.The results of operational and resource tests of motor oils of gasoline engines carried out by methods of measuring their physical and chemical properties are presented.Results. In this paper, based on the analysis of the problem, recommendations for changing oil in gasoline engines by motorcycle hours for the conditions of the Republic of Dagestan (RD) are developed.The use of external and built-in technical means for calculating the motor hours allows you to determine the recommended oil change interval.Discussion and conclusion. In this paper, on the basis of research on a certain number of vehicles operating in various (including difficult) conditions, recommendations are developed that allow you to determine the rules of car maintenance for various operating conditions.

A schematic and structural solution of regenerative-utilization heat use in centralized heat supply systems was previously proposed in order to increase the efficiency of operation of heating networks located in non-passable channels. The impossibility of creating a full-scale experimental setup covering the required range of factors and the area of their change, the complexity of a passive experiment on existing heating mains led to the need to develop a virtual model based on the ANSYS sofware package. A six-factor experiment has been carried out on this virtual model. Regression equations have been obtained to determine the pressure required to provide air purging of the channel, as well as heat exchange with pipelines of direct and return network water located in the channel, and heat exchange with soil around the channel. In addition, a regression relationship has been derived to find the integral heat flux from the listed washed surfaces to the air flow. The transition from dimensionless to natural factors has been made in the paper. The most significant factors are identified with the help of Pareto cards. The obtained dependencies have been verified in Part 1 of the paper. The adequacy of the obtained regression equations has been determined using standard statistical estimation methods based on the calculated values of the Fisher’s, Student’s and other criteria. The response surfaces are presented and analyzed using two dimensional sections for a number of factor values at fixed values of one and a change in two most characteristic, physically significant for a given response function. They have been validated on the basis of the analysis of regression dependencies. The obtained regression equations cover almost the entire range of possible diameters of heating mains, which makes it possible to use them in the development of energy-saving projects.

The mixed problem for the telegraph equation well-known in electrical engineering and electronics, provided that the line is free from distortions, is reduced to a similar problem for one-dimensional inhomogeneous wave equation. An effective way to solve this problem is based on the use of special functions – polylogarithms, which are complex power series with power coefficients, converging in the unit circle. The exact solution of the problem is expressed in integral form in terms of the imaginary part of the first-order polylogarithm on the unit circle, and the approximate one – in the form of a finite sum in terms of the real part of the dilogarithm and the imaginary part of the third-order polylogarithm. All the indicated parts of the polylogarithms are periodic functions that have polynomial expressions of the corresponding degrees on an interval of length in the period, which makes it possible to obtain a solution to the problem in elementary functions. In the paper, we study a mixed problem for the telegrapher’s equation which is well-known in applications. This problem of linear substitution of the desired function witha time-exponential coefficient is reduced to a similar problem for the Klein – Gordon equation. The solution of the latter can be found by dividing the variables in the form of a series of trigonometric functions of a line point with time-dependent coefficients. Such a solution is of little use for practical application, since it requires the calculation of a large number of coefficients-integrals and it is difficult to estimate the error of calculations. In the present paper, we propose another way to solve this problem, based on the use of special He-functions, which are complex power series of a certain type that converge in the unit circle. The exact solution of the problem is presented in integral form in terms of second-order He-functions on the unit circle. The approximate solution is expressed in the final form in terms of third-order He-functions. The paper also proposes a simple and effective estimate of the error of the approximate solution of the problem. It is linear in relation to the line splitting step with a time-exponential coefficient. An example of solving the problem for the Klein – Gordon equation in the way that has been developed is given, and the graphs of exact and approximate solutions are constructed.

The paper deals with determining a temperature field of an isotropic solid with inclusion represented as a spherical layer that absorbing penetrating radiation. A hierarchy of simplified analogues of the basic model of the heat transfer process in the system under study was developed, including a “refined model of concentrated capacity”, a “concentrated capacity” model, and a “truncated model of concentrated capacity”. Each of the mathematical models of the hierarchy is a mixed problem for a second-order partial differential equation of the parabolic type with a specific boundary condition that actually takes into account the spherical layer available in the system under study.The use of the Laplace integral transform and the well-known theorems of operational calculus in analytically closed form enabled us to find solutions to the corresponding problems of unsteady heat conduction. The “concentrated capacitance” model was in detail analysed with the object under study subjected to the radiation flux of constant density. This model is associated with a thermally thin absorbing inclusion in the form of a spherical layer. It is shown that it allows us to submit the problem solution of unsteady heat conduction in the analytical form, which is the most convenient in terms of both its practical implementation and a theoretical assessment of the influence, the spherical layer width has on the temperature field of the object under study.Sufficient conditions are determined under which the temperature field of the analysed system can be identified with a given accuracy through the simplified analogues of the basic mathematical model. For simplified analogues of the basic model, the paper presents theoretical estimates of the maximum possible error when determining the radiated temperature field.

When fighting against terrorism in modern armed conflicts, combat vehicles, including tanks, are widely used. To minimise own losses of vehicles and personnel for overthrowing enemy is a relevant task. To solve it, the paper considers certain events in the history of the Great Patriotic War, which are associated with battle of tanks that spring an ambush. A mathematical model of the battle is built. The state graph of the system is given. Using this graph, a probability of tank kills and a ratio of mathematical expectations of losses have been calculated. This mathematical model generalizes the models, previously published in this journal, based on the Markov chain apparatus. The paper gives an example of calculations for this model in the particular case in which experimental data are used as a basis. The ratios of mathematical expectations of losses of the warring parties are obtained. Further, we consider the mathematical models, in which it is assumed that probabilities for tank crews to provide operations of targets detection in firing are known. With technology development and its mathematical support it becomes increasingly more real. The formulas to obtain the probability of tank kills are given according to the graph of states using the known probabilities of transition from one state to another. In each of the three mathematical models under consideration there is a graph of the system state, which allows calculation of the tank kills probability. We have analysed the models to prove a significant dependence of the loss ratio of the warring parties on the number of firing positions used by the tank in ambush in case re-siting is unnoticeable for the enemy. The authors-considered models that use the examples of historical events confirm that the tactics of organising and conducting ambushes in tank battles can be successfully used nowadays, when the technology intensiveness of the opposing forces significantly grows. The obtained results can be applied to organise and conduct tank ambushes in modern armed conflicts and fight against terrorist army.

