Pub Date : 2022-01-01DOI: 10.17721/2706-9699.2022.1.09
A. Y. Shavlyuk, V. Semenov
The asymptotic behavior of the gradient system, which is a continuous analogue of the variant of the gradient method from [16] for the minimization of strongly convex functions, is studied. Using the Lyapunov analysis, estimates of the rate of convergence of the gradient system were established.
{"title":"CONVERGENCE OF GRADIENT-LIKE DYNAMICAL SYSTEM","authors":"A. Y. Shavlyuk, V. Semenov","doi":"10.17721/2706-9699.2022.1.09","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.09","url":null,"abstract":"The asymptotic behavior of the gradient system, which is a continuous analogue of the variant of the gradient method from [16] for the minimization of strongly convex functions, is studied. Using the Lyapunov analysis, estimates of the rate of convergence of the gradient system were established.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"131 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75059707","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.2.09
P. Malachivskyy, L. Melnychok, Y. Pizyur
A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p to infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.
提出了一种利用多变量函数的有理表达式和插值构造切比雪夫近似的方法。该方法基于在空间范数$L_p$ ($p to infty$)中具有插值条件的有理表达式构造最终平均-功率近似。为了构造这样的近似，采用了一种基于最小二乘法的具有两个可变权函数的迭代方案。
{"title":"CHEBYSHEV APPROXIMATION MULTIVARIABLE FUNCTIONS BY THE RATIONAL EXPRESSION WITH THE INTERPOLATION","authors":"P. Malachivskyy, L. Melnychok, Y. Pizyur","doi":"10.17721/2706-9699.2022.2.09","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.09","url":null,"abstract":"A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p to infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"41 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78222979","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.2.06
O. Kashpur
In a linear infinite-dimensional space with a scalar product and in a finite-dimensional Euclidean space the interpolation Hermite polynomial with a minimal norm, generated by a Gaussian measure, contains fundamental polynomials are shown. The accuracy of Hermit’s interpolation formulas on polynomials of the appropriate degree are researched.
{"title":"UNDAMENTAL POLYNOMIALS OF HERMITE’SINTERPOLATION FORMULA IN LINEAR NORMAL AND INEUCLIDEAN SPACES","authors":"O. Kashpur","doi":"10.17721/2706-9699.2022.2.06","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.06","url":null,"abstract":"In a linear infinite-dimensional space with a scalar product and in a finite-dimensional Euclidean space the interpolation Hermite polynomial with a minimal norm, generated by a Gaussian measure, contains fundamental polynomials are shown. The accuracy of Hermit’s interpolation formulas on polynomials of the appropriate degree are researched.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89269467","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.1.04
G. Sandrakov
Computational algorithms for modeling of multiphase hydrodynamics processes with take of phase transitions will be discussed. The algorithms are based on discretization of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial discretization is natural and numerical simulations are realized as direct computer experiments. The experiments are implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite–diamond phase transitions and calculations are given. Modification of the algorithms have also been developed to take into account the influence of viscosity when simulating the dynamics of a multiphase fluid in porous media.
{"title":"COMPUTATIONAL ALGORITHMS FOR MULTIPHASE HYDRODYNAMICS MODELS AND FILTRATION","authors":"G. Sandrakov","doi":"10.17721/2706-9699.2022.1.04","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.04","url":null,"abstract":"Computational algorithms for modeling of multiphase hydrodynamics processes with take of phase transitions will be discussed. The algorithms are based on discretization of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial discretization is natural and numerical simulations are realized as direct computer experiments. The experiments are implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite–diamond phase transitions and calculations are given. Modification of the algorithms have also been developed to take into account the influence of viscosity when simulating the dynamics of a multiphase fluid in porous media.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90960941","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.1.01
A. Hulianytskyi, Kostiantyn Tokar
In the work considered process of continuous-time random walk, that has fat-tailed jump waiting time, on an equispaced grid of one-dimensional domain with absorbing boundary. Deduced fractional equation w.r.t. cumulative distribution function of first passage time. Obtained asymptotic of density of this variable and shown that it has fat tail.
