Table of contents

This conference keeps the tradition of having regular scientific and technical conferences on the urgent issues of applied mathematics, computer science and mechanics at the Voronezh State University, which has been developed over the past 20 years. Every year, well-known authorities, who represent various scientific areas, educational organizations, industrial enterprises and IT companies, gather at this scientific forum.

Within the framework of the conference, thorough analyses of modern scientific advances in fundamental and applied areas are made, original reports on the current trends in the development of modern mathematics, computer science and mechanics are made. In general, the work of the conference is aimed at identifying and systematizing the issues and trends in the development of the scientific areas of modern mathematics, computer science and mechanics; discussion of the results of solving scientific problems and projects; development of scientific cooperation; involving students and graduate students in scientific work.

List of Organizing Institutions, Supporting Institutions, Organizing and Program Committees and Conference Paper Review Process are available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The paper proposes an algorithm for the formation of a linguistic integrated assessment of the resource sustainability of an enterprise, based on the theory of extensive and intensive use of resources and methods of aggregating linguistic information using linguistic ordinal operators that formalize sequential averaging strategies for multicriteria estimation. The assessment of the extent of extensive and intensive use of resources in the work is carried out through groups of models that re ect the dependence of the resulting indicators of the enterprise on the quantity and quality of resources of various types. Quantitative indicators of the intensity of resource use are estimated by the method of chain substitutions; the Harrington function is used to switch to linguistic values. The integrated linguistic assessment obtained as a result of the work of the considered algorithm aggregates the linguistic values of the resource use intensity by all models and is interpreted as an integral indicator of resource stability, which is achieved due to intensive production factors.

In this paper, we analyse basic facts of infinite matrix theory. We construct a similarity transform which allows one to represent matrices in a certain class of 5-th diagonal matrices of a difference operator in a diagonal or block-diagonal form. For such matrices, asymptotic estimates of eigenvalues and eigenvectors are obtained. Such matrices are considered in game theory. They are also used in the study fourth-order difference operators with growing potential. The problem of invariant subspaces is also considered.

The article is devoted to the development of a set of mathematical models and algorithms to support the formation of income tax rates in the regional budget, which provide a compromise for the interests of regional authorities, business leaders and the public. To support the formation of effective options for compromise income tax rates, a two-level algorithm is proposed based on mathematical models and methods. The proposed models differ in the level of aggregation of enterprises in the region's economic system. At the upper level, options for income tax rates in the regional budget for enterprise groups are determined. Rates are formed on the basis of the principle of harmonizing tax revenues to the regional budget, the number of jobs and profits of the group's enterprises. At the lower level, optimization models are proposed for targeted adjustment of the income tax rate for socially significant enterprises in the region. The software implementation of the proposed models and algorithms allows a reasonable calculation of income tax rates using statistical information.

Developed search algorithm for the optimal control of multilevel hierarchical systems. The basis of the algorithm are the theory of fuzzy sets together with the Bellman optimality principle. The computational experiment confirms the convergence of the algorithm.

We study a mathematical model describing the steady-state non-isothermal flow of a viscous fluid between two parallel plates under the Navier slip boundary condition. The flow is driven by an applied pressure gradient. The dependence of the viscosity, thermal conductivity and slip coefficients on the temperature is taking into account. The model under consideration is a boundary value problem for a system of nonlinear coupled ordinary differential equations. We give the weak formulation of this problem and establish sufficient conditions for the existence and uniqueness of a weak solution. To construct weak solutions, we propose an algorithm based on the Galerkin procedure, methods of the topological degree theory, and compactness arguments. Moreover, explicit expressions for the velocity and the temperature on the plates are obtained.

The article shows that the difficulties encountered in solving thermal conductivity problems in a multilayer medium by the Fourier analytic method can be overcome by using the apparatus of complex functions. These are the problems of finding the eigenvalues, normalizing the basis functions and finding the expansion coefficients in a Fourier series. The results can be used to solve other non-stationary problems of transport theory.

The article is devoted to the issue of effective management in fire rescue units of the Ministry of Emergency Situations of Russia based on application of functional modeling. Data on functional model of activity of standard fire rescue unit are given. The example of application of functional modeling and business process management in day-to-day operations of fire rescue units, which allows increasing efficiency of management, is considered. The method of assessing the day-to-day activities of the fire rescue unit based on functional modeling described. Problems in the increase of enhancement of the efficiency in the activity of the fire and rescue units related to the Ministry of Emergency Situations (MES) of Russia as well as similar units that are not involved in the federal group of forces and assets is an ultimately burning problem.

In the paper, there are defined continuous-valued logical functions defined on [0, 1] as natural reactions of swarm to several stimuli detected at one time step. In this model, the logical duality represented by squares or cubes of opposition is realizable by own swarm patterns based on lateral inhibition and lateral activation. Swarm reactions are considered not certain, but with a probability of their intensity in respect to the distance to an appropriate biologically active substance. At the same time, we can formalize cases when the swarm members are partly inhibited and partly activated. In other words, we assume that they can be less or more inhibited and less or more activated, etc. So, we can deal with a fuzzy mix of conjunction and disjunction at one time.

We describe some operators for solving model elliptic pseudo-differential equations in special canonical domains. It helps us to write a general solution of corresponding pseudo-differential equation in an explicit form. Moreover, knowing a general solution we can choose additional (possibly boundary) conditions to determine uniquely the solution. All considerations we give in Sobolev–Slobodetskii spaces.

The article discusses the features of split testing and usability testing. The stages of these two types of testing are proposed. To create a web resource convenient for the user and practical for the business, analytics helps. Ergonomics test (usability testing) is a type of software testing that is aimed at exploring the convenience for users of a web page, user interface or device. At the end of the usability testing, a split (A / B testing) is performed (or not). A / B testing involves setting up two different options for a web page or landing page and sending the same amount of traffic to each page option. Then, the number of conversions for each option is measured and the best is revealed. The best option generates the most conversions. The stages of these two types of testing are proposed. An application is described that allows usability testing of information resources. The developed application supports the function of analysing images according to the main colour schemes, collect statistics selected by the user and upload their PC to an Excel document, independently define areas for collecting statistics.

The principle possibility of two metal pendulums synchronization oscillating in the parallel planes, the distance between the suspension points of which is fixed, is proved. This behavior is possible only due to the taking into account two physical factors. The first one is an effect of electromagnetic interaction between them. The second one is accounting the electromagnetic radiation of each pendulum, which leads to nonlinear attenuation. The system of nonlinear dynamical equations of the movement is obtained and its decision are numerically analyzed.

The article considers the problem of assessing the level of uncertainty in the behavior of the short time series. The approach to solving this problem, based on the use of the fuzzy linear regression equation with the asymmetric parameters has been proposed. The methods for assessing the level of uncertainty in the behavior of the short time series using the fuzzy similarity measures have been considered. A herewith, the time series which describes the equation of the classical linear regression is used as the standard time series. The presented results of experimental studies confirm the effectiveness of using the proposed approach to assess the level of uncertainty in the behavior of the short time series.

The article proposes a methodological approach to reducing the dimensionality of the problem of forming the requirements for the security of information processed in organizational-technical systems with complex architecture. The methodological approach is based on the structural analysis of graphs that formalize the structural scheme of organizational-technical systems and on the construction of the adjacency matrix of the graph. Using the selected elements of strong connectiveness, which form the clusters of architecture, allows further to solve the problem of formation of requirements to the information protection system against unauthorized access and to go from the architecture of organizational-technical system as a whole to the consideration of individual clusters. In this case, the task of forming requirements is significantly simplified. With the use of the proposed method of clustering the architecture of organizational-technical systems, the problem of forming the sets of information protection of objects of biological activity during molecular-biological and genetic - engineering studies is solved.

The multicriteriality problem has many aspects. The paper is dedicated to one of them, namely: development of the methodology for building and using dynamically changing multi-level vector criteria for optimization of engineering and manufacturing complexes. The approach applied most frequently involves vector to scalar conversion of the optimization criterion. When multi-level criteria are used we have to deal with a system of embedded convolutions forming a hierarchical system of vectors. The current principles of making convolutions for such systems can be implemented in different ways depending on peculiarities of the controlled object and management goalsThis study discusses building of hierarchical criteria in mathematical setting up of engineering and manufacturing complex optimization problems. A method of forming and scalarization of a hierarchical vector criterion following a recurrent procedure based on an invariant representing a linear combination of Holder norms of partial criteria is suggested. An example of techniques usage in the development of software for multi-criterial optimization of refinery is given.

The article defines the goals and discusses the principles for the formation of control circuits for managing an MIS enterprise. The contours of operational and financial planning, the general scheme of extrapolatory planning of MIS enterprises are considered. A theoretical information contour has been developed for coordinating the distribution of resources based on the goals of the enterprise's commercial activities.

Shelf life and quality of raw materials depend on optimal conditions for long-term storage. The optimal storage time, is the longest period, at which the loss of quality and nutritional value of raw materials do not exceed the allowable limit, depends on the temperature and humidity conditions. Throughout the entire storage period, the constant temperature should be maintained as long as possible, since its fluctuations even within +5°C can seriously affect the storage duration. On the territory of the Russian Federation, the temperature of outdoor air changes during the day from about 5 to 15°C, reaching 30°C in some regions. The seasonal temperature also varies significantly. Optimal conditions for storing pectin-containing raw materials are temperature limits of 0−5°C. One of the modes of storage of raw materials is storage in a refrigerated state, when the temperature of the raw materials and the surrounding space is lowered to −10°C. Such conditions can be achieved by equipping storage facilities with artificial cooling. Using thermophysical methods, it is possible to objectively assess the optimal storage conditions for raw materials and predict storage periods.

Relational DBMS are often used to store fuzzy values, but problems arise with putting such data in a tabular form. Moreover, there appears a problem of storing both the crisp and fuzzy data related to one subject domain in one column of a relational table. This article considers the mechanism of storing crisp and fuzzy values and linguistic variables in the document-oriented Mongo DBMS. The data are stored in the collection as GeoJSON geometry; different geometries are used for different data options. The possibility of storing crisp scalar values, crisp value sets, crisp value intervals and fuzzy values in the collection documents is described. For data processing by means of SQL queries, the context-free grammar of the SQL subset is described, according to which lexer and parser are generated. In order to form the structure of an abstract syntactic tree, a corresponding object model has been implemented. A translator application has been developed, which allows converting SQL queries related to the crisp and fuzzy data into Mongo QL queries. The algorithm of fuzzy queries translation process is suggested; the geometrical interpretation of data comparison operations is described. The examples show the options of fuzzy comparison operations for different value options.

The motion of a mechanical system consisting of a carrier and a load is considered. The carrier, located all the time in a horizontal plane, can move translationally along a rectilinear trajectory. The carrier has a rectilinear channel through which the load can move. The load is considered further on as a material point. The load can move in the channel according to a predetermined motion law. The channel axis is located in a vertical plane passing through the trajectory of the carrier. The Coulomb dry friction model is applied for simulation the forces of resistance to the motion of the carrier from the side of the underlying plane. In the conditions of the carrier motion along horizontal plane without detachment, the carrier motion differential equations are a system of three linear second-order differential equations. The influence of the system parameters on the motion of the carrier from the rest state is studied in the point of view of determining functions. An important property of the determining expressions is proved: the existence of a single intersection point of the curves given by the determining equations, which corresponds to the zero angle of setting of the channel along which the load moves.