Block ciphers form one of the main classes of cryptographic algorithms. One of the challenges in development of block ciphers, like any other cryptographic algorithms, is the analysis of their cryptographic security. In the course of such analysis, statistical testing of block ciphers is often used. The paper reviews literature on statistical testing of block ciphers.The first section of the paper briefly and informally discusses approaches to the definition of the concept of a random sequence, including the Kolmogorov, von Mises, and Martin-Löf approaches and the unpredictability-related approach. However, all these approaches to the definition of randomness are not directly applicable in practice.The second section describes statistical tests of binary sequences. It provides brief descriptions of the tests included in the DieHard, NIST STS, RaBiGeTe statistical test suites.The third section provides the appropriate information to present further the operation modes of block ciphers.The fourth section deals with techniques for statistical testing of block ciphers. Usually such techniques lie in the fact that based on the block cipher under test, various generators of the pseudorandom sequences are built, with their output sequences being tested using any suite of statistical tests. The approaches to the construction of such generators are given.The paper describes the most known statistical test technique for block ciphers among the submitted for the AES competition. It is a technique the NIST uses for statistical testing of ciphers. In addition, there are other techniques mentioned in the literature.In conclusion the paper states that there is a need to develop new techniques for statistical testing of block ciphers.The paper support was provided from the Russian Foundation for Basic Research in the framework of the research project No. 16-07-00542 supported

For the processes described by dynamical systems, closed trajectories of dynamical systems are in line with periodic oscillations. Therefore, there is a considerable interest in describing the bifurcations of the generation of closed trajectories from equilibrium when the parameters change. In typical one-parameter and two-parameter families of smooth dynamical systems on a plane, closed trajectories can be generated only from equilibrium – weak focus. In mathematical modeling in the theory of automatic control, in mechanics and in other applications, piecewise smooth dynamical systems are often used. For them, there are other bifurcations of the generation of closed trajectories from equilibrium. The paper describes one of them, which is a typical family of dynamical systems specified by a piecewise smooth vector field on a two-dimensional manifold depending on two small parameters. It is assumed that for zero values of the parameters the vector field has a singular point O on the line of discontinuity of the field, and the point O is stable; in one half-neighborhood of the point O the field coincides with a smooth vector field for which the point O is a weak focus with positive (negative) first Lyapunov value, and in the other half-neighborhood it coincides with a smooth vector field directed at the points of the line of discontinuity inside the first of the semi-neighborhoods. The paper describes bifurcations in the neighborhood of the point O as the parameters change, in particular, indicating the regions of the parameters for which the vector field has a stable closed trajectory.

WENO schemes (weighted, essentially non oscillating) are currently having a wide range of applications as approximate high order schemes for discontinuous solutions of partial differential equations. These schemes are used for direct numerical simulation (DNS) and large eddy simmulation in the gas dynamic problems, problems for DNS in MHD and even neutron kinetics. This work is dedicated to clarify some characteristics of WENO schemes and numerical simulation of specific tasks. Results of the simulations can be used to clarify the field of application of these schemes. The first part of the work contained proofs of the approximation properties, stability and convergence of WENO5, WENO7, WENO9, WENO11 and WENO13 schemes. In the second part of the work the modified wave number analysis is conducted that allows to conclude the dispersion and dissipative properties of schemes. Further, a numerical simulation of a number of specific problems for hyperbolic equations is conducted, namely for advection equations (one-dimensional and two-dimensional), Hopf equation, Burgers equation (with low dissipation) and equations of non viscous gas dynamics (onedimensional and two-dimensional). For each problem that is implying a smooth solution, the practical calculation of the order of approximation via Runge method is performed. The influence of a time step on nonlinear properties of the schemes is analyzed experimentally in all problems and cross checked with the first part of the paper. In particular, the advection equations of a discontinuous function and Hopf equations show that the failure of the recommendations from the first part of the paper leads first to an increase in total variation of the solution and then the approximation is decreased by the non-linear dissipative mechanics of the schemes. Dissipation of randomly distributed initial conditions in a periodic domain for one-dimensional Burgers equation is conducted and a comparison with the spectral method is performed. It is concluded that the WENO7-WENO13 schemes are suitable for direct numerical simulation of turbulence. At the end we demonstrate the possibility of the schemes to be used in solution of initial-boundary value problems for equations of non viscous gas dynamics: Rayleigh-Taylor instability and the reflection of the shock wave from a wedge with the formation a complex configuration of shock waves and discontinuities.

Introduction. The paper deals with the calculation of wooden arches taking into account the nonlinear relationship between stresses and instantaneous deformations, as well as creep and geometric nonlinearity, are considered. The analysis is based on the integral equation of the viscoelastoplastic hereditary aging model, originally proposed by A.G. Tamrazyan [1] to describe the nonlinear creep of concrete. Materials and Methods. The creep measure is taken in accordance with the work of I.E. Prokopovich and V.A. Zedgenidze [2] as a sum of exponential functions. The transition from the integral form of the creep law to the differential form is shown. The relationship between stresses and instantaneous deformations for wood under compression is determined from the Gerstner formula, and elastic work is assumed under tension. The solution is carried out using the finite element method in combination with the Newton-Raphson method and the Euler method according to the scheme that involves a stepwise increase in the load with correction of the stiffness matrix taking into account the change in the coordinates of the nodes with the sequential calculation of additional displacements of the nodes, which are due to the residual forces. The proposed approach for increasing the accuracy of determination of creep deformations at each step provides using the fourth-order Runge-Kutta method instead of the Euler method. Results. Based on the Lagrange variational principle, expressions are obtained for the stiffness matrix and the vector of additional dummy loads due to creep. The method developed by the authors is implemented in the form of a program in the MATLAB environment. Calculation examples are given for parabolic arches simply supported at the ends without an intermediate hinge and with an intermediate hinge in the middle of the span under the action of a uniformly distributed load. The results obtained are compared in the viscoelastic and viscoelastic formulation. The reliability of the results is validated through the calculation in the elastic formulation in the ANSYS software package. Discussion and Conclusions. For the arches considered, it is found that even with a load close to the instant critical, the growth of time travel is limited. Thus, the nature of their work under creep conditions differs drastically from the nature of the deformation of compressed rods.

The current paper has presented the estimation results of ecological adaptability of the alfalfa samples. The purpose of the work was to assess the productivity and quality of green mass of the alfalfa samples from the IPI plant genetic resources gene bank and to identify the most adaptive ones according to the trait ‘green mass productivity’ and ‘raw protein percentage’. The study of the collection alfalfa samples was carried out in the southern part of the Rostov region on the plots of the “ARC “Donskoy” in the breeding crop rotation of perennial grasses in 2016–2018. The objects of study were 30 alfalfa samples from the collection of N.I. Vavilov IPI from different countries (Canada, the USA, Peru, France). The variety ‘Rostovskaya 90’ was used as a standard one. The estimation of alfalfa samples on the presence of adaptive properties in them according to the trait ‘green mass productivity’ showed that the most valuable samples in present practical breeding work are the samples ‘K-32873’, ‘K-33299’, ‘K-42684’, ‘K-42249’, ‘K-78803’ with weak responsiveness to changes in environmental conditions; the samples ‘K-36104’, ‘K-48778’, ‘K-42694’, ‘K-45715’, ‘K-47800’, ‘K-47802’, ‘K-43260’ with high resistance to stress; the samples ‘K-43272’, ‘K-50545’, ‘K-47806’, ‘K-47807’ with genetically flexible genotypes. When breeding according to the trait ‘raw protein percentage’, the samples ‘K-47807’, ‘K-47804’, ‘K-42712’ possessing a high raw protein percentage and resistance to changes in this trait are important for further work.

