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Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika最新文献

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Algebraic equations and polynomials over the ring of p-complex numbers p复数环上的代数方程和多项式
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-12-21 DOI: 10.33581/2520-6508-2022-3-37-44
V. V. Dovgodilin
{"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}
引用次数: 0
On the theory of operator interpolation in spaces of rectangular matrixes 矩形矩阵空间中的算子插值理论
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-12-19 DOI: 10.33581/2520-6508-2022-3-91-106
M. V. Ignatenko, L. Yanovich
{"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}
引用次数: 0
Application of the real Hardy – Sobolev space on the line to study the order of uniform rational approximations of functions 应用实Hardy - Sobolev空间在直线上研究函数一致有理逼近的阶数
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-12-12 DOI: 10.33581/2520-6508-2022-3-16-36
Tatsiana S. Mardvilko, Aleksandr A. Pekarskii
{"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}
引用次数: 0
Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus 电渗析装置三维脱盐通道中盐离子转移的数学模型
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-08-03 DOI: 10.33581/2520-6508-2022-2-70-81
A. Kovalenko, A. Ovsyannikova
{"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}
引用次数: 0
Detection of human body parts on the image using the neural networks and the attention model 利用神经网络和注意力模型检测图像上的人体部位
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-08-03 DOI: 10.33581/2520-6508-2022-2-94-106
V. Sorokina, S. Ablameyko
{"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}
引用次数: 1
Classical solution of one problem of a perfectly inelastic impact on a long elastic semi-infinite bar with a linear elastic element at the end 一端有线弹性单元的半无限长弹性杆的完全非弹性冲击问题的经典解
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-08-01 DOI: 10.33581/2520-6508-2022-2-34-46
V. I. Korzyuk, J. V. Rudzko
{"title":"Classical solution of one problem of a perfectly inelastic impact on a long elastic semi-infinite bar with a linear elastic element at the end","authors":"V. I. Korzyuk, J. V. Rudzko","doi":"10.33581/2520-6508-2022-2-34-46","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-34-46","url":null,"abstract":"In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. This mixed problem models the propagation of displacement waves during a longitudinal impact on a bar, when the load remains in contact with the bar and the bar has a linear elastic element at the end. On the lower boundary, the Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. The boundary condition, including the unknown function and its first and second order partial derivatives, is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proven and the conditions are established under which a piecewise-smooth solution exists. The problem with matching conditions is considered.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45538486","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}
引用次数: 1
The non-axisymmetric loading of an elastoplastic three-layer plate in its plane 弹塑性三层板在其平面上的非轴对称载荷
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-08-01 DOI: 10.33581/2520-6508-2022-2-57-69
E. Starovoitov, Alina V. Nesterovich
{"title":"The non-axisymmetric loading of an elastoplastic three-layer plate in its plane","authors":"E. Starovoitov, Alina V. Nesterovich","doi":"10.33581/2520-6508-2022-2-57-69","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-57-69","url":null,"abstract":"The statement of the boundary value problem on the deformation of a circular three-layer plate in its plane under the action of a non-axisymmetric load is herein presented. The materials of thin carrier layers obey the hypotheses of the theory of small elastoplastic deformations. The relatively thick filler is physically non-linearly elastic. A system of non-linear differential equilibrium equations in partial derivatives is obtained. A general technique for solving the problem in displacements based on the Fourier method and Ilyushin’s method of elastic solutions is proposed. The case of an external cosine load is considered. An iterative solution of a boundary value problem for a physically non-linear plate is obtained. The corresponding solution of the elastic problem is written out in the final form. The obtained solution is numerically tested.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41901243","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}
引用次数: 0
On meromorphic solutions of the equations related to the first Painlevé equation 关于第一个Painlevé方程的亚纯解
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-07-27 DOI: 10.33581/2520-6508-2022-2-15-22
E. V. Gromak
