Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-13
N. Aralova, L. Shakhlina, A. Aralova, Svetlana Kalytka, O. Roda, L. Vasylchenko
One of the most important tasks in modern sport's training for the sport of highest achievements is the ability to control the state of the athlete's body in the process of training and competitive activities. For this purpose, the use of systems registering and analyzing information about the functional capabilities of an athlete in the dynamics of his activity, allows you to provide an individual approach when planning and correcting training loads. This is especially important for medical and pedagogical examination. The development of methods and means for increasing physical performance and, in particular, in the practice of high-performance sports, is one of the most important principles of modern sports medicine, physiology of labor and sports. In the practice of modern sports medicine, when carrying out mass examinations of athletes, the approach based on the proposed A.Z. Kolchinskaya concept on the regulation of the body's oxygen regimes, which allows to give a general characteristic of gas homeostasis, to diagnose the main syndromes associated with disorders of the transport of respiratory gases in the body, to assess the functional state of the body at all stages of the annual cycle of sports training and during the post-exercise recovery period. Since this work is associated with a large number of calculations and subsequent processing of the information received, it is necessary to use modern means of modern information support. Thus, the automated information system (AIS) for the functional diagnostics of athletes allows many times to speed up the processing of data obtained during the examination of athletes, centrally accumulate information for its preprocessing, storage and collective use of the AIS, is equipped with convenient services for graphical and tabular presentation of data, allows analyzing the dynamics of functional the state of athletes in the annual cycle of their training, as well as at the stage of the 4-year training Olympic cycle.
{"title":"AUTOMATED WORKPLACES FOR FUNCTIONAL DIAGNOSTICS OF ATHLETES","authors":"N. Aralova, L. Shakhlina, A. Aralova, Svetlana Kalytka, O. Roda, L. Vasylchenko","doi":"10.34229/1028-0979-2021-4-13","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-13","url":null,"abstract":"One of the most important tasks in modern sport's training for the sport of highest achievements is the ability to control the state of the athlete's body in the process of training and competitive activities. For this purpose, the use of systems registering and analyzing information about the functional capabilities of an athlete in the dynamics of his activity, allows you to provide an individual approach when planning and correcting training loads. This is especially important for medical and pedagogical examination. The development of methods and means for increasing physical performance and, in particular, in the practice of high-performance sports, is one of the most important principles of modern sports medicine, physiology of labor and sports. In the practice of modern sports medicine, when carrying out mass examinations of athletes, the approach based on the proposed A.Z. Kolchinskaya concept on the regulation of the body's oxygen regimes, which allows to give a general characteristic of gas homeostasis, to diagnose the main syndromes associated with disorders of the transport of respiratory gases in the body, to assess the functional state of the body at all stages of the annual cycle of sports training and during the post-exercise recovery period. Since this work is associated with a large number of calculations and subsequent processing of the information received, it is necessary to use modern means of modern information support. Thus, the automated information system (AIS) for the functional diagnostics of athletes allows many times to speed up the processing of data obtained during the examination of athletes, centrally accumulate information for its preprocessing, storage and collective use of the AIS, is equipped with convenient services for graphical and tabular presentation of data, allows analyzing the dynamics of functional the state of athletes in the annual cycle of their training, as well as at the stage of the 4-year training Olympic cycle.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44409272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-4
M. Mamatov, Jalolkon Nuritdinov, Egamberdi Esonov
The article deals with the problem of pursuit in differential games of fractional order with distributed parameters. Partial fractional derivatives with respect to time and space variables are understood in the sense of Riemann - Liouville, and the Grunwald-Letnikov formula is used in the approximation. The problem of getting into some positive neighborhood of the terminal set is considered. To solve this problem, the finite difference method is used. The fractional Riemann-Liouville derivatives with respect to spatial variables on a segment are approximated using the Grunwald-Letnikov formula. Using a sufficient criterion for the existence of a fractional derivative, a difference approximation of the fractional-order derivative with respect to time is obtained. By approximating a differential game to an explicit difference game, a discrete game is obtained. The corresponding pursuit problem for a discrete game is formulated, which is obtained using the approximation of a continuous game. The concept of the possibility of completing the pursuit, a discrete game in the sense of an exact capture, is defined. Sufficient conditions are obtained for the possibility of completing the pursuit. It is shown that the order of approximation in time is equal to one, and in spatial variables is equal to two. It is proved that if in a discrete game from a given initial position it is possible to complete the pursuit in the sense of exact capture, then in a continuous game from the corresponding initial position it is possible to complete the pursuit in the sense of hitting a certain neighborhood. A structure for constructing pursuit controls is proposed, which will ensure the completion of the game in a finite time. The methods used for this problem can be used to study differential games described by more general equations of fractional order.
