bluuebunny/crossref_metadata_2025_split huggingface dataset:
Correction of the model dynamics for the Northern seas using observational altimetry data
Authors: Belyaev K , Chetverushkin B , Kuleshov A , Smirnov I 
Published: December 2021

Abstract
The earlier derived data assimilation method called Generalized Kalman filter (GKF) is applied in conjunction with the Nucleus for European Modelling of the Ocean (NEMO) circulation model to the calculation of the dynamics in the North Seas of Russia. By assimilating the satellite altimetry data from archive AVISO (Archiving, validating and interpolating of satellite observations) this method corrects the direct model calculations and improves the ocean state. The model fields, in particular, sea level and sea surface temperature with and without assimilation are constructed and compared with each other. The brief analysis of the results is also performed.
Change in the amplitude of strong discontinuity wave propagating in a rod made of Murnaghan material
Authors: Major M , Major I , Yazyev B 
Published: December 2021

Abstract
The paper presents calculations of the change in amplitude of strong discontinuity wave propagating in a thin rod made of hyperelastic Murnaghan material. Two functions were assumed for the calculations, describing the change of the cross-section of the rod with the constant scaling parameter?for both decreasing cross-sections of the analysed steel rods. A numerical analysis was performed based on analytical solutions. The analytical form of solution for both rods with decreasing cross-sections allowed for preparation of contour maps for the propagating wave of strong discontinuity. Furthermore, the changes in the relative amplitude of the propagating shock wave in a thin rod were determined for two rods analysed in the study, for which the differences in the values of the relative amplitude in the final cross-section were found.
Features of using a two-point crossover for solving an inhomogeneous minimax problem modified by the Goldberg model
Authors: Kobak V G , Porksheyan V M , Jukovskiy A G , Shkabriy R S 
Published: December 2021

Abstract
The relevance of the topic of this work is the strong growth of multiprocessor systems, for which it is important to solve a large volume of tasks in a minimum time. There are various algorithms for solving such a problem, which can be divided into classes of exact and approximate. The representative of approximate algorithms is the algorithm of the Goldberg model, which gives acceptable results, the modifications of the crossovers of which are studied in this paper.
Properties of prime numbers and their relation to sound vibrations
Authors: Pinevich Elena , Agishev Timur , Belyakov Yefim , Gargatsova Svetlana 
Published: December 2021

Abstract
The article introduces new properties of prime numbers. An alternative method for finding prime numbers using linear algebra tools is discussed. The probabilistic approach is used to analyze the use of a new property as a means of finding prime numbers. Mathematical calculations of determinants composed of prime numbers were converted to sound according to a given pattern. To optimize the process of calculating and converting numbers to, a software implementation was performed. A MIDI format saved in a folder has been created. In the process of processing the received data, the program recorded a melody, which, when changing scales, gives a beautiful sound.
Compiler for physical and geometric construction of sets
Authors: Pinevich Elena , Mayorov Denis , Safaryan Olga , Lagunova Elena , Fisenko Konstantin 
Published: December 2021

Abstract
This article is devoted to the geometric representation of sets. The paper presents an implementation that allows using operations on sets to build any images. For this algorithm, the equations of first-and second-order lines on the plane and first-and second-order surfaces in space are used. Restrictions are introduced by setting segments on the coordinate axes, indicating whether lines or surfaces belong to these segments. Inequalities are used to create the shaded area of the drawings. In the course of research on this topic, a software tool was developed that allows you to model drawings using the entered formulas, build images based on a set of operations on given sets of points, which allows you to have an analytical description of the drawings. This software tool can be used both in the educational process to test the correctness of the assimilation of the material, and to create flat geometric shapes and three-dimensional bodies for the purpose of engineering the optimal forms of structures and various parts. This application allows the user, performing operations with mathematical expressions and inequalities, to get a graphical display of the result with a mathematical description of any part of the figure.
The execution complexity of logical formulas with restricted quantifiers based on CF-grammars
Authors: Korovina K S , Sh Rudova I 
Published: December 2021

Abstract
The polynomial realized formulas are introduced with quantifiers acting on hierarchy lists described by CF-grammars. Upper estimates of execution complexity are obtained depending from the sort of grammar. These formulas have been applied for formal definition of context-dependent syntax of programming languages and describing dynamic discrete system.
Strict convexity of the objective function and uniqueness of the maximum point in a model with three arbitrary random priorities
Authors: Pavlov I V , Neumerzhitskaia N V , Uglich S I , Volosatova T A 
Published: December 2021

