bluuebunny/crossref_metadata_2025 huggingface dataset:
Poisson processes directed by subordinators, stuttering poisson and pseudo-poisson processes, with applications to actuarial mathematics
Authors: Rusakov O , Yakubovich Yu
Published: December 2021

Weconsider a PSI-process, that is a sequence of random variables (&), i = 0.1,…, which is subordinated by a continuous-time non-decreasing integer-valued process N(t): <K0 = ÇN(ty Our main example is when /V(t) itself is obtained as a subordination of the standard Poisson process 77(s) by a non-decreasing Lévy process S(t): N(t) = 77(S(t)).The values (&)one interprets as random claims, while their accumulated intensity S(t) is itself random. We show that in this case the process 7V(t) is a compound Poisson process of the stuttering type and its rate depends just on the value of theLaplace exponent of S(t) at 1. Under the assumption that the driven sequence (&) consists of i.i.d. random variables with finite variance we calculate a correlation function of the constructed PSI-process. Finally, we show that properly rescaled sums of such processes converge to the Ornstein-Uhlenbeck process in the Skorokhod space. We suppose that the results stated in the paper mightbe interesting for theorists and practitioners in insurance, in particular, for solution of reinsurance tasks.
Modelling of manufacturing process on the example of electro-pneumatic control unit
Authors: Tkachenko S N , Shpilevoy A A , Zakharov A I , Burmistrov V I , Stavitskaya E P
Published: December 2021

The work describes the developed imitative model of manufacturing process on the example of control unit, specifically a plate, and testing of its performance. The process of model development is performed in AnyLogic software. Authors demonstrate modeling results and formulate manufacturing process optimization recommendations on its basis. The article shows expediency of imitative model applying for checkout of technological operations.
Interval forecasting of time series using orderstatistics
Authors: Misyura V , Bogacheva M , Misyura E
Published: December 2021

In the traditional approach of obtaining time series forecasts based on the selected model, the model parameters are first estimated, then a point forecast using the obtained estimatesis made and then an interval forecast with a given probability is made. In the article the authors propose a nonparametric method for obtaining a single-stage interval forecasting of a time series based on constructing predictive and target variables sets using robust statistics and obtaining the forecast boundaries by constructing linear regression models. The predictive algorithm is based on the problems of estimating the parameters of linear multiple regression using a model regularization methods. The results of forecasting prove the expediency and effectiveness of the proposed method.
RUN-BOT: mobile robot for running exercises
Authors: Kudinov Ya , Izumov A , Lobanov S , Obuhov P , Marchenko E
Published: December 2021

This article describes the operating principle of a mobile robot for running exercises RUN-BOT, shows a visual model, demonstrates photos of a testing prototype, describes the algorithm of the robot’s work on a real work-area. The functional model of the robot’s operation and a brief justification for the choice of electronic components are also described.
Planar kinematic grids created on the basis of triangulation
Authors: Buzalo N , Kurbanov A , Sheina S , Tsaritova N , Tumasov A
Published: December 2021

Activities to protect historic cities and the revival of areas of historical importance are accompanied by a desire to maximize the entry of the natural environment into the city. Architects and builders often go on the use of non-standard design solutions to create a beautiful, healthy, beloved city. They widely use spatial coating constructions as the forms closest to natural. Construction with curvilinear outlines, that V.G. Shuhov had invented and patented in XIX century, had become the basis of modern architecture. The reticulated shells have unlimited possibilities for creating new architectural forms. The growing number of structures constructed using this technology indicates the prospects for the use of such structures, especially at low temperatures, in seismic and remote areas. The design of reticulated shells is self-supporting and has higher bearing properties compared to other types of structures. This is due to the uniform distribution of loads on all the rods of the structure, which virtually eliminates brittle fracture. The aerodynamic shape of the reticulated shells provides the best wind flow compared to other structures, which makes them stable during destructive hurricanes and tornadoes.
Digital models of parametric structures
Authors: Kravchenko G , Panasyuk L , Trufanova E , Pudanova L
Published: December 2021

Formation of parametric structure digital model are considered. Investigation was based on the analysis of the shaping evolution of the analytical surface in the form of a hyperboloid of rotation. Finite element frame represents a spatial plate-rod system has been developed during creation of the digital model. This scheme allows to study the effectiveness of constructive solutions under dynamic influence at the design stage. Dynamic characteristics of various design solutions are considered in process of choosing a rational variant of the building frame. The influence of the inclusion of outrigger floor in the model of the frame at various levels of the building are investigated. The proposed method of research and application of the possibilities of the shaping evolution allows to proceed to the modernization of BIM technologies in the design of unique buildings. Recommendations for refining the algorithm for studying parametric object digital models were developed.
An illegal user model of communication channel with error correction codeс
Authors: Mogilevskaya N S , Dolgov V V
Published: December 2021