{"title":"DIFFERENTIAL GAMES OF FRACTIONAL ORDER WITH DISTRIBUTED PARAMETERS","authors":"M. Mamatov, Jalolkon Nuritdinov, Egamberdi Esonov","doi":"10.34229/1028-0979-2021-4-4","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-4","url":null,"abstract":"The article deals with the problem of pursuit in differential games of fractional order with distributed parameters. Partial fractional derivatives with respect to time and space variables are understood in the sense of Riemann - Liouville, and the Grunwald-Letnikov formula is used in the approximation. The problem of getting into some positive neighborhood of the terminal set is considered. To solve this problem, the finite difference method is used. The fractional Riemann-Liouville derivatives with respect to spatial variables on a segment are approximated using the Grunwald-Letnikov formula. Using a sufficient criterion for the existence of a fractional derivative, a difference approximation of the fractional-order derivative with respect to time is obtained. By approximating a differential game to an explicit difference game, a discrete game is obtained. The corresponding pursuit problem for a discrete game is formulated, which is obtained using the approximation of a continuous game. The concept of the possibility of completing the pursuit, a discrete game in the sense of an exact capture, is defined. Sufficient conditions are obtained for the possibility of completing the pursuit. It is shown that the order of approximation in time is equal to one, and in spatial variables is equal to two. It is proved that if in a discrete game from a given initial position it is possible to complete the pursuit in the sense of exact capture, then in a continuous game from the corresponding initial position it is possible to complete the pursuit in the sense of hitting a certain neighborhood. A structure for constructing pursuit controls is proposed, which will ensure the completion of the game in a finite time. The methods used for this problem can be used to study differential games described by more general equations of fractional order.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46934130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-12
L. Movchan, S. Movchan
The paper considers two types of boundaries of the D-partition in the plane of one parameter of linear continuous systems given by the characteristic equation with real coefficients. The number of segments and intervals of stability of the X-partition curve is estimated. The maximum number of stability intervals is determined for different orders of polynomials of the equation of the boundary of the D-partition of the first kind (even order, odd order, one of even order, and the other of odd order). It is proved that the maximum number of stability intervals of a one-parameter family is different for all cases and depends on the ratio of the degrees of the polynomials of the equation of the D-partition curve. The derivative of the imaginary part of the expression of the investigated parameter at the initial point of the D-partition curve is obtained in an analytical form, the sign of which depends on the ratio of the coefficients of the characteristic equation and establishes the stability of the first interval of the real axis of the parameter plane. It is shown that for another type of the boundary of the D-partition in the plane of one parameter, there is only one interval of stability, the location of which, as for the previous type of the boundary of the stability region (BSR), is determined by the sign of the first derivative of the imaginary part of the expression of the parameter under study. Consider an example that illustrates the effectiveness of the proposed approach for constructing a BSR in a space of two parameters without using «Neimark hatching» and constructing special lines. In this case, a machine implementation of the construction of the stability region is provided. Considering that the problem of constructing the boundary of the stability region in the plane of two parameters is reduced to the problem of determining the BSR in the plane of one parameter, then the given estimates of the maximum number of stability regions in the plane of one parameter allow us to conclude about the number of maximum stability regions in the plane of two parameters, which are of practical interest. In this case, one of the parameters can enter nonlinearly into the coefficients of the characteristic equation.