The problems of mathematical modeling of effective control of heat and mass transfer and friction on permeable cylindrical and spherical surfaces of hypersonic aircraft are considered. The systems of ordinary differential equations are obtained by A.A.Dorodnicyn generalized integral relations method to approximate the systems of partial differential equations describing laminar boundary layers on permeable cylindrical and spherical surfaces of hypersonic aircraft. The joint systems are applied in the mathematical model. The parameters of the mathematical model at the flow stagnation point are determined from the joint systems of nonlinear algebraic equations. The blowing into boundary layer, temperature factor and magnetic field are used as controls. Dependences of hypersonic aerodynamics functionals (the total heat flow, the total Newton friction force and total blowing system power) on controls (the linear blowing into boundary layer, the constant temperature factor, the constant magnetic field) are investigated. The domains of allowed values of functionals of hypersonic aerodynamics are obtained. The results of the computational experiments are presented: the dependences of total heat flow on controls; the dependences of total Newton friction force on controls; the dependences of blowing system power on controls; the mutual dependences of functionals (as the domains of allowed values "Heat and Friction").

The problems of mathematical modeling of effective control of heat and mass transfer and friction on permeable cylindrical and spherical surfaces of hypersonic aircraft are considered. The systems of ordinary differential equations are obtained by A.A.Dorodnicyn generalized integral relations method to approximate the systems of partial differential equations describing laminar boundary layers on permeable cylindrical and spherical surfaces of hypersonic aircraft. The joint systems are applied in the mathematical model. The parameters of the mathematical model at the flow stagnation point are determined from the joint systems of nonlinear algebraic equations. The blowing into boundary layer, temperature factor and magnetic field are used as controls. Dependences of hypersonic aerodynamics functionals (the total heat flow, the total Newton friction force and total blowing system power) on controls (the constant blowing into boundary layer, the linear temperature factor, the constant magnetic field) are investigated. The domains of allowed values of functionals of hypersonic aerodynamics are obtained. The results of the computational experiments are presented: the dependences of total heat flow on controls; the dependences of total Newton friction force on controls; the dependences of blowing system power on controls; the mutual dependences of functionals (as the domains of allowed values "Heat and Friction").

This article through simulation provides the functioning mathematical model of information security system (ISS) from unauthorized access (UAA) in automated systems (AS). The model is developed in CPN Tools software environment for its analysis, getting probabilistic-temporal characteristics and its further comparison with the analytical model. The systematic analysis of functional components in ISS from UAA highlighted its key subsystems. Integrated CPN Tools breaks the model into subsystems by preserving ISS functioning logics from UAA, and observes the taking processes. This model performs the computation experiment, namely, researches ISS real consumer properties from UAA in AS, which in following researches provides the analysis software complex development and qualitative assessment of the similar systems functioning. Simulation results of ISS functioning process from UAA in AS can be various characteristics of each state, describing the system work both generally and for its subsystems. The programming Metalanguage, used in CPN Tools adjusts the simulation model and controls the marker random transition from the initial state to final through intermediate, determines transition properties, enters different marker types, sets time delays, etc. The article substantiates the required transitions by ISS simulation model from UAA in AS to get reliable characteristics as the further research direction.

The article completes the cycle the articles by the authors assessing reliability of information security systems from the unauthorized access to automated systems. In includes previously unpublished materials. The article discloses main directions to improve methods and procedures for assessing reliability of the information security systems from the unauthorized access to automated systems. There is modification of the traditional static method to assess the functional reliability of the information security systems from the unauthorized access to investigate their operation in the dynamic (real) functioning mode and to quantify reliability of the information security systems, including development of adequate indicators, models and algorithms. Main stages and procedures for forming the reliability assessment method were developed as a technological scheme with demonstration of the main stages to implement the proposed methods in the current normative-technical documentation.

The sixth-order nonlinear spectral problem with nonsmooth solutions is studied. It is proved that the set of non-negative values for which the nonlinear spectral problem has at least one non-trivial non-negative solution is nonempty and coincides with a certain interval. We use the pointwise approach proposed by Yu. V. Pokorny analyzing solutions to a boundary value problem. This approach shown to be effective in the study of the second-order problems. Based on the previously obtained estimates of the Green's function of the boundary-value problem, it was possible to show that the operator inverting the studied nonlinear problem, representable as a superposition of completely continuous and continuous operators, acts from the cone of nonnegative continuous functions to a narrower set. The last fact allows us to prove the uniqueness of a solution of a nonlinear boundary value problem using the theory of spaces with a cone.

The problem of simplifying solution of linear dynamic systems with preset conditions at the edges and internal points of the segment is considered. In this regard a modification technique of the existing cascade decomposition method based on obtaining a general formula for the system state and control functions is described. Coefficients of this formula are identified in a recursive way. The formula is presented to obtain the cascade decomposition method and kernel functions of the intermediate step matrices being important for the last step function. Illustratively, a practice-oriented example proves the method advantages in convenience and speed comparing with the conventional method of cascade decomposition.

Numerical modeling of fractal sets using randomized iterated function systems can be implemented in two ways. The first of them is known as the chaos game, and the other is associated with the construction of a transformation matrix, the elements of which are the sums of terms of a converging series, divided by given classes. The last way allows us to relatively easily generate realizations of homeomorphic prefractal sets with similar topological properties.

The main purpose of this study is to identify, using various methods of machine learning, the most effective markers of atherosclerosis and their main predictors, which can accurately determine the risk of this disease in the human body. In this study, various models and balancing techniques of the initial data set were used, which allowed us to develop the efficient classifiers according to the criteria of sensitivity, specificity and ROC AUC.

In this paper, computer simulations of the hardness of ordered and disordered alloys of Cu−Ag and Au−Ag were performed using the Sutton-Chen potential and the GULP software package within several models. In addition, Poisson ratios were estimated. When simulating a chemical disorder, a super-cell containing 108 atoms was built. Numerical experiments have shown that chemical disorder in the studied alloys leads to hardness degradation.

On directed graphs defined a new kind of reachability restriction – table constraints on reachability. Each edge of the graph assigned a certain element of the monoid. Some element of the monoid selected and fixed. This element does not equal to the unit of the monoid. This element is called forbidden. Each way on the graph is associated with characteristic – a vector, whose length is equal to the number of way edges. First element of the characteristic is equal to the element of the monoid which corresponded to the first edge of the way. Each successive element of the characteristic is equal to the previous element of the characteristics plus the value of an element of the monoid, corresponding to the next edge of the way. A way on the graph is considered as valid if the way characteristic does not contain a forbidden element. The construction of the scan-graph, which is built on the original graph, is described. The transition to the scan-graph allows you to solve the problems of the reachability on such graphs, shortest ways and random walks on the graphs with table constraints on reachability.

This paper presents the results of numerical modeling by the finite element method (FEM) of convective heat and mass transfer during the growth of single crystals by the vertical Bridgman method with a submerged heater. Numerical calculations were performed using the implicit matrixless finite element method based on the iterative process of conjugate gradients and significantly reducing the requirements for RAM and computer speed. The effects of gravity, rotation, crystallization rate and vibration on heat and mass transfer in the melt, the geometry of the crystallization front, and the thickness of the boundary layers were studied. It is shown that the above effects can be effectively used to control the distribution of impurities in crystals grown by the vertical Bridgman method.

A rarefied gas flow trough a long circular tube due to pressure and temperature gradients is studied on the basis of the S-model kinetic equation. The Maxwellian mirror-diffuse reflection model is used as the boundary condition on the channel walls. The mass flow rate is calculated as a function of the small pressure and temperature gradients. Similar results presented in the literature are compared. The thermomolecular pressure effect has been modeled and the coefficient of the thermomolecular pressure difference has been calculated at various values of the accommodation coefficient and in whole range of the Knudsen number.

Currently, information systems have become an integral part of critical information infrastructure. In particular in the energy sector, developed and successfully operated information system in the management of technological, industrial and security measures. Systems in this class are subject to destructive impact and above all by cybercriminals seeking to infiltrate their database, block, or disable electronic equipment control and management. The main feature behind the concept of structural-parametric synthesis and optimization of information systems is that the systems of this class are objects for a formal description, which there is no unambiguous analytical dependencies. In addition, there are significant limitations on the choice of the optimization parameters that cannot be precisely determined at the stage of examination of the object of the synthesis, since they depend on the design solutions. Therefore, structural-parametric synthesis of the information systems cannot be reduced to the solution of the optimization math problems. Requires a special approach, which is able to resolve the difficulties due to the operational management of the course of the synthesis.

The paper presents a systematic approach to the selection of methods and algorithms suitable for modeling the dynamics of market indicators. The directions and stages of modeling and forecasting market dynamics in the study of short time series based on the use of fictitious and lag variables, as well as adaptive methods, are formulated. It is shown how the specificity of the data and the size of the series of observations affect the choice of suitable mathematical methods. A range of models suitable for approximating short time series has been determined. Studying the example of labor market research, the choice of the Holt-Winters multiplicative model as the best is substantiated. The model makes it possible to adequately approximate the damping of the oscillation amplitude synchronously with the initial process. When studying the dynamics of real estate market prices, the possibilities of using lag variables as a leading indicator for the purpose of short-term forecasting are shown.

The article proposes an approach to metallographic research based on solving the problem of semantic segmentation using a trained neural network classifier. To solve the problem of isolating grains in micrographs of longitudinal and transverse slices of metal, the neural network model U-Net was adapted. In order to obtain closed image contours, a post-processing algorithm was developed using the OpenCV open source computer vision library. The article describes the training of a neural network and the conversion of its results, as well as the comparative analysis of the histograms between the reference grain area distribution and the distribution obtained using the proposed algorithm.

The features of the numerical solution of the two-dimensional equation of stationary heat conduction are considered taking into account nonlocal effects. The finite element method using isoparametric finite elements was chosen as the numerical solution scheme. A method for approximating the zone of nonlocal influence was proposed, and an estimate of the time for calculating the coefficients of the thermal conductivity matrix was also constructed. The influence of the main parameters of the model on the final results is studied, and a polynomial family of functions of non-local influence is also studied. The results are compared with the results obtained with the classical approach.

We describe one of the possible methods for organizing a control and communications system for agents such as unmanned aerial vehicles with directional antennae. A special kind of cellular automaton was proposed with an adjacency between cells changing every cycle to describe the group movement of agents forced to synchronize, as well as the corresponding game.

