Pub Date : 2023-01-01DOI: 10.17721/2706-9699.2023.1.01
D. I. Symonov
The paper considers several methods of analyzing opportunities for optimizing supply chains. An iterative method of finding the optimal structure is proposed, considering the power of the supply chain links and the capacity of the paths between them. The theorem on the value of the maximum flow in the combined path is proved. A numerical simulation of the operation of the proposed algorithm for finding directions for the optimization of the network structure was performed.
{"title":"NETWORK FLOW ANALYSIS AS A METHOD OF SUPPLY CHAIN MANAGEMENT OPTIMIZATION","authors":"D. I. Symonov","doi":"10.17721/2706-9699.2023.1.01","DOIUrl":"https://doi.org/10.17721/2706-9699.2023.1.01","url":null,"abstract":"The paper considers several methods of analyzing opportunities for optimizing supply chains. An iterative method of finding the optimal structure is proposed, considering the power of the supply chain links and the capacity of the paths between them. The theorem on the value of the maximum flow in the combined path is proved. A numerical simulation of the operation of the proposed algorithm for finding directions for the optimization of the network structure was performed.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89536954","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 : 2023-01-01DOI: 10.17721/2706-9699.2023.1.04
O. Pokutnyi
The boundary value problems for the Lyapunov equation in the resonant (irregular) case in Banach and Hilbert spaces, when the solution of the equation does not exist for all right-hand sides and its uniqueness may be violated, have been investigated. The conditions for bifurcation and branching of solutions in linear and nonlinear cases, including with a moving right end of the segment on which the corresponding boundary value problem is considered, are found.
{"title":"BOUNDARY VALUE PROBLEMS FOR THE LYAPUNOV EQUATION","authors":"O. Pokutnyi","doi":"10.17721/2706-9699.2023.1.04","DOIUrl":"https://doi.org/10.17721/2706-9699.2023.1.04","url":null,"abstract":"The boundary value problems for the Lyapunov equation in the resonant (irregular) case in Banach and Hilbert spaces, when the solution of the equation does not exist for all right-hand sides and its uniqueness may be violated, have been investigated. The conditions for bifurcation and branching of solutions in linear and nonlinear cases, including with a moving right end of the segment on which the corresponding boundary value problem is considered, are found.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76808002","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 : 2023-01-01DOI: 10.17721/2706-9699.2023.1.03
V. A. Kolesnykov
In the work numerical methods for solving the Richards–Klute equation and methods of their construction are considered. A new method of constructing an adaptive grid in space is also proposed and numerical methods using it are constructed. A comparative analysis of the data of numerical methods in the conditions of a problem with a known analytical solution was carried out.
{"title":"ANALYSIS OF THE CONSTRUCTION OF NUMERICAL METHODS FOR SOLVING THE RICHARDS–KLUTE EQUATION","authors":"V. A. Kolesnykov","doi":"10.17721/2706-9699.2023.1.03","DOIUrl":"https://doi.org/10.17721/2706-9699.2023.1.03","url":null,"abstract":"In the work numerical methods for solving the Richards–Klute equation and methods of their construction are considered. A new method of constructing an adaptive grid in space is also proposed and numerical methods using it are constructed. A comparative analysis of the data of numerical methods in the conditions of a problem with a known analytical solution was carried out.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86638727","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 : 2023-01-01DOI: 10.17721/2706-9699.2023.1.02
V. Semenov, O. Kharkov
This work is devoted to the study of new algorithm for solving variational inequalities in Hilbert spaces. The proposed algorithm is a variant of the operator extrapolation method regularized using the Halpern scheme. The algorithm has an advantage over the Korpelevich extragradient method and the method of extrapolation from the past in terms of the amount of calculations required for the iterative step. For variational inequalities with monotone, Lipschitz continuous operators acting in Hilbert space, a theorem on strong convergence of the method is proved.
