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Generalization of the Artin-Hasse logarithm for the Milnor -groups of -rings -环的Milnor群的Artin-Hasse对数的推广
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9520
D. N. Tyurin
{"title":"Generalization of the Artin-Hasse logarithm for the Milnor -groups of -rings","authors":"D. N. Tyurin","doi":"10.1070/SM9520","DOIUrl":"https://doi.org/10.1070/SM9520","url":null,"abstract":"Let be a -adically complete ring equipped with a -structure. We construct a functorial group homomorphism from the Milnor -group to the quotient of the -adic completion of the module of differential forms . This homomorphism is a -adic analogue of the Bloch map defined for the relative Milnor -groups of nilpotent extensions of rings of nilpotency degree for which the number is invertible. Bibliography: 12 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72461436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition 匀化狄利克雷条件下沿规定流形细穿孔区域问题的一致收敛性和渐近性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9435
Denis Borisov, A. I. Mukhametrakhimova
{"title":"Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition","authors":"Denis Borisov, A. I. Mukhametrakhimova","doi":"10.1070/SM9435","DOIUrl":"https://doi.org/10.1070/SM9435","url":null,"abstract":"A boundary value problem for a second-order elliptic equation with variable coefficients is considered in a multidimensional domain which is perforated by small holes along a prescribed manifold. Minimal natural conditions are imposed on the holes. In particular, all of these are assumed to be of approximately the same size and have a prescribed minimal distance to neighbouring holes, which is also a small parameter. The shape of the holes and their distribution along the manifold are arbitrary. The holes are divided between two sets in an arbitrary way. The Dirichlet condition is imposed on the boundaries of holes in the first set and a nonlinear Robin boundary condition is imposed on the boundaries of holes in the second. The sizes and distribution of holes with the Dirichlet condition satisfy a simple and easily verifiable condition which ensures that these holes disappear after homogenization and a Dirichlet condition on the manifold in question arises instead. We prove that the solution of the perturbed problem converges to the solution of the homogenized one in the -norm uniformly with respect to the right-hand side of the equation, and an estimate for the rate of convergence that is sharp in order is deduced. The full asymptotic solution of the perturbed problem is also constructed in the case when the holes form a periodic set arranged along a prescribed hyperplane. Bibliography: 32 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76113533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Orthogonality in nonseparable rearrangement-invariant spaces 不可分重排不变空间中的正交性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9543
S. V. Astashkin, E. Semenov
{"title":"Orthogonality in nonseparable rearrangement-invariant spaces","authors":"S. V. Astashkin, E. Semenov","doi":"10.1070/SM9543","DOIUrl":"https://doi.org/10.1070/SM9543","url":null,"abstract":"Let be a nonseparable rearrangement-invariant space and let be the closure of the space of bounded functions in . Elements of orthogonal to , that is, elements , , such that for each , are investigated. The set of orthogonal elements is characterized in the case when is a Marcinkiewicz or an Orlicz space. If an Orlicz space is considered with the Luxemburg norm, then the set is the algebraic sum of and . Each nonseparable rearrangement-invariant space such that is shown to contain an asymptotically isometric copy of the space . Bibliography: 17 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88596082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The maximum tree of a random forest in the configuration graph 配置图中随机森林的最大树
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9481
Yu. L. Pavlov
{"title":"The maximum tree of a random forest in the configuration graph","authors":"Yu. L. Pavlov","doi":"10.1070/SM9481","DOIUrl":"https://doi.org/10.1070/SM9481","url":null,"abstract":"Galton-Watson random forests with a given number of root trees and a known number of nonroot vertices are investigated. The distribution of the number of direct offspring of each particle in the forest- generating process is assumed to have infinite variance. Branching processes of this kind are used successfully to study configuration graphs aimed at simulating the structure and development dynamics of complex communication networks, in particular the internet. The known relationship between configuration graphs and random forests reflects the local tree structure of simulated networks. Limit theorems are proved for the maximum size of a tree in a random forest in all basic zones where the number of trees and the number of vertices tend to infinity. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89781693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Uniform -stability modulo a subgroup 子群的一致稳定模