This article discusses an example of using the algorithm for finding the shortest path to determine the strength of the connection between different words and phrases of the subject area in the tasks of Internet marketing, such as website promotion, thematic traffic, contextual advertising. The input data is words and phrases obtained from search queries and the frequency of their use in the network. Based on the initial data, a weighted graph is constructed, a adjacency matrix is drawn up. The shortest path is determined by the algorithm Floyd-Warshall. The algorithm finds links between words and the force of communication. This approach allows you to find unique semantic combinations and make the necessary search queries. Based on the analysis of the adjacency matrix and the definition of the coherence of words, marketers get a unique tool for solving problems in the field of digital marketing.

The paper considers logical approach to solution of multi-objective optimization problems, which consists in representing a certain optimality principle in the form of a predicate with subsequent generalization in the form of a membership function of a fuzzy set of optimal solutions. The results of the study of the dependence of the optimal solution of the fuzzy multi-objective problem on the principle of optimality, functional representation and parameters of fuzzy logical connectives are presented.

Verification of facts refers to the task of verifying textual content. Taking into account the growth of false information on the Internet, fact-checking becomes not only the activity of only journalists. The problem in computer-based fact-checking on the Internet is the lack of universal mathematical models for extracting useful textual information. Proposed the algorithms and mathematical models for extracting useful textual information in order to further verify facts. Presented results of experiments with the practical application of the developed mathematical model for extracting useful text from Internet resources.

We consider a general method to derive an optimization algorithms based on potential theory. This theoretical approach is based on the randomization of an objective function and the computation of directional derivatives of the randomized functional. Using the gradient of the potential field we consider algorithm in terms of the means of the underlying movements in the space of random vectors. Effectively, this process combines the exploration power of random-search algorithms with the exploitation power of direct-search algorithms. At the end we offer the results of a computational expert.

The error in the planar projection of the principal components of a multidimensional data array strongly depends on the number and dimension of the column vectors of this array and the correlation between the vectors. In this work, we investigate the dependence of the error on the planar projection of the principal components of fractal Brownian functions on the number of statistically independent realizations in the multidimensional data array. As a result, we show that, under certain assumptions, the number of statistically independent realizations of fractal Brownian functions coincides with the effective dimension of the projection of the principal components.

Pattern recognition is one of the most important tasks of both intelligent control systems and arti cial intelligence. The paper substantiates the relevance of the study of computer modelling of statistical, structural and neural network methods of pattern recognition. The article presents a comparative analysis of the quality of pattern recognition using the Hamming neural network and the statistical algorithm. The analysis shows that the use of the Hamming neural network is preferable in most cases. Computer modelling of the structural method using the Freeman code gives a description that allows us to unambiguously assign an object to its class. Based on the analysis of the results of computer modelling, the positive and negative aspects of each method are revealed. As a result, the structural method is the most optimal.

We consider the macroeconomic model of T. Puu, describing the fluctuations of gross income in a given region. With a special combination of savings and investment rates, income deviations will take place only for a finite period of time, after which the income will return to a stationary state. This e˙ect is known in mathematical physics as the Huygens principle. We investigated this model using statistical methods of data analysis. The obtained results suggest that the Huygens effect hypothesis in certain historical periods of the Russian economy is plausible. We have also considered the structure of the set of stationary zeros for nontrivial solutions to a stationary equation.

In the article results of charged particles identification for BM@N experiment being performed at NICA acceleration complex of Joint Institute for Nuclear Research are presented. A standard neural network-based technique of constructing a classificator is applied to the data sets obtained both from modelling of a realistic experimental setup and three synthetic data sets. The carried-out analysis demonstrates that the estimated data accuracy is insufficient to make a clear distinction between electrons, muons and pions, and also between -particles and deutrons. The problem could be solved by using an extra data from the detector or by improving the accuracy of the experimental data by two orders of magnitude.

In the present paper, the growth rate of eigenvalues for the fourth-order spectral problem with nonsmooth solutions is obtained. It arises when we apply the Fourier method to the mathematical model, describing small free vibrations of a mechanical system consisting of pivotally connected rods. We assume that at the connection points there are springs that respond to rotation, while the system is in the external environment with localized features, leading to a loss of smoothness of the solution. The analysis of the problem is based on the pointwise approach proposed by Yu. V. Pokorny, and proved to be effective in studying linear boundary problems of the second and fourth orders with continuous solutions (an exact parallel with oscilation theory of ordinary differential equations is constructed).

The problem of finding the centers and scattering matrices for a finite set of points containing outliers in a multidimensional space is considered. A new approach is considered in which instead of the arithmetic mean, differentiable mean values are used that are insensitive to outliers. An iterative reweighting scheme for searching for centers and corresponding scattering matrices for the Mahalanobis distance is considered. The examples presented in the article show the robustness property of the proposed method and algorithm with respect to a large number of outliers.

In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite–rank approximations by linear systems. The main result for this approach is to establish correctness of the finite–rank linear system under consideration. And the main result of the paper is to prove correctness of the finite–rank linear system approximation. For that an explicit formula for the main determinant of the linear system is derived to demonstrate that it is non–zero.

In this paper we describe new algorithm of calculating total density of electromagnetic states in one-dimensional photonic dielectric crystals. Our algoritm do not use unitary transformations and have low computational complexity. We are implemented it on Fortran in sequential and parallel variants.

The problem of starting control of the vibration of points of a rectangular membrane with fixed boundaries is considered. The concept of implemented functions for these membrane points is introduced. For each function being implemented, valid controls are defined that form the control sets. The structure of the control set is studied. The problem is solved in the game setting, the initial player controls the initial position of the membrane, the second, the initial speed. The criterion of the quality of control is determined by the control standards with which the functional is built. The saddle point of the functional and the equilibrium situation of the game are found.

The article presents the research results on the computational theory of semantic interpretation in Russian language. These interpretations represent a generalizing formalization of a scientific and technical style sentences. Furthermore, the concept of a partition system of a word scale, its classes and a method of forming partition classes is defined. We showed that the word scale corresponds to many partition systems that are specified by a special rule for selecting instances from classes. Additionally, we proposed generalized algorithms for constructing a partition system.

The article considers the application of the mathematical modeling method to describe the dynamics of the catalytic layer state variables of the styrene production reactor. This method was carried out using a kinetic approach for description of chemical transformations, which occurs in a multicomponent gas mixture. The main physical processes, affecting the decrease in catalytic activity during operation, are considered and the relationship between them is described. A method for increasing the efficiency of the catalytic system in terms of ACS (automated controlling system) synthesis is proposed. The mathematical formulation of the problem of creating a predictive program control system under unsteady conditions is completed. Mathematical software has been developed that allows us to evaluate activity and predict the dynamics of changes in such production efficiency indicators as ethylbenzene conversion and styrene selectivity. In that framework, the blocking of catalyst active centers, proceeding by the sequential mechanism of coke formation, is classified as a deactivating factor. The distribution patterns of carbon along the length of the reaction space at different times of the catalyst inter-reactivation period, depending on changes in the mixture component concentrations and the temperature condition, are revealed. Based on the production data, the calculation and approximation of raw materials conversion values and selectivity for the target product were carried out taking into account the accumulation of carbon on the layer surface, as well as the variation of process parameters such as temperature, pressure of the reaction mixture and partial pressures of the components.

The iterative method for automated synthesis of band-pass filters with current to voltage conversion with a given transfer gain is developed. The structure of the synthesis system of LC circuits with a given voltage transfer coefficient is presented. The implementation of the proposed method in SimOne Circuit Designer plugin is shown. Further ways for method development are suggested.

A mathematical model of the current density distribution in an axially symmetric system of superconductors in an external magnetic field is formulated within the framework of the integral form of London equations. The discretization of the model is carried out and the stability and convergence of the computational scheme are investigated. The distribution of magnetic induction, the density of currents in the ring and the sphere and the attractive force between them are calculated. The possibility of stable levitation of the sphere near the center of the ring is shown.

Graphostructural modeling is an effective tool for the analysis and control of social and economics systems. Graphs, hypergraphs and metagraphs are used to simulate complex hierarchical structures. In this paper we consider metagraphs and their matrices associated with 2D and 3D systems and cellular automatons; and their relationship with the transition from basic to associated models of cellular automatons. The transition to an associated model is a key step in developing the theory of discrete argument systems. In this paper with the simple examples of discrete-argument systems we demonstrate that matrix characteristics of the models, associated with such systems, are closely related to the matrix characteristics of associated metagraphs.

The problem of estimating the average risk in Bayesian Belief Networks is considered, taking into account the uncertainty of the initial data. For estimation of parameters of functional dependences taking into account errors in values of functions and arguments it is offered to use methods of the confluent analysis. The necessity of obtaining interval estimates of functional dependencies and average risk to increase the reliability of decision-making is shown. The Bayesian Belief Network is modeled taking into account random errors.

The development of uranium and hydrocarbon deposits is a rather complex technological process consisting of several related sub-processes. One of them is the dissolution of solid soil by acid (in-situ leaching). The aim of this article is to model this process at the macroscopic level. The approach is based on the detailed consideration of fundamental laws of mechanics and chemistry at the pore scale. It is clear that the mathematical model obtained at the pore scale cannot be used in practical applications, but its simple and mathematically correct form allows further approximation by a system of homogenized equations. The dynamics of the liquid and the concentration of the reagent is described by a system of Darcy equations and the convection-diffusion equation respectively, obtained by homogenization the initial microscopic problem at the pore level. To solve the system of equations numerically, the method of finite differences on a uniformly spaced staggered grid is used. Temporal and spatial discretization of the equations is carried out. The results of numerical experiments are presented. The obtained results can help to analyse the active solution front motion in a porous medium and physical and chemical processes there.

Sources (generators) of random processes (signals) are widely used in various technology areas as software modules in computer simulations or hardware blocks in experimental works. The equipment can be built on analog or digital bases. Noise physical sources (generators) form random processes of a certain type (Gaussian noise), which properties and characteristics are set very approximately. Digital generators (sensors) of pseudo-random processes have better technical characteristics, but the range of their types is very limited. The random signal simulator should form its values with specified statistical characteristics (probability distribution and its parameters, correlation properties, etc.) and the possibility of changing them. From this point of view, the Markov model of random process (a simple Markov chain) provides good results. It is the base for a structural scheme of the simple digital algorithm to form pseudo-random numbers and the hardware simulator implementation, to research its capabilities and effectiveness.

The mathematical model for calculation of the ion density in the gas-discharge chamber of a radio-frequency ion thruster is developed. The model is based on the assumption of higher potential of the central plasma volume comparing to the chamber walls due to higher mobility of electrons. Firstly, the initial approximation for the plasma potential is set and parameters of the ion trajectories in quasistationary electric field are computed. Then, from the assumption of keeping the total ion flow for each trajectory, the ion density is computed as well as the next approximation for plasma potential. The computation is performed iteratively until the change in the ion density is less than the predefined small value. The model was verified by comparing the results of numerical simulation with the analytical solution for spherical volume. The high accuracy of the numerical model is shown. Also, the ion density in the discharge chamber of a radio-frequency ion thruster was calculated with the uniform distribution of neutral atom density and coefficient of ionization rate. It was shown that at such conditions the ion density has a maximum in central part of the discharge chamber and it decreases towards the walls.