Introduction. As is known, the selection of optimal conditions for the analysis of extracts from medicinal plant raw materials (MPМ), as well as medicinal herbal preparations and pharmaceutical substances of plant origin, characterized by a complex variable composition of biologically active substances (BAS) by TLC, presents certain difficulties. For the design of mobile phases for the separation of mixtures of BAS of plant origin, in a thin layer of sorbent, the following approaches are used: literary sources; standard mobile phases; spot elution method; the scheme proposed by the firm Camag (Switzerland); model "PRISMA"; variocameras and others. In foreign literature, there are publications on the generalization of the available experimental data on the determination of various natural groups of BAS in objects of plant origin. However, such reviews did not reveal the regularities of the chromatographic behavior of individual BAS in a thin layer, as well as the influence of various factors on the reproducibility of Rf values. The study of the possibility of a theoretical approach to the choice of optimal conditions for chromatography of groups of BAS of different polarity, allowing them to separate, identify and quantify by TLC is a relevant and poorly developed area of chromatography in general.Aim. The aim of this work was to develop a theoretical approach to the choice of optimal conditions for the chromatographic separation of various groups of BAS of plant origin in a thin layer of sorbent.Materials and methods. To study the regularities of chromatographic behavior in a thin layer of representatives of the main classes of BAS present in MPМ (amino acids, flavonoids, tannins, simple sugars, ascorbic acid, fat-soluble vitamins), the value of the main factor affecting the parameters of the efficiency of the chromatographic process, the polarity of the eluent, was studied. As objects of research, we used ready-made chopped raw material of nettle leaves, produced by a domestic manufacturer, that meets the requirements of regulatory documents, as well as sea buckthorn fruits collected on the territory of the Voronezh region, according to the rules for harvesting MPМ of various morphological groups in fresh and dried form.Results and discussion. The regularities of elution and mathematical models describing the chromatographic behavior of plant BAS in a thin layer of sorbent have been established. Based on the totality of the results obtained, from the standpoint of the efficiency of the chromatographic process, the optimal conditions for their TLC analysis were selected and theoretically substantiated. To study the qualitative composition of BAS and to achieve a clear separation of zones on chromatograms, TLC methods were developed and tested on the studied MPМ using simple, frontal or two-dimensional chromatography.Conclusion. It is shown that the determination and separation in a thin layer of the sorbent of hydrophilic and lipophilic BAS of MPМ in the presence of a joint requires different approaches and techniques. The paper proposes an algorithm for the selection of the mobile phase and methods of chromatography of BAS of medicinal products. The revealed mathematical models describing the chromatographic behavior of BAS will make it possible to select the conditions under which it is possible to determine the individual components of multicomponent mixtures without preliminary separation. The developed methods for the determination of BAS can also be used for standardization and quality assessment of other types of MPМ, phytopreparations and pharmaceutical substances of plant origin.

So far, there are no efficient algorithms to solve a problem of finding the low degree annihilators for arbitrary Boolean function. In the paper we present a new algorithm to find affine annihilators for an arbitrary Boolean function. We start with considering the identity fg ≡ 0 or the arbitrary Boolean function f and its possible affine annihilator g. We use a special representation of the Boolean function in sum of its sub-functions to reduce degrees of considering functions in previous identity. As a result, we establish equivalence between the identity fg ≡ 0 for Boolean functions of n variables and the system of Boolean equations of n-1 variable.An algorithm for finding the affine annihilators for the arbitrary Boolean function f must find all the affine functions g so that fg ≡ 0. Our algorithm is based on reducing the problem of finding the affine annihilators for the Boolean function f of n to the similar problem for its sub-functions of n-1 variable. The presented algorithm has the following advantages:An input function can be presented in different ways;Output can be also presented in different ways;The algorithm can be effectively parallelized.It should be noted that the result we have obtained is not final and highlights some development directions: first, to study the impact of its input and output on the efficiency of the algorithm of various representations and, second, to use our idea of constructing the algorithm for development of algorithms, which allow finding the 2nd, 3rd, etc. degree annihilators for a specified Boolean function.

The total probability formula for continuous random variables is the integral of product of two probability density functions that defines the unconditional probability density function from the conditional one. The need for calculation of such integrals arises in many applications, for instant, in statistical decision theory. The statistical decision theory attracts attention due to the ability to formulate the problems in a strict mathematical form. One of the technical problems solved by the statistical decision theory is the problem of dual control that requires calculation of integrals connected with the multivariate probability distributions. The necessary integrals are not available in the literature. One theorem on the total probability formula for vector Gaussian distributions was published by the authors earlier. In this paper we repeat this theorem and prove a new theorem that uses more familiar form of the initial data and has more familiar form of the result. The new form of the theorem allows us to obtain the unconditional mathematical expectation and the unconditional variance-covariance matrix very simply. We also confirm the new theorem by direct calculation for the case of the simple linear regression.

Introduction. Currently, the development of safe helicopter landing systems as the most complex and dangerous stage of a flight is one of the priority tasks. A significant number of companies in Russia and abroad are engaged in its solution. Landing on unprepared (unequipped) sites with snow-ice cover may be caused by the need to deliver units, cargo and ammunition in combat conditions, search and rescue operations, evacuations of victims, etc. A key factor for a landing decision is information about the height of snow and about the depth of ice cover. In the paper remote identification of the state of snow-ice cover, excluding the need to present any person (crew member or rescue worker) on a landing site is proposed.Aim. To develop a method for the remote identification of the state of snow-ice cover used to determine the possibility of a helicopter - type aircraft safe landing on a reservoir with snow-ice cover.Materials and methods. Numerical simulation of echo signals Fresnel reflection coefficients polarization ratio was realized in MatLab. Vertical and horizontal polarizations in the range from 25 to 45 degrees were simulated.Results. Intervals of polarization relations correspond to the interval density of snow-ice layers for fixed angles. For example, when θ = 34 for dry snow ρds = 100…500 kg/m3 (ε'ds = 1.162…1.984) – Prm = 5.6915...3.3266, dry firn ρdf = 500…700 kg/m3 (ε'df = 1.984…2.51) – Prm = 3.3266...2.8311, dry ice ρdi = 700…913 kg/m3 (ε'di = 2.51…3.179) – Prm = 2.8311...2.4753. A layer reconstruction inverse problem was solved by indirect determining of complex relative permittivity of each successive underlying layer with 10-2 real part resolution. The identity of the obtained characteristics of snow-ice layers with calculated (standard) values was established.Conclusion. Remote identification of components of a snow-ice cover structure allows one to automate the process of evaluating of landing possibility. Thereby it reduces a decision-making time and increases a level of safety. In contrast to the known methods of identification of the surface layer the identification of multilayer medium layers was carried out.

