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.
{"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":"55 2","pages":"1746 - 1764"},"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}
It is proved that in each homotopy class of continuous mappings of the two-dimensional torus to itself that induce a hyperbolic action on the fundamental group, as long as it is free of expanding mappings, there exists an -endomorphism whose nonwandering set consists of an attracting hyperbolic sink and a nontrivial one-dimensional collapsing repeller, which is a one-dimensional orientable lamination, locally homeomorphic to the direct product of a Cantor set and a line segment. Moreover, the unstable -invariant subbundle of the tangent space to the repeller has the property of uniqueness. Bibliography: 23 titles.
{"title":"On -endomorphisms of the two-dimensional torus","authors":"V. Grines, E. Zhuzhoma, E. D. Kurenkov","doi":"10.1070/SM9372","DOIUrl":"https://doi.org/10.1070/SM9372","url":null,"abstract":"It is proved that in each homotopy class of continuous mappings of the two-dimensional torus to itself that induce a hyperbolic action on the fundamental group, as long as it is free of expanding mappings, there exists an -endomorphism whose nonwandering set consists of an attracting hyperbolic sink and a nontrivial one-dimensional collapsing repeller, which is a one-dimensional orientable lamination, locally homeomorphic to the direct product of a Cantor set and a line segment. Moreover, the unstable -invariant subbundle of the tangent space to the repeller has the property of uniqueness. Bibliography: 23 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"5 1","pages":"698 - 725"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87117880","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}
Виктор Владимирович Пржиялковский, V. Przyjalkowski, Константин Александрович Шрамов, Сonstantin Aleksandrovich Shramov
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.
{"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":"7 1","pages":"112-127"},"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}
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.
在本文中，我们证明了一对关于约化李群模的子群的一致稳定性的一个版本。参考书目:7篇。
{"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":"43 1","pages":"332 - 350"},"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}
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.
{"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":"79 1","pages":"1553 - 1570"},"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}
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.
{"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":"33 1","pages":"1329 - 1346"},"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}
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.
{"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":"26 1","pages":"274 - 287"},"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}
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.
{"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":"37 1","pages":"887 - 920"},"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}
We generalize a construction due to Mironov. Some time ago he presented new examples of minimal and Hamiltonian minimal Lagrangian submanifolds in and . His construction is based on the considerations of a noncomplete toric action of , where , on subspaces that are invariant with respect to the action of a natural antiholomorphic involution. This situation takes place for a rather broad class of algebraic varieties: complex quadrics, Grassmannians, flag varieties and so on, which makes it possible to construct many new examples of Lagrangian submanifolds in these algebraic varieties. Bibliography: 4 titles.
{"title":"Mironov Lagrangian cycles in algebraic varieties","authors":"N. Tyurin","doi":"10.1070/SM9407","DOIUrl":"https://doi.org/10.1070/SM9407","url":null,"abstract":"We generalize a construction due to Mironov. Some time ago he presented new examples of minimal and Hamiltonian minimal Lagrangian submanifolds in and . His construction is based on the considerations of a noncomplete toric action of , where , on subspaces that are invariant with respect to the action of a natural antiholomorphic involution. This situation takes place for a rather broad class of algebraic varieties: complex quadrics, Grassmannians, flag varieties and so on, which makes it possible to construct many new examples of Lagrangian submanifolds in these algebraic varieties. Bibliography: 4 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"109 1","pages":"389 - 398"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86371116","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}
The phenomenon of support shrinking with a time delay for the solution of a doubly nonlinear degenerate parabolic equation is studied in the case of slow diffusion and strong absorption. For a nonnegative solution, a sufficient condition for support shrinking beginning with some moment of time is deduced in terms of the local behaviour of the mass of the initial datum. It is also proved that the solution vanishes identically in finite time. Bibliography: 21 titles.
{"title":"On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution","authors":"S. P. Degtyarev","doi":"10.1070/SM9377","DOIUrl":"https://doi.org/10.1070/SM9377","url":null,"abstract":"The phenomenon of support shrinking with a time delay for the solution of a doubly nonlinear degenerate parabolic equation is studied in the case of slow diffusion and strong absorption. For a nonnegative solution, a sufficient condition for support shrinking beginning with some moment of time is deduced in terms of the local behaviour of the mass of the initial datum. It is also proved that the solution vanishes identically in finite time. Bibliography: 21 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"14 1","pages":"170 - 184"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81831635","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：