This work is devoted to the numerical solution of the acoustic problem. It has a lot of important applications, for example, direct and inverse problems of the seismic survey process. The grid-characteristic approach was used to transform the problem into a set of independent linear transport equations. In one-dimensional case explicit numerical schemes for continuous and discontinuous materials were derived. Using differential sequences of initial equations, the new compact scheme on the two-point spatial stencil was proposed. A set of numerical experiments with different initial conditions and materials were carried out. Direct numerical simulations proved the third order of the approximation.

The article is devoted to solving the practical problem of assessing the quality characteristic of the information protection system –«usability». In the course of his/her work, the security administrator of the automated system, built in a secure execution, makes a number of technological operations restricted by regulatory and administrative documents. At this, the prompt of such operations is determined by the characteristics of the interfaces of the software modules of the information protection system (IPS). In this regard, the assessment of the quality characteristic of the IPS «usability» becomes relevant for the category of users - security administrators. A meaningful analysis of the activities of this category users of information systems showed that it is appropriate to assess the "usability" based on operational, temporal and probabilistic indicators. The methodological basis for assessing these indicators is an experimental measurement of the average execution time of each operation by a representative group of users, followed by an analytical prediction of the probability of their execution.

At the current paper the system of signal type automatic recognition for the problem of automated testing of radar stations based on collaborative usage of production system and neural network set is presented. The main approaches for solving the problem of automated recognition digital and analog modulation types are shortly outlined. Characteristics calculated based on time-domain and frequency-domain signal representation, typical for the radar impulses are considered. The structural schema of the software for automated classification of radar impulses is presented.

We establish algorithmic undecidability of "simple" (with respect to the quantifier-prefix and the quantifier-free part of the formulas) fragments of positive theories of finitely generated semigroups and elementary theory of a free countably generated semigroup.

Ergatic systems have found their application in those areas where operator's participation is an integral part of the effective functioning of these systems, that is, it has the ability to quickly solve problems and contingencies that arise during work process. Critical application systems are one of the varieties of ergatic systems. For their successful functioning, it is necessary to choose the optimal set of alternative functions of multifunctional elements. The relevance of this problem lies in the wide distribution of this type systems, as well as in their special importance. So this article provides a description of the structural and parametric models and functional capabilities of ergatic systems. As a model, it is proposed to use weighted hypergraphs. The statement of the problem of optimizing the choice of a combination of alternative functions of multifunctional elements of such systems is given. The description of the developed numerical method based on the use of the scheme of branches and boundaries is also given. The final part of the article presents a numerical example, divided into initial, intermediate and final stages of optimization, for demonstration of the described numerical method operation.

An approach is proposed for the integrated processing of the data of multispectral aerial photography and a geophysical survey; this approach is based on the consistent application of the principal component analysis and the fuzzy c-means clustering algorithm. Its use provides the identification of thick humus layer areas, clarification of the boundaries of a thick occupation layer, as well as the localization of sites presumably containing buried archaeological objects. This approach was successfully applied in identifying an occupation layer and modeling its boundaries in the test area of the archaeological site – Kushmanskoye fortified settlement Uchkakar (Udmurt Republic, Yarsky district).

A model for studying the movement of avalanche-hazardous snow masses based on the method of smoothed particles is presented. This approach has been shown to be most appropriate in modelling environments prone to fragmentation. The impact of the snow avalanche on vehicles and the dependence of the affecting factors on the thickness of the snow cover and the terrain have been investigated. It has been found that with snow cover thickness up to 0.5 m, avalanche does not lead to loss of vehicle controllability. The results of the modelling at a qualitative level coincide with the real effects of the avalanche on the vehicle, which confirms the adequacy of the model developed.

When solving applied problems, an important aspect of the analysis is the stability of the obtained solution with respect to experimental data errors. Empirical experimental data, although a priori inaccurate, can be represented by intervals of their range of values. In some cases, the limits of their variation may also be known. Obviously, the degree of inaccuracy of input data influences the solution of the parametric identification problem. Therefore, in the case when this solution is not the only one, methods for assessing the influence of experimental error on the stability of each potential solution are of interest as they may provide additional arguments in favour of choosing one of them. In the case of models formalized in the form of systems of linear algebraic equations, a similar effect can be investigated using the condition number. In a case of quantitative analysis of multicomponent mixtures, the paper presents an approach to the parametric identification of linear models based on the calculation of the maximum permissible parameter estimates in combination with the study of the coefficient stability of the system.

The article deals with methods of teaching incremental classifiers capable to adapt to incoming online streaming data, using the example of environmental monitoring systems. It is proposed to use Cascade ARTMAP neural network architecture, compatible with symbolic representation based on IF- THEN rules. The knowledge gained during Cascade ARTMAP network training can be transformed into a compact set of decisive rules for classification of source data that can be easily interpreted by experts in the field of environmental assessment.

Using the finite element model of the shock system, the efficiency of the shock pulse energy transfer to the deformation zone under wave strain hardening is studied. It was established, that conducting research from the point of view of the efficiency of transferring the shock pulse energy to the deformation zone, and from the point of view of the design of the shock pulse generator, is advisable on shock systems in which the contacting ends of the striker and the waveguide have equal diameters. Studies showed that with ratios 1<L1/L2<10; 5<L1/d1<10, an increase in the fraction of the shock pulse energy transmitted to the deformation zone n exceeds 80% for the striker and waveguide with diameters of 30, 48, 60, 90 mm. According to the adopted optimization criteria, the geometrical dimensions of the striker and the waveguide are determined, which ensure the transfer of the largest amount of shock pulse energy to the deformation zone.

The study of radon migration in geological environments is relevant for the search and contouring of oil and gas deposits, the search for uranium and thorium ores, environmental mapping when choosing sites for the construction of industrial and residential structures, and for predicting events in seismic activity zones. The paper considers a mathematical model of the three-dimensional problem of radon diffusion-advection in piecewise constant layered media with inclusions, taking into account the anisotropy of the diffusion properties of subregions of the geological environment. A combined method for solving the problem is described, based on a combination of the methods of Laplace integral transformations, integral representations with the construction of the Green function of the host layered medium, and Fredholm integral equations of the second kind arising at the boundaries of local inclusions. The results of a comparison of the data of computational and natural experiments for some special cases are presented. A mathematical model of the inverse geometric problem of search for the boundary of a local inclusion is presented.

Operation is devoted the decision of the task increase of structural stability and information efficiency of network information systems on the basis of mathematical apparatus of the theory of fuzzy sets and the spectral theory of graphs. For this purpose introduction of two variants fuzzy structural (channel and nodal) is offered to redundancy of the determined regular topology of network information systems. Functions of an accessory of separate structural elements to which in correspondence the modes of an information exchange which are representing itself as requirements to structural characteristics of system are defined. Analytical and imitative modeling for research of influence fuzzy redundancy on the main structural parameters of the determined topology and estimation of information efficiency of the received structures of network information systems is conducted. Results of modeling showed perspectivity of the offered approach at implementation of structural adaptation of systems to changing conditions of an information exchange.

Operation is devoted obtaining, on the basis of the spectral theory of graphs, the adaptive algorithm of conversion of basic structural models of network information systems for synthesis of topology with the minimum redundancy meeting requirements of structural stability by the given criteria. On the basis of switchings of Zajdel the method providing on each step of operation of cycles of algorithm a finding cospectral structures of high stability is developed. During researches concepts cospectral structures in narrow and wide sense are formulated. Modeling of operation of algorithm and an estimation of information efficiency cospectral network information systems on the basis of the generalized index – performance coefficient of information transfer taking into account influence of noises is led. Results of modeling confirmed a realizability and serviceability of the received algorithm, and also allowed to generate practical recommendations about its application in a structural circuit of complex multiple loop adaptation.

The article describes the worked on numerical technique for forming alternative coalitions of experts relating to solving weakly formalized problems and the results of verification of the proposed method by the example of the studying the attributes of violators in the field of physical protection of critical information infrastructure objects. The proposed methodology for conducting preliminary examination on the basis of the worked on numerical method for identifying coalitions of experts allows to perform the procedure for forming an agreed group of experts and obtaining preliminary estimates of the significance of the attributes of a violator during a single survey of experts, that significantly saves time and reduces the complexity of the expertise of objects. Using the worked on numerical method, the main and two alternative coalitions were identified. Taking into account the alternative opinion of experts allowed 31 experts to be identified as agreed upon, which more precisely determines the results of the expertise.

In the research is represented the mathematical model of the periodic process of isoprene polymerization in the presence of titanium-containing catalyst systems. By the process of constructing of the mathematical model was taken into account the polycentric nature of the applied catalytic system. On purpose of organization of the possibility to describe a continuous process in a cascade of ideal mixing reactors, the mathematical model was supplemented by the corresponding hydrodynamic mechanism. For the resulting system of differential equations, a numerical solution method was programmatically implemented and was conducted a computational experiment to predict the main molecular characteristics of the resulting product.

The article presents the results of a study of the process of copolymerization in an industrial environment gathered by the software developed by the authors. The software is based on the modeling of the copolymerization process by the Monte Carlo method. The core algorithm is the simulation of the growth of each macromolecule of the resulting copolymer and tracking processes occurring with it. At the same time, we took into account that the industrial copolymerization process is carried out continuously in a cascade of reactors, which is reflected in the use of the residence time distribution of particles in the algorithm. The developed model makes it possible to calculate the molecular weight distribution, to construct the compositional distribution of macromolecules depending on the proportion of monomers, the distribution of macromolecules in size and composition for various variants of the ratio of monomers, as demonstrated by the results of computational experiments on modeling the process of copolymerization of butadiene with styrene in a cascade of reactors.

The development of a new piezoelectric fatigue machine operating in pure torsion is presented in this paper. The proposal for implementation of a testing machine to research on very-high cycle fatigue at biaxial bending is studied. Results of pure torsion tests on titanium alloy VT3-1 processed by forging and extrusion are shown. Evaluations of specimens shapes made of aluminum alloy D16T and titanium alloy VT3-1 were conducted as well as the possibility to conduct VHCF bi-axial bending tests was confirmed.

Tasks of automated text analysis are increasingly moving from theoretical research and experimental systems into practice. Increased volumes of text information for manual processing caused the need to use automated tools to solve a variety of tasks for a wide range of users operating not only desktop computers but more and more often mobile devices. There is the need of creating new automated systems and services for a wide variety of applications and the lack of universal algorithms for text analysis. In addition, in connection with different performance requirements of the large data volumes processing, it is urgent to develop integrated tools of automated text analysis, quickly solve user problems on any device, tools for deeper text study and create a basis for further research in the field of computational linguistics and testing of new algorithms of analysis. The proposed toolset includes an open system of automated text analysis, web-portal "Automated text analysis," a set of services and mobile applications. Its use will provide an ability to create and use software tools to solve practical problems, taking into account the interests of a wide range of users, and promotes research in the field of computer linguistics and deploying their results into various applications.