Abstract
The main result of this paper is the proof of the strict concavity of some function of integral form depending on three random variables, which we call priorities. This function is an objective function in the so-called model with priorities, in which the arbiter, following expert opinions, distributes funds among the enterprises and institutions under his jurisdiction. This result implies an important corollary about the existence and uniqueness of a local maximum point (which is also a global maximum point) of the objective function. This is a significant generalization of the corresponding result of N.V. Neumezhitskaia, S.I. Uglich and T.A. Volosatova, published in December 2020.
Logic prototyping: approach and use cases
Authors: Il’icheva O A , Ilicheva V V 
Published: December 2021

Abstract
In this article, we present an approach to prototyping complex systems and processes using classical predicate logic. The prototype is built by the interpreter based on a logical description of the properties and/or behavior of the designed system. The description contains the definitions of the prototype elements and the constraints that the correct prototype must satisfy. Definitions are used to build a prototype, and constraints are used to analyze it and check the required properties. Definitions are interpreted using direct logic inference, constraints are only checked on the resulting model. A wider class of formulas is used than in well-known logical languages. Computable logical and denotational semantics are defined for them. In the process of building a prototype, logical errors of uncertainty, redefinition of functions, and contradictions are diagnosed. We are given examples of prototype descriptions used for semantic program analysis, space training, transport system design.
Increasing the contact line operational reliability by forecasting its constructive elements’ failures
Authors: Bodrov P A , Popova N A , Ganashek A L 
Published: December 2021

Abstract
The article discusses the issues of calculating the indicators of the power supply systems’ reliability. The analysis of the existing problem and options for its solution are given. To assess the patterns, the authors proposed a mathematical tool. The method based on the rectangular scores’ technique is adopted as a forecasting method. The development belongs to the class of specialized method-oriented software tools.
Simulation modelling of operational tests to assess the reliability of railway automation software systems
Authors: Maslov A A , Maslov An A 
Published: December 2021

Abstract
A simulation model for in-servicetesting of software reliability assessment for railway automation systems is described in this paper. As a basic concept, the reliability indicators are calculated using the concept of a reference object, being the most common element of the respective train protection systems on the road network. We are aware that this concept is embedded in the subsystem for the formation of the reference object-element infrastructure of JSC “Russian Railways”, involving the function of bringing all track, electrification and power supply facilities as well as automation and telemechanics facilities to the reference objects. In order to develop this approach, the “Performance Test Simulation” application was developed on the Windows Presentation Foundation (WPF) platform, using the object- and component-oriented programming language C#, allowing the practical simulation of performance tests of reference objects of various types, during the design phase, using the Monte Carlo method.
Algorithms for forming the coefficient matrix of a system of differential equations Chapman-Kolmogorov models of non-stationary service systems
Authors: Bubnov V P , Sultonov Sh Kh 
Published: December 2021

Abstract
The paper considers a new approach to building models of nonstationary service systems based on: the formation of all possible states of a nonstationary service system with a finite number of applications and rules of transition between them; the formation of the coefficient matrix of Chapman-Kolmogorov differential equation system; the numbering procedure for all states. A critical analysis is made of the algorithms for the formation of the coefficient matrix and the numbering procedure for all states: sequential, recursive and recursive with grouping. Its comparison with the recursive algorithm is given, as well as the optimal structure for storing the list of states for the sequential algorithm. Recommendations for the practical application of software implementations of the considered algorithms are discussed. Theoretical foundations for building and calculating models of nonstationary service systems have been developed. It is compared to the recursive algorithm. The optimal structure for storing the list of states for a sequential algorithm is given.
Processing of strain gauge control signals by the Kalman filter
Authors: Vyplaven V , Kolomeets A , Popkov A 
Published: December 2021

Abstract
One of the methods for detecting defects in the rolling surface of the wheels of freight cars is to measure the deformations of the rail under the passing train. The method is based on the analysis of a strain gauge signal. The main task of the strain gauge signal analysis is the selection of informative components and the removal (filtering) of interference. The paper presents methods of filtering diagnostic signals of strain gauge control and the selection of informative components. The useful signal component can be used to measure the mass of cars, to determine the dynamic load on the rails and to detect defects in the rolling surface of the wheels. The method of adaptive Kalman filtering and linear convolution are proposed as signal processing tools. Based on these algorithms, a software module based on the.NET Framework has been developed using the C# programming language. The algorithms were tested on the signals received when the train was moving along the active section of the track, with a strain gauge control system located on it. The computational complexity and speed of the algorithms are assessed, and the possibility of their further application in the autonomous mode of the system is investigated. The results show that the use of the Kalman filtering algorithm provides a significant performance advantage over the linear convolution algorithm.
Degree estimates of one class cut-offs for improper integrals
Authors: Pozhidaev A , Khaustova O 
Published: December 2021