The situation when an illegal user intercepts data from the communication channel of two legal users is considered. The data in the legal channel is protected from distortion by error correction codes. It is assumed that the intercept channel may be noisier than the legal channel. And, consequently, the interceptor receives low-quality data. The possibility of using a special type of error-correction code decoders by an illegal user to restore damaged data is discussed. The interceptor model is constructed. The model includes a receiving block of the intercept channel, as well as several auxiliary blocks, such as a memory device, a block for determining the quality of communication in the legal channel, databases with possible decoders and their parameters. Examples are given that show the potential capabilities of the interceptor. The examples demonstrate the difference in decoding quality between different decoders for LDPC codes and Reed-Muller codes. These examples show that an illegal user with the various decoders described in the open press can receive information with satisfactory quality even at a weak signal level in the intercept channel. The constructed model can be useful in the tasks of developing methods of protection against intruders who organize illegitimate data interception channels.
Decision-making system with homo and hetero elements
Authors: Fathi V A , Ganzhur A P , Ganzhur M A , Dyachenko N V , Shabanov R M
Published: December 2021

Experts from all over the world provide an opportunity in filling decision-making systems. But the filling of decision-making systems with data does not have an exact quantitative characteristic. It is good when the expert is completely confident in the decision. But some decisions can add up to their own internal assessment without justification or experimentation. Other decisions are hampered by past experience. To overcome this type of problem, it is necessary to develop a system that will be based on clear and fuzzy data behaviour. This article is aimed at describing the method for constructing a decision-making system on clear and fuzzy data using Petri nets.
The list algorithms accuracy characteristics improvement based on Krohn’s algorithm and its modifications
Authors: Kobak V G , Zolotykh O A , Zolotykh I A , Poliev A V
Published: December 2021

The research of algorithms for uniform loading of devices for homogeneous information processing systems is a very important science-intensive task. An experimental approach was chosen for the research. This is primarily due to the fact that the analytical solution of the distribution problem gives solutions that are far from reality, since it is unable to take into account many factors that affect the computing machine during its operation. The aim of this research is to improve the accuracy characteristics of the list algorithms through the use of heuristic algorithms, such as Krohn’s algorithm and its modifications. This made it possible to obtain a more even distribution of tasks among executive devices, which can be networked workstations, processors or processor cores. The work uses list algorithms, such as the Critical Path algorithm and Pashkeev’s algorithm, as well as heuristic algorithms - Krohn’s algorithm and its modifications. The main idea of the research is to obtain the best suboptimal solution by improving the quality of the resulting distribution. In this case, with the help of the list algorithms, the initial distribution is formed, and its refinement is carried out through the application of the Krohn’s algorithm and its modifications. In fact, in the work, a number of symbiotic algorithms are examined and analyzed. For this, many computational experiments were carried out and a large amount of output data were collected, on the basis of which conclusions were drawn about the effectiveness of the solution obtained for each symbiotic group and for all groups as a whole.
Experimental modeling of the interaction of hard and aeriform body and the onset of a drag crisis with a significant change in velocity
Authors: Kudinov N V , Atayan A M
Published: December 2021

The paper deals with the possibilities and prospects of experimental modeling of the interaction of a solid and a gaseous body. It is assumed that reliable experimental data have already been obtained and published. The problem of approximating the complex aerodynamic characteristics of air flow around a spherical body is posed and solved. The study was carried out using the «Cut-Glue» method for approximating numerical information about blowing experiments. Generally, this information reflects the dependence of the drag coefficient on the Reynolds number. The choice of the Cut-Glue method for the approximation of complex, multiextremal characteristics that can be obtained in physical experiments is substantiated.
Nonlinear stochastic filtration of satellite measurements
Authors: Reshetnikova I V , Sokolov S V , Manin A A , Polyakova M V , Gerasimenko M S
Published: December 2021