{"title":"INVESTIGATION OF THE GEOMETRY OF THE D-PARTITION OF ONE-DIMENSIONAL PLANE OF PARAMETER OF THE CHARACTERISTIC EQUATION OF A CONTINUOUS SYSTEM","authors":"L. Movchan, S. Movchan","doi":"10.34229/1028-0979-2021-4-12","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-12","url":null,"abstract":"The paper considers two types of boundaries of the D-partition in the plane of one parameter of linear continuous systems given by the characteristic equation with real coefficients. The number of segments and intervals of stability of the X-partition curve is estimated. The maximum number of stability intervals is determined for different orders of polynomials of the equation of the boundary of the D-partition of the first kind (even order, odd order, one of even order, and the other of odd order). It is proved that the maximum number of stability intervals of a one-parameter family is different for all cases and depends on the ratio of the degrees of the polynomials of the equation of the D-partition curve. The derivative of the imaginary part of the expression of the investigated parameter at the initial point of the D-partition curve is obtained in an analytical form, the sign of which depends on the ratio of the coefficients of the characteristic equation and establishes the stability of the first interval of the real axis of the parameter plane. It is shown that for another type of the boundary of the D-partition in the plane of one parameter, there is only one interval of stability, the location of which, as for the previous type of the boundary of the stability region (BSR), is determined by the sign of the first derivative of the imaginary part of the expression of the parameter under study. Consider an example that illustrates the effectiveness of the proposed approach for constructing a BSR in a space of two parameters without using «Neimark hatching» and constructing special lines. In this case, a machine implementation of the construction of the stability region is provided. Considering that the problem of constructing the boundary of the stability region in the plane of two parameters is reduced to the problem of determining the BSR in the plane of one parameter, then the given estimates of the maximum number of stability regions in the plane of one parameter allow us to conclude about the number of maximum stability regions in the plane of two parameters, which are of practical interest. In this case, one of the parameters can enter nonlinearly into the coefficients of the characteristic equation.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45082949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-3
A. Nakonechnyi, G. Kudin, T. Zinko, Petr N. Zinko
The issues of parameter estimation in linear regression problems with random matrix coefficients were researched. Given that random linear functions are observed from unknown matrices with random errors that have unknown correlation matrices, the problems of guaranteed mean square estimation of linear functions of matrices were investigated. The estimates of the upper and lower guaranteed standard errors of linear estimates of observations of linear functions of matrices were obtained in the case when the sets are found, for which the unknown matrices and correlation matrices of observation errors are known. It was proved that for some partial cases such estimates are accurate. Assuming that the sets are bounded, convex and closed, more accurate two-sided estimates have been gained for guaranteed errors. The conditions when the guaranteed mean squared errors approach zero as the number of observations increases were found. The necessary and sufficient conditions for the unbiasedness of linear estimates of linear functions of matrices were provided. The notion of quasi-optimal estimates for linear functions of matrices was introduced, and it was proved that in the class of unbiased estimates, quasi-optimal estimates exist and are unique. For such estimates, the conditions of convergence to zero of the guaranteed mean-square errors were obtained. Also, for linear estimates of unknown matrices, the concept of quasi-minimax estimates was introduced and it was confirmed that they are unbiased. For special sets, which include an unknown matrix and correlation matrices of observation errors, such estimates were expressed through the solution of linear operator equations in a finite-dimensional space. For quasi-minimax estimates under certain assumptions, the form of the guaranteed mean squared error of the unknown matrix was found. It was shown that such errors are limited by the sum of traces of the known matrices. An example of finding a minimax unbiased linear estimation was given for a special type of random matrices that are included in the observation equation.