Abstract
The paper considers a normalized non-integral integral of the first kind with a variable lower bound. In this case the integrand is a generalization of the standard Gaussian distribution density. Such integrals are often called cutoffs or incomplete functions. The purpose of this paper is to obtain power inequalities for this kind of integrals. The necessity of obtaining this type of estimations is due to the fact that incomplete functions have become widespread in applications and theoretical studies. The peculiarity of the results established in the article consists in the fact that arbitrary degrees of a given integral for any value of an argument are evaluated from above not by means, of the value of integrable functions at a certain point, but by the value of the integral in question at some point proportional to this argument. The coefficient of proportionality, a parameter, can take any value from some closed interval. The main difficulty in obtaining these inequalities is that the integrand is a logarithmically concave function, that is, its logarithm is a concave function. The paper also proves that both limits of the closed interval for the parameter cannot be extended. This shows that the obtained estimates are unimprovable.
Study of the soil stability theory problems by the simplex method
Authors: Karaulov A , Nemtzev D , Konkov A , Shekhov V 
Published: December 2021

Abstract
The questions of linear programming methods application to the main problems of stability theory - problems on slope stability, problems on ultimate pressure of soil on enclosures (case of landslide pressure), and problems on bearing capacity of horizontal base of a die are considered. The problems of stability theory are formulated as linear programming tasks. It is shown that the given systems of equations are linear with respect to the unknowns and may be solved by the Simplex method. The results of soil stability problems calculation by Simplex method are compared with the results of calculations according to the most known classical schemes. It is shown that a great scatter of final results is observed in calculating the stability of slopes by classical methods, and in this case, the results obtained by the Simplex method are the most trustworthy ones. The situation with landslide pressure definition is especially complicated in this sense where classical methods give a scatter of landslide pressure values by several times. It is established that with increasing discretization of the computational domain, the results tend to exact solutions of the limit equilibrium theory, obtained, for example, by the method of characteristics. The latter point is illustrated using the example of the problem of a die pushing into a ground massif with a Hill scheme bulge.
The use of fuzzy sets to determine the parameters of genetic algorithms that provide approximately the same execution time on the CPU and GPU
Authors: Agibalov Oleg , Ventsov Nikolay 
Published: December 2021

Abstract
The problem under consideration consists in choosing the number of k individuals, so that the time for processing k individuals by the genetic algorithm (GA) on the CPU architecture is close to the time for processing l individuals on the GPU architecture by the genetic algorithm. The initial information is data arrays containing information about the processing time of a given number of individuals by the genetic algorithm on the available hardware architectures. Fuzzy numbers are determined based on these arrays?~? and?~?, describing the processing time of a given number of individuals, respectively, on the CPU and GPU architectures. The peculiarities of the subject area do not allow considering the well-known methods of comparison based on the equalities of the membership functions and the nearest clear sets as adequate. Based on the known formula “close to Y (around Y)” the way to compare fuzzy numbers?~? and?~? was developed in order to determine the degree of closeness of the processing time of k and l individuals, respectively, on the hardware architectures of the CPU and GPU.
Modeling and visualization of the forecast trajectory for the decision support system for controlling the movement of a river displacement vessel
Authors: Galeev R E , Soloviev A V , Fedosenko Y S 
Published: December 2021

Abstract
An approach to dynamic modeling of the predicted trajectory of movement of a displacement vessel and its continuous visualization on an electronic panel is considered, superimposed on the actual digital twin of the real scene of the environment along the course of the vessel. The hardware and software implementation of the developed approach as a decision support system for the navigator in the form of a standard option of the integrated control panel located in the wheelhouse provides an opportunity to objectively assess the safe distance to potential navigation obstacles within the ship’s course at the free distance of the vessel by means of combined visualization.
As part of the organizational and technical measures to ensure the safety of navigation, the proposed innovative approach to continuous joint visualization of the digital twin of the current scene of the surrounding sailing situation and the predicted trajectory of the vessel’s movement acquires significant importance in the operation of automatic vessels as an option for the supervisor to intervene in the operation of an integrated automatic control system in complex navigating conditions.
Orbital stability analysis of trajectories of highly nonlinear dynamic systems with feedback coupling
Authors: Annakulova G K 
Published: December 2021