A computer modeling system of chemical processes in tubular reactors has been developed. The system helps researchers (technologists, designers) to determine rational modes of operation of tubular reactors, which ensure compliance with the requirements for efficiency indices of chemical processes carried out by various mechanisms. The system includes a module for setting the mechanism of the chemical process, modules for structural synthesis and parameters adjustment of the dynamic mathematical model of the chemical process, a library of finite-difference methods for solving the equation of convective transfer of substance, a module for calculating distributions of concentrations of raw substances and reaction products along the length of the reactor and during time, a module for calculating efficiency indices, a module for generating and storing a modeling report. The information ware of the system includes databases of geometric parameters of tubular reactors and procedural ranges of technological parameters of chemical processes. Databases allow the system to be adjusted according to the tubular reactor brand. The results of the modeling are presented in tables, 2D and 3D graphs of the concentration distributions of raw substances and reaction products. The system has been tested according to the data of thermal decomposition of ethylene, benzene oxidation, pyrolysis of mixture of ethane, butane and propane, production of vinyl acetate. The testing results have confirmed the adequacy of the proposed mathematical description of chemical processes in tubular reactors and the operability of the created software solution.

A hybrid computer modeling system of extrusion processes has been developed, which includes mathematical models of various types. The system helps operators to solve the problems of quality control of multi-assortment polymeric films during change-over of production lines and in the mode of film production. The system includes a module for choice of extruder brands, a designer of virtual 3D extruder screw models, and modules for structural and parametric synthesis of mathematical models of extrusion processes and calculation of throughput, energy consumption of extruders, extrudate quality indices determining consumer characteristics of the film. The model library contains geometric models of screw elements of various types, static functional models of physical processes in channels of screw elements, empirical models of rheological properties of polymers, dynamic models for estimation of residence time, models for calculation of mixing degree, index of thermal destruction and color characteristics of extrudate. Static models have been developed on the basis of conservation and rheology laws. The method of synthesis of a cell-type hydrodynamic model with recycles has been developed. The system is adjusted according to the production method, the film type, throughput and energy consumption requirements. Modeling results are presented as tables, 2D and 3D graphs. Testing of the system according to the data of the productions of polyvinyl chloride and polyethylene films at plants in Russia, Germany has confirmed its operability.

The article is devoted to the research of the effects of wave processes on shore protection structures using mathematical model of wave processes based on the system of Navier-Stokes equations, which includes three equations of motion in areas with dynamically changing geometry of the computational domain. The pressure correction method is used for the approximation of a hydrodynamic model. The difference schemes describing the mathematical model of the wave propagation towards the shore are constructed on the basis of the integro-interpolation method using the scheme with weights. An adaptive alternating-triangular iterative method is used to solve the system of grid equations. The model presented in the article gives more realistic description of the physical wave process near the coastline. The practical significance of the numerical algorithms and program complex for their implementation is the possibility of their application in the study of hydrophysical processes in the coastal water systems, as well as to build the velocity and pressure fields of the water environment and the evaluation of hydrodynamic effects on shore protection structures and coastal structures.

We propose a new method for calibrating tempered stable Lévy processes based on an artificial neural network (ANN), which takes probabilities of crossing a number of fixed barriers by a random walk as input data, and demonstrate its performance for the widely used CGMY model. To train the network we use real historical data and a synthetic dataset. We download and prepare the former to create a sequence of histograms with historical probabilities of crossing the set of barriers by log-returns of the underlying asset. To construct the synthetic dataset, we generate the values of the CGMY model's parameters and calculate the respective probabilities of crossing the barriers as prices of synthetic one-touch-digital options by means of an effective numerical method, which is based on the fast Wiener-Hopf factorization technique. After that, we become able to calibrate the parameters for this model by means of the trained ANN, using the probabilities as input data. As the result, we obtain a fast method to calibrate the CGMY Lévy model, which can be used to solve risk management problems on financial markets – especially for the case where the asset under consideration is highly liquid and highly volatile at the same time (e.g. cryptocurrencies).

The paper considers the problem of multi-frame super-resolution under applicative noise which generates distributed regions of outlying observations in low resolution images. The analysis of existing solutions is performed. They include algorithms based on spin-glass models and Markov random fields used to remove applicative noise. The authors suggest their own approach, which involves using a recurrent algorithm of quasi-linear optimal filtering of a sequence of low resolution images together with superpixel segmentation performed in order to determine the regions damaged by applicative noise. The considered algorithms are compared as applied to a set of test images. The results of the experiment demonstrate that the suggested approach allows for more accurate recovery of HR images than the existing analogues.

The present work is devoted to the study of three-dimensional model of transport and sedimentation of suspended matter in the coastal zone. The model takes into account the following processes: advective transport due to the movement of the aquatic environment, microturbulent diffusion and gravitational sedimentation of particles of the suspension, and changes in the geometry of the bottom caused by sedimentation of the suspension or the rise of bottom sediments. The aim of the work was to conduct an analytical study of the uniqueness of the initial-boundary-value problem corresponding to the constructed model. In accordance with the stated aim, an initial-boundary-value problem is considered for a parabolic type equation with lower derivatives in the domain for which a quadratic functional is constructed and the uniqueness of the solution is proved by the energy method.

The paper considers the application of the scheme based on linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation error. The proposed difference scheme has shown its effectiveness in solving diffusion-convection problems in the range of grid Peclet numbers 2 ≥ Pe ≥ 20, which allows us to apply this class of schemes for the numerical solution of computational Oceanology problems. The problem of soil dumping was considered as a practical example of application of the proposed schemes.

The paper covers the development and research of computational structure for mathematical modelling of hydrobiological processes for water with complex bottom geometry, based on the modern information technologies and computational methods. The models used in modelling take into account following: microturbulent diffusion; gravitational settling of pollutants; plankton populations nonlinear interaction; the salinity impact, temperature. The scheme with weights was proposed for discretization of the developed model, that allowed significantly reduce the error and the computational time. Practical significance of the work is that the proposed model was software implemented; the limits and prospects of its use were defined. The experimental software was designed on the basis of a graphics accelerator for mathematical modelling of possible development scenarios of the waters with complex bottom geometry, taking into account the environment influence. Parallel implementation was performed using the decomposition methods for computationally labours diffusion-convection problems taking into account the CUDA architecture characteristics.

Recently, the number of vehicles on the roads has increased significantly, including within high-speed transportation corridors. Furthermore, the volume of cargo transportation increases annually not only within the country, but also between different countries. Taking into account these factors, as well as the possibility that unmanned vehicles will soon appear within high-speed transportation corridors, it is necessary to develop intelligent transportation systems that will effectively control traffic flows. Traffic flows are controlled by directional changes in its capacity. In order to interact with road users and road infrastructure, it is necessary to develop an expert system that will make recommendations using the predicted capacity value and information about the current value of the parameters describing the high-speed transport corridor. The article presents a neuro-fuzzy model for predicting capacity by known system parameters and conditions of its functioning, built using the concept of mathematical remodeling. There is also given the results of Sensitivity Analysis based on applying Analysis of Finite Fluctuations depending on external factors. In addition the conceptual and functional models of the developed expert system for regional intelligent transportation system module are proposed.

This article considers the classification problems using the decision trees. It suggests the improved CART algorithm version called clean CART (CCART). The key feature of this algorithm is the reducing of the hardware memory for the tree storing. The main ideas of the CCART algorithm software implementation have been presented. The experimental results of comparison of the original and the presented algorithms for constructing the decision trees confirm that the proposed CCART algorithm has the stated advantage. Therefore, the proposed CCART algorithm is recommended for use in the ensembles of classifiers construction.

Cardiovascular disease is one of the leading causes of death worldwide. Currently, there is an increase in the percentage of people with various heart rhythm disorders. There are permanent (chronic), persistent and paroxysmal form of atrial fibrillation, and the most severe violation is the permanent form. Since the reasons for the development of a certain form of atrial fibrillation are not completely clear, this article presents an analysis of various characteristics that affect the formation of arrhythmias of these species. The most significant signs that can potentially be predictors of different forms of the disease have been identified. Four machine learning methods were used for the analysis: classification trees, logistic regression, random forest, and gradient boosting. The highest cross-validation accuracy was obtained using logistic regression.

In this paper we study the properties of one class of nonlinear means, including a geometric mean, a harmonic mean, and also a power mean of random variables. The considered random variables are assumed to be positive and have finite mathematical expectations. The asymptotics and extremal properties, as well as algebraic properties and inequalities between means are also studied below.

The results of modeling the interaction of a multicomponent thermal cosmic plasma consisting of oxygen ions, hydrogen and electrons with a charged CubeSat 1U microsatellite are considered. For the simulation was used method of molecular dynamics. The characteristic features of the spatial distribution of hydrogen and oxygen ions are considered. Near a positively charged spacecraft, there is a region of negative charge, which eliminate a satellite charge. Behind the satellite is the region of the "ion shadow" in which the concentration of ions is close to zero. The spatial features of the "ion shadow" depend on the type of ion, the temperature of the plasma, the velocity and charge of the satellite relative to the plasma. The process of formation of an "ion shadow" for a number of parameters is considered.

In paper, neural net decoders of nonbinary error correction codes are considered. Analytic methods for calculating of synapse weight coefficients are proposed. It is shown that for codes (n, k) with a small number of corrected errors (n − k ≪ k), it is advisable to use a 6-layer universal classifier based on the feature space of parity symbols. For codes with k ≪ n − k, it is proposed to use a 3-layer classifier on feature space of information symbols.

Solving problems of parametric identification with uncertainty in the initial data due to their inaccuracy and incompleteness complicates, and, in some cases, even rules out the possibility of using classic mathematical and statistical methods as the latter are meant to deal with sufficiently large amounts of observations. These conditions involve the use of specific methods to directly determine the exact type of functional link and to verify its qualitative characteristics. A set of such characteristics also forms an idea of the informativeness of a model. This paper considers the characterization of this concept in relation to parametric identification problems and presents a method of their solution where the procedure of the analysis of informativeness of the obtained models is formalized. Approbation of the developed technique was carried out on the example of parametric identification of the time series model. This time series cannot be linearized. A small number of observations were also known. All these conditions precluded the use of statistical methods to construct a time series model.

One of the approaches to solving parametric identification problems is based on numerical methods. In fact, their use is reduced to the process of iterating over the elements of multidimensional areas of the desired parameters. Increasing the density of the introduced grid increases the amount of calculations and time spent on the process of their implementation. Increasing the density of the introduced grid increases the amount of calculations and time spent on the process of their implementation. In this regard, it is desirable to improve the efficiency of the computer systems used. An important direction in the context of the above is the development of procedures for parallelization of programs. The article presents an algorithm for searching the nodal points of multidimensional areas based on the principle of data decomposition. In regard to solving the problem of parametric identification of the diffuse Bass model of the spread of innovation, its practical implementation has been carried out.