Existing methods for processing satellite measurements are based on the use of either the least squares method in different versions, or with the known model of motion of an object – various modifications of the Kalman filter. At the same time, the Kalman approach is more accurate, since it takes into account the dynamics of the movement of the object and the history of estimates, but its significant drawback is the need for a priori knowledge of the equations of motion of the object. In this regard, a new approach is proposed to assess the navigation parameters of the object by satellite measurements. On the one hand, this approach takes into account the dynamic nature of motion parameters and the history of estimates, and on the other hand, free from restriction in the form of accurate knowledge of the equations of motion of an object. The effectiveness of the considered approach in comparison with the existing traditional methods of processing satellite measurements is confirmed by the results of numerical modeling.
Optical digital-to-analog converter for N-digit logic-based processing circuits
Authors: Reshetnikova I V , Sokolov S V , Manin A A , Polyakova M V , Sokolova O I
Published: December 2021

The possibility of synthesis of ultra-fast universal optical digital-to-analog converter (DAC) providing conversion of digital information into analog information in giga- and terahertz ranges, including in digital systems based on N-digit logic, is considered. The functional diagram of the optical DAC containing technologically well-developed optical elements is given, the principle of operation is described in detail. The possibility of implementing this DAC with the speed potentially possible for optical data processing circuits is shown.
On one case of quasi-correctness of the static boundary value problem for shells of rotation
Authors: Tyurikov E V , Polyakov A S
Published: December 2021

Within the framework of the membrane theory of convex shells, a static boundary value problem is studied for one class of spherical domes.
About the features of the least squares method with linearization when determining nonlinear parameters of functional dependencies
Authors: Azarova Lidia V
Published: December 2021

The features of approximation of empirical data by functional dependence with nonlinear parameters using the two-stage least squares method are considered in this paper. A method of simplified parameter estimation by constructing a new expression that depends on the parameters in a linear way is described. To obtain the final solution, the least squares estimation of the main dependence linearized in terms of parameters is performed. The influence of various forms of noise imposed on the theoretical dependence on the approximations is modeled.
Modeling of the processes of extracting rules from Neural Network components with Petri nets
Authors: Marshakov D V
Published: December 2021

The paper deals with the use of extended Petri nets in modeling the processes of extracting rules from neural network components. The mathematical model for extracting rules from neural network components based on a modified timed Petri net is constructed, followed by an analysis of its dynamic behavior based on a timed reachability graph, which is a set of all its states that can be reached when a finite number of transitions are fired. The proposed model allows us to move from the initial detailed structure to its simplified description, which preserves the possibility of obtaining information about the structure and dynamic behavior of the neural network system. The proposed approach can be used in the synthesis of cognitive systems with a neural network organization to provide computational support for the functions of forming, learning, and correcting cognitive networks that display neural network models.
Method of creation of a two-level neural network structure for solving problems in mechanical engineering
Authors: Volkov A , Varlamov O
Published: December 2021

There is an industrial trend of increasing technological effectiveness of production and growing autonomy of factories, resulting in generation of huge amounts of raw data that can be used to improve efficiency and continuity of industrial plants operation. Big data collection, processing and analysis technologies are already being actively implemented. Further use of big data will help with a variety of tasks, such as optimization and process monitoring, quality control of equipment and produced parts, modeling and forecasting of the facility operation and other mechanical engineering challenges. A new method of creation of a two-level neural network structure is proposed, designed to solve a number of problems by training individual neural networks for each subset of data used in the task at hand. This method combines two levels of information processing: the first level of the neural network classifier and the second level, which includes several neural network analyzers. Depending on the specific subject area and the data sets available, it is possible to use the method to solve various problems in mechanical engineering. The method allows to add new neural network analyzers and expand the scope of application. The practical application of the method in solving the problem of text message sentiment analysis is shown and an example of the Python programming language software implementation of the two-level structure is given. Use cases for the two-level structure method in mechanical engineering tasks are proposed. In addition, the proposed method can be used as a part of the hybrid intelligent information system that includes mivar expert systems. Combining neural networks with mivar expert systems as part of a hybrid intelligent information system is a promising direction for the development of artificial intelligence for mechanical engineering.
Modeling of complex structured processes using discrete iterative networks and petri nets
Authors: Korneev A , Lavrukhina T , Smetannikova T , Glazkova Yu
Published: December 2021

The paper considers the use of discrete iterative networks and Petri nets in the modeling of complex structured processes. In general, the production process is represented as a composition of machines. Probabilistic finite machine are modeled to select optimal solutions from a certain set of alternative solutions. Alphabets of finite and probabilistic machines are formed on the basis of discrete optimization methods when modeling multi-stage productions. The processing mode adaptation block is used to change the alphabets when the production conditions are changed. Using the alphabet generation block allows you to choose the optimal value of the alphabets of the random variables under study. During modeling complex systems and developing algorithms for managing them, the presence of ambiguous functional relationships between factors and quality indicators is taken into account. Methods of modeling complex spatially distributed objects based on a hierarchy of machines belonging to a predetermined finite number of machine types using iterative networks and Petri nets are described.
Calculation of accuracy with the coordinate-positional method of basing
Authors: Kovalevich M , Neypert T , Davydov P
Published: December 2021