{"title":"MINIMAX ROOT–MEAN–SQUARE ESTIMATES OF MATRIX PARAMETERS IN LINEAR REGRESSION PROBLEMS UNDER UNCERTAINTY","authors":"A. Nakonechnyi, G. Kudin, T. Zinko, Petr N. Zinko","doi":"10.34229/1028-0979-2021-4-3","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-3","url":null,"abstract":"The issues of parameter estimation in linear regression problems with random matrix coefficients were researched. Given that random linear functions are observed from unknown matrices with random errors that have unknown correlation matrices, the problems of guaranteed mean square estimation of linear functions of matrices were investigated. The estimates of the upper and lower guaranteed standard errors of linear estimates of observations of linear functions of matrices were obtained in the case when the sets are found, for which the unknown matrices and correlation matrices of observation errors are known. It was proved that for some partial cases such estimates are accurate. Assuming that the sets are bounded, convex and closed, more accurate two-sided estimates have been gained for guaranteed errors. The conditions when the guaranteed mean squared errors approach zero as the number of observations increases were found. The necessary and sufficient conditions for the unbiasedness of linear estimates of linear functions of matrices were provided. The notion of quasi-optimal estimates for linear functions of matrices was introduced, and it was proved that in the class of unbiased estimates, quasi-optimal estimates exist and are unique. For such estimates, the conditions of convergence to zero of the guaranteed mean-square errors were obtained. Also, for linear estimates of unknown matrices, the concept of quasi-minimax estimates was introduced and it was confirmed that they are unbiased. For special sets, which include an unknown matrix and correlation matrices of observation errors, such estimates were expressed through the solution of linear operator equations in a finite-dimensional space. For quasi-minimax estimates under certain assumptions, the form of the guaranteed mean squared error of the unknown matrix was found. It was shown that such errors are limited by the sum of traces of the known matrices. An example of finding a minimax unbiased linear estimation was given for a special type of random matrices that are included in the observation equation.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48304685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-6
N. Yakovenko, A. Bondarchuk, O. Kovalchuk
Axisymmetric problem of heat pulse irradiation of a cylindrical solid is considered. Nonlinear behavior of the material is described by the generalized Bodner-Partom model of flow. The nature of generalization lies in applying the rule of mixtures for the determination of parameters of the model responsible for yield point and ultimate strength. The considered model enables one to estimate the residual stress-strain state more exactly. During subsequent in-service loading of cylindrical solids, this state strongly affects the fatigue resistance of elements. The problem is solved by the time step integration method, iterative method, and finite element method. In each time step, we realize a double iteration process. The first is connected with the integration of the system of nonlinear equations of flow, the second with the solution of equations of motion and heat conduction. The calculations are performed on a grid FEM, especially in the region of irradiation, for the correct modeling of thermomechanical behavior of the material. The grid parameters are chosen with the help of the criterion of practical convergence of the solutions. The investigation of the stress-strain state of an inelastic material with regard for the dependence of parameters of the flow model on the phase composition of a material is carried out by using of numerical simulation. The main result is the following: qualitative and quantitative effects of phase composition influence on inelastic characteristics are established, namely change of tensile residual stresses on compression. The results obtained in the work can be used in calculations of parameters of surface hardening technologies.
{"title":"THE INVESTIGATION OF DYNAMIC EFFECTS UNDER MICROSCALE PULSE LOAD","authors":"N. Yakovenko, A. Bondarchuk, O. Kovalchuk","doi":"10.34229/1028-0979-2021-4-6","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-6","url":null,"abstract":"Axisymmetric problem of heat pulse irradiation of a cylindrical solid is considered. Nonlinear behavior of the material is described by the generalized Bodner-Partom model of flow. The nature of generalization lies in applying the rule of mixtures for the determination of parameters of the model responsible for yield point and ultimate strength. The considered model enables one to estimate the residual stress-strain state more exactly. During subsequent in-service loading of cylindrical solids, this state strongly affects the fatigue resistance of elements. The problem is solved by the time step integration method, iterative method, and finite element method. In each time step, we realize a double iteration process. The first is connected with the integration of the system of nonlinear equations of flow, the second with the solution of equations of motion and heat conduction. The calculations are performed on a grid FEM, especially in the region of irradiation, for the correct modeling of thermomechanical behavior of the material. The grid parameters are chosen with the help of the criterion of practical convergence of the solutions. The investigation of the stress-strain state of an inelastic material with regard for the dependence of parameters of the flow model on the phase composition of a material is carried out by using of numerical simulation. The main result is the following: qualitative and quantitative effects of phase composition influence on inelastic characteristics are established, namely change of tensile residual stresses on compression. The results obtained in the work can be used in calculations of parameters of surface hardening technologies.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44084800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-2