Abstract
Orbital stability and qualitative study of the oscillations of a highly nonlinear dynamic system with feedback coupling are considered. For a highly nonlinear dynamic system with feedback coupling that satisfies Liénard’s theorem (on the existence and uniqueness of a periodic solution), a complete study of the phase pattern of the system is conducted. Applying the Poincaré criterion, the conditions for the existence of limit cycles and their Lyapunov stability are determined. The diagrams of phase trajectories are constructed numerically using the Mathcad 15 software package. Limit cycles are established, which are consistent with the limit cycles obtained by the Poincaré method. The behavior of trajectories outside the limit cycles is investigated. Recurrent homogeneous Pfaff equations are obtained, which determine the behavior of the systems “at infinity”. It was determined that the infinitely distant point of the horizontal axis is the only singular point for these equations. Linear approximations of recurrent homogeneous equations are obtained, which make it possible to determine the nature of the singular points. It was found that the trajectories then wind like a spiral on the limit cycles. Images of trajectories on the phase plane outside the limit cycles for the cases of degrees of nonlinearity under consideration are constructed.
Using multivalued logic for qualitative data analysis
Authors: Lyutikova L A 
Published: December 2021

Abstract
The paper considers a logical approach to data analysis to solve the classification problem. The studied data is a set of objects and their features. As a rule, this is scattered heterogeneous information and it is not enough for a reasonable application of probabilistic models. Therefore, logical algorithms are considered, which under certain conditions may be more adequate. For an expressive formal representation of the relationship between objects and their attributes, multivalued logic is used, and the number of values depends on a specific attribute. Therefore, a system of operations is proposed for variables with different domains of definition. As a result, a decisive function is built, which is a classifier of objects that are present in the studied data. The properties and capabilities of this function are analyzed. It is shown that the logical function, which is a conjunction in the space of rules connecting given objects with their characteristic features, uniquely characterizes the initial data, divides the subject area into classes, possesses modifiability properties, meets the requirements of completeness and consistency in a given area. The paper also proposes an algorithm for its implementation.
Mathematical modeling of the pollutant distribution process in the Gelendzhik Bay
Authors: Litvinov V N , Rudenko N B , Filina A A , Nikitina A V 
Published: December 2021

Abstract
Currently, the pollution problem of coastal sea waters in the resort areas of the Black Sea is becoming increasingly urgent. Thousands of chemicals, industrial and household waste enter the water basins every year, which significantly worsens the state of marine waters. Storm drains are saturated with pollutants at precipitation, washing out various chemical compounds, garbage and transporting them to the sea. In addition, a separate problem is poorly self-cleaning of the Gelendzhik Bay. A complete water change occurs in the period from 1 to 6 days. This paper covers the development, research and numerical implementation of a mathematical model of the pollution transport, including petroleum products, in the Gelendzhik Bay taking into account a number of important hydrodynamic and hydrophysical factors, methods of its numerical implementation, which allow predictive modeling of the pollution spread in shallow water systems in a limited time. A hydrobiological model of a coastal system characterized by significant depth differences has been developed. A three-dimensional mathematical model is designed to research the transformation of the phosphorus, nitrogen and silicon forms in the plankton dynamics problem. It takes into account the convective and diffusive transports, absorption and release of nutrients by phytoplankton, salinity, temperature, oxygen regime, etc. Using a spatial-three-dimensional hydrodynamics model, taking into account the physical properties of water environment of the coastal system, calculation results are used as input data for the development of scenarios for the dynamics of transport processes and the transformation of pollution biogenic elements in the water.
Organization of parallel-pipeline calculations for modeling the pollutant distribution process in a reservoir
Authors: Litvinov V N , Gracheva N N , Filina A A , Nikitina A V 
Published: December 2021

Abstract
One of the most acute problems for today is the water pollution. For rapid decision in emergency situations, it is necessary to develop effective software and algorithmic tools that allow us to make accurate forecasts of the environmental situation changing of coastal systems. Water pollution of the Azov and Black Seas by storm drains and human waste products leads to an increase of toxic substances concentrations that significantly exceed the maximum permissible values. The pollution transport problem is solved on the basis of the Navier-Stokes and the diffusion-convection-reaction equations. As a result of discretization of the continuous problem of transport of pollutants using the finite-difference approach for a rectangular grid, we obtain a system of linear algebraic equations (SLAE) of large dimension, which require significant time costs. To increase the efficiency of calculations (to reduce the time) on a multiprocessor computer system (MCS), there is a need to develop effective parallel algorithms for solving SLAE. The decomposition method for a two-dimensional computational domain is proposed in this paper, which allows organizing a parallel-pipeline process of calculations as follows: at each stage of calculations, each processor core simultaneously processes fragments of the computational domain that are offset from each other. This process is described in the form of a graph, in which each node corresponds to fragments of the computational domain, and the edges – a sign of the adjacency of fragments.