Introduction. Rubber bushings are important parts of the spring systems of modern vehicles. The properties determine not only the comfort of car movement, but also affect the elastic suspension characteristics. When a bushing is deformed, linear sections appear in characteristics. It is advisable to describe such characteristics using a mathematical model based on the classical elements of Hooke and Saint-Venant. The paper presents a mathematical description of the bushing simulation functioning results, accuracy of approach, areas of application of the mathematical model.Materials and methods. The initial data was the experimental characteristic of a cylindrical automobile rubber bushing, obtained in harmonic mode at the 0.03 to 51 Hz frequency and the 0.4 to 10 mm amplitude. The force balance of the two Hooke elements and one Saint-Venant element interacting with each other determined the mathematical model description. The authors carried out the calculations using numerical and optimization methods.Results. As a result, the authors determined functions characterizing the change in the parameters of the Hooke and Saint-Venant elements from the rubber bushings’ deformation amplitude. Moreover, the authors calculated power characteristics in the form of dependences of the rubber bushing effort and also found quantitative indicators of the reliability of the experimental data approximation by the developed mathematical model.Discussion and conclusions. The analysis of the operating modes shows the possibility of the model application to describe the rubber bushing functioning in a stationary harmonic mode with small and medium strain amplitudes. The simulation results of the Hooke’s and Saint-Venant’s parameters reveals the theoretical prerequisites for the possibility of using the model to calculate the bushing force in an unsteady mode.The authors have read and approved the final manuscript. Financial transparency: the authors have no financial interest in the presented materials or methods. There is no conflict of interest.

The paper studies linear differential operators in derivatives with respect to one variable. Such operators include, in particular, operators defined on infinite prolongations of evolutionary systems of differential equations with one spatial variable. In this case, differential operators in total derivatives with respect to the spatial variable are considered. In parallel, linear differential operators with one independent variable are investigated. The known algorithms for reducing the matrix to a stepwise or diagonal form are generalized to the operator matrices of both types. These generalizations are useful at points, where the functions, into which the matrix components are divided when applying the algorithm, are nonzero.In addition, the integral operator is defined as a multi-valued operator that is the right inverse of the total derivative. Linear operators that involve both the total derivatives and the integral operator are called integro-differential. An invertible operator in the integro-differential sense is an operator for which there exists a two-sided inverse integro-differential operator. A description of scalar differential operators that are invertible in this sense is obtained. An algorithm for checking the invertibility in the integro-differential sense of a differential operator and for constructing the inverse integro-differential operator is formulated.The results of the work can be used to solve linear equations for matrix differential operators arising in the theory of evolutionary systems with one spatial variable. Such operator equations arise when describing systems that are integrable by the inverse scattering method, when calculating recursion operators, higher symmetries, conservation laws and symplectic operators, and also when solving some other problems. The proposed method for solving operator equations is based on reducing the matrices defining the operator equation to a stepwise or diagonal form and solving the resulting scalar operator equations.

Nowadays there is a need to develop new recipes and technologies that allow the production of chopped semi-finished products with a relatively low cost, original taste and long shelf life. Various curing mixtures, marinades, acid-containing products, seasonings and spices are used to improve the organoleptic characteristics of chopped semi-finished products. They include beer, red wine, lemon juice, marinade (laurel leaves, salt, black peppers, onions, lemon juice or vinegar).Today marinades are a new and little studied raw material for the production of semi-finished products. They give the meat a delicate texture, a pleasant aroma and can eliminate or weaken the undesirable odor, which is achieved by various spices and seasonings adding. The problem of chopped semi-finished products assortment expanding was considered in this paper. The recipe for chopped semi-finished products “Nur” based on several types of marinades with the application of fresh pomegranate seeds was developed to obtain an “original” and unusual new-generation food product. Fresh pomegranate seeds, which give the cutlets an unusual sweet and sour taste, were used in the recipe for all types of cutlets. The composition of the seeds of this fruit includes 15 amino acids and a large amount of fatty acids. Pomegranate is rich in carbohydrates, important B vitamins and vitamin C, minerals (calcium, magnesium, iron). Four types of chopped "Nur" cutlets with pomegranate and Lingonberry, Basil, Picantillo marinades and without adding marinade were made for research. The developed assortment of chopped semi-finished products has high nutritional and biological value, good organoleptic characteristics with a pronounced taste. According to the organoleptic indicators, the best is the chopped Nur cutlet with pomegranate and the addition of Picantillo marinade. Analyzing the data of studies on storage capacity, it should be noted that, subject to the established regime, changes in organoleptic indicators during storage are insignificant. When developing chopped "Nur" cutlets with pomegranate, the Lingonberry, Basil, Picantillo marinades, produced under the Cetrina trademark, cope successfully with the task of flavoring improving.

The paper deals with a mixed problem for the telegraph equation well-known in electrical engineering and electronics, provided that the line is free from distortion. This problem is reduced to the analogous one for the one-dimensional inhomogeneous wave equation. Its solution can be found as the sum of the solution for a mixed homogeneous boundary value problem for the corresponding homogeneous wave equation and for the solution of a non-homogeneous wave equation with homogeneous boundary data and zero initial conditions. Solutions to both problems can be found by separating the variables in the form of a series of trigonometric functions of the line point with time-dependent coefficients. Such solutions are inconvenient for real application because they require calculation of a large number of integrals, and it is difficult to estimate the miscalculation. An alternative method for solving this problem is proposed, based on the use of special functions, viz. polylogarithms, which are complex power-series with power coefficients converging in a unit circle. The exact solution of the problem is expressed in the integral form via the imaginary part of the first-order polylogarithm on the unit circle, and the approximate one is expressed in the form of a finite sum via the real part of the dilogarithm and the imaginary part of the third-order polylogarithm. All these parts of the polylogarithms are periodic functions that have polynomial expressions of the corresponding powers on the segment of the length equal to the period. This makes it possible to effectively find an approximate solution to the problem. Also, a simple and convenient error estimate of the approximate solution of the problem is found. It is linear with respect to the step of splitting the line and the step of splitting the time range in which the problem is considered. The score is uniform along the length of the line at each fixed point of time. A concrete example of solving the problem according to the proposed mode is presented; graphs of exact and approximate solutions are constructed.