V. Legeza, Alexander Neshchadym
The article proposes a solution to the well-known Zermelo navigation problem by classical variational methods. The classical Zermelo problem within the framework of optimal control theory is formulated as follows. The ship must pass through the region of strong currents, the magnitude and direction of the current velocity are set as functions of phase variables. In this case, the relative speed of the ship is set, the module of which remains constant during movement. It is necessary to find such an optimal control that ensures the arrival of the ship at a given point in the minimum time, i.e. control of the ship by fast-action should be determined. In this paper, we consider the brachistochronic motion of a material point in a plane vector field of a mobile fluid, for which the classical variational problem of finding extreme trajectories is formulated. The aim of the study is to obtain equations of extreme trajectories along which a material point moves from a given starting point to a given finish point in the least amount of time. The solution to the problem was carried out using the classical methods of the theory of the calculus of variations. For a given variant of the boundary conditions, algebraic equations of extremals of motion of a material point were established in the form of segments of a power series. A comparative analysis of the fast-action was carried out both along extreme trajectories and along an alternative path — along a straight line that connects two given start and finish points. Analysis of the results showed that the considered variational problem has two solutions, which differ only in sign. However, only one solution provides the minimum time for moving a material point between two given points. It was also found that the extreme trajectory of the brachistochronic motion of a point is not straight, but has an oscillatory character.
{"title":"DETERMINATION OF THE FASTEST TRAJECTORIES OF MATERIAL POINT MOTION IN A HORIZONTAL VECTOR FIELD","authors":"V. Legeza, Alexander Neshchadym","doi":"10.34229/1028-0979-2021-4-2","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-2","url":null,"abstract":"The article proposes a solution to the well-known Zermelo navigation problem by classical variational methods. The classical Zermelo problem within the framework of optimal control theory is formulated as follows. The ship must pass through the region of strong currents, the magnitude and direction of the current velocity are set as functions of phase variables. In this case, the relative speed of the ship is set, the module of which remains constant during movement. It is necessary to find such an optimal control that ensures the arrival of the ship at a given point in the minimum time, i.e. control of the ship by fast-action should be determined. In this paper, we consider the brachistochronic motion of a material point in a plane vector field of a mobile fluid, for which the classical variational problem of finding extreme trajectories is formulated. The aim of the study is to obtain equations of extreme trajectories along which a material point moves from a given starting point to a given finish point in the least amount of time. The solution to the problem was carried out using the classical methods of the theory of the calculus of variations. For a given variant of the boundary conditions, algebraic equations of extremals of motion of a material point were established in the form of segments of a power series. A comparative analysis of the fast-action was carried out both along extreme trajectories and along an alternative path — along a straight line that connects two given start and finish points. Analysis of the results showed that the considered variational problem has two solutions, which differ only in sign. However, only one solution provides the minimum time for moving a material point between two given points. It was also found that the extreme trajectory of the brachistochronic motion of a point is not straight, but has an oscillatory character.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42796851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-8
B. Borsuk, A. Khanin
The paper is devoted to a behavior investigation of the upper bound of deviation of functions from Zygmund classes from their biharmonic Poisson integrals. Systematic research in this direction was conducted by a number of Ukrainian as well as foreign scientists. But most of the known results relate to an estimation of deviations of functions from different classes from operators that were constructed based on triangular l-methods of the Fourier series summation (Fejer, Valle Poussin, Riesz, Rogozinsky, Steklov, Favard, etc.). Concerning the results relating to linear methods of the Fourier series summation, given by a set of functions of natural argument (Abel-Poisson, Gauss-Weierstrass, biharmonic and threeharmonic Poisson integrals), in this direction the progress was less notable. This may be due to the fact that the above-mentioned linear methods the Fourier series summation are solutions of corresponding integral and differential equations of elliptic type. And, therefore, they require more time-consuming calculations in order to obtain some estimates, that are suitable for a direct use for applied purposes. At the same time, in the present paper we investigate approximative characteristics of linear positive Poisson-type operators on Zygmund classes of functions. According to the well-known results by P.P. Korovkin, these positive linear operators realize the best asymptotic approximation of functions from Zygmund classes. Thus, the estimate obtained in this paper for the deviation of functions from Zygmund classes from their biharmonic Poisson integrals (the least studied and most valuable among all linear positive operators) is relevant from the viewpoint of applied mathematics.
