{"title":"The Non-Classical Models of Mathematical Physics the Multipoint Initial-Final Value Condition","authors":"S. Zagrebina, A. S. Konkina","doi":"10.14529/mmp220104","DOIUrl":"https://doi.org/10.14529/mmp220104","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"32 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73360695","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}
E. Bychkov, S. Zagrebina, A. Zamyshlyaeva, N. Manakova, M. Sagadeeva, G. Sviridyuk, A. Keller
{"title":"Development of the Theory of Optimal Dynamic Measurements","authors":"E. Bychkov, S. Zagrebina, A. Zamyshlyaeva, N. Manakova, M. Sagadeeva, G. Sviridyuk, A. Keller","doi":"10.14529/mmp220302","DOIUrl":"https://doi.org/10.14529/mmp220302","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"75 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72679918","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}
Мельцайкин Евгений Андреевич, Meltsaykin Evgeniy, Andreevich, Ushakov Andrey, Leonidovich
. The article describes the analysis of biharmonic models by iterative extension methods. Various stationary physical systems in mechanics are modeled using boundary value problems for inhomogeneous Sophie Germain. Using the biharmonic model, i.e. boundary value problem for the inhomogeneous Sophie Germain equation, describe the deflection of plates, flows during fluid flows. With the help of the developed methods of iterative extensions, efficient algorithms for solving the problems under consideration are obtained.
{"title":"Analysis of Biharmonic and Harmonic Models by the Methods of Iterative Extensions","authors":"Мельцайкин Евгений Андреевич, Meltsaykin Evgeniy, Andreevich, Ushakov Andrey, Leonidovich","doi":"10.14529/mmp220304","DOIUrl":"https://doi.org/10.14529/mmp220304","url":null,"abstract":". The article describes the analysis of biharmonic models by iterative extension methods. Various stationary physical systems in mechanics are modeled using boundary value problems for inhomogeneous Sophie Germain. Using the biharmonic model, i.e. boundary value problem for the inhomogeneous Sophie Germain equation, describe the deflection of plates, flows during fluid flows. With the help of the developed methods of iterative extensions, efficient algorithms for solving the problems under consideration are obtained.","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"93 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80468901","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 considers the problem of dynamic control to a portfolio for a binary model with disorder. The a posteriori approach is considered, that is a disorder is detected with the subsequent clustering of the tree nodes in the process of solving the problem. On the basis of this clustering, we construct an algorithm for calculating the optimal dynamic portfolio, which is applicable for binary models with disorder. We use both symmetric and asymmetric penalties for not achieving the set control goal. Further, we analyze the possibility of using a binary model to approximate the Black–Scholes model with disorder, and investigate the possibility of reducing an NP -complete problem to P -complete problem with loss of information.
{"title":"Control in Binary Models with Disorder","authors":"G. Beliavsky, N. Danilova","doi":"10.14529/mmp220305","DOIUrl":"https://doi.org/10.14529/mmp220305","url":null,"abstract":"The paper considers the problem of dynamic control to a portfolio for a binary model with disorder. The a posteriori approach is considered, that is a disorder is detected with the subsequent clustering of the tree nodes in the process of solving the problem. On the basis of this clustering, we construct an algorithm for calculating the optimal dynamic portfolio, which is applicable for binary models with disorder. We use both symmetric and asymmetric penalties for not achieving the set control goal. Further, we analyze the possibility of using a binary model to approximate the Black–Scholes model with disorder, and investigate the possibility of reducing an NP -complete problem to P -complete problem with loss of information.","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"9 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77804749","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}
This article is a survey devoted to inverse problems of recovering sources and coefficients (parameters of a medium) in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of the inverse problems with pointwise overdetermination conditions. The questions of this type arise in the heat and mass transfer theory, in environmental and ecology problems, when describing diffusion and filtration processes, etc. As examples, we note the problems of determining the heat conductivity tensor or sources of pollution in a water basin or atmosphere. We describe three types of problems. The first of them is the problem of recovering point or distributed sources. We present conditions for existence and uniqueness of solutions to the problem, show non-uniqueness examples, and, in model situations, give estimates on the number of measurements that allow completely identify intensities of sources and their locations. The second problem is the problem of recovering the parameters of media, in particular, the heat conductivity. The third problem is the problem of recovering the boundary regimes, i. e. the flux through a surface or the heat transfer coefficient.
{"title":"On Inverse Problems with Pointwise Overdetermination for Mathematical Models of Heat and Mass Transfer","authors":"S. Pyatkov","doi":"10.14529/mmp220303","DOIUrl":"https://doi.org/10.14529/mmp220303","url":null,"abstract":"This article is a survey devoted to inverse problems of recovering sources and coefficients (parameters of a medium) in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of the inverse problems with pointwise overdetermination conditions. The questions of this type arise in the heat and mass transfer theory, in environmental and ecology problems, when describing diffusion and filtration processes, etc. As examples, we note the problems of determining the heat conductivity tensor or sources of pollution in a water basin or atmosphere. We describe three types of problems. The first of them is the problem of recovering point or distributed sources. We present conditions for existence and uniqueness of solutions to the problem, show non-uniqueness examples, and, in model situations, give estimates on the number of measurements that allow completely identify intensities of sources and their locations. The second problem is the problem of recovering the parameters of media, in particular, the heat conductivity. The third problem is the problem of recovering the boundary regimes, i. e. the flux through a surface or the heat transfer coefficient.","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"13 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74872142","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 Models of Sobolev Type. Non-Uniqueness of Solution to the Showalter-Sidorov Problem","authors":"N. Manakova, O. Gavrilova, K. V. Perevozchikova","doi":"10.14529/mmp220105","DOIUrl":"https://doi.org/10.14529/mmp220105","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"64 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90412002","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":"A Model for Competition of Technologies for Limiting Resources","authors":"Almaz Mustafin, Aliya Kantarbayeva","doi":"10.14529/mmp220203","DOIUrl":"https://doi.org/10.14529/mmp220203","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"4 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90541480","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 a Limit Pass from Two-Point to One-Point Interaction in a One Dimensional Quantum Mechanical Problem Giving Rise to a Spontaneous Symmetry Breaking","authors":"A. Restuccia, A. Sotomayor, V. Strauss","doi":"10.14529/MMP210106","DOIUrl":"https://doi.org/10.14529/MMP210106","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"2 1","pages":"75-90"},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79908290","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":"Algorithm of Reconstruction of Three-Dimensional Images in X-Ray Computed Tomography with a Cone Beam","authors":"E. N. Simonov, A. V. Prokhorov","doi":"10.14529/MMP210108","DOIUrl":"https://doi.org/10.14529/MMP210108","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"20 1","pages":"104-117"},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90162745","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":"Generalized Kelly Strategy","authors":"V. Rodin, S. V. Sinegubov","doi":"10.14529/mmp210211","DOIUrl":"https://doi.org/10.14529/mmp210211","url":null,"abstract":"","PeriodicalId":44106,"journal":{"name":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming & Computer Software","volume":"97 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82898832","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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