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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series最新文献

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Stability investigation of an implicit difference scheme for a nonlinear transport equation 非线性传输方程隐式差分方案的稳定性研究
Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series Pub Date : 2024-01-05 DOI: 10.29235/1561-2430-2023-59-4-279-290
M. Chuiko, O. M. Korolyova
{"title":"Stability investigation of an implicit difference scheme for a nonlinear transport equation","authors":"M. Chuiko, O. M. Korolyova","doi":"10.29235/1561-2430-2023-59-4-279-290","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-279-290","url":null,"abstract":"In this paper, we investigate the stability with respect to initial data in the uniform norm of an implicit difference scheme approximating a nonlinear transport equation. An iterative process is used to implement the difference scheme. The convergence of the iterative process and the stability of the difference scheme are proven in the case of initial data guaranteeing the absence of shock waves. In the case of the occurrence of shock waves, estimates of the growth of spatial derivatives at each time layer are obtained. An adaptive computational algorithm for solving the transfer equation during the formation of shock waves is built.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"59 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536151","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 kinetic model of a quantum-dot microlaser 量子点微型激光器动力学模型
Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series Pub Date : 2024-01-05 DOI: 10.29235/1561-2430-2023-59-4-328-337
E. V. Timoshchenko, V. A. Yurevich
{"title":"A kinetic model of a quantum-dot microlaser","authors":"E. V. Timoshchenko, V. A. Yurevich","doi":"10.29235/1561-2430-2023-59-4-328-337","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-328-337","url":null,"abstract":"The results of a qualitative analysis of a semiclassical model of light generation in low-dimensional solidstate lasers, including quantum-dot microlasers and, on its basis, a numerical modelling of the regular pulsation regime that occurs under conditions of nonlinear shift and broadening of the resonant spectral gain line due to the influence of dipoledipoles interaction and absorption in quasi-resonant transitions on the dielectric susceptibility of the active medium are herein presented. The modelling of lasing was carried out for the parameters of semiconductor quantum-dot structures.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"15 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536192","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
An isomorphism problem for objects in categories related to finite dimensional division algebras having henselian valuations 与具有亨塞尔值的有限维划分代数相关的范畴中的对象的同构问题
Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series Pub Date : 2024-01-04 DOI: 10.29235/1561-2430-2023-59-4-271-278
V. Yanchevskiĭ
{"title":"An isomorphism problem for objects in categories related to finite dimensional division algebras having henselian valuations","authors":"V. Yanchevskiĭ","doi":"10.29235/1561-2430-2023-59-4-271-278","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-271-278","url":null,"abstract":"Abstract. Let K be a field. In this paper, we found the necessary and sufficient conditions for K-homomorphisms of noncommutative finite-dimensional central division K-algebras with henselian valuations being K-isomorphisms. A similar result is obtained for the case of algebras with involutions. A category interpretation of these results is given.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"29 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536257","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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