本文研究了Zygmund类函数偏离双调和泊松积分上界的行为。一些乌克兰和外国科学家在这方面进行了系统的研究。但是，大多数已知的结果与基于傅立叶级数求和的三角l-方法(Fejer, Valle Poussin, Riesz, Rogozinsky, Steklov, Favard等)构造的不同类别的函数的偏差估计有关。关于傅里叶级数和的线性方法的结果，由一组自然参数函数(Abel-Poisson, Gauss-Weierstrass，双调和和三调和泊松积分)给出，在这个方向上的进展不太显著。这可能是由于上述线性方法的傅里叶级数求和是相应的椭圆型积分方程和微分方程的解。因此，它们需要更耗时的计算，以便获得一些适合直接用于应用目的的估计。同时，本文研究了Zygmund函数类上线性正泊松型算子的近似性质。根据P.P. Korovkin的著名结果，这些正线性算子实现了Zygmund类中函数的最佳渐近逼近。因此，本文对Zygmund类的函数偏离其双调和泊松积分(所有线性正算子中研究最少但最有价值的一种)的估计具有应用数学的意义。
{"title":"ON APPROXIMATION OF FUNCTIONS FROM ZYGMUND CLASSES BY BIHARMONIC POISSON INTEGRALS","authors":"B. Borsuk, A. Khanin","doi":"10.34229/1028-0979-2021-4-8","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-8","url":null,"abstract":"The paper is devoted to a behavior investigation of the upper bound of deviation of functions from Zygmund classes from their biharmonic Poisson integrals. Systematic research in this direction was conducted by a number of Ukrainian as well as foreign scientists. But most of the known results relate to an estimation of deviations of functions from different classes from operators that were constructed based on triangular l-methods of the Fourier series summation (Fejer, Valle Poussin, Riesz, Rogozinsky, Steklov, Favard, etc.). Concerning the results relating to linear methods of the Fourier series summation, given by a set of functions of natural argument (Abel-Poisson, Gauss-Weierstrass, biharmonic and threeharmonic Poisson integrals), in this direction the progress was less notable. This may be due to the fact that the above-mentioned linear methods the Fourier series summation are solutions of corresponding integral and differential equations of elliptic type. And, therefore, they require more time-consuming calculations in order to obtain some estimates, that are suitable for a direct use for applied purposes. At the same time, in the present paper we investigate approximative characteristics of linear positive Poisson-type operators on Zygmund classes of functions. According to the well-known results by P.P. Korovkin, these positive linear operators realize the best asymptotic approximation of functions from Zygmund classes. Thus, the estimate obtained in this paper for the deviation of functions from Zygmund classes from their biharmonic Poisson integrals (the least studied and most valuable among all linear positive operators) is relevant from the viewpoint of applied mathematics.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43217200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-7
V. Sobchuk, Galina Kharkevych
Machine translation is widely used in the translation of commercial, technical, scientific information that is connected with the process of globalization and, accordingly, the expansion of the network of business relations. Mathematical methods related to machine translation of the texts have recently received new development due to the intensive development of Fourier transformation theory. Thus, the requirements for filtering accuracy in the processing of contrast signals and images have increased, allowing to create efficient filtering algorithms. Frequency algorithms are the most efficient of all the existing filtering algorithms, i.e., those where the coefficients of decomposition of the noisy signal by Fourier basis are the subject to processing. When using Fourier filtering algorithms, the properties of Fourier transformation play an important role, that depend on belonging to a particular class of differential functions. The necessary condition for the existence of the continuous Fourier transformation is the absolute convergence of some functions by means of which the real studied process is describing. In practice, the so-called “summation functions” are often used as simulated functions, which can be constructed using a linear matrix summation of Fourier series. As for the latter, scientists distinguish between both triangular and rectangular linear matrix methods. This paper is devoted to the study of the convergence conditions of Fourier transformations of both triangular and rectangular linear matrix methods for summing Fourier series. Moreover, this article shows that the rate of convergence of Fourier transformation of the rectangular linear Abel-Poisson method is at times faster than the rate of convergence of the analogous triangular linear Abel-Poisson method. This result can further significantly influence the choice of the more effective Fourier transformation used in the process of machine translation of the text.
