{"title":"Construction of Schedules for the Performance of Task Packages in Multi-Stage Systems when Forming Sets of Results and Limitations","authors":"K. Krotov, A. Skatkov","doi":"10.14529/mmp220206","DOIUrl":"https://doi.org/10.14529/mmp220206","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"5 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80073516","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}
{"title":"On One Routing Problem Oriented on the Problem of Dismantling Radiation-Hazardous Objects","authors":"A. Chentsov, A. Chentsov","doi":"10.14529/mmp220306","DOIUrl":"https://doi.org/10.14529/mmp220306","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"23 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77454859","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}
The paper presents an approach to the modelling of the dynamic behavior of a piezoelectric transducer of a complex shape in a three-dimensional case based on the spectral element method. The proposed mathematical model will be a part of the hybrid approach to the modelling of the guided waves excitation and sensing in an elongated structure in a three-dimensional case. Different types of electrodes of piezoelectric transducers as well as various boundary value conditions for the modelling of the actuation and sensing operations are considered. Unknown displacements are approximated with Lagrange polynomials at the Gauss-Legendre-Lobatto nodal points and the system of linear algebraic equations is obtained in terms of the displacement vector and electric potential at the nodal points. The results are compared with the standard finite element calculations provided with the finite-element COMSOL Multiphysics software. The electro-mechanical characteristics of the dynamic behaviour of piezoelectric transducers are analysed depending on the operational conditions and the kind of electrodes. The eigenfrequencies of the piezoelectric transducers are calculated and the corresponding eigenforms are constructed and analysed.
{"title":"Simulation of the Vibrations of a Piezoelectric Transducer with a Wrapped Electrode Using the Spectral Element Method","authors":"A. Shpak, S. A. Siuhina, M. Golub","doi":"10.14529/mmp220307","DOIUrl":"https://doi.org/10.14529/mmp220307","url":null,"abstract":"The paper presents an approach to the modelling of the dynamic behavior of a piezoelectric transducer of a complex shape in a three-dimensional case based on the spectral element method. The proposed mathematical model will be a part of the hybrid approach to the modelling of the guided waves excitation and sensing in an elongated structure in a three-dimensional case. Different types of electrodes of piezoelectric transducers as well as various boundary value conditions for the modelling of the actuation and sensing operations are considered. Unknown displacements are approximated with Lagrange polynomials at the Gauss-Legendre-Lobatto nodal points and the system of linear algebraic equations is obtained in terms of the displacement vector and electric potential at the nodal points. The results are compared with the standard finite element calculations provided with the finite-element COMSOL Multiphysics software. The electro-mechanical characteristics of the dynamic behaviour of piezoelectric transducers are analysed depending on the operational conditions and the kind of electrodes. The eigenfrequencies of the piezoelectric transducers are calculated and the corresponding eigenforms are constructed and analysed.","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"3 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73872232","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}
The article discusses a mathematical model of the production activity of PJSC “Fortum”, which is the main supplier of electrical and thermal energy in the Southern Urals. The model is constructed on the basis of the modified production function of Cobb Douglas for 2010-2020. The author’s algorithm for constructing the model is given, according to which a computer program for modelling the operating activities of an enterprise was written and registered in the State Register of computer programs in the Java language. The adequacy of the constructed model was checked by the coefficient of determination, the value of which showed its high reliability. The analysis of the constructed mathematical model made it possible to draw the following conclusions: the strategic goal of reducing tariffs declared in the course of the restructuring of OJSC “RAO UES of Russia” was not fulfilled, on the contrary, their steady growth is observed; the efficiency of operating activities does not meet modern requirements – during the entire analyzed period, there is a diminishing economies of scale; the sustainable development strategy implemented by PJSC “Fortum” does not have a proper economic power supply unit due to a decrease in the return on resources involved in production; relatively high financial results of PJSC “Fortum” are associated with an unreasonable increase in tariffs; consumers of electric and thermal energy of the Urals and Western Siberia, in the conditions of the monopoly on the energy market, finance the richest country in the world – the Netherlands – through payments from Fortum Holding B.V., which directly and indirectly owns 98% of the shares of PJSC “Fortum”; with the existing management mechanism and state control by the antimonopoly service, PJSC “Fortum” has no incentives to replace the outdated cogeneration option based on hydrocarbon fuels with modern, progressive green technologies. The results of the study are recommended to the Federal Antimonopoly Service to strengthen control over the activities of PJSC “Fortum”, reduce tariff pressure on consumers of electric and thermal energy and unjustified enrichment of foreign subjects of the electric power industry at the expense of Russian consumers.