{"title":"SUBDIFFUSION FIRST-PASSAGE TIME ON DISCRETE GRID","authors":"A. Hulianytskyi, Kostiantyn Tokar","doi":"10.17721/2706-9699.2022.1.01","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.01","url":null,"abstract":"In the work considered process of continuous-time random walk, that has fat-tailed jump waiting time, on an equispaced grid of one-dimensional domain with absorbing boundary. Deduced fractional equation w.r.t. cumulative distribution function of first passage time. Obtained asymptotic of density of this variable and shown that it has fat tail.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86030960","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.2.12
O. Nakonechnyi, G. Kudin, P. Zinko, T. Zinko
The problems of guaranteed mean square estimation of unknown rectangular matrices based on observations of linear functions from random matrices with random errors are considered in the paper. Asymptotic distributions of guaranteed errors and guaranteed estimates are obtained in the case of small perturbations of the matrices. A test example of the asymptotic distribution is given.
{"title":"GUARANTEED ROOT MEAN SQUARE ESTIMATES OF OBSERVATIONS WITH UNKNOWN MATRICES","authors":"O. Nakonechnyi, G. Kudin, P. Zinko, T. Zinko","doi":"10.17721/2706-9699.2022.2.12","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.12","url":null,"abstract":"The problems of guaranteed mean square estimation of unknown rectangular matrices based on observations of linear functions from random matrices with random errors are considered in the paper. Asymptotic distributions of guaranteed errors and guaranteed estimates are obtained in the case of small perturbations of the matrices. A test example of the asymptotic distribution is given.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83591873","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.1.08
A. Tymoshenko, D. Klyushin, S. Lyashko
The article is dedicated to several gradient based methods for solving a two-dimensional humidification problem, described by Richards equation. Several assumptions are made: water is assumed incompressible, external pressure and temperature are constant. The initial state and desired function are known, while the optimal source power should be calculated. Kirchhoff transformation is applied to the initial equation to simplify the stated problem. Time and space coordinates are scaled to get linear dimensionless equation, which can be easily discretized over space and time. Numerical methods are applied to rewrite and solve the system. Also gradient methods are applied for cases, where it is possible to define the optimization functional for every allowed source power.
{"title":"GRADIENT METHODS FOR IDENTIFICATION OF POINT SOURCE POWER IN POROUS MEDIUM","authors":"A. Tymoshenko, D. Klyushin, S. Lyashko","doi":"10.17721/2706-9699.2022.1.08","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.08","url":null,"abstract":"The article is dedicated to several gradient based methods for solving a two-dimensional humidification problem, described by Richards equation. Several assumptions are made: water is assumed incompressible, external pressure and temperature are constant. The initial state and desired function are known, while the optimal source power should be calculated. Kirchhoff transformation is applied to the initial equation to simplify the stated problem. Time and space coordinates are scaled to get linear dimensionless equation, which can be easily discretized over space and time. Numerical methods are applied to rewrite and solve the system. Also gradient methods are applied for cases, where it is possible to define the optimization functional for every allowed source power.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"71 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83334698","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.2.13
Y. Pelekh, A. Kunynets, R. Pelekh
Using the continued fractions and the method of constructing Runge-Kutta methods, numerical methods for solving the Cauchy problem for nonlinear Volterra non-linear integrodifferential equations are proposed. With appropriate values of the parameters, one can obtain an approximation to the exact solution of the first and second order of accuracy. We found a set of parameters for which we obtain two-sided calculation formulas, which at each step of integration allow to obtain the upper and lower approximations of the exact solution.