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Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-11
A. Tkachenko
An in-flight geometric calibration (further — calibration) is interpreted here as a procedure of making more preceise mutual attitude parameters of the onboard imaging camera and the star tracker. The problem of calibration is solved with using of observations of the landmarks from the orbit. In this work, the landmarks are considered as unknown in the sense that they may be identified on the several snapshots, they may be associated with synchronous data of the star tracker and GPS, but their location in the Earth coordinate frame is unknown. While unknown markers are used, it is more complicated to provide high accuracy of calibration than when geo-referenced markers are observed. In such a situation, improvement of the onboard devices and gauges and increasing of their accuracy strenghtens advisability of agreement of attainable accuracy of calculations while in-flight geometric calibration with accessible measurings accuracy. It concerns properly calibration so as geo-referencing of space snaps using results of calibration. In particular, it is important to consider how accuracy of calibration depends on the accuracy of specific measurings and initial data. Actuality of the considered problem is indisputable. Without its solution, attraction of high-accurate measurings is senseless. A main means of investigation is computer simulanion and analysis of its results. The combined algorithm is proposed for the processing of the calibration measuring equations. It consists of two independent parts. The first one belongs to author of this work and is based on photogrammetric condition of collinearity The second part belongs to D.V. Lebedev and is based on photogrammetric condition of coplanarity. The method of state estimation with high convergence characteristics — fuzzy state observer — is used for resolving of measuring equations. The results of above-mentioned calibration are fully fit for the geo-referencing of the unknown ground objects with acceptable accuracy. Computer simulation had demonsrated good accuracy of the proposed method of the in-flight geometric calibration using unknown landmarks in a combination with high-precise characteristics of used technical means. The simulation had shown the calibration accuracy on the level of 5 arc sec and accuracy of the geo-referencing on the level of 10–20 m. It is fully comparable with accuracy when geo-referenced markers are observated.
{"title":"HIGH-PRECISION IN-FLIGHT CALIBRATION USING UNKNOWN LANDMARKS","authors":"A. Tkachenko","doi":"10.34229/1028-0979-2021-4-11","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-11","url":null,"abstract":"An in-flight geometric calibration (further — calibration) is interpreted here as a procedure of making more preceise mutual attitude parameters of the onboard imaging camera and the star tracker. The problem of calibration is solved with using of observations of the landmarks from the orbit. In this work, the landmarks are considered as unknown in the sense that they may be identified on the several snapshots, they may be associated with synchronous data of the star tracker and GPS, but their location in the Earth coordinate frame is unknown. While unknown markers are used, it is more complicated to provide high accuracy of calibration than when geo-referenced markers are observed. In such a situation, improvement of the onboard devices and gauges and increasing of their accuracy strenghtens advisability of agreement of attainable accuracy of calculations while in-flight geometric calibration with accessible measurings accuracy. It concerns properly calibration so as geo-referencing of space snaps using results of calibration. In particular, it is important to consider how accuracy of calibration depends on the accuracy of specific measurings and initial data. Actuality of the considered problem is indisputable. Without its solution, attraction of high-accurate measurings is senseless. A main means of investigation is computer simulanion and analysis of its results. The combined algorithm is proposed for the processing of the calibration measuring equations. It consists of two independent parts. The first one belongs to author of this work and is based on photogrammetric condition of collinearity The second part belongs to D.V. Lebedev and is based on photogrammetric condition of coplanarity. The method of state estimation with high convergence characteristics — fuzzy state observer — is used for resolving of measuring equations. The results of above-mentioned calibration are fully fit for the geo-referencing of the unknown ground objects with acceptable accuracy. Computer simulation had demonsrated good accuracy of the proposed method of the in-flight geometric calibration using unknown landmarks in a combination with high-precise characteristics of used technical means. The simulation had shown the calibration accuracy on the level of 5 arc sec and accuracy of the geo-referencing on the level of 10–20 m. It is fully comparable with accuracy when geo-referenced markers are observated.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45761863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-01DOI: 10.34229/1028-0979-2021-4-1