The performed theoretical studies obtained by computer modeling and calculations performed by the semi-empirical method using the MNDO calculation scheme showed the possibility of creating sensitive chemically active probes, which are semiconductor sensor systems with boundary modification, which can act as the tip of the cantilever of the atomic force microscope. These studies allow us to predict that such a sensor based on a modified borocarbon nanotube will react to the presence of ultra-small amounts of substances, which opens up prospects for its use in the field of chemistry, biology, medicine, etc. The use of chemically modified nanotubes, including in atomic force microscopy, is the way to create probes with distinct chemical characteristics.

During the study of adsorption interaction by computer modeling, it was found that adsorption of oxygen, fluorine and chlorine atoms is possible on the surface of a carbon nanotube. In the course of comparing the surface sorption activity of BC₅ nanotubes with respect to various chemical elements, it was found that the interaction of the oxygen atom with the surface of the borocarbon nanotube is the most energetically advantageous. The introduction of boron atoms promotes a more active addition of oxygen, fluorine and chlorine atoms to the surface of the nanotube, that is, structural modification leads to an increase in the sorption activity of carbon nanotubes.

In the paper a review of investigations related to a boiling process at normal conditions of microgravity and at a vibration forcing is presented. The effect of vibrations and a bubble boiling to heat transfer in water was studied. A decrease in temperature of heated wall in both cases as compared to the cases without boiling and vibrations has been shown. The results of modeling the problem on influence of the area of a vapor film on a heat flux of heated surface at various dimensionless governing parameters are presented. It has been shown the influence of the Grashof, Marangoni numbers and the contact angle on heat flux during formatting a bubble from air film.

The article is devoted to the recognition of sound signals, including cough jerks, using various mathematical methods. The paper presents an information system for the diagnosis of patients with pulmonary diseases. The main problem of this system is to determine the parameters of cough fragments in the monitoring record recorded with a dictaphone. Criteria of recognition of cough moments are given, the analysis of processing of sound record is carried out and results of research are systematized. This system can be used by doctors to diagnose the condition of patients, as well as to monitor the treatment process.

The article covers clustering algorithms for dynamic Bayesian networks based on the construction of join tree. Investigated problems associated with simplifying the topology of dynamic Bayesian networks using clustering methods and consider various semantic approaches of junction trees construction. The paper presents a junction tree constructing algorithm for the dynamic Bayesian network that takes into account the transition and perception models applied to the process of network formation. Analyzed The relationship between the complete joint probability distribution for the dynamic Bayesian network and the complete joint distribution obtained for the junction tree. It is shown that the required complete joint distribution of the junction tree for the dynamic Bayesian network can be obtained as a product of local probability distributions for each node associated with the resulting junction tree, and proved that this distribution will be equivalent to the probability distribution of the original dynamic Bayesian network. Introduced the main structural approaches to the construction of junction tree for the discrete dynamic Bayesian network and inspected the use of junction tree for solving similar problems for continuous dynamic Bayesian networks with Gaussian and exponential distribution functions of network variables.

Given article presents a generalized equation for calculating the average coordination number from the density of a random sphere packing, supplemented by a dependence on the threshold value of the interparticle distance in two- and three-dimensional spaces. It is shown that the calculation of the average coordination numbers according to the proposed equation gives an unambiguous correspondence between the simulated, calculated and experimental data for threshold values of more than 1.02 particle diameters. An explanation of the weak dependence of the average coordinate number on the packing density for small threshold values of the interparticle distance is given in this work.

The article describes the results of modeling the oscillation of the impact device elements in the presence of hysteresis damping together with dissipative. The influence of the symmetrical and asymmetric power characteristics on the oscillation mode is considered. For a single-mass model, initial problems are formulated and solved. Under the condition of continuity, an analytical solution is obtained that practically coincides with the numerical one. Initial-boundary value problems are formulated for the tool of an impact device, as a rod of variable section. Problem solving is found by the finite difference method. The properties of two-layer and three-layer difference schemes are estimated. The limiting amplitudes of the oscillations of the rod cross-sections are controlled by the initial-boundary-value problem, which is obtained by the Fourier method. The stress distribution over the rod length is obtained.

In this paper some approaches to solving the problems of flow past around thin profiles are presented. We consider the problem of flow past around a contour defined by a set of segments, each of which is close to the segment ( a; a). A formula that gives an approximate velocities distribution in a flow flowing around a system of thin profiles is obtained. A mixed boundary-value problem for an analytic function in the upper half-plane is studied. A system of singular integral equations having a unique solution up to two arbitrary constants in the class of functions that are boundary values of analytic functions in the upper half-plane is obtained. Considered the generalized problem of flow past around thin profiles for infinite numbers of thin profiles.

The paper is devoted to numerical modeling of the deformed state of physically nonlinear transversely isotropic bodies with an aperture. To solve the problem of the theory of plasticity, a simplified theory of small elastoplastic deformations for a transversely isotropic body is used. In work, to describe the anisotropy of the mechanical properties of transversely isotropic materials, a structural-phenomenological model is used. It allows you to represent the source material in the form of a complex of two jointly working isotropic materials. The main material is considered from the standpoint of continuum mechanics. The fiber material is oriented along the anisotropy direction of the starting material. It is assumed that the fibers perceive only the axial tensile-compression forces and are deformed together with the main material. The presentation of fibrous composites in the form of homogeneous anisotropic materials with effective mechanical parameters allows a fairly accurate calculation of structures with stress concentrators. Based on a simplified theory and finite element method, a computer model of nonlinear deformation of fibrous composites is constructed. The influence of the configuration of holes and a rectangular crack on the distribution of deformation and stress fields in the vicinity of these concentrators is investigated.

The article is devoted to the creation of an algorithm for finding the optimal temperature regime of a chemical reaction based on evolutionary calculations. The problem of optimal control for a chemical process is formulated in a general way. A genetic algorithm for solving the problem is described. A computational experiment was carried out for the synthesis reaction of benzylidenebenzylamine in order to obtain the maximum yield of the product during the reaction. The optimum temperature profile and the optimal concentration of reagents were obtained. Based on the formulated genetic algorithm, a program was developed in the visual programming environment Delphi, which allows finding the optimal temperature profile of the chemical process.

The article reviews the most important results in the field of numerical mathematics obtained by Professor V. V. Strygin's disciples and the disciples of his disciples in 2000–2019 in the city of Samara. We present the results on spline interpolation of functions with a boundary layer, methods and algorithms for a posteriori adaptation of computational grids for singularly perturbed boundary value problems and the results on applied wavelet analysis based on spline wavelets.

This article proposes a method of stability analysis in the sense of Liapunov for systems of ordinary differential equations. The method is based on matrix multiplicative stability criteria obtained from transformations of numerical integration difference schemes. Criteria are formed in the form of necessary and sufficient conditions. A distinctive feature of the criteria is that they do not employ the methods of the qualitative theory of differential equations. Specifically, for the case of linear systems, the evaluation of characteristic numbers and characteristic indicators is not necessary. When analyzing the stability of nonlinear systems, the construction of Liapunov functions is not required. Matrix multiplicative form of the criteria allows computerization of stability analysis. The software implementation of the criteria is performed in real time and, based on its results, allows to make an unambiguous conclusion about the nature of stability of the system under study.

Samples of independent identically distributed random non-negative values ${\mathop{r}\limits^{\sim }}_{1},\ldots,{\mathop{r}\limits^{\sim }}_{N}$ with a finite size $N\ge 2$ are studied. It is posed the problem to find the sufficient conditions for their common probability distribution $Q(x)=\Pr \{{\mathop{r}\limits^{\sim }}_{j}\lt x\},j=1{\div}N$ which guarantee the unimodality of the probability distributions ${F}_{N}^{(+)}(x)=\Pr \{{\mathop{r}\limits^{\sim }}_{+}\lt x\}$ and ${F}_{N}^{(-)}(x)=\Pr \{{\mathop{r}\limits^{\sim }}_{-}\lt x\}$ which correspond to the maximum ${\mathop{r}\limits^{\sim }}_{+}=\max \{{\mathop{r}\limits^{\sim }}_{j};j=1{\div}N\}$ and to the minimum ${\mathop{r}\limits^{\sim }}_{-}=\max \{{\mathop{r}\limits^{\sim }}_{j};j=1{\div}N\}$ of the sample, respectively. It is proved that if the distribution Q is determined by a continuously differentiable Erlang probability density q of an arbitrary order $n\in \boldsymbol{\rm{N}}$ then distributions ${F}_{N}^{(\pm )}$ are unimodal.

Despite the importance of resolving issues related to predicting the formation of heat-moisture fields during storage of grain, seeds and bulk-stored roots and tubers and the changes in technological properties of food raw materials that depend on them, currently, the mathematical descriptions of these associated phenomena do not suffice. This is due to the complexity and poor knowledge of the storage processes for bulk-stored food products at both the micro and macro levels. Such masses are a system with distributed parameters. In this regard, the possibility of predicting the fields of heat and moisture content depends, on the one hand, on the completeness of the necessary information about the moisture and temperature of the components of the mass at the initial moment, and on the other hand, on the reliability of the mathematical model capable of describing the real processes of heat transfer in bulk based on this information, which is used to set boundary conditions and thermophysical constants. An analysis of the nature of the features of heat and mass transfer in a discrete bulk of food product can be carried out only on the basis of the developed analytical models. This is the subject of this paper.

This work is devoted to the study of the distribution of residual plastic strains on outer and inner surface over the length of a cylindrical shell in the process of dynamic deformation generated by a longitudinal impact on its end face. As a mathematical model, the Timoschenko's model was used to describe the dynamic deformation of elastic thin shells, modified for the case of plastic deformations using the Bingham's model. As the boundary conditions, we selected a longitudinal impact applied at the end face of the shell with longitudinal strains constant in time. As a method for solving the resulting system of differential equations in partial derivatives of a hyperbolic type, the third–order ray method was implemented. The paper represents options for the numerical calculation of the distribution of residual plastic strains for various thicknesses, as well as the corresponding shell shape after unloading.

This work is devoted to analysis and research of OLS-estimates properties when identifying parameters of distributed dynamic processes. The study showed that at a low level of observation errors (1% and lower), the use of direct OLS estimates to identify parameters of distributed dynamic processes gives satisfactory results. At the same time, the displacement value is always slightly higher than the value of the standard deviation of the parameter estimate, which does not allow to neglect the displacement, especially at a high and average level of observation errors. The method of obtaining so-called alternative OLS-estimates is also proposed, which allows to reduce multicollinearity in sample statistics and at any level of observation errors significantly reduce standard error of parameter estimation.

The problem of estimating unknown signal parameters in the presence of noise is a classical problem in statistical radio engineering. There are many algorithms for solving this problem. Many of these algorithms are based on the use of well-known statistical optimality criteria in order to improve the estimation efficiency. Therefore, they acquire a high computational complexity. In this article, in order to reduce computational complexity, it is proposed to modernize the classical correlation algorithm based on the new Compressive Sensing theory, which has been actively developed in recent decades. The article presents a new simplified algorithm of signal parameters estimation, outlines operational speed benefits, and compares the efficiency of the proposed algorithm to the efficiency of the classical algorithm as well as some other algorithms. The proposed algorithm has also been compared to the classical one according to computational complexity. Practical implementation of the proposed algorithm requires much smaller number of arithmetical operations with some deterioration in unknown parameter estimation accuracy.