{"title":"THE REGULARIZED OPERATOR EXTRAPOLATION ALGORITHM","authors":"V. Semenov, O. Kharkov","doi":"10.17721/2706-9699.2023.1.02","DOIUrl":"https://doi.org/10.17721/2706-9699.2023.1.02","url":null,"abstract":"This work is devoted to the study of new algorithm for solving variational inequalities in Hilbert spaces. The proposed algorithm is a variant of the operator extrapolation method regularized using the Halpern scheme. The algorithm has an advantage over the Korpelevich extragradient method and the method of extrapolation from the past in terms of the amount of calculations required for the iterative step. For variational inequalities with monotone, Lipschitz continuous operators acting in Hilbert space, a theorem on strong convergence of the method is proved.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"56 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81489076","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 : 2023-01-01DOI: 10.17721/2706-9699.2023.1.05
V. Samoilenko, Y. Samoilenko
The issue of the existence of solutions of the Cauchy problem for a first-order quasi-linear differential equation with partial derivatives and variable coefficients is considered. The studied equation is a generalization of the classic Hopf equation, which is used in the study of many mathematical models of hydrodynamics. This equation arises when constructing approximate (asymptotic) solutions of the Korteweg–de Vries equation and other equations with variable coefficients and a singular perturbation, in particular, when finding their asymptotic step-type soliton-like solutions. For the mentioned differential equation of the first order, the solution of the Cauchy problem is obtained in analytical form, and the statement about sufficient conditions for the existence of solutions of the initial problem in the space of rapidly decreasing functions is proved. A similar problem for a first-order differential equation with partial derivatives with variable coefficients and quadratic nonlinearity is considered.
{"title":"EXISTENCE IN SCHWARTZ SPACE AND SOLUTIONS PROPERTIES OF THE HOPF–TYPE EQUATION WITH VARIABLE COEFFICIENTS","authors":"V. Samoilenko, Y. Samoilenko","doi":"10.17721/2706-9699.2023.1.05","DOIUrl":"https://doi.org/10.17721/2706-9699.2023.1.05","url":null,"abstract":"The issue of the existence of solutions of the Cauchy problem for a first-order quasi-linear differential equation with partial derivatives and variable coefficients is considered. The studied equation is a generalization of the classic Hopf equation, which is used in the study of many mathematical models of hydrodynamics. This equation arises when constructing approximate (asymptotic) solutions of the Korteweg–de Vries equation and other equations with variable coefficients and a singular perturbation, in particular, when finding their asymptotic step-type soliton-like solutions. For the mentioned differential equation of the first order, the solution of the Cauchy problem is obtained in analytical form, and the statement about sufficient conditions for the existence of solutions of the initial problem in the space of rapidly decreasing functions is proved. A similar problem for a first-order differential equation with partial derivatives with variable coefficients and quadratic nonlinearity is considered.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90227966","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: 10.17721/2706-9699.2022.2.14
M. Savkina
At the paper a linear regression model whose function has the form $f (x)=ax + b$, $a$ and $b$ — unknown parameters, is studied. Approximate values (observations) of functions $f(x)$ are registered at equidistant points $x_0,x_1,...,x_n$ of a line segment. It is also assumed that the covariance matrix of deviations is the symmetric Toeplitz matrix. Among all Toeplitz matrices, a family of matrices is selected for which all diagonals parallel to the main, starting from the $(k+1)$th, are zero, $k=n/2$, $n$ — even. Elements of the main diagonal are denoted by $lambda$, elements of the $k$th diagonal are denoted by $c$, elements of the $j$th diagonal are denoted by $c_{k-j}$, $j=1,2,...,k-1$. The theorem proved in the article states that the following condition on the elements of such covariance matrix $c_j=bigl(k/(k+1)bigr)^j c$, $j=1,2,...,k-1$, is necessary for the coincidence of the LS and Aitken's estimations of the parameter $a$ of this model. Values $lambda$ and $c$ are any that ensure the positive definiteness of such matrix.
{"title":"THE NECESSARY CONDITION FOR COINCIDENCE OF LS AND AITKEN ESTIMATIONS OF THE HIGHER COEFFICIENT OF THE LINEAR REGRESSION MODEL IN THE CASE OF CORRELATED DEVIATIONS","authors":"M. Savkina","doi":"10.17721/2706-9699.2022.2.14","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.14","url":null,"abstract":"At the paper a linear regression model whose function has the form $f (x)=ax + b$, $a$ and $b$ — unknown parameters, is studied. Approximate values (observations) of functions $f(x)$ are registered at equidistant points $x_0,x_1,...,x_n$ of a line segment. It is also assumed that the covariance matrix of deviations is the symmetric Toeplitz matrix. Among all Toeplitz matrices, a family of matrices is selected for which all diagonals parallel to the main, starting from the $(k+1)$th, are zero, $k=n/2$, $n$ — even. Elements of the main diagonal are denoted by $lambda$, elements of the $k$th diagonal are denoted by $c$, elements of the $j$th diagonal are denoted by $c_{k-j}$, $j=1,2,...,k-1$. The theorem proved in the article states that the following condition on the elements of such covariance matrix $c_j=bigl(k/(k+1)bigr)^j c$, $j=1,2,...,k-1$, is necessary for the coincidence of the LS and Aitken's estimations of the parameter $a$ of this model. Values $lambda$ and $c$ are any that ensure the positive definiteness of such matrix.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"57 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74174966","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: 10.17721/2706-9699.2022.1.05
V. Semenov, Yana Vedel, S. Denisov
New iterative extra-proximal algorithms have been pro-posed and investigated for approximate solution of problems of equilibrium in Hadamard metric spaces. The para-meter update rule does not use the values of the Lipschitz constants of the bifunction. In contrast to the rules of the linear search type, it does not require calculations of the bifunction values at additional points. In addition, at the initial stages of the algorithms, the step size parameter can increase from iteration to iteration. For pseudo-monotone bifunctions of the Lipschitz type we proved convergence theorems. It is shown that the proposed algorithms are applicable to pseudo-monotone variational inequalities in Hilbert spaces.
