Pub Date : 2022-12-27DOI: 10.33581/2520-6508-2022-3-54-66
S. V. Chebakov, L. V. Serebryanaya
An algorithm for solving the knapsack problem based on the proposed multicriteria model has been developed. The structure of admissible subsets is presented for the value of the non-dominance depth of the Pareto layer equal to zero. The sum of the resource of the elements of this layer is greater than or equal to the value of the volume of the knapsack. Based on the structure, the form of the optimal admissible subset with the maximum total value of the weight of its elements is determined. It is shown that at a certain stage the developed algorithm includes the solution of a number of knapsack subtasks. Their knapsack volumes are smaller than in the original problem with input data sets. The definition of the redundancy of the set of initial data and the condition for the existence of redundancy for a given value of the depth of non-dominance of the Pareto layer are introduced.
{"title":"Algorithm for solving the knapsack problem with certain properties of Pareto layers","authors":"S. V. Chebakov, L. V. Serebryanaya","doi":"10.33581/2520-6508-2022-3-54-66","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-54-66","url":null,"abstract":"An algorithm for solving the knapsack problem based on the proposed multicriteria model has been developed. The structure of admissible subsets is presented for the value of the non-dominance depth of the Pareto layer equal to zero. The sum of the resource of the elements of this layer is greater than or equal to the value of the volume of the knapsack. Based on the structure, the form of the optimal admissible subset with the maximum total value of the weight of its elements is determined. It is shown that at a certain stage the developed algorithm includes the solution of a number of knapsack subtasks. Their knapsack volumes are smaller than in the original problem with input data sets. The definition of the redundancy of the set of initial data and the condition for the existence of redundancy for a given value of the depth of non-dominance of the Pareto layer are introduced.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45515349","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 : 2022-12-26DOI: 10.33581/2520-6508-2022-3-79-90
Yauheni V. Audzeichyk, P. Konon
The paper investigates the shapes of relative rest of limited layers of liquid on a rotating horizontal plane in the field of gravity in the presence of surface tension. The layers under consideration have a simply connected free surface and rotational symmetry with respect to the line of action of the angular velocity. The mathematical formulation of this problem is reduced to a system of first-order ordinary differential equations with boundary and integral closing conditions. A new algorithm for the numerical solution of the resulting system is proposed, the influence of various dimensionless parameters on the characteristics of equilibrium droplet shapes is studied, and criteria for the existence of such shapes are determined. The paper is of theoretical interest, since the problem under consideration is one of the fundamental ones in the research of capillary phenomena. The developed numerical scheme can also be applied in a wider class of differential equations. The results of the article can be used in practical tasks related to coating, fiber and powder production by the centrifugal-disk method.
{"title":"Numerical study of the relative equilibrium of a droplet with a simply connected free surface on a rotating plane","authors":"Yauheni V. Audzeichyk, P. Konon","doi":"10.33581/2520-6508-2022-3-79-90","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-79-90","url":null,"abstract":"The paper investigates the shapes of relative rest of limited layers of liquid on a rotating horizontal plane in the field of gravity in the presence of surface tension. The layers under consideration have a simply connected free surface and rotational symmetry with respect to the line of action of the angular velocity. The mathematical formulation of this problem is reduced to a system of first-order ordinary differential equations with boundary and integral closing conditions. A new algorithm for the numerical solution of the resulting system is proposed, the influence of various dimensionless parameters on the characteristics of equilibrium droplet shapes is studied, and criteria for the existence of such shapes are determined. The paper is of theoretical interest, since the problem under consideration is one of the fundamental ones in the research of capillary phenomena. The developed numerical scheme can also be applied in a wider class of differential equations. The results of the article can be used in practical tasks related to coating, fiber and powder production by the centrifugal-disk method.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47626637","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 : 2022-12-23DOI: 10.33581/2520-6508-2022-3-67-78
Shibsankar Das, S. Rai
A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based topological indices such as the Wiener index, hyper-Wiener index, Harary index, and Tratch – Stankevitch – Zefirov index. In the present study, we determine a closed form of the Hosoya polynomial for the third type of the chain hex-derived network of dimension n and derive the distance-based topological indices of the network with the help of their direct formulas and alternatively via using the obtained Hosoya polynomial. Finally, we graphically represent the computed distance-based topological indices and the Hosoya polynomial of the underlying network to comprehend their geometrical pattern. This study of the Hosoya polynomial and the corresponding indices can set the basis for more exploration into chain hex-derived networks and their properties.