Local vegetable raw materials have good prospects in developing new balanced foods with high nutrition value. As a rule, local vegetable raw materials are environmentally friendly and contain a wide range of biologically and physiologically active agents. Fruit liqueurs possess a balanced chemical composition and a high nutrition and physiological value. They produce a recreational or preventive effect on human organism. However, the level of consumption of fresh fruit and berries remains low because of their seasonality. Moreover, the range of fruit and berry products is usually very poor, and very few of them are beneficial for human health and can prevent diseases. The research featured the formulations and production technology for new multicomponent fruit liqueurs of high nutrition value. The liqueurs were made from Dagestan garden and wild fruit and berries with a high content of macro- and micronutrients. The nutrition value and quality of the liqueurs were estimated according to the mass concentration of sugars, titrable acids, vitamins C and P, β-carotene, mineral elements, and phenolic and pectinaceous substances. The sensory properties were measured according to a 10-score system. The paper introduces formulations and technologies for three types of liqueur (Zhivitel’naya, Garmoniya, and Uslada). They involved alcoholized and fermentation-alcoholized juices of grapes, fruit and berry fruit drinks and extracts that mutually complemented each other according to valuable components. The new liqueurs have a high nutrition since 100 cm3 of the liqueur per day partially satisfies the daily requirements for some nutrients: phenolic substances – for 37.5–55.0%; pectinaceous substances – 17.5–32.5%; in vitamin C – 13.7–38.7%, β-carotene – 17.6–43.0%, and a microelement iron – for 14.0–26.0%. The multicomponent fruit liqueurs possess a wide range of biologically and physiologically active agents. As a result, they improve physical activity and increase resistance to bad ecological environment.

The studies were conducted on the experimental field of the FSBSI “Federal Russian Agricultural Research Center”, whose soils are ordinary blackearth (chernozem). 25 productive shoots of each sample were taken in their full ripeness, and, when the seeds reached standard humidity, there was performed a structural analysis in the laboratory. T. petropavlovskyi and spontaneous macromutant forms emerged from cultivation were used as the objects of study. In the process of a long-term cultivation of T. petropavlovskyi in the collection, there were identified numerous spontaneous macromutant forms of a specific nature. The paper presents the study results of the product characteristics of T.petropavlovskyi and spontaneous macromutant forms which are phenotypically close to T. spelta and soft-like T. aestivum and typical soft wheat T. aestivum. It has been established that product characteristics of speltoid macromutant wheat are significantly inferior to the original T. petropavlovskyi and macromutant soft wheat T. aestivum. Product features of soft-like macromutant T. aestivum is similar to the original T. petropavlovskyi, but has a smaller sprout weight and, correspondingly, lower grain productivity. The most promising variety for breeding process is the macromutant typical soft wheat T. aestivum, which forms a larger number of grains and, due to this, has an advantage in ‘kernel weight per head’ over all samples, including the initial form. The value of this macromutant form can also be determined by the high coefficient of specific productivity (Csp), which indicates a more efficient work of its vegetative organs. Consequently, the macromutant T. aestivum, which is phenomenally similar to the existing varieties of soft wheat, promises a high hybridization efficiency with the latter. Thus, the macromutant form of T. aestivum, developed on the basis of the T. petropavlovskyi genotype, is of some value as an initial material for breeding practice.

The paper has presented the study results of the effect of chelated micronutrients on the yield structure of pea varieties. Field experiments was laid in 2015–2017 in the scientific crop rotation of the Agrotechnological Center of the Azov-Blacksea Engineering Institute of FSBEI HE “Donskoy SAU” in Zernograd. There were performed seed treatment with recommended 2 liters of ORMISS Cu/B per ton and peas sprouts were treated with 2 liters of ORMISS Cu/Mo per hectare. There has been found that some variants of seed treatment resulted in an increase in number of productive nodes to 3.4, number of beans to 5.8, kernels per a bean to 5.9, 1000-kernels weight to 237.1 g, kernels weight per plant to 5.8 g.

Aim. This paper is aimed at studying the relative light conditions (RLC) for lawns in the crown shade of light‐requiring and shade‐tolerant trees from the landscaping sites of Stavropol.Methods. The illuminance incident on the lawn surface was measured using a TKA‐LUX light meter from 7 a.m. to 5 p.m., every two hours.Results. It is shown that lawns under the crowns of light‐requiring tree species (Larix sibirica), received the highest RLC. During three calendar periods (22.05–15.06–18.09.2017, from 7 a.m. to 5 p.m.), its value amounted to 8.2‐9.2% (9.2% – at 1 p.m.); 4.6‐6.8% (6.8%); 7.0‐12.9% (12.9%). The projective cover of the lawns reached 75‐90%. In case of Betula pendula, the RLC values were as follows: 2.6‐3.7% (3.7%); 1.9‐3.2% (3.0%); 3.6‐5.7% (5.6%), with the projective cover amounting to 75‐90%. Under the crowns of shade‐tolerant species, Abies nordmanniana, the RLC values reached 1.0‐1.5% (1.0%), 0.6‐1.5% (0.6%), 0.7‐3.0 (0.7%), with the projective cover of lawns amounting to 10‐25%. For Aesculus hip‐ pocastanum, these values were equal to 0.6‐0.8% (0.6%); 0.6‐0.8% (0.6%); 9.0‐11.5% (11.2%), with dead patches being frequently formed. Projective cover values for shaded lawns correlate with the RLC value (r = 0.89).Conclusions. Under present conditions, ground covers consisting of Vinca minor shrubs and Hedera helix vines can be used in urban greening for intensively shaded sites.

This paper presents the results of the identification procedure certification and subsequent quantitative determination of the active ingredients of two-component injectable medicines (active ingredient and solvent) using Raman spectroscopy. The main objective of the research was to select approaches for estimating the metrological characteristics of the measurement procedure, which include consideration of the methodological parameters and provide the metrological traceability of measurement results to SI units. According to this purpose, the GVET 176‑1‑2010 State Secondary Measurement Standard for units of mass fraction, mass (molar) concentration of components in solid and liquid substances and materials based on volumetric titration was used. The following substances were chosen as the research objects for estimating the metrological characteristics of the measurement procedure: ascorbic acid, novocaine and sodium thiosulphate. The authors of the work have demonstrated the measurement-procedure certification results, whose accurate determination was confirmed by the results of interlaboratory comparisons. The obtained results confirmed the accuracy of the identification procedure and subsequent quantitative determination, which proves its applicability for the determination of the active ingredients in two-component injectable medicines. In addition, the possibility of developing reference materials based on the medicines under study is indicated. Further development of this study may be directed at the development of an identification procedure and its certification, with subsequent quantitative determination of the active ingredients of injectable medicines having three components as well as those having a more complex composition.