{"title":"CONVERGENCE OF ADAPTIVE EXTRA-PROXIMAL ALGORITHMS FOR EQUILIBRIUM PROBLEMS IN HADAMARD SPACES","authors":"V. Semenov, Yana Vedel, S. Denisov","doi":"10.17721/2706-9699.2022.1.05","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.05","url":null,"abstract":"New iterative extra-proximal algorithms have been pro-posed and investigated for approximate solution of problems of equilibrium in Hadamard metric spaces. The para-meter update rule does not use the values of the Lipschitz constants of the bifunction. In contrast to the rules of the linear search type, it does not require calculations of the bifunction values at additional points. In addition, at the initial stages of the algorithms, the step size parameter can increase from iteration to iteration. For pseudo-monotone bifunctions of the Lipschitz type we proved convergence theorems. It is shown that the proposed algorithms are applicable to pseudo-monotone variational inequalities in Hilbert spaces.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"4 3","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72592623","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: 10.17721/2706-9699.2022.2.16
Y. V. Semenova, S. G. Solodky
The problem of numerical differentiation for non-periodic bivariate functions is investigated. For the recovering mixed derivatives of such functions an approach on the base of truncation method is proposed. The constructed algorithms deal with Legendere polynomials, the degree of which is chosen so as to minimize the approximation error. It is established that these algorithms are order-optimal both in terms of accuracy and in the sense of the amount of Galerkin information involved.
{"title":"OPTIMAL METHODS FOR RECOVERING MIXED DERIVATIVES OF NON-PERIODIC FUNCTIONS","authors":"Y. V. Semenova, S. G. Solodky","doi":"10.17721/2706-9699.2022.2.16","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.16","url":null,"abstract":"The problem of numerical differentiation for non-periodic bivariate functions is investigated. For the recovering mixed derivatives of such functions an approach on the base of truncation method is proposed. The constructed algorithms deal with Legendere polynomials, the degree of which is chosen so as to minimize the approximation error. It is established that these algorithms are order-optimal both in terms of accuracy and in the sense of the amount of Galerkin information involved.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"118 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85852603","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: 10.17721/2706-9699.2022.2.04
V. Begun
The implementation of information technologies in Ukraine in the field of security and the state of education in this direction were studied. A comparison of the degree of informatization in this field and education in this field with developed countries in the nuclear field is made. The problems and tasks of teaching the direction of digital management in the field of security and the main method of modeling dangerous systems and processes — probabilistic structural and logical models — are analyzed. Conclusions were made about the need for more widespread education in the applied field of security, formulation and solution of actual problems, creation of special software.
{"title":"IMPLEMENTATION OF DIGITAL MANAGEMENT IN THE SECURITY FIELD","authors":"V. Begun","doi":"10.17721/2706-9699.2022.2.04","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.04","url":null,"abstract":"The implementation of information technologies in Ukraine in the field of security and the state of education in this direction were studied. A comparison of the degree of informatization in this field and education in this field with developed countries in the nuclear field is made. The problems and tasks of teaching the direction of digital management in the field of security and the main method of modeling dangerous systems and processes — probabilistic structural and logical models — are analyzed. Conclusions were made about the need for more widespread education in the applied field of security, formulation and solution of actual problems, creation of special software.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"2003 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89522075","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: 10.17721/2706-9699.2022.2.05
S. Denisov, V. Semenov, O. Kharkov
This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.
{"title":"WEAK CONVERGENCE OF THE OPERATOR EXTRAPOLATION METHOD FOR VARIATIONAL INEQUALITIES IN UNIFORMLY CONVEX BANACH SPACES","authors":"S. Denisov, V. Semenov, O. Kharkov","doi":"10.17721/2706-9699.2022.2.05","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.05","url":null,"abstract":"This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"165 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74213130","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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