Vladislav Hrygorenko, D. Klyushin, S. Lyashko
ADMM (alternating direction methods of multipliers) is widely used to solve many optimization problems. This method is especially important for solving problems arising in great variety of fields, especially in machine learning, mathematical statistics and pattern recognition, signal denoising and big data analysis using parallel computations. ADMM also useful for solving optimization problems in cases when objective function presented as sum of smooth and non-smooth functions. Standard two block ADMM can be extended for solving problems where objective function can be represented as sum of N functions (multiblock approach). In this paper we described some most common used technics used for acceleration of ADMM and reviewed most significant works related to this topic. The aim of this paper is to develop an improved version of the ADMM with better convergence rate. For this, we used a combination of two already existing approaches: splitting the initial optimization problem into subtasks and solving them in parallel using multiblock approach and calculating the Nesterov acceleration at each iteration step. We provided a theoretical justification for the convergence of this method, defined necessary for convergence conditions, and also implemented the proposed algorithm in the Python programming language and applied it to solve the problem of exchange with random data, basis pursuit problem and LASSO with restrictions problem. The article presents the results of comparing the effectiveness of the multiblock ADMM method with Nesterov acceleration and the existing multiblock and standard two-block ADMM method. Multiblock ADMM with Nesterov acceleration demonstrates better performance that already existing methods and also can be easily adopted for parallel calculation. Proposed method has great practical value due to necessity to solve optimization problems with great volumes of data, which requires high performance, because it works much more faster than well-known analogies. The use of the proposed method will make it possible to solve practically important problems of large volume using parallel calculations.
{"title":"MULTI-BLOCK ADMM METHOD WITH NESTEROV ACCELERATION","authors":"Vladislav Hrygorenko, D. Klyushin, S. Lyashko","doi":"10.34229/1028-0979-2021-4-1","DOIUrl":"https://doi.org/10.34229/1028-0979-2021-4-1","url":null,"abstract":"ADMM (alternating direction methods of multipliers) is widely used to solve many optimization problems. This method is especially important for solving problems arising in great variety of fields, especially in machine learning, mathematical statistics and pattern recognition, signal denoising and big data analysis using parallel computations. ADMM also useful for solving optimization problems in cases when objective function presented as sum of smooth and non-smooth functions. Standard two block ADMM can be extended for solving problems where objective function can be represented as sum of N functions (multiblock approach). In this paper we described some most common used technics used for acceleration of ADMM and reviewed most significant works related to this topic. The aim of this paper is to develop an improved version of the ADMM with better convergence rate. For this, we used a combination of two already existing approaches: splitting the initial optimization problem into subtasks and solving them in parallel using multiblock approach and calculating the Nesterov acceleration at each iteration step. We provided a theoretical justification for the convergence of this method, defined necessary for convergence conditions, and also implemented the proposed algorithm in the Python programming language and applied it to solve the problem of exchange with random data, basis pursuit problem and LASSO with restrictions problem. The article presents the results of comparing the effectiveness of the multiblock ADMM method with Nesterov acceleration and the existing multiblock and standard two-block ADMM method. Multiblock ADMM with Nesterov acceleration demonstrates better performance that already existing methods and also can be easily adopted for parallel calculation. Proposed method has great practical value due to necessity to solve optimization problems with great volumes of data, which requires high performance, because it works much more faster than well-known analogies. The use of the proposed method will make it possible to solve practically important problems of large volume using parallel calculations.","PeriodicalId":54874,"journal":{"name":"Journal of Automation and Information Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41777413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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