To study an arithmetic nature of the values of hyper-geometric functions (and their derivatives including those with respect to parameter), it is common practice to use one either Siegel's method or the method based on the effective construction of the linear approximating form. The main distinction between these methods consists in the mode of construction of the first approximating form. Applying Siegel's method allows us to construct such a form by means of a pigeonhole principle that makes it possible to establish, in certain cases, the algebraic independence of the values of corresponding functions. The Siegel's method can be usually applied just while considering hyper-geometric functions with rational parameters. The effective method has a certain advantage here, for in some cases this method enables us to carry out corresponding investigation also for the functions with irrational parameters. Another advantage of the effective method is that it provides obtaining of high- accuracy quantitative results. By quantitative results one usually implies the estimates of the moduli of the linear forms in the values of corresponding functions. The effective method has made it possible to obtain, in some cases, estimates being precise regarding the height of such forms with calculation of the corresponding constants. A drawback of the effective method is the narrow domain of its applications. The effective construction of the linear approximating form, which initiates reasoning, is always a challenge. So far, an effective construction of the approximating form for the product of powers of hyper-geometric functions (with the rare exceptions) failed.In both aforementioned methods one proves previously linear independence (in Siegel's method, as a rule, algebraic independence,) of the functions under consideration. Such a proof is often considered as an independent result.In this paper, by means of the method especially elaborated for this purpose we establish linear independence of some hyper-geometric functions and their derivatives (including those with respect to parameter) over the field of rational fractions. Subsequently, it will be possible to apply this result to investigate arithmetic properties of the values of such functions. Herewith we mean the application of the effective method to achieve the sufficiently accurate quantitative result.

The creation of methods for the study of nonlinear phase systems has a long history, since the 60s of the last century (V.I. Tikhonov, V. Lindsay, M.V. Kapranov, B.I. Shakhtarin, etc.). By now, rigorous and approximate analysis methods of such systems have been developed. However, most methods are limited to the analysis of low order systems. Only in recent years attempts have been made to create methods, which allow to carry out the analysis of high-order phase systems. The material of this article deals with these methods. The article considers the construction of solutions of phase systems on the example of phase-locked frequency of arbitrary dimension with piecewise linear approximation of the nonlinear function. This approximation allowed to use an explicit form of solutions in the linearity and to obtain analytical conditions for the existence of various types of system behavior. The analytical conditions for the existence of solutions leading to the emergence of complex limit sets of the trajectories of phase systems and their bifurcations are obtained. These are homoclinic trajectories in the case of the saddle-focus equilibrium state, which play a decisive role in the occurrence of chaos. It is also shown that it is possible to obtain analytical conditions for the bifurcation of the birth and the existence of multi-pass rotational cycles in a piecewise linear phase system, on the basis of which a criterion for the transition to chaos through bifurcations cascade of doubling the stable cycle period can be obtained; in accordance with the Sharkovsky theorem it ends with the bifurcation of the cycle birth of the period three and the occurrence of developed chaos. It should be noted that the research methods of piecewise linear systems described in the paper were applied by the authors not only to phase systems, but, for example, to the Chua system, allowing various chaotic behavior.

In this paper we introduce a new class of foliations on Rie-mannian 3-manifolds, called B-foliations, generalizing the class of foliations of non-negative curvature. The leaves of B-foliations have bounded total absolute curvature in the induced Riemannian metric. We describe several topological and geometric properties of B-foliations and the structure of closed oriented 3-dimensional manifolds admitting B-foliations with non-positive curvature of leaves.

Let $M$ be a compact two-dimensional manifold and, $f \in C^{\infty}(M,\mathbb{R})$ be a Morse function, and $\Gamma_f$ be its Kronrod-Reeb graph. Denote by $\mathcal{O}_{f}=\{f \circ h \mid h \in \mathcal{D}\}$ the orbit of $f$ with respect to the natural right action of the group of diffeomorphisms $\mathcal{D}$ on $C^{\infty}(M,\mathbb{R})$, and by $\mathcal{S}(f)=\{h\in\mathcal{D} \mid f \circ h = f\}$ the corresponding stabilizer of this function. It is easy to show that each $h\in\mathcal{S}(f)$ induces a homeomorphism of $\Gamma_f$. Let also $\mathcal{D}_{\mathrm{id}}(M)$ be the identity path component of $\mathcal{D}(M)$, $\mathcal{S}'(f)= \mathcal{S}(f) \cap \mathcal{D}_{\mathrm{id}}(M)$ be group of diffeomorphisms of $M$ preserving $f$ and isotopic to identity map, and $G_f$ be the group of homeomorphisms of the graph $\Gamma_f$ induced by diffeomorphisms belonging to $\mathcal{S}'(f)$. This group is one of the key ingredients for calculating the homotopy type of the orbit $\mathcal{O}_{f}$. Recently the authors described the structure of groups $G_f$ for Morse functions on all orientable surfaces distinct from $2$-torus $T^2$ and $2$-sphere $S^2$. The present paper is devoted to the case $M=S^{2}$. In this situation $\Gamma_f$ is always a tree, and therefore all elements of the group $G_f$ have a common fixed subtree $\mathrm{Fix}(G_f)$, which may even consist of a unique vertex. Our main result calculates the groups $G_f$ for all Morse functions $f:S^{2}\to\mathbb{R}$ whose fixed subtree $\mathrm{Fix}(G_f)$ consists of more than one point., Comment: 5 pages

The study of non-stationary rarefied gas flows is, currently, attracting a great deal of attention. Such an interest arises from creating the pulsed jets used for deposition of thin films and special coatings on the solid surfaces. However, the problems of non-stationary rarefied gas flows are still understudied because of their large computational complexity. The paper considers the computational aspects of investigating non-stationary movement of gas reflected from a wall and flowing through a suddenly formed gap. The study objective is to analyse the possible numerical kinetic approaches to solve such problems and identify the difficulties in their solving. When modeling the gas flows in strong rarefaction one should consider the Boltzmann kinetic equation, but its numerical implementation is rather time-consuming. In order to use more simple approaches based, for example, on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference between the solutions of the model equations and of the Boltzmann equation. For this purpose, two auxiliary problems are considered, namely reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas.A numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but at the same time a strong dependence of a behavior of the macro-parameters on the velocity grid step. The detailed velocity grid is necessary to avoid a non-monotonous behavior of the macro-parameters caused by so-called ray effect. To reduce computational costs of the detailed velocity grid solution, a hybrid method based on the synthesis of model equations and the Boltzmann equation is proposed. Such an approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The article presents the results obtained using two different software packages, namely a Unified Flow Solver (UFS) [13] and a Nesvetay 3D software complex [14-15]. Note that the UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility to calculate both the Boltzmann equation and the model equations is realized. The Nesvetay 3D software complex was created to solve the Shakhov model equation (S-model) for calculations based on non-structured non-uniform grids, both in velocity space and in physical one.