{"title":"On meromorphic solutions of the equations related to the first Painlevé equation","authors":"E. V. Gromak","doi":"10.33581/2520-6508-2022-2-15-22","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-15-22","url":null,"abstract":"In this paper, we consider the generalised hierarchy of the first Painlevé equation which is a sequence of polynomial ordinary differential equations of even order that have a uniform differential-algebraic structure determined by the operator L~n. The first member of this hierarchy for n = 2 is the first Painlevé equation, and the subsequent equations of order 2n – 2 contain arbitrary parameters. They are named as higher analogues of the first Painlevé equation of 2n – 2 order. The article considers the analytical properties of solutions to the equations of the generalised hierarchy of the first Painlevé equation and the related linear equations. It is established that each hierarchy equation has one dominant term, and an arbitrary meromorphic solution of any hierarchy equation cannot have a finite number of poles. The character of the mobile poles of meromorphic solutions is determined. Using the Frobenius method, sufficient conditions are obtained for the meromorphicity of the general solution of the second-order linear equations with a linear potential defined by meromorphic solutions of the first three equations of the hierarchy.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46371905","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}
引用次数: 0
A queueing system with a batch Markovian arrival process and varying priorities 具有批马尔可夫到达过程和变优先级的排队系统
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-07-27 DOI: 10.33581/2520-6508-2022-2-47-56
V. Klimenok
{"title":"A queueing system with a batch Markovian arrival process and varying priorities","authors":"V. Klimenok","doi":"10.33581/2520-6508-2022-2-47-56","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-47-56","url":null,"abstract":"We consider herein a single-server queueing system with a finite buffer and a batch Markovian arrival process. Customers staying in the buffer may have a lower or higher priority. Immediately after arrival each of the customer is assigned the lowest priority and a timer is set for it, which is defined as a random variable distributed according to the phase law and having two absorbing states. After the timer enters one of the absorbing states, the customer may leave the system forever (get lost) or change its priority to the highest. When the timer enters another absorbing state, the customer is lost with some probability and the timer is set again with an additional probability. If a customer enters a completely full system, it is lost. Systems of this type can serve as mathematical models of many real-life medical care systems, contact centers, perishable food storage systems, etc. The operation of the system is described in terms of a multidimensional Markov chain, the stationary distribution and a number of performance characteristics of the system are calculated.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49573826","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}
引用次数: 0
Tools for the analysis and visualisation of distributions and vector fields in surface forest fires modelling 用于分析和可视化地表森林火灾建模中的分布和矢量场的工具
Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika Pub Date : 2022-07-20 DOI: 10.33581/2520-6508-2022-2-82-93
D. Barovik, V. Taranchuk
{"title":"Tools for the analysis and visualisation of distributions and vector fields in surface forest fires modelling","authors":"D. Barovik, V. Taranchuk","doi":"10.33581/2520-6508-2022-2-82-93","DOIUrl":"https://doi.org/10.33581/2520-6508-2022-2-82-93","url":null,"abstract":"The problem of computer modelling of the spread of surface forest fires in a two-dimensional formulation is herein considered. We describe the initial-boundary value problem in the form of a system of partial differential equations in the accepted approximation of the corresponding physical and chemical processes with refinements of the mutually agreed defining functions and the coefficients included in the equations. The Wolfram Mathematica computer algebra system is used as a platform for developing the computer model, performing calculations, and creating a database with the outcomes of computations. The results of numerical experiments investigating possible scenarios of how a fire zone spreads in different directions and its behaviour near the fuelbreaks are presented. Several qualitative features of the structure, the evolution of the temperature front, and the vector fields of the oxygen concentration gradient over the forest area are identified and illustrated with multidimensional graphics in the presence of areas of the low content of combustible materials of various shapes and sizes, including the demonstration of the influence of the equilibrium wind speed in the forest canopy. Possible variants of the fire front movement in the direction of the wind velocity and against it are identified and explained using representative examples.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47025543","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}
引用次数: 0
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