The article describes the results of mathematical simulation and quantitative analysis of the biological property of diversity. The purpose of this work is a methodological generalization of this wildlife property in the form of a cybernetic concept of multialternativity as an evolutionary strategy of functioning of complex systems. The process of mathematical simulation of evolutionary processes in a complex hierarchical ecosystem with the closed-loop trophic cycle is carried out on the basis of the differential equations of mass balance. Several substantive principles given in the conclusions formulate the concept of multialternativity, i.e., the principles of multilevelness, division of functions and discretization. The constructive nature of these principles opens the way to a practical realization of a strategy of multialternativity in the creation of complex control systems realizing various functions.

This article deals with the method of approximate solution of the Cauchy problem for the transport equation based on the Newton interpolation polynomial of two variables with iterative refinement. In each element of the division of a rectangular domain into subdomains, a polynomial approximation of the partial time derivative is constructed. The interpolation polynomial is transformed into the form of an algebraic polynomial with numerical coefficients. In the integrated form, the polynomial is substituted for the dependent variable in the right side of the expression of the partial time derivative. Iterative renewal of the process at a fixed polynomial degree leads to the analogue of Picard's method of successive approximations.

The work is devoted to the construction of effective computational algorithms for modeling vibrations of elastically supported load-bearing systems. An approach is developed based on the representation of a mathematical model in the form of partial differential equations for generalized functions. With this approach, the presence of elements with a very high stiffness in the design made it necessary to carry out the calculation with a very small time step. To build a computational algorithm, a fundamental solution to the problem operator is used, which allows one to obtain a solution at the next time step for each point of the spatial grid independently. The need to carry out the calculation with a very small time step arises only in nodes that coincide with the location of structural elements with very high stiffness. The proposed approach allows simulating impact forces and instantaneous change of boundary conditions. The possibility of using the model with an absolutely rigid restraining support as a limit transition from a model of elastic bond of high rigidity was researched on.

This paper presents the methodology and results of an experimental estimation of the channel width required to transfer traffic from VoIP subscribers connected via VPN technology to IP ATC Asterisk. OpenVPN technology with typical settings (tun interfaces, routed network segments and TCP transport protocol) was used. An updated tool for estimating the volumes of transmitted and received traffic was used, based on data processing from the ipcad sensor — an emulator of the Cisco NetFlow mechanism for linux routers. The operator representation of extracting information about single network sessions is used.

The paper considers a mathematical model for managing a website of a company operating in a competitive environment. Management is carried out in order to maximize profits. Optimal control actions is determined using Pontryagin's maximum principle. Numerical solution is obtained using iteration algorithm based on gradient descent method. The obtained results form the basis of a software application that can be used as a management decision support system.

The model problem about the axisymmetric quasistatic motion of an elastic sphere considering the interaction with inner surface of a rigid cone die is investigated. The constitutive model is represented by the physically nonlinear generalization of the linear model of Hencky's elastic material. The tensor of logarithmic strains is used by way of strain measure due to described below special properties. The influence of friction on macro characteristics of a process is studied using proposed numerical model of accounting of mixed boundary conditions on time-changing contact surface.

A mathematical model of the axisymmetric flow of cohesive granular materials is considered. A plastically compressible material is considered as a mathematical model. This material has an additional characteristic - its own rotation of particles. The existence of this characteristic leads to the asymmetry of the stress tensor and the presence of torque stresses. Asymmetric components of the stress tensor are balanced by normal pressure due to the presence of rolling friction. It is shown that the distinctive characteristic of the axisymmetric state is the layering of its flow. The condition for the flow of cohesive bulk material is obtained.

An analytical matrix method that makes it possible to calculate the distributions of nonequilibrium minority charge carriers generated in multilayer planar semiconductor structures by external influence is described. For the case of generation of nonequilibrium minority charge carriers by a wide electron beam in a two-layer structure, the results of model calculations using the analytical matrix method with the results of calculations using a numerical conservative difference scheme are compared. It is shown that the method allows to carry out calculations of the distributions of nonequilibrium minority charge carriers in a relatively short time with an accuracy sufficient for practical use in electron probe technologies.

The paper considers the plane strain of a compressed elastic strip made from incompressible material. The deviation of the cross-section contour from the rectangle, as well as the intensity of the force applied to the upper and the lower edge of the section are known up to small parameters. The authors have carried out a study of the problem solution analyticity with respect to small near zero parameters. With the help of the perturbation method, they have found a solution for a particular case of the function describing the deviations up to the second order of smallness. It has been shown that if an experimental research is carried out and the applied force meets the condition described, the average stress and displacement values will differ from those typical for homogeneous state only by a second order infinitesimal.

The study on the optomechanical effect (photostriction) in the material used in 3D printing by layer-by-layer photopolymerization is performed. The calculation - experimental model in the form of a steel console plate with the one-sided photopolymeric coating is developed for studying of this effect. The experimental setup including UV source, the set of irradiated identical consoles, part of which had the photopolymer coating, the speckle-interferometer device for registration of bending micro displacements of the consoles called by photostriction shrinkage of the coating, is collected. The temperature bending of the plate during is irradiation by the UF-source was determined. The Magnitude of the optomechanical shrinkage in comparison with the temperature bending of the plate with a photopolymeric coating at the fixed radiation time is experimentally determined. The technique is developed for calculation and allocation of the optomechanical effect against the background of temperature bending of the plate with a photopolymeric coating and value of earlier undetermined coefficient of linear dilatation of the photopolymer is obtained. Also the residual stresses which generate in the coating owing to optomechanical effect are defined.

In the present paper, we describe a model of a prestressed inhomogeneous body and provide the variational and weak statements. On its basis, we study a problem of mixed vibrations of a non-uniform plate with inclusions and a sandwich-structured three-ply plate under the conditions of the residual stress-strain state. We build the numerical finite-element solution on the basis of the weak problem statement and analyze the effect of the prestress states on its frequency response functions. In addition, we identify the prestress level in the middle layer of the composite plate by the data on frequency characteristics measurements.

A model device of the liquid rocket engine mixing head for experimental determination of hydraulic non-uniformity of fuel distribution is described. Schemes of hydraulic and gas-dynamic test benches are given. The results of the planned factor experiment to determine the array of flow rates through individual sprayers are presented. Neural network regression factor models were created to evaluate the criterion of non-uniformity. The influence of various factors on the parameters of non-uniformity is estimated

Numerical procedure for analysis of eigenfrequencies and eigenfunctions of ultrasonic medical instrument waveguide is presented. A curved beam of variable cross-section is considered as a design scheme for the waveguide with respect to different boundary conditions. Test analysis for clamped-free curved waveguide is developed with MathCAD complex.

We consider the problem of a rapidly rotating disk in the elastic-plastic state. The piecewise linear plasticity condition in general form is chosen. It is believed that all plastic curves have the common point of intersection which corresponds to uniaxial tension. For external parameters, we obtain the conditions that determine the probability of inception of plastic zones. It is shown that plastic zones could incept in the center of the disk and/or on the boundary of it. The problem in the plastic zone is statically determinate. The case when the plastic zone occupies some central part (core) of the disk, where one regime of plastic condition is fulfilled, is considered. In order to estimate the stress state inside the elastic zone of the disk, equivalent stress which is equal to the chosen plasticity function is defined. In order to define the relationship between plastic deformations and stresses, the piecewise linear plastic potential being equal to the plasticity function is chosen. The plastic incompressible body is considered. The associated flow rule can be integrated so that the problem of getting displacements turns into quasistatic one. The problem of determining displacements in the plastic region leads to a first-order differential equation with respect to the radial component of the displacement vector. Therefore the continuity condition for displacements at the elastic-plastic boundary and the assumption that the displacements in the center of the disk are equal to zero leads to an overdetermined problem. So, only the continuity condition for displacements at the elasto-plastic boundary is accepted. It is assumed that plastic deformations at the elastic-plastic boundary are equal to zero. It is shown that displacements at the center of the disk are equal to zero automatically for all piecewise linear conditions of plasticity apart from the Tresca yield criterion. For the Schmidt–Ishlinskii yield criterion, all deformations at the center of the disk attain finite values. Meanwhile, for other piecewise linear conditions, plastic deformations at the center of the disk attain infinitely large values. This explains the discontinuity of displacements at the center of the disk for the Tresca yield criterion. The calculation results are presented as graphs of stresses, displacements, and deformations.

The modeling of the phenomenon of reflection of the front edge of a longitudinal shear crack from a stressed boundary is considered. The front edge of crack is modeled by an extreme along the edge rupture of rates and stresses exceeding the plastic limit propagating as an orthogonal trajectory of a longitudinal wave of plastic loading. The dependence of the intensity of the reflected cracks of a simple shear and detachment (as a function of the angle of incidence of the initiating crack) on the stress at the boundary at the moment of reflection and on the physical constants of the material is investigated. The conditions for the absence of reflected cracks of shear and detachment and criteria for boundary stresses initiating the cracks of various types are obtained.

Mathematical modeling of branching of the leading edge of a longitudinal shear crack on a porous inclusion is proposed. The leading edge of the crack is approximated by the δ-neighborhood of the plastic deformation of the material with the front of longitudinal or shear waves, at which the longitudinal or transverse velocities break when passing through the leading edge of the crack. Expressions are obtained and graphs of the relative intensity of the leading edges of the reflected cracks of longitudinal and transverse shear and the conditions for the generation of reflected cracks depending on the angle of intersection of the crack with inclusion and physical parameters of the material are constructed.

On the basis of the viscoplastic fluid rheological model, which takes into account the manifestation of the "solidification" effect, a flow has been simulated in the annular cross section channel. It is shown that, depending on the pressure drop level, three different flow patterns are possible. For each pattern, the expressions that determine the fluid velocity distribution in the channel's cross section have been obtained. It is shown that the dependence of the volume fluid flow rate on the pressure drop is not monotonic. Moreover, the increase in the pressure drop critical level ultimately leads to the flow rate decrease due to the narrowing of the channel's passage section, which is caused by the formation of the "solidified" liquid layers.

The paper adopts an approach to predicting the laminar-turbulent transition onset, which is based on the hypothesis of a threshold "connection" of the transverse viscosity factor and the subsequent transverse velocity components "generation". In the framework of this approach, certain empirical local transition conditions are proposed and imposed on the dimensionless invariant complexes that characterize the laminar flow under study. Based on these conditions, an analysis of the Poiseuille flow transition onset in the flat channel in the presence of the stationary velocity field periodic background perturbation is carried out. A comparison with the known experimental data is presented.

This paper exposes the strain potential of the quadratic theory of elasticity for isotropic media. The strain potential is represented as a sum of the quadratic and the cubic part. A system of experiments, carried out to define five constants included in the potential, is exposed. Different variants of building quasi-linear correlations are discussed. The rationality of linearizing constitutive correlations by reducing the degree of the potential's cubic part by division by the quadratic convolution module of stress tensor components is doubted because the correlations thus found are lengthier than the correlations from the quadratic elasticity theory.