The purpose of this paper is to compare the shortcomings of the widely used inequality coefficients that appear when working with real (ie, knowingly incomplete) data and searching for alternative quantitative methods for describing inequalities that lack these shortcomings.Research methods:– consideration of an extensive range of as full as possible real data on the population distribution by income, expenditure, property (ie data on the economic structure of society);– revealing the specific shortcomings of these data on the economic structure of society, finding out which information is missing or presented disproportionately;– comparison of the values of the most widely used indices of inequality calculated on real data on the economic structure, with a view to establishing the suitability of these indicators for problems of inequality estimation;– development of an index of inequality that adequately describes the real economic structure of society.Research data:– official data of Rosstat and the Federal Tax Service on incomes of Russian citizens;– specialized sites of announcements about the prices for real estate and cars;– Credit Suisse Research Institute data on the distribution of Russian citizens by property level;– Forbes data on income and wealth of the richest people in Russia.It is shown that the income data are essentially incomplete and fragmentary – the width of the income range (i.e., the income of therichest member of society) is known, but the filling of rich cohorts is not known, since the incomes of the richest members of society are hidden.We proposed the next (criteria as) requirements for an inequality index:– possibility of calculating the index of inequality for arbitrary quantization;– invariance of the value of the inequality index for different quantization of the same data;– sensitivity of the index to the width of the income range.It is noted that only the exponential function describes societies with high social inequality enough well (the intensity of the exponential distribution is more than 10).For the presented population distributions, the next indices of inequality are calculated:– decile coefficient of funds;– Gini coefficient;– Pareto index;– indicators of total entropy (zero, first or Tayle index, and second orders);– the ratio of maximum income (property value) to the modal;– intensity of exponential distribution.It is shown, that:– the value of the Pareto index does not have a unique relationship with the inequality;– the coefficients of the funds (decile, quintile, etc.) are not computable for arbitrary quantization, and therefore are unsuitable for comparing data from various sources and have different quantization;– The Gini index requires complete data on the rich;– from all considered criteria of inequality the first three indicators of the total entropy, as well as the ratio of maximum income (property) to the modal strongly depend on data quantization.Therefore they are unsuitable for comparison data from various sources with different quantization. It is concluded that the intensity of the exponential distribution does not possess the listed disadvantages and can be recommended as an index of inequality.

A numerically stable direct multiplicative method for solving systems of linear equations that takes into account the sparseness of matrices presented in a packed form is considered. The advantage of the method is the calculation of the Cholesky factors for a positive definite matrix of the system of equations and its solution within the framework of one procedure. And also in the possibility of minimizing the filling of the main rows of multipliers without losing the accuracy of the results, and no changes are made to the position of the next processed row of the matrix, which allows using static data storage formats. The solution of the system of linear equations by a direct multiplicative algorithm is, like the solution with LU-decomposition, just another scheme for implementing the Gaussian elimination method. The calculation of the Cholesky factors for a positive definite matrix of the system and its solution underlies the construction of a new mathematical formulation of the unconditional problem of quadratic programming and a new form of specifying necessary and sufficient conditions for optimality that are quite simple and are used in this paper to construct a new mathematical formulation for the problem of quadratic programming on a polyhedral set of constraints, which is the problem of finding the minimum distance between the origin ordinate and polyhedral boundary by means of a set of constraints and linear algebra dimensional geometry. To determine the distance, it is proposed to apply the known exact method based on solving systems of linear equations whose dimension is not higher than the number of variables of the objective function. The distances are determined by the construction of perpendiculars to the faces of a polyhedron of different dimensions. To reduce the number of faces examined, the proposed method involves a special order of sorting the faces. Only the faces containing the vertex closest to the point of the unconditional extremum and visible from this point are subject to investigation. In the case of the presence of several nearest equidistant vertices, we investigate a face containing all these vertices and faces of smaller dimension that have at least two common nearest vertices with the first face.

Darboux theorem to more general context of Frechet manifolds we face an obstacle: in general vector fields do not have local flows. Recently, Fr\'{e}chet geometry has been developed in terms of projective limit of Banach manifolds. In this framework under an appropriate Lipchitz condition The Darboux theorem asserts that a symplectic manifold $(M^{2n},\omega)$ is locally symplectomorphic to $(R^{2n}, \omega_0)$, where $\omega_0$ is the standard symplectic form on $R^{2n}$. This theorem was proved by Moser in 1965, the idea of proof, known as the Moser’s trick, works in many situations. The Moser tricks is to construct an appropriate isotopy $ \ff_t $ generated by a time-dependent vector field $ X_t $ on $M$ such that $ \ff_1^{*} \omega = \omega_0$. Nevertheless, it was showed by Marsden that Darboux theorem is not valid for weak symplectic Banach manifolds. However, in 1999 Bambusi showed that if we associate to each point of a Banach manifold a suitable Banach space (classifying space) via a given symplectic form then the Moser trick can be applied to obtain the theorem if the classifying space does not depend on the point of the manifold and a suitable smoothness condition holds. If we want to try to generalize the local flows exist and with some restrictive conditions the Darboux theorem was proved by Kumar. In this paper we consider the category of so-called bounded Fr\'{e}chet manifolds and prove that in this category vector fields have local flows and following the idea of Bambusi we associate to each point of a manifold a Fr\'{e}chet space independent of the choice of the point and with the assumption of bounded smoothness on vector fields we prove the Darboux theorem.

The paper presents a method for solving a mixed problem with homogeneous initial conditions for a loaded hyperbolic equation with an integral natural degree modulus of unknown function. An approximate solution is sought for by means of a priori estimates of the solution to the problem. A formula expressing the solution through the solution to the ordinary differential equation associated with the initial loaded equation is obtained.

We considered the problem of obtaining upper bounds for the mathematical expectation of the $q$-norm ($2\leqslant q \leqslant \infty$) of the vector which is uniformly distributed on the unit Euclidean sphere. We finish the paper with numerical experiments illustrating our results., Comment: in Russian, 10 pages, 2 figures

The paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approximated by a finite dimensional problem with mesh approximation of the state equation by the explicit (forward Euler) mesh scheme with variable time steps. The existence of unique solutions for the continuous and mesh optimal control problems is proved. The Uzawa-type iterative method is used for solving the finite dimensional optimal control problem. The results of numerical experiments are presented.

In this paper we classify all potentially G-birationally rigid del Pezzo threefolds of degree 4 and their automorphism groups and prove the G-birational rigidity of one of them, Old article in Russian. Published in Math. Sb

In 1994, in [13], N. Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of CR- and slant-submanifolds. In particular, he considered this submanifold in Kaehlerian manifolds, [13]. Then, in 2007, V. A. Khan and M. A. Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, [11]. Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and gave a necessary and sufficient conditions for two distributions (holomorphic and slant) to be integrable. Moreover, we considered these submanifolds in a locally conformal Kaehler space form, [4]. In this paper, we define 2-kind warped product semi-slant submanifolds in a locally conformal Kaehler manifold and consider some properties of these submanifolds.