{"title":"TWO-SIDED METHODS FOR SOLVING INITIAL VALUE PROBLEM FOR NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS","authors":"Y. Pelekh, A. Kunynets, R. Pelekh","doi":"10.17721/2706-9699.2022.2.13","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.13","url":null,"abstract":"Using the continued fractions and the method of constructing Runge-Kutta methods, numerical methods for solving the Cauchy problem for nonlinear Volterra non-linear integrodifferential equations are proposed. With appropriate values of the parameters, one can obtain an approximation to the exact solution of the first and second order of accuracy. We found a set of parameters for which we obtain two-sided calculation formulas, which at each step of integration allow to obtain the upper and lower approximations of the exact solution.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83008510","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.2.03
S. Baranovsky, A. Bomba
A model of viral biinfection has been modified to predict the development of the disease process, taking into account diffusion perturbations, concentrated influences, as well as the logistic dynamics of antigen and antibody populations. The solution of the original model singularly perturbed problem with a delay is presented in the form of numerically asymptotic approximations of solutions to the corresponding sequence of problems without delay. The results of computer experiments are presented, which demonstrate a decrease in the rate of model growth of the antigenic population, taking into account the diffusion «scattering» of the active factors of the process. Also illustrated is the exacerbation of the nature of the course of a previously stabilized chronic disease due to the redistribution of the resources of the immune system to overcome infection with another viral infection. It was noted that such exacerbation significantly increases under conditions of low model levels of logistical limitation of the volume of antibody synthesis. It is emphasized that an excessive increase in the model concentration of chronic disease antigens due to a too low level of logistical limitation of the antibody population leads to a significant predictive damage to the target organ and a corresponding decrease in the overall power of the immune response. Taking into account such an effect is important when predicting the development of the disease in practical decision-making situations regarding the formation of the most effective treatment programs, including the use of various concentrated effects of immunotherapy.
{"title":"MODIFIED MODEL OF VIRAL BIINFECTION TAKING INTO ACCOUNT DIFFUSION PERTURBATIONS, CONCENTRATED INFLUENCES AND LOGISTIC DYNAMICS","authors":"S. Baranovsky, A. Bomba","doi":"10.17721/2706-9699.2022.2.03","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.03","url":null,"abstract":"A model of viral biinfection has been modified to predict the development of the disease process, taking into account diffusion perturbations, concentrated influences, as well as the logistic dynamics of antigen and antibody populations. The solution of the original model singularly perturbed problem with a delay is presented in the form of numerically asymptotic approximations of solutions to the corresponding sequence of problems without delay. The results of computer experiments are presented, which demonstrate a decrease in the rate of model growth of the antigenic population, taking into account the diffusion «scattering» of the active factors of the process. Also illustrated is the exacerbation of the nature of the course of a previously stabilized chronic disease due to the redistribution of the resources of the immune system to overcome infection with another viral infection. It was noted that such exacerbation significantly increases under conditions of low model levels of logistical limitation of the volume of antibody synthesis. It is emphasized that an excessive increase in the model concentration of chronic disease antigens due to a too low level of logistical limitation of the antibody population leads to a significant predictive damage to the target organ and a corresponding decrease in the overall power of the immune response. Taking into account such an effect is important when predicting the development of the disease in practical decision-making situations regarding the formation of the most effective treatment programs, including the use of various concentrated effects of immunotherapy.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88924407","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 : 2022-01-01DOI: 10.17721/2706-9699.2022.2.07
O. Y. Kosukha, I. Shevchuk
This research paper provides a description of the system of intellectual analysis and prediction of reactions to news based on data from Telegram channels. In particular, the features of collecting and pre-processing datasets for the system, the methodology of thematic analysis of the received data, and the model used to obtain predictions of reactions to Telegram messages depending on their text are described.
{"title":"A SYSTEM OF INTELLECTUAL ANALYSIS AND PREDICTION OF REACTIONS TO NEWS BASED ON DATA FROM TELEGRAM CHANNELS","authors":"O. Y. Kosukha, I. Shevchuk","doi":"10.17721/2706-9699.2022.2.07","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.07","url":null,"abstract":"This research paper provides a description of the system of intellectual analysis and prediction of reactions to news based on data from Telegram channels. In particular, the features of collecting and pre-processing datasets for the system, the methodology of thematic analysis of the received data, and the model used to obtain predictions of reactions to Telegram messages depending on their text are described.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75425338","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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