{"title":"On the Hosoya polynomial of the third type of the chain hex-derived network","authors":"Shibsankar Das, S. Rai","doi":"10.33581/2520-6508-2022-3-67-78","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-67-78","url":null,"abstract":"A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based topological indices such as the Wiener index, hyper-Wiener index, Harary index, and Tratch – Stankevitch – Zefirov index. In the present study, we determine a closed form of the Hosoya polynomial for the third type of the chain hex-derived network of dimension n and derive the distance-based topological indices of the network with the help of their direct formulas and alternatively via using the obtained Hosoya polynomial. Finally, we graphically represent the computed distance-based topological indices and the Hosoya polynomial of the underlying network to comprehend their geometrical pattern. This study of the Hosoya polynomial and the corresponding indices can set the basis for more exploration into chain hex-derived networks and their properties.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44117091","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 : 2022-12-21DOI: 10.33581/2520-6508-2022-3-37-44
V. V. Dovgodilin
In this paper, we study the algebraic equations over the ring of p-complex numbers. Remainder division theorems and an analogue of Bezout’s theorem for p-complex polynomials are represented. For equations of the 2nd and 3rd degrees, conditions for the existence of roots are obtained, in some cases solutions are given in an explicit form. For polynomials of an arbitrary degree with an invertible leading coefficient, theorems on factorisation with a unit leading coefficient are proven in the cases where there are simple roots, multiple roots, and no roots. It is shown that in the absence of multiple roots, this decomposition will be unique, and in the case of the presence of multiple roots, the polynomial admits an infinite number of expansions.
{"title":"Algebraic equations and polynomials over the ring of p-complex numbers","authors":"V. V. Dovgodilin","doi":"10.33581/2520-6508-2022-3-37-44","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-37-44","url":null,"abstract":"In this paper, we study the algebraic equations over the ring of p-complex numbers. Remainder division theorems and an analogue of Bezout’s theorem for p-complex polynomials are represented. For equations of the 2nd and 3rd degrees, conditions for the existence of roots are obtained, in some cases solutions are given in an explicit form. For polynomials of an arbitrary degree with an invertible leading coefficient, theorems on factorisation with a unit leading coefficient are proven in the cases where there are simple roots, multiple roots, and no roots. It is shown that in the absence of multiple roots, this decomposition will be unique, and in the case of the presence of multiple roots, the polynomial admits an infinite number of expansions.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41512605","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 : 2022-12-19DOI: 10.33581/2520-6508-2022-3-91-106
M. V. Ignatenko, L. Yanovich
The problem of constructing and studying interpolation operator polynomials of an arbitrary fixed degree, defined in spaces of rectangular matrices, which would be generalisations of the corresponding interpolation formulas in the case of square matrices, is considered. Linear interpolation formulas of various structures are constructed for rectangular matrices. Matrix polynomials, with respect to which the resulting interpolation formulas are invariant, are indicated. As a generalisation of linear formulas, formulas for quadratic interpolation and interpolation by polynomials of arbitrary fixed degree in the space of rectangular matrices are constructed. Particular cases of the obtained formulas are considered: when square matrices are chosen as nodes or when the values of the interpolated function are square matrices, as well as the case when both of these conditions are satisfied. For the last variant, the possibilities of different and identical matrix orders for nodes and function values are explored. The obtained results are based on the application of some well-known provisions of the theory of matrices and the theory of interpolation of scalar functions. The presentation of the material is illustrated by a number of examples.
{"title":"On the theory of operator interpolation in spaces of rectangular matrixes","authors":"M. V. Ignatenko, L. Yanovich","doi":"10.33581/2520-6508-2022-3-91-106","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-91-106","url":null,"abstract":"The problem of constructing and studying interpolation operator polynomials of an arbitrary fixed degree, defined in spaces of rectangular matrices, which would be generalisations of the corresponding interpolation formulas in the case of square matrices, is considered. Linear interpolation formulas of various structures are constructed for rectangular matrices. Matrix polynomials, with respect to which the resulting interpolation formulas are invariant, are indicated. As a generalisation of linear formulas, formulas for quadratic interpolation and interpolation by polynomials of arbitrary fixed degree in the space of rectangular matrices are constructed. Particular cases of the obtained formulas are considered: when square matrices are chosen as nodes or when the values of the interpolated function are square matrices, as well as the case when both of these conditions are satisfied. For the last variant, the possibilities of different and identical matrix orders for nodes and function values are explored. The obtained results are based on the application of some well-known provisions of the theory of matrices and the theory of interpolation of scalar functions. The presentation of the material is illustrated by a number of examples.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41359797","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 : 2022-12-16DOI: 10.33581/2520-6508-2022-3-45-53
B. Kalitine
This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.
{"title":"Pseudo-prolongations in the qualitative theory of dynamical systems","authors":"B. Kalitine","doi":"10.33581/2520-6508-2022-3-45-53","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-45-53","url":null,"abstract":"This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47587675","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 : 2022-12-13DOI: 10.33581/2520-6508-2022-3-6-15
A. P. Shilin
A new hypersingular integro-differential equation is considered on a closed curve located on the complex plane. The equation refers to linear equations with variable coefficients of a special kind. A characteristic feature is the presence of constant multipliers in the coefficients, given by some recurrent relations. The equation is first reduced to solving the Riemann boundary value problem on the original curve. A class of functions is established for solving the Riemann problem, after which this problem is solved. Next, it is necessary to solve two linear differential equations of arbitrary order for analytical functions in two different regions of the complex plane. The corresponding fundamental systems of solutions are found, after which the method of variation of arbitrary constants is used for the solution. Restrictions are imposed on the obtained solutions of differential equations in order to achieve their analyticity. As a result, all the resulting solvability conditions of the original equation are written explicitly. The solution of the original equation after solving the differential equations can be written explicitly. Solved the example.
