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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":"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}
引用次数: 0
On -endomorphisms of the two-dimensional torus 关于二维环面的-自同态
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9372
V. Grines, E. Zhuzhoma, E. D. Kurenkov
{"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}
引用次数: 1
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":"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}
引用次数: 0
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":"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}
引用次数: 0
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":"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}
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":"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}
引用次数: 2
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":"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}
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":"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}
引用次数: 1
Mironov Lagrangian cycles in algebraic varieties 代数变异中的Mironov拉格朗日循环
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9407
N. Tyurin
{"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}
引用次数: 2
On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution 论时滞解的支点收缩现象及解的消光
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2021-01-01 DOI: 10.1070/SM9377
S. P. Degtyarev
{"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}
引用次数: 0
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