The article is devoted to the assessment of assembly accuracy when positioning with the use of industrial manipulators (robots). Classic assembly technologies are outdated and have many disadvantages that can be solved by the automation of industrial processes, which became possible due to the rapid development of robotization. In the material there are investigation the possibility of using industrial robots for positioning structural elements of aircraft from the point of view of achieving the required assembly accuracy. For the analysis, foreign literature sources and the current experience of introducing similar technologies by large aircraft manufacturers were used. To assess the assembly accuracy, the formulas for the functional size error were used. An enlarged technological assembly process is presented, graphic materials with basing schemes are presented. Based on the data obtained, the advantages and disadvantages of basing with the help of industrial robots at this stage of technology development are formulated, taking into account the existing production experience.
Fuzzy modelling of the transportation logistics processes
Authors: Chislov O , Lyabakh N , Kolesnikov M , Bakalov M , Bezusov D
Published: December 2021

The relevance of mechanisms and fuzzy modeling methods used in transport and logistics processes is justified. The logic of the transport and logistics chains study by their decomposition into separate economic entities with subsequent synthesis, with taking into account their conflicting interests, is presented. The task of managing transport and logistics processes is set within the framework of the conceptual positions of the fuzzy sets theory: the use of linguistic variables, the concept of a fuzzy set, fuzzy inference, implemented on the basis of fuzzy sets operations. In this study, the fuzzy modeling on the bottom-up conclusions from the premises to the conclusion was used. Various methods of implication and defuzzification have been analyzed. An iterative procedure for managing transport and logistics chains and their links has been proposed, which ensures the adaptation of the process to the specified performance indicators. A calculated example is given for a marshalling yard as a link in the transport and logistics chain.
Ford-Fulkerson algorithm refinement for the cooperation effectiveness increase of intensive and low-density lines
Authors: Kovalev K E , Novichikhin A V
Published: December 2021

The article describes tools of the railway control on intensive and low-density lines which is directed on the effectiveness increase of low-density line functioning, for the solution of perspective tasks of the railway network functioning and development. For the too realization the oriented graph with the Ford-Fulkerson algorithm which allows determining the maximum flow and the minimum cut for non-oriented graphs. Firstly as values of graph tops inverse values of the station rating and as graph edges inverse values of the railway line class are accepted. The use of this approach allows determining the maximum flow in the system and provides the clear view of relations of transportation capacities of railway lines and stations.
Approach to formalization of the intelligent information control systems based on the topos theory
Authors: Avsykevich D , Tupitsin Yu , Shishkin E
Published: December 2021

The approach to formalization of complex organizational and technical systems based on the toposes theory is substantiated. The article presents a review of the literature on the formalization of knowledge. An integrated control system for technical complexes is considered. The description of blocks of intelligent information and control systems based on the toposes theory is developed. An algorithm for formalizing intelligent information and control systems and an example of constructing toposes and functors for the general case are presented. The conclusion is made about the possibility of applying the proposed approach to the formalization of the intelligent information and control systems in the process of formation of their appearance.
Mathematical model for organizing storage and providing access to files in distributed information systems
Authors: Egorov A , Makshanov A , Krupenina N , Tyndykar L
Published: December 2021

Existing solutions for data exchange problem are considered. Installation feasibility and use FTP-server as an effective tool for storing and providing access to files is analyzed. Technical aspects of its work, as well as the tasks range that can be solved with its help are specified. Within the adaptive information system limits the general interaction functional structures scheme of the distributed FTP-server is resulted, and as the presence concealment scheme of storehouses by a controlling server at connection at the client. The mathematical storage model organization and access to files, allowing to realize rational files distribution sent by the client among available storages, is described.
Mathematical model for the reinforced concrete with nonlinearity behaviour of bond
Authors: Samoshkin A , Tikhomirov V
Published: December 2021