{"title":"Hypersingular integro-differential equation with recurrent relations in coefficients","authors":"A. P. Shilin","doi":"10.33581/2520-6508-2022-3-6-15","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-6-15","url":null,"abstract":"A new hypersingular integro-differential equation is considered on a closed curve located on the complex plane. The equation refers to linear equations with variable coefficients of a special kind. A characteristic feature is the presence of constant multipliers in the coefficients, given by some recurrent relations. The equation is first reduced to solving the Riemann boundary value problem on the original curve. A class of functions is established for solving the Riemann problem, after which this problem is solved. Next, it is necessary to solve two linear differential equations of arbitrary order for analytical functions in two different regions of the complex plane. The corresponding fundamental systems of solutions are found, after which the method of variation of arbitrary constants is used for the solution. Restrictions are imposed on the obtained solutions of differential equations in order to achieve their analyticity. As a result, all the resulting solvability conditions of the original equation are written explicitly. The solution of the original equation after solving the differential equations can be written explicitly. Solved the example.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48464715","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 : 2022-12-12DOI: 10.33581/2520-6508-2022-3-16-36
Tatsiana S. Mardvilko, Aleksandr A. Pekarskii
The real space of Hardy – Sobolev on a straight line is considered and some sufficient conditions for belonging to functions to this space are described. Estimates of the norm of functions from this space are also obtained. Various examples of functions from the Hardy – Sobolev space are given and the order of their best uniform rational approximations are investigated. Estimates of the best rational approximations for even and odd continuations of functions with monotonous derivatives are obtained. The order of the best rational approximations of the even and odd continuations of functions in the general case have also been studied. Estimates are given both considering the continuity module and without it. The obtained results are also used to study the best rational approximations of functions with a kink, introduced by A. A. Gonchar.
{"title":"Application of the real Hardy – Sobolev space on the line to study the order of uniform rational approximations of functions","authors":"Tatsiana S. Mardvilko, Aleksandr A. Pekarskii","doi":"10.33581/2520-6508-2022-3-16-36","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-3-16-36","url":null,"abstract":"The real space of Hardy – Sobolev on a straight line is considered and some sufficient conditions for belonging to functions to this space are described. Estimates of the norm of functions from this space are also obtained. Various examples of functions from the Hardy – Sobolev space are given and the order of their best uniform rational approximations are investigated. Estimates of the best rational approximations for even and odd continuations of functions with monotonous derivatives are obtained. The order of the best rational approximations of the even and odd continuations of functions in the general case have also been studied. Estimates are given both considering the continuity module and without it. The obtained results are also used to study the best rational approximations of functions with a kink, introduced by A. A. Gonchar.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48711852","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 : 2022-08-03DOI: 10.33581/2520-6508-2022-2-70-81
A. Kovalenko, A. Ovsyannikova
A new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed.
{"title":"Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus","authors":"A. Kovalenko, A. Ovsyannikova","doi":"10.33581/2520-6508-2022-2-70-81","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-70-81","url":null,"abstract":"A new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42946085","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 : 2022-08-03DOI: 10.33581/2520-6508-2022-2-94-106
V. Sorokina, S. Ablameyko
Human body parts detection is a challenging task, which has a lot of applications. In this paper, we propose an algorithm to detect human body parts on images using the OpenPose neural network and the attention model. The novelty of the proposed algorithm is that it is based on a convolutional neural network that uses non-parametric representation to associate the body parts with people in an image in combination with the attention model that learns to focus on specific regions of the input image. The algorithm is part of the Smart Cropping system developed by the authors with the aim to cut necessary pieces of clothing in images and prepare e-commerce catalogues.
{"title":"Detection of human body parts on the image using the neural networks and the attention model","authors":"V. Sorokina, S. Ablameyko","doi":"10.33581/2520-6508-2022-2-94-106","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-94-106","url":null,"abstract":"Human body parts detection is a challenging task, which has a lot of applications. In this paper, we propose an algorithm to detect human body parts on images using the OpenPose neural network and the attention model. The novelty of the proposed algorithm is that it is based on a convolutional neural network that uses non-parametric representation to associate the body parts with people in an image in combination with the attention model that learns to focus on specific regions of the input image. The algorithm is part of the Smart Cropping system developed by the authors with the aim to cut necessary pieces of clothing in images and prepare e-commerce catalogues.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49461430","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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