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9430
Y. Li, G. Tian, X. Zhu
{"title":"Uniform -stability modulo a subgroup","authors":"Y. Li, G. Tian, X. Zhu","doi":"10.1070/SM9430","DOIUrl":"https://doi.org/10.1070/SM9430","url":null,"abstract":"In this paper, we prove a version of uniform -stability for a pair with respect to a reductive Lie group modulo a subgroup of . Bibliography: 7 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75163034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Об автоморфизмах квазигладких взвешенных полных пересечений 准平滑全交叉的自同构
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.4213/SM9451
Виктор Владимирович Пржиялковский, V. Przyjalkowski, Константин Александрович Шрамов, Сonstantin Aleksandrovich Shramov
{"title":"Об автоморфизмах квазигладких взвешенных полных пересечений","authors":"Виктор Владимирович Пржиялковский, V. Przyjalkowski, Константин Александрович Шрамов, Сonstantin Aleksandrovich Shramov","doi":"10.4213/SM9451","DOIUrl":"https://doi.org/10.4213/SM9451","url":null,"abstract":"Показано, что действие любой редуктивной подгруппы в группе автоморфизмов квазигладкого хорошо сформированного взвешенного полного пересечения размерности не меньше $3$ индуцировано действием подгруппы в группе автоморфизмов объемлющего взвешенного проективного пространства. Приведены примеры, показывающие, что группа автоморфизмов квазигладкого хорошо сформированного взвешенного полного пересечения Фано может быть бесконечной и даже нередуктивной. Библиография: 25 названий.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77482096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local controllability and optimality 局部可控性和最优性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9434
E. R. Avakov, G. Magaril-Il'yaev
{"title":"Local controllability and optimality","authors":"E. R. Avakov, G. Magaril-Il'yaev","doi":"10.1070/SM9434","DOIUrl":"https://doi.org/10.1070/SM9434","url":null,"abstract":"The concept of local controllability is introduced for a dynamical system; sufficient conditions for such controllability are presented. As a consequence, necessary conditions for a local infimum in an optimal control problem are obtained. These strengthen Pontryagin’s maximum principle and extend it to more general classes of problems. Bibliography: 8 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89573916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Versal families of elliptic curves with rational 3-torsion 具有有理3-扭转的椭圆曲线的一般族
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9429
B. Bekker, Y. Zarhin
{"title":"Versal families of elliptic curves with rational 3-torsion","authors":"B. Bekker, Y. Zarhin","doi":"10.1070/SM9429","DOIUrl":"https://doi.org/10.1070/SM9429","url":null,"abstract":"For an arbitrary field of characteristic different from 2 and 3, we construct versal families of elliptic curves whose 3-torsion is either rational or isomorphic to as a Galois module. Bibliography: 10 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85673180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation by simple partial fractions in unbounded domains 无界域上的简单部分分式近似
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9298
P. Borodin, K. Shklyaev
{"title":"Approximation by simple partial fractions in unbounded domains","authors":"P. Borodin, K. Shklyaev","doi":"10.1070/SM9298","DOIUrl":"https://doi.org/10.1070/SM9298","url":null,"abstract":"For unbounded simply connected domains in the complex plane, bounded by several simple curves with regular asymptotic behaviour at infinity, we obtain necessary conditions and sufficient conditions for simple partial fractions (logarithmic derivatives of polynomials) with poles on the boundary of to be dense in the space of holomorphic functions in (with the topology of uniform convergence on compact subsets of ). In the case of a strip bounded by two parallel lines, we give estimates for the convergence rate to zero in the interior of of simple partial fractions with poles on the boundary of and with one fixed pole. Bibliography: 16 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72481708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Approximation of resolvents in homogenization of fourth-order elliptic operators 四阶椭圆算子均匀化的近似解
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9413
S. Pastukhova
{"title":"Approximation of resolvents in homogenization of fourth-order elliptic operators","authors":"S. Pastukhova","doi":"10.1070/SM9413","DOIUrl":"https://doi.org/10.1070/SM9413","url":null,"abstract":"We study the homogenization of a fourth-order divergent elliptic operator with rapidly oscillating -periodic coefficients, where is a small parameter. The homogenized operator is of the same type and has constant coefficients. We apply Zhikov’s shift method to obtain an estimate in the -operator norm of order for the difference of the resolvents and . Bibliography: 25 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75039105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
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