本文讨论了乌拉尔南部主要的电力和热能供应商PJSC“Fortum”生产活动的数学模型。该模型是在Cobb Douglas 2010-2020年修正生产函数的基础上构建的。本文给出了构建模型的算法，并据此编写了一个企业经营活动建模的计算机程序，并用Java语言在国家计算机程序库中进行了登记。通过确定系数对模型的充分性进行了检验，确定系数的取值表明模型具有较高的可靠性。对构建的数学模型进行分析，可以得出以下结论:在OJSC“俄罗斯的RAO UES”重组过程中宣布的降低关税的战略目标没有实现，相反，它们的稳步增长;经营活动的效率不符合现代要求- -在整个分析期间，规模经济在减少;PJSC“Fortum”实施的可持续发展战略由于生产所涉及的资源回报减少而没有适当的经济供电单元;PJSC“Fortum”相对较高的财务业绩与不合理的关税增加有关;乌拉尔和西伯利亚西部的电力和热能消费者，在垄断能源市场的条件下，通过直接或间接拥有PJSC“Fortum”98%股份的Fortum Holding b.v.的付款，为世界上最富有的国家荷兰提供资金;在现有的管理机制和反垄断机构的国家控制下，PJSC“Fortum”没有动力用现代先进的绿色技术取代过时的基于碳氢化合物燃料的热电联产选择。研究结果建议联邦反垄断局加强对PJSC“Fortum”活动的控制，减少对电力和热能消费者的关税压力，并以牺牲俄罗斯消费者的利益为代价，使电力工业的外国主体不合理地致富。
{"title":"Mathematical Modelling and Analysis of Activities of PJSC \"Fortum\"","authors":"V. Mokhov, G. Chebotareva","doi":"10.14529/mmp220209","DOIUrl":"https://doi.org/10.14529/mmp220209","url":null,"abstract":"The article discusses a mathematical model of the production activity of PJSC “Fortum”, which is the main supplier of electrical and thermal energy in the Southern Urals. The model is constructed on the basis of the modified production function of Cobb Douglas for 2010-2020. The author’s algorithm for constructing the model is given, according to which a computer program for modelling the operating activities of an enterprise was written and registered in the State Register of computer programs in the Java language. The adequacy of the constructed model was checked by the coefficient of determination, the value of which showed its high reliability. The analysis of the constructed mathematical model made it possible to draw the following conclusions: the strategic goal of reducing tariffs declared in the course of the restructuring of OJSC “RAO UES of Russia” was not fulfilled, on the contrary, their steady growth is observed; the efficiency of operating activities does not meet modern requirements – during the entire analyzed period, there is a diminishing economies of scale; the sustainable development strategy implemented by PJSC “Fortum” does not have a proper economic power supply unit due to a decrease in the return on resources involved in production; relatively high financial results of PJSC “Fortum” are associated with an unreasonable increase in tariffs; consumers of electric and thermal energy of the Urals and Western Siberia, in the conditions of the monopoly on the energy market, finance the richest country in the world – the Netherlands – through payments from Fortum Holding B.V., which directly and indirectly owns 98% of the shares of PJSC “Fortum”; with the existing management mechanism and state control by the antimonopoly service, PJSC “Fortum” has no incentives to replace the outdated cogeneration option based on hydrocarbon fuels with modern, progressive green technologies. The results of the study are recommended to the Federal Antimonopoly Service to strengthen control over the activities of PJSC “Fortum”, reduce tariff pressure on consumers of electric and thermal energy and unjustified enrichment of foreign subjects of the electric power industry at the expense of Russian consumers.","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"33 1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90450855","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}
{"title":"Invariant Manifolds of Semilinear Sobolev Type Equations","authors":"O. G. Kitaeva","doi":"10.14529/mmp220106","DOIUrl":"https://doi.org/10.14529/mmp220106","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"184 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80526153","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}
{"title":"Calculation of the Three-Dimensional Magnetic Field of a System of Permanent Magnets and Ferromagnets Based on the Integral Magnetization Equation and the Jills-Atterton Model","authors":"R.V. Harutyunyann","doi":"10.14529/mmp220204","DOIUrl":"https://doi.org/10.14529/mmp220204","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"27 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78701382","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}
{"title":"Application of an Implicit Scheme of the Discontinuous Galerkin Method to Solving Gas Dynamics Problems on NVIDIA Graphic Accelerators","authors":"V. F. Masyagin, R. V. Zhalnin, V. Tishkin","doi":"10.14529/mmp220207","DOIUrl":"https://doi.org/10.14529/mmp220207","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"48 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76978136","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}
{"title":"Semilinear Sobolev Type Mathematical Models","authors":"A. Zamyshlyaeva, E. Bychkov","doi":"10.14529/mmp220103","DOIUrl":"https://doi.org/10.14529/mmp220103","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"48 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77248459","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}
The aim of this study is to construct the exact solutions of the (2+1)-dimensional Kundu–Mukherjee–Naskar (KMN) equation via Improved Bernoulli Sub-Equation Function Method (IBSEFM). The physics of this model describes optical dromions in (2+1)-dimensional case. It is also studied in fluid dynamics. Applying the proposed method, we obtain new exact solutions of (2+1)-dimensional KMN equation. Moreover, we plot the 2D-3D figures and contour surfaces according to the suitable parameters by the aid of computer software. The results confirm that IBSEFM is powerful, effective and straightforward for solving nonlinear partial differential equations arising in mathematical physics.
{"title":"Exact Solutions of the (2+1)-Dimensional Kundu-Mukherjee-Naskar Model via IBSEFM","authors":"K. Mamedov, U. Demirbilek, V. Ala","doi":"10.14529/mmp220202","DOIUrl":"https://doi.org/10.14529/mmp220202","url":null,"abstract":"The aim of this study is to construct the exact solutions of the (2+1)-dimensional Kundu–Mukherjee–Naskar (KMN) equation via Improved Bernoulli Sub-Equation Function Method (IBSEFM). The physics of this model describes optical dromions in (2+1)-dimensional case. It is also studied in fluid dynamics. Applying the proposed method, we obtain new exact solutions of (2+1)-dimensional KMN equation. Moreover, we plot the 2D-3D figures and contour surfaces according to the suitable parameters by the aid of computer software. The results confirm that IBSEFM is powerful, effective and straightforward for solving nonlinear partial differential equations arising in mathematical physics.","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"36 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91213046","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}
{"title":"Sobolev Type Equations in Spaces of Differential Forms on Riemannian Manifolds Without Boundary","authors":"D. E. Shafranov","doi":"10.14529/mmp220107","DOIUrl":"https://doi.org/10.14529/mmp220107","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"16 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85704347","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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