The article developed a mathematical model describing the deformation of reinforced concrete, taking into account its adhesion to reinforcement. The model consists of three layers: concrete, contact layer, reinforcement. The contact layer surrounding the reinforcement takes into account the complex deformation of the concrete when interacting with the profiled reinforcement. Arguments are presented for criteria that determine the transition of concrete, reinforcement and contact layer to limit states. A diagram of testing of reinforced concrete specimen has been proposed and a procedure for processing experimental data, which allow you to determine the bond parameters. Equations that bind the mechanical characteristics of the contact layer with two the bond parameters of concrete with reinforcement are obtained. The developed model was used in the numerical solution of the problem of static pull-out of reinforcement from concrete. The calculation of the finite element method showed a good correspondence with the experimental data, including during plastic deformation of the reinforcement. This shows the correctness of theoretical provisions and developed mathematical algorithms used to model the deformation of reinforced concrete.
Control device synthesis by polynomial matrix fractional descriptions method with limitation on controller structure
Authors: Voevoda A , Shipagin V , Bobobekov K
Published: December 2021

Modification of the algorithm for the polynomial synthesis of a multi-channel controller was proposed to preserve all control channels in this article. In order to test the functionality of the proposed modification, an example of a linear model of an unstable multi-channel plant is considered. The choice of the plant was determined by the possibility of a visual algorithm demonstration for polynomial synthesis of the controller, taking into account the proposed modifications.The plant was represented as three series-connected standard links: an aperiodic link of the first order, an unstable link, and an integrator, and has three input and two output channels. The control in the system is carried out in the feedback of the system and is summed up with the input impact. The feature of the plant is to limit the task to the second output, since it is essentially a derivative of the first output. In addition, the plant has a direct input–output channel. That is, the traversal matrix of the system is nonzero (when described through the state space). The synthesis task was set as follows: it is necessary to achieve certain quality indicators of the output vector value while maintaining all three control channels of the plant.
Polynomial matrix synthesis method of a subordinate control system
Authors: Voevoda A , Filiushov V
Published: December 2021

The main difference between controlsyn thesis approaches is the various mathematical representation of a plant or system model. The aim of the work is to represent a single channel control plant model by a multichannel one and to obtain an identical design result for a single channel multiloop synthesis method by a multichannel one. For these purposes, direct current motor model is used as an example of a single channel plant. Classical approach to design control system for that kind of plant is to describe it as a serial connected transfer functions and design a multiloop system in accordance with subordinate concept. Polynomial matrix synthesis method with Sylvester matrix is utilized to make identical subordinate regulator. By several transformations, polynomial matrix description was obtained, that describe the plant as one input and three output model and subordinate regulator as a three input and one output model. Arbitrary parameters of regulator were introduced for extended null placement.
On thermoelastic deformation of a transversally isotropic medium in 3D construction printing
Authors: Chirkunov Yu , Pikmullina E , Gasenko I
Published: December 2021

A three-dimensional dynamic model of a thermoelastic transversely isotropic medium is used to describe the thermoelastic deformation of materials with anisotropy of elastic properties with a selected direction of anisotropy. Such materials are layered and composite materials used in construction, mechanical engineering, aircraft and shipbuilding, soils in permafrost conditions, glaciers, as well as rocks (basalt, sandstone, marble, limestone, shale, and others). The study of this model, in particular, is relevant in connection with the use of 3D printers in construction. This is due to the fact that it is necessary to select the heating mode of the 3D printer head, in which cracks will not form during the cooling of the polystyrene concrete layers.We study this model using the group analysis methods, which is one of the most powerful and effective tools for obtaining exact solutions. The group stratification of the system of second-order differential equations defining this model is carried out. A system of first-order differential equations is obtained, which is equivalent to the equations of the original model. The solution describing a traveling wave for this system is obtained, that depends on arbitrary elements: parameters and function. For the specific sets of these elements, we study a deformation of a sphere and cube located inside a thermoelastic transversely isotropic medium with increasing time is found. The corresponding graphs are given.
Predictive Temporal Analytics Method in Situational Modeling of the Evolution of Complex Systems
Authors: Kurnosov A
Published: December 2021