This paper considers spectral-difference methods of a high-order of accuracy for solving the one-way wave equation using the Laguerre integral transform with respect to time as the base. In order to provide a high spatial accuracy and calculation stability, the Richardson method can be employed. However such an approach requires high computer costs, therefore we consider alternative algorithms based on the Adams multistep schemes. To reach the stability first for the 1D one-way equation and then for the 2D case, the stabilizing procedures using the spline interpolation were developed. This made possible to efficiently implement a predictor-corrector type method in terms of which a boundary value problem for high-order elliptic equations is substituted for a sequence of inversions of second order elliptic operators thus decreasing computer costs. To assess the accuracy and stability of difference approximations for the 1D one-way wave equation, the analytical solution based on the double Laguerre transform was obtained. This solution can be efficiently calculated if for summation one makes use of fast algorithms of computing a discrete linear convolution. For the 2D one-way wave equation the stability and accuracy of the procedures proposed have been studied on implementing the migration algorithm within a problem of seismic prospecting., In Russian. arXiv admin note: substantial text overlap with arXiv:1605.03292

The paper introduces and investigates partial orders that are finer than the minus partial order and are based on inverses along an element and other specific outer inverses. It turns out that in this way a number of classical partial orders can be equivalently defined.

To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately supported by computer algebra systems. In this paper, we distinguish between two stages of working with a mathematical model: model development and model usage. Each of these stages implies its own computer algebra system. As a model problem, we consider the problem of geometrization of Maxwell's equations. Two computer algebra systems---Cadabra and FORM---are selected for use at different stages of investigation., in Russian; in English

A.A. Levin, Energy Systems Institute SB EAS (Irkutsk, Russian Federation), lirt@mail.ru, V.F. Chistyakov, Institute for System Dynamics and Control Theory SB RAS (Irkutsk, Russian Federation), chist@icc.ru, E.A. Tairov, Energy Systems Institute SB RAS (Irkutsk, Russian Federation), tairov@isem.irk.ru Левин Анатолий Алексеевич, кандидат технических наук, ведущий научный сотрудник, Институт систем энергетики им. Л.А. Мелентьева СО РАН (г. Иркутск, Российская Федерация), lirt@mail.ru. Чистяков Виктор Филимонович, доктор физико-математических наук, главный научный сотрудник, Институт динамики систем и теории управления СО РАН (г. Иркутск, Российская Федерация), chist@icc.ru. Таиров Эмир Асгадович, доктор технических наук, главный научный сотрудник, Институт систем энергетики им. Л.А. Мелентьева СО РАН (г. Иркутск, Российская Федерация), tairov@isem.irk.ru. This paper presents the results of applying the methods of the hydraulic circuit theory in the interactive modeling of hydrogasdynamic and thermal processes that occur in the equipment of thermal power plants. The problem statement of flow distribution in the energy plants with different pressure drop laws in the branches of complex gas air and steam-water ducts is formulated. The research shows that the application of traditional methods of hydraulic circuit theory is challenging for such problems. Some aspects of solvability of the related systems of nonlinear equations are studied. The numerical methods for solving these systems as applied to the problems that require calculations in real time are considered. A computation scheme is proposed. The scheme makes it possible to reduce the initial statement of the problem to the classical scheme of the nodal pressure method. The method of decomposition of the hydraulic circuit configuration into interconnected circuits of smaller dimension is considered to reduce the computational effort. The results of tests that demonstrate high reliability of the method developed for the flow distribution calculation are presented. В статье представлены результаты применения методов теории гидравлических цепей для интерактивного моделирования гидрогазодинамических и тепловых процессов в оборудовании тепловых электрических станций. Сформулирована постановка задачи расчета потокораспределения в трактах энергоустановок с различными законами падения давления на ветвях в сложных газовоздушных и пароводяных трактах. Показано, что применение традиционных способов расчета потокораспределения методами теории гидравлических цепей затруднительно для задач. Исследованы некоторые аспекты разрешимости соответствующих систем нелинейных уравнений. Рассмотрены численные методы решения этих систем применительно к задачам, требующим выполнения расчетов в масштабе реального времени. Предложена расчетная схема, позволяющая свести исходную постановку задачи к классической схеме метода узловых давлений. Рассмотрен способ декомпозиции структуры гидравлической цепи на взаимосвязанные цепи меньшей размерности для уменьшения вычислительных затрат. Приведены результаты тестов, демонстрирующих высокую надежность разработанного способа расчета потокораспределения. This work has been supported by the Russian Foundation for Basic Research, grant No. 15-01-03228-a.

Let $A_j,B_j$ $(j=0,1,\ldots)$ be $m \times m$ matrices, whose elements are complex numbers, $A_j$ are selfadjoint matrices and $B_j^{-1}$ exist. We study the deficiency index problem for minimal closed symmetric operator $L$ with domain $D_L$, generated by the Jacobi matrix $\textbf{J}$ with entries $A_j,B_j$ in the Hilbert space $l_m^2$ of sequences $ u=(u_0,u_1, \ldots), u_j \in C^m$ by mapping $u \rightarrow \textbf{J}u$, i.e. by the formula $Lu=lu$ for $u \in D_L$, where $lu=((lu)_0,(lu)_1, \ldots)$ and $$ (lu)_0:=A_0u_0+B_0u_1, \quad (lu)_j:=B^*_{j-1}u_{j-1}+A_ju_j+B_ju_{j+1}, \;\; j=1,2, \ldots $$ It is well known that the case of the minimal deficiency numbers of the operator $L$ corresponds to the determinate case, and the case of the maximal deficiency numbers of this operator corresponds to the completely indeterminate case of the matrix power moment problem. In this paper we obtain new conditions of the minimal, maximal and not maximal deficiency numbers of the operator $L$ in terms of the entries of the matrix $\textbf{J}$. The special attention is paid to the case $m=1$, i.e. we present some conditions on the elements of the numerical tridiagonal Jacobi matrix, which ensure the realization of the determinate case of the classical power moment problem., 9 pages, in Russian

In this paper, we consider iterative propositional calculi, which are finite sets of propositional formulas together with the rules of modus ponens and weak substitution (when formula being substituted must be already inferred). We construct an undecidable iterative propositional calculus using axioms in 3 variables. Particulary, we show that the general problem of derivability for these calculi is undecidable., 10 pages, in Russian

International audience; http://mech.math.msu.su/~fpm/ps/k14/k143/k14303.pdfIn this paper, a computerized model for morphological analysis of languages with word-formation based on affixation processes is proposed. The main idea consists in defining structural patterns of words and corresponding lists of suffixes. First, a detaileddescription of a stemming algorithm, its modification, and the technique of determining grammatical characteristics of word-forms are given. The next part of this work focuses on the application of the proposed algorithms for the French language. Finally, some results of execution of these algorithms are provided.; http://mech.math.msu.su/~fpm/ps/k14/k143/k14303.pdfВ работе предлагается метод структурных схем в качестве модели морфологического анализа словоформ естественного языка с развитым аффиксальным словообразованием и словоизменением. Дано описание алгоритма выделения псевдоосновы, его модификация, а также алгоритм восстановления грамматических характеристик словоформ. Описано применение предложенного метода для анализа словоформ французского языка. Представлены результаты работы предложенных алгоритмов.