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Contemporary Mathematics. Fundamental Directions最新文献

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Maslov complex germ and semiclassical contracted states in the Cauchy problem for the Schrödinger equation with delta potential 具有δ势的Schrödinger方程的柯西问题中的马斯洛夫复胚和半经典收缩态
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-12-15 DOI: 10.22363/2413-3639-2022-68-4-704-715
A. Shafarevich, O. A. Shchegortsova
{"title":"Maslov complex germ and semiclassical contracted states in the Cauchy problem for the Schrödinger equation with delta potential","authors":"A. Shafarevich, O. A. Shchegortsova","doi":"10.22363/2413-3639-2022-68-4-704-715","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-4-704-715","url":null,"abstract":"We describe the semiclassical asymptotic behavior of the solution of the Cauchy problem for the Schrödinger equation with a delta potential localized on a surface of codimension 1. The Schrödinger operator with a delta potential is defined using the theory of extensions and is given by the boundary conditions on this surface. The initial data are selected as a narrow peak, which is a Gaussian packet localized in a small neighborhood of the point. To construct the asymptotics, we use the Maslov complex germ method. We describe the re ection of the complex germ from the carrier of the delta potential.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124818993","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
Numerical analysis of stationary solutions of systems with delayed argument in mathematical immunology 数学免疫学中时滞参数系统平稳解的数值分析
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-12-15 DOI: 10.22363/2413-3639-2022-68-4-686-703
M. Y. Khristichenko, Y. Nechepurenko, D. Grebennikov, G. Bocharov
{"title":"Numerical analysis of stationary solutions of systems with delayed argument in mathematical immunology","authors":"M. Y. Khristichenko, Y. Nechepurenko, D. Grebennikov, G. Bocharov","doi":"10.22363/2413-3639-2022-68-4-686-703","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-4-686-703","url":null,"abstract":"This work is devoted to the technology developed by the authors that allows one for fixed values of parameters and tracing by parameters to calculate stationary solutions of systems with delay and analyze their stability. We discuss the results of applying this technology to Marchuk-Petrov's antiviral immune response model with parameter values corresponding to hepatitis B infection. The presence of bistability and hysteresis properties in this model is shown for the first time.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127432451","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
Explicit solution of a Dirichlet problem in nonconvex angle 非凸角Dirichlet问题的显式解
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-12-15 DOI: 10.22363/2413-3639-2022-68-4-653-670
A. Merzon, P. Zhevandrov, J. E. de la Paz Méndez, M. Romero Rodríguez
{"title":"Explicit solution of a Dirichlet problem in nonconvex angle","authors":"A. Merzon, P. Zhevandrov, J. E. de la Paz Méndez, M. Romero Rodríguez","doi":"10.22363/2413-3639-2022-68-4-653-670","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-4-653-670","url":null,"abstract":"In the present work, we give an explicit solution of the Dirichlet boundary-value problem for the Helmholtz equation in a nonconvex angle with periodic boundary data. We present uniqueness and existence theorems in an appropriate functional class and we give an explicit formula for the solution in the form of the Sommerfeld integral. The method of complex characteristics [14] is used.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"66 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125950628","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
Chaos in Topological Foliations 拓扑叶状中的混沌
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-424-450
Удк, В Хаос, Топологических Слоениях
{"title":"Chaos in Topological Foliations","authors":"Удк, В Хаос, Топологических Слоениях","doi":"10.22363/2413-3639-2022-68-3-424-450","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-424-450","url":null,"abstract":"We call a foliation (M,F) on a manifold M chaotic if it is topologically transitive and the union of closed leaves is dense in M. A foliated manifold M is not assumed to be compact. The chaotic foliations can be considered as multidimensional generalization of chaotic dynamical systems in the sense of Devaney. For foliations covered by fibrations we prove that a foliation is chaotic if and only if its global holonomy group is chaotic. We introduce the concept of the integrable Ehresmann connection for a foliation as a natural generalization of the integrable Ehresmann connection for smooth foliations. A description of the global structure of foliations with integrable Ehresmann connection and a criterion for the chaotic behavior of such foliations are obtained. Applying the method of suspension, a new countable family of pairwise nonisomorphic chaotic foliations of codimension two on 3-dimensional closed and nonclosed manifolds is constructed.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132513236","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
Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces Pontryagin空间中自伴随算子和幺正算子的模型
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-522-552
V. Strauss