The article discusses the main characteristics of complex systems, as well as the structures, domains and interactions occurring in the course of evolution. The main properties of complex systems are defined to include openness, non-ergodicity, disequilibrium, activity and multiplicity of goals. The classification attributes are defined to include free energy, anthropic factor, incomplete observability, computational irreducibility, dominant coded interactions, dynamic structure and transformable environments. A variety of primary entities, which form complex systems, are represented by two classes, possible individuals and abstract individuals. The space-time structure as a 6D continuum is formulated; spatial and temporal vacuums and quanta of interaction are defined. The three-dimensional time is presented in terms of three orthogonal components: coordinate time, structural time and discrete time. The coordinate time corresponds to the variability of a system when individuals move in space; the structural time corresponds to the variability of a system when the structure of individuals changes; the discrete time corresponds to the variability of the system caused by informational interaction between or within individuals. A model of a one-time ideal event and a continuous event is defined. The interaction between individuals is presented through a two-way reflexive model of cyclic interaction of an actor and an acceptor. The occurrence of post-causes and post-effects of physical interactions is shown to result in unpredictable chains of effects. The essence of the predictive temporal analytics method is presented. The use of the method involves the construction of a six-dimensional hypergraph of cause-and-effect relations with subsequent analysis of a body of causes and effects. The optimal way of evolution of a system is considered a way that maximizes diversity (in terms of liberty of actions, states, goals achieved) and minimizes the energy costs in a certain time perspective.
Minimization of power and energy consumption of mechatronic drives in robotics and technological equipment
Authors: Volkov A , Matsko O , Mosalova A
Published: December 2021

The maximum instantaneous power consumption of robot drives determines the requirements for the energy supply system and the dimensions of the machine. For numerous machines, there are no technological restrictions on the types of applied motion laws and their numerical characteristics i.e. maximum speeds and accelerations. The type of the motion law and especially its parameters are traditionally determined according to the preferences of the design engineer without any justification, though some-times restrictions on maximum accelerations or speeds are considered. The restrictions on maximum accelerations are related to ensuring the strength and accuracy of the drive, and the restrictions on maximum speeds are related to the safety of personnel in the workplace. The motor power is selected according to the maximum value of the instantaneous power and thermal load, which depends on the duration of switching on. The article analyzes the ways of minimizing of this maximum (peak) of instantaneous power inside the cycle for different laws and different loads. The main parameter by which the maximum (peak) power is minimized for all types of laws is the acceleration and braking times. On the example of the most common motion laws, the dependence of instantaneous power and energy consumption on accelerating time and braking time for various types of loads are studied. In this article, the dependence of instantaneous power and energy consumption on accelerating time and braking time for various types of loads are studied on the example of the most common motion laws. The research results are intended to create a design technique for drives of modern equipment.
Digital information system for inland water transport vessels based on AIS
Authors: Bazylev A V , Plyushchaev V I
Published: December 2021

The most important role in ensuring navigation safety on inland waterways is played by the timely provision of navigators with timely and reliable navigational, meteorological and track information, as well as safety information. To solve this problem, the complexes of automatic identification stations’ coastal and ship networks deployed currently can be used. This communication channel (with free traffic for inland waterway transport) is currently used extremely ineffectively due to a small number of serviced vessels. The article substantiates the structure of a digital information system based on deployed networks of automatic identification stations for inland navigation vessels and its functional purpose. The issues of algorithmic and software support development for the process of preparation, transmission, reception and processing of transmitted information are considered. The structure of the database and algorithms for the formalized information packets’ formation in the direction of bank-to-ship are proposed. The formats of address and broadcast messages are presented. A variant of transmitting differential corrections to ships from control-correcting stations via networks of automatic identification stations without using the currently used radio channel is considered. The options for the dialog boxes of the digital information system for the dispatcher and the navigator are given.
Some properties of Glisson distances in the upper half-plane
Authors: Ovchintsev M
Published: December 2021

The author compares the Gleason distance with the distance of Euclid in the unit disk in the upper half plane. The concept of “the Gleason distance” was formulated in the work of H.S. Bear [1] The Gleason distance is defined as follows (see [1]): d = sup |f(z2)-f(z1)|, f(Z)εB1(K) where B
1 (K) is the unit ball in the space of bounded analytic in K functions. The author of the article proves that in the circle K the distances of Gleason and Euclid are equal only when the points are opposite. He found necessary and sufficient conditions, when the distances are equal for the two given points which are symmetrical about the ordinate axis.
Method of lines for solving linear equations of mathematical physics with the third and first types boundary conditions
Authors: Kh Eshmurodov M , Shaimov K M , Khujaev I , Khujaev J
Published: December 2021

The use of the method of lines in solving multidimensional problems of mathematical physics makes it possible to eliminate the discrepancies caused by the use of the sweep method in certain coordinates. As a result, the solution of the Poisson equation, for example, is obtained without using the relaxation method. In the article, the problem on the eigenvalues and vectors of the transition matrix is solved for boundary conditions of the third and first types, used to solve a one-dimensional equation of parabolic type by the method of lines. Due to the features of boundary conditions of the third type for determining the eigenvalues, a mixed method was proposed based on the Vieta theorem and the representation of the characteristic equation in trigonometric form typical for the method of lines. To solve the eigenvector problem, a simple sweep method was used with the algebraic compliments to the transition matrix. Discontinuous solutions of a one-dimensional parabolic equation were presented for various values of complex 1 -αl; the method for solving the characteristic equation was selected based on these values. The calculation results are in good agreement with the analytical solution.
Fujita type global solvability to double nonlinear parabolic equation with nonlinear gradient term for the salt transfer process
Authors: Aripov M M , Baltabaeva R B
Published: December 2021