In this paper the earlier elaborated finite-element method of calculating the stress intensity factor for stationary cracks at dynamic loading by means of cohesion finite elements and on the basis of the method of lines is generalized for high-velocity cracks. The method in question does not require rearranging the finite-element mesh. The crack growth is modeled by consecutively releasing the nodes located on the crack line. The calculated data are compared with the analytical solutions of other researchers and with the experimental data.

The free vibrations of cylindrical shells with rectangular cross-section are studied in the work. The precision of Rayleigh method for various admissible functions and different boundary conditions is evaluated. Using finite element method, the natural frequencies in the case of deviation of the cross-section shape from square to rectangular are examined, and the vibration frequencies and modes for the shell joined with the plate are studied for various plate thicknesses. Additionally, fundamental frequency behavior is analyzed in the case of fixed support, as one of the cross-section sides approaches zero.

Many recent studies have focused on specifics of behavior of materials under dynamic loading as it is considerably different from cases with quasi-static loading. This paper considers the method of magnetic pulse deformation of metal rings, which is a continuation of the authors' research. [1]. The methods used in the experiment, which are described in this paper, allow to carry out laboratory studies into material deformation at a speed reaching the values of around 10⁷c⁻¹. This paper is dedicated to building a mathematical model for determining the stress in the test samples under dynamic loading of materials by the magnetic pulse method.

The paper deals with the possibility of modifying pyrolyzed polyacrylonitrile with amorphizing additives. Adsorption features of the boron atom on the surface of the monolayer of polymer are studied, and the geometric and electron-energy characteristics of the composite obtained are established. The calculations were performed using the semi-empirical MNDO method within the framework of the molecular cluster model.

Separation of two meteoroid bodies is studied using modelling method based on a system of grids and solving adjoint aerodynamic and ballistic problems. Bodies of the same mass but different shapes were considered. Calculations were done for different combinations of the cylindrical bodies with their cross sections having a shape of square, elongated rectangular and circle. Initially the bodies were placed near each other on the line perpendicular to the flight direction. The lowest value of separation velocity was obtained for the bodies with circular cross section; the separation velocity is significantly increased for the bodies with elongated rectangular cross section due to rotation. Stable aerodynamic position of the bodies with elongated cross sections occurs when the bodies fly with a large side perpendicular to the flight direction. The lateral velocity acquired by each body appears to be primary determined by its own geometry and show no dependency on the shape of a neighboring body.

The torsion of inhomogeneous rods made of ideal rigid plastic material is investigated in this work. The integrals determining the stress and strain states of a rod under linearized plasticity condition are obtained. The field of characteristics of the basic relations is constructed, the rupture lines of stresses are found.

The study looks upon the process of physically nonlinear deformation of isotropic and transversely isotropic homogeneous continuous solid bodies made from fibre composites where the reinforcing elements are far more rigid than the binder. The study offers an approach to writing out an explicit solution to a problem that effectively links a small parameter to the method of boundary states. Equations of the medium are presented as power series of small parameters. Each decomposition step calls for a solution of a linear elasticity problem, which is adequately addressed by the method of boundary states. Below are the results of solving test problems featuring an isotropic cube and a transversely isotropic cylinder with homogeneous boundary conditions. In both cases high accuracy is achieved as early on as the third iteration. Also presented is an axisymmetry problem for a transtropic cylinder with inhomogeneous boundary conditions. In this case accuracy depends on the values of small parameters. For all of the problems described we provide a detailed accuracy analysis and draw conclusions as to convergence.

The study considers a statement of geometrically non-linear problems of isotropic theory of elasticity for a simply connected bounded body. The Lindstedt–Poincaré method reduces the problem to a weakly non-linear variation containing a small parameter. The solution is then effected at each step of the perturbations method through the means of the method of the boundary states with perturbations (MBSP). Each iteration is accompanied by a generation of fictitious volume forces of a polynomial nature. The study proposes a strict particular solution and a solution of an elasticity problem for iteration. The approach is also applicable to thermoelasticity problems. The method is tested on classical axially symmetrical bodies, i.e., cylinders subjected to uniaxial tensioning or twisting. The study confirms the applicability of flat section hypotheses to linear engineering calculations. Nonlinear distortions mostly happen at the first iteration, followed by a weak correction. We also provide a calculation for and an illustration of a stress-strain state (SSS) of a semicylinder under unbalanced axial loads and a concentration of compression stresses in extended bodies' middle areas that are remote from load-free surfaces.

An approximation of matrix Green's function for a hyperbolic system of linear differential equations of the first order has been created. An algorithm for an approximate solution of the generalized Riemann problem of discontinuity decay in the presence of additional conditions at the boundaries has been proposed. A computational algorithm for the approximate solution of boundary value problems for hyperbolic systems of equations has been set up on the basis of these solutions. The algorithm is implemented for a system of equations describing the propagation of elastic waves in a block-fractured medium. The results of the numerical experiments aimed at studying the possible mechanisms of propagation of elastic waves to a considerable depth without scattering have been presented.

A variant of the relations of nonlinear elasticity is considered for anisotropic materials which are supposed to be crystals of cubic syngony with respect to the type of elastic symmetry. The proposed model takes into account the physical nonlinearity in the behavior of such materials under the condition of small deformations. Based on the representation of the elastic potential in the form of a tensor polynomial in third-order strains, relations for stresses with elastic constants of the second and third orders are obtained. On the basis of the concept of the elastic eigenstates of materials, in the case of a cubic material, representations for the elastic tensors of the fourth and sixth ranks in eigentensor bases are obtained. The proposed variant of constitutive relations takes into account the mutual influence of the processes occurring in various eigenspaces of cubic material.

In this paper, the stability of a cylinder with circular and elliptical section made of compressible and incompressible nonlinear elastic materials under finite perturbations is considered. A set of computational experiments was performed. The permissible boundaries of the region with respect to final and initial perturbations for given parameters of loading and structures are established. Finite sequences of bifurcation points are constructed, confirming, in contrast to stability at small perturbations, the existence of a hierarchy of stable equilibrium states. Classical linearized stability theories are evaluated. New phenomena and characteristic effects are established.

An experimental program has been developed to identify the type of initial elastic anisotropy of the material. The program includes a series of compression experiments to determine the orientation of the principal axes of anisotropy of the material and additional experiments to find the orientation of the canonical axes of anisotropy. In order to distinguish isotropic and cubic materials, it is necessary to fulfill an experiment on biaxial tension-compression in the direction of two canonical axes of anisotropy, and a shear experiment in the same plane. Similar experiments make it possible to identify trigonal, tetragonal and hexagonal materials. To identify triclinic, monoclinic, and rhombic materials, three shear experiments in planes determined by the canonical axes of anisotropy are required.

The paper aims to clarify the rules of calculation of steel-reinforced concrete bridge superstructures on the basis of generalization of modern scientific achievements in conjunction with the possibilities of computational software and computer technology in the field of calculations of multi-component sections without the need to use simplifying hypotheses that affect the accuracy of the calculation. An algorithm for calculating continuous multi-span beams of bridge structures with the possibility of taking into account the flexibility of the shear joint between concrete and steel structural elements is proposed, which increases the accuracy of determining the stress-strain state (SSS) of the structure. The results of the work can be used in the design of steel-concrete bridge superstructures. The significance of the work lies in the fact that the proposed analytical dependences in the joint use of modern computing power will clarify the calculation of steel-concrete bridges, thereby increasing the level of reliability of bridge structures, laid at the design stage.

The stress distribution in shells of variable thickness must be taken into account when designing various elements of general and transport engineering, aviation, rocket and space technology, structures. The paper presents one of the possible approaches to the dynamic calculation of a thin-walled non-circular conical structure rigidly fixed along a beveled end section. The resolving system of ordinary differential equations was obtained in the framework of the technical theory of shells using the variational Lagrange principle. The boundary-value problem of determining dynamic stresses in the structure under consideration under the influence of a harmonic load is solved numerically by the method of orthogonal sweeping of a system of linear ordinary differential equations of the first order. In contrast to the known works, a variable thickness of the structure along the length is considered.

The paper reveals the ideas of assessing the road condition on the basis of risk theory, which allows predicting the rate of the road structure destruction and its actual life. The regularities of the influence of physicomechanical parameters of road construction materials, as well as the coefficient of variation of the required modulus of elasticity of the subgrade on the value of the equivalent modulus of elasticity and the rate of destruction of pavement are established.

The statement of the problem and the algorithms for calculating thin-walled rods of arbitrary section under spatially variable loading based on the theory of small elastoplastic deformations and the refined theory of rods are presented. Using the variational Lagrange principle, mathematical models are developed for the deformation and damage of thin-walled rods in a cylindrical coordinate system. A system of differential equilibrium equations for a rod with spatially variable loading in vector form is obtained. To solve the boundary-value problem, the central difference scheme of the second order of accuracy and the matrix sweep method are used. An example of calculation is given.

The article is devoted to the digital processing interferograms (isochromatic fringe patterns) obtained by the photoelasticity method. The application to interpretate the isochromatic fringe patterns allows us to automate image processing, gets to avoid the routine and time-consuming work. The features of the developed software package are described in detail by means the problem of stretching plate with two symmetrical edge notches. The application's algorithm includes following main steps: image pre-processing, localization interference fringe, fringe tracing. The application creates a text file containing all the necessary data to further determine the stress-strain state (isochromatic fringe's number and locus of fringes).

With the help of current approaches in mechanics of additively manufactured deformable solids, a non-classical mathematical model is developed to predict the stress-strain state of layers being gradually formed on a rotating substrate in an arbitrary number of continuous stages of ageing viscoelastic material application. On the basis of numerous calculations performed, the qualitative and quantitative features of the internal technological stresses distributions in the finished cylindrical product for different variants of its release from the mechanical loading and the kinematic bonds acting during the manufacturing process are analyzed in detail. Previously unknown mechanical effects are found. The appropriate recommendations of a practical nature are given.

Using the fast expansion method, we obtained several exact solutions of the boundary value problem for the Poisson equation in a rectangular domain. We have given graphs of exact solutions corresponding to different boundary conditions and different types of the Poisson equation free term. We showed the influence of the type of boundary conditions and the right-hand side on the type of exact solution. We obtained a solution to the problem of membrane deflections under the action of variable load. We have given graphs of the stress components, from the analysis of which it follows that the greatest stress is in the middle of the rectangular membrane long sides.

Formulas are given for the fast expansion of a smooth function on a segment, which allows one to increase the rate of convergence of the Fourier series unlimitedly depending on the order of expansion. The theorems on the convergence of a series in fast expansion, the possibility of its multiple termwise differentiation, the uniqueness of fast expansion, are proved, and the error in the residual series in fast expansion is estimated. Algorithms for applying fast expansion are given, the concept of the fast expansion operator, which is necessary for solving nonlinear integro-differential problems, is introduced.