{"title":"Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces","authors":"V. Strauss","doi":"10.22363/2413-3639-2022-68-3-522-552","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-522-552","url":null,"abstract":"This paper represents a revised version of the lectures, delivered by the author at KROMSH-2019. These lectures are devoted to describing a few different ways of constructing a model representation for self-adjoint and unitary operators acting in Pontryagin spaces, and a comparison between them. Two of these models are based on the regularized integral Krein-Langer representation of a numerical sequence generated by the powers of a self-adjoint (in the sense of Pontryagin spaces) operator. The steps to deduce both this representation and the spectral function of the corresponding operator are given. In both models (first of which belongs to the author of this paper), the operator is realized as an operator of multiplication by an independent variable, but the space of functions in which it acts is different for each of the models. The third model, introduced by V. S. Shulman, is based on his own concept of a quasi-vector.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121621670","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
Multistability for a Mathematical Model of the Dynamics of Predators and Preys in a Heterogeneous Area 非均质区捕食者与被捕食者动力学数学模型的多稳定性
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-509-521
Удк, Мультистабильность Для, Математической Модели
{"title":"Multistability for a Mathematical Model of the Dynamics of Predators and Preys in a Heterogeneous Area","authors":"Удк, Мультистабильность Для, Математической Модели","doi":"10.22363/2413-3639-2022-68-3-509-521","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-509-521","url":null,"abstract":"We consider the system of reaction-diffusion-advection equations describing the evolution of the spatial distributions of two populations of predators and two prey populations. This model allows us to consider directed migration, the Holling functional response of the second kind, and the hyperbolic prey growth function. We obtain conditions on the parameters under which cosymmetries exist. As a result, multistability is realized, i.e., the one- and two-parameter families of stationary solutions appear. For a homogeneous environment, we analytically derive explicit formulas for equilibria. With a heterogeneous habitat, we computed distributions of species using the method of lines and the scheme of staggered grids. We present the results of violation of cosymmetry and transformation of the family in the case of invasion of a predator.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127582087","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
Order Projection in OAr(E,F) OAr(E,F)中的阶投影
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-407-423
N. Dzhusoeva, S. Y. Itarova, M. Pliev
{"title":"Order Projection in OAr(E,F)","authors":"N. Dzhusoeva, S. Y. Itarova, M. Pliev","doi":"10.22363/2413-3639-2022-68-3-407-423","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-407-423","url":null,"abstract":"We investigate order projections onto different bands in the space of all regular orthogonally additive operators. In particular, we obtain formulas for calculation of the order projections onto the band generated by a directed set of positive orthogonally additive operators and onto the band of all laterally continuous operators.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125200129","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
Asymptotic Behavior of Solutions of a Complete Second-Order Integro-Differential Equation 一类完全二阶积分-微分方程解的渐近性质
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-451-466
D. Zakora
{"title":"Asymptotic Behavior of Solutions of a Complete Second-Order Integro-Differential Equation","authors":"D. Zakora","doi":"10.22363/2413-3639-2022-68-3-451-466","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-451-466","url":null,"abstract":"In this paper, we study a complete second-order integro-differential operator equation in a Hilbert space. The difference-type kernel of an integral perturbation is a holomorphic semigroup bordered by unbounded operators. The asymptotic behavior of solutions of this equation is studied. Asymptotic formulas for solutions are proved in the case when the right-hand side is close to an almost periodic function. The obtained formulas are applied to the study of the problem of forced longitudinal vibrations of a viscoelastic rod with Kelvin-Voigt friction.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122756693","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
Optimal Control of the Behavior of Solutions to an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuum Systems 离散连续系统力学中初边值问题解行为的最优控制
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-488-508
E. P. Kubyshkin
{"title":"Optimal Control of the Behavior of Solutions to an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuum Systems","authors":"E. P. Kubyshkin","doi":"10.22363/2413-3639-2022-68-3-488-508","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-488-508","url":null,"abstract":"<jats:p>-</jats:p>","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116669493","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 Spaces of Vector Functions that Are Holomorphic in an Angular Domain 角域上全纯向量函数的空间
Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-393-406
V. Vlasov, N. Rautian
{"title":"On Spaces of Vector Functions that Are Holomorphic in an Angular Domain","authors":"V. Vlasov, N. Rautian","doi":"10.22363/2413-3639-2022-68-3-393-406","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-393-406","url":null,"abstract":"In this paper, we study spaces of vector functions that are holomorphic in the angular domain of the complex plane and with values in a separable Hilbert space. We show that, equipped with the appropriate norms, these spaces are Hilbert spaces.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134408127","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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