In this paper we investigated the qualitative properties of non-negative and bounded continuous solutions to problem Cauchy for a degenerate parabolic equation with nonlinear gradient term. We based on splitting algorithm suggest estimate of weak solution for slowly, fast diffusion and critical cases, Fujita type global solvability of the Cauchy problem to degenerate type parabolic equation with nonlinear gradient term established. The theorems proven with comparison principle.
Mathematical modeling of double nonlinear problem of reaction diffusion in not divergent form with a source and variable density
Authors: Aripov M , Matyakubov A S , Khasanov J O , Bobokandov M M
Published: December 2021

In this paper the properties of solutions of nonlinear parabolic equation not in divergence form

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are studied. Depending on values of the numerical parameters and the initial value, the existence of the global solutions of the Cauchy problem is proved. Constructed asymptotic representation of self-similar solutions of nonlinear parabolic equation not in divergence form, depending on the value in the equation of the numerical parameters necessary and sufficient signs of their existence. The compactly supported solution of the Cauchy problem for a cross-diffusion parabolic equation not in divergence form with a source and a variable density is obtained.
Geometric models of the run method
Authors: Dubanov A
Published: December 2021

This article discusses models of the run method in the pursuit problem. The considered models are based on the correction of the direction vector. Let’s assume that the intended direction on a plane is the line of sight between the pursuer and the target. The direction correction consists in the rotation of the velocity vector until it coincides with the line of sight. When constructing trajectories on the surface, a line of sight is built on the horizontal projection plane. After calculating horizontal projections, all points are projected back onto the surface. On the basis of the research carried out proposed a mathematical model, proposed mathematical models of the method of pursuit on a plane and on a surface given in an explicit form. Mathematical models are the development of chase and parallel approach methods. A modification of these methods is that the speed of the pursuer and the target are directed at random. These models can be in demand by developers of autonomous unmanned vehicles equipped with artificial intelligence systems.
Fault simulation in networks with isolated neutral to find the fault location in power transmission lines
Authors: Belitsyn I V , Pestov M I , Pavlichenko I A , Belitsyn A I
Published: December 2021

The paper deals with an urgent problem - determining the location of damage to an overhead power transmission line. In particular, the application of the wavelet transform is considered, which makes it possible to localize the temporal position of the frequencies and to determine the time interval of the presence of the frequency in the event of damage to the power line. The paper presents a mathematical model that makes it possible to determine the amplitude-frequency spectrum, by which it is possible to determine the presence of a certain frequency in the signal under study, by which it is possible to determine the fault location. Based on the wavelet transform, the spectra of the current and voltage in the damaged phase in the isolated neutral mode are obtained. It is shown that when the neutral mode is switched, there are no dangerous overvoltage or current surges in the network, and the overvoltage level is reduced.
Methodological approaches to the use of the law of inertia in the development of socio-economic systems
Authors: Ivanova N A
Published: December 2021

The relevance of the proposed study is due to the application of Newton’s laws on the determination of speed and acceleration, which reflects the establishment of the actual specific weights of production factors by phases (stages) of the economies’ development of the countries in the world. By applying the laws of physics, the simplest methods have been developed for decomposing the absolute growth of GDP per capita, according to the factors that determine it. A model of economic growth is determined, which is similar in content to Newton’s first law of measuring the paths traveled with uniformly accelerated motion of matter. By calculation, the forecast parameters of the Russian economy can be determined, which determine the GDP per capita until 2030. At the same time, the basic factors of development (45%), investment in fixed assets (35%) and innovative (20%) remain the main factor in the development of global competitiveness in Russia. To do this, you need to gain the proper acceleration. We propose a new approach for assessing the economic stability of socio-economic systems, based on taking into account the mutual influence of the elements of large systems on each other. The novelty of the research lies in the use of the laws of inertia in the development of the economy, since the existing forecasting activity does not provide for obtaining promising changes in the volume and structure of the forecast. As the competitiveness of the countries of the world develops, the share of basic factors such as labor, capital and natural resources decreases significantly (from 50% in the first stage to 40% in the second, and up to 30% in the third stage of economic development). In the stage of high-tech development of the countries in the world, the proportion of factors of innovative development grows up to 30% comparing with 10% in the first two stages of its development. To illustrate the applied value, Newton’s second law was applied as an alternative method for preliminary estimation of the specific weights of three groups of production factors.
˄C˄C
4
He and ˄C˄C
4
H hypernuclei
Authors: Matskevich E E
Published: December 2021

In our article we consider charmed hypernuclei states having the number of baryons B = 4 and containing two Ae hyperons. To do this we use the technique of the dispersion relations. We obtain the relativistic equations which describe these states. The relativistic amplitudes for 12-quark states, including the constituent quarks of three flavors u, d, c are considered. We find the approximate solutions of these equations and take into account main singularities of the amplitudes. We calculate masses and binding energies of the hypernuclei states ˄C˄C
4
He, ˄C˄C
4
H.
Coastal wave processes numerical modeling for large valley-type reservoirs
Authors: Sukhinov A I , Sidoryakina V V , Protsenko S V
Published: December 2021

The problem of modeling sediment transport and wave processes of large valley-type reservoir under non-stationary conditions of the hydrological cycle active phase (spring-autumn period) is considered. Coupled 2D sediment transport model and 3D wave hydrodynamics was considered to describe these processes, which uses the Navier-Stokes equations. The wave hydrodynamics model is applied to large reservoir of the valley type, such as Tsimlyansky reservoir. Detailed numerical experiments were performed taking into account the real coastline geometry and the bottom relief of the Tsimlyansk reservoir southwestern part. The developed complex of models and programs allows to predict reshaping the bottom relief and coastline under various hydrometeorological conditions. The results of modeling can be in demand when planning water management activities in valley-type reservoirs.
Algorithm for monitoring the plankton population dynamics based on satellite sensing data
Authors: Panasenko N D , Yu Poluyan A , Motuz N S
Published: December 2021

The scientific work describes the algorithms for processing the multispectral water coastal imagery from satellite sensing data with the aim of identifying the phytoplankton population of a spotted structure: determining the contour, distributing color gradation and as a result - determining the concentration of phytoplankton distribution inside the zones and mass centers. Such characteristics let determine the speed of changing contours spots and their concentration, the mass center shift as a consequence of the water masses movement and the processes of phytoplankton growing and dying. All these may be done on the base of the processed image series of the same water area over different time (different dates). The combination of LBP and neural network methods are observed as algorithms for image processing and the results of computer experiments are presented.
Detection of water surface natural objects based on the satellite sensing data
Authors: Panasenko N D , Motuz N S
Published: December 2021

The article shows an application of satellite sensing data method in geoenvironmental monitoring of water surface. It is expected to apply combination of LBP and neural network approaches for detection and identification objects of natural and anthropogenic origin. The applying of satellite images, the implementation and operation of the filtration method and satellite sensing data assimilation in real or near-real time are considered to detect the blooming areas and their coordinates. The research demonstrates the need and possibility to apply neural approach and the theory of deep learning for solving the tasks. The results of computer experiments are presented basing on the images from satellites Resurs-P, WorldView and Landsat over the Azov sea area.
Image processing algorithms application for the modeling biogeochemical cycles of the Azov Sea
Authors: Belova Y V , Rahimbaeva E O , Timofeeva E F
Published: December 2021

In the article biogeochemical processes of the Azov Sea were researched. Mathematical non-stationary 3D model is proposed which describes the development dynamics of the two most common species of phytoplankton populations in the summer, the growth of which is limited by a single biogenic element, is proposed the linearization of continuous mathematical model on a uniform temporal grid is made. For a continuous model, a discrete analogue is constructed and an optimal method for grid equations solving is selected. To determine the boundary of the considered computational domain of a complex shape an image processing algorithm has been developed, implemented as a software module on Python, which makes it possible to obtain a dynamically changing contour of the Azov Sea from satellite images.
Physical and mathematical modeling of cleaning fibrous material from coarse-grained litter
Authors: Tashpulatov D , Plehanov A , Madumarov I , Tashpulatov S , Cherunova I
Published: December 2021

The article provides a recommended scheme and principle of operation of the cleaner of fibrous material from large litter. The results of theoretical studies to determine the laws of motion and the recommended parameters of the working bodies of the cleaning machine are presented. The results of comparative production tests of a fibrous material cleaner from large litter are given. Substantiated the receipt of parameters and modes of operation of the working bodies of the cleaner of fibrous material, in particular cotton.