Russian Mathematical Surveys最新文献_第10页

Iterated Laurent series over rings and the Contou-Carrère symbol 在环和contou - carr<e:1>符号上迭代Laurent级数

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-01 DOI: 10.1070/RM9975

S. Gorchinskiy, D. Osipov

{"title":"Iterated Laurent series over rings and the Contou-Carrère symbol","authors":"S. Gorchinskiy, D. Osipov","doi":"10.1070/RM9975","DOIUrl":"https://doi.org/10.1070/RM9975","url":null,"abstract":"This article contains a survey of a new algebro-geometric approach for working with iterated algebraic loop groups associated with iterated Laurent series over arbitrary commutative rings and its applications to the study of the higher-dimensional Contou-Carrère symbol. In addition to the survey, the article also contains new results related to this symbol. The higher-dimensional Contou-Carrère symbol arises naturally when one considers deformation of a flag of algebraic subvarieties of an algebraic variety. The non-triviality of the problem is due to the fact that, in the case 1$?> , for the group of invertible elements of the algebra of -iterated Laurent series over a ring, no representation is known in the form of an ind-flat scheme over this ring. Therefore, essentially new algebro-geometric constructions, notions, and methods are required. As an application of the new methods used, a description of continuous homomorphisms between algebras of iterated Laurent series over a ring is given, and an invertibility criterion for such endomorphisms is found. It is shown that the higher- dimensional Contou-Carrère symbol, restricted to algebras over the field of rational numbers, is given by a natural explicit formula, and this symbol extends uniquely to all rings. An explicit formula is also given for the higher-dimensional Contou-Carrère symbol in the case of all rings. The connection with higher-dimensional class field theory is described. As a new result, it is shown that the higher-dimensional Contou-Carrère symbol has a universal property. Namely, if one fixes a torsion-free ring and considers a flat group scheme over this ring such that any two points of the scheme are contained in an affine open subset, then after restricting to algebras over the fixed ring, all morphisms from the -iterated algebraic loop group of the Milnor -group of degree to the above group scheme factor through the higher-dimensional Contou-Carrère symbol. Bibliography: 67 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48732400","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

The spectral radius of a certain parametric family of functional operators 某参数泛函算子族的谱半径

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.1070/RM9967

N. B. Zhuravlev, L. Rossovskii

引用次数: 0

Caucasus Mathematical Olympiad 高加索奥数竞赛

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.4171/NEWS/104/8

D. Mamiy

引用次数: 0

Ramsey theory in the -space with Chebyshev metric 具有Chebyshev度量的-空间中的Ramsey理论

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.1070/RM9958

A. Kupavskii, A. Sagdeev

引用次数: 14

Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes 充液膜管中类孤子结构的动力学和光谱稳定性

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.1070/RM9953

A. Il'ichev

{"title":"Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes","authors":"A. Il'ichev","doi":"10.1070/RM9953","DOIUrl":"https://doi.org/10.1070/RM9953","url":null,"abstract":"This survey presents results on the stability of elevation solitary waves in axisymmetric elastic membrane tubes filled with a fluid. The elastic tube material is characterized by an elastic potential (elastic energy) that depends non-linearly on the principal deformations and describes the compliant elastic media. Our survey uses a simple model of an inviscid incompressible fluid, which nevertheless makes it possible to trace the main regularities of the dynamics of solitary waves. One of these regularities is the spectral stability (linear stability in form) of these waves. The basic equations of the ‘axisymmetric tube – ideal fluid’ system are formulated, and the equations for the fluid are averaged over the cross-section of the tube, that is, a quasi-one-dimensional flow with waves whose length significantly exceeds the radius of the tube is considered. The spectral stability with respect to axisymmetric perturbations is studied by constructing the Evans function for the system of basic equations linearized around a solitary wave type solution. The Evans function depends only on the spectral parameter , is analytic in the right-hand complex half-plane , and its zeros in coincide with unstable eigenvalues. The problems treated include stability of steady solitary waves in the absence of a fluid inside the tube (the case of constant internal pressure), together with the case of local inhomogeneity (thinning) of the tube wall, the presence of a steady fluid filling the tube (the case of zero mean flow) or a moving fluid (the case of non-zero mean flow), and also the problem of stability of travelling solitary waves propagating along the tube with non-zero speed. Bibliography: 83 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43539043","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: 3

Extreme value theory for triangular arrays of dependent random variables 相依随机变量三角形阵列的极值理论

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.1070/RM9964

M. Isaev, I. Rodionov, Ruizhe Zhang, M. Zhukovskii

引用次数: 2

Anatolii Iserovish Neishtadt Anatolii Iserovish Neishtadt

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.1070/RM9965

A. Artem’ev, S. Bolotin, D. Vainchtein, A. Vasiliev, S. Dobrokhotov, L. Zelenyi, V. V. Kozlov, A. Petrukovich, V. V. Sidorenko, D. Treschev, A. I. Shafarevich

{"title":"Anatolii Iserovish Neishtadt","authors":"A. Artem’ev, S. Bolotin, D. Vainchtein, A. Vasiliev, S. Dobrokhotov, L. Zelenyi, V. V. Kozlov, A. Petrukovich, V. V. Sidorenko, D. Treschev, A. I. Shafarevich","doi":"10.1070/RM9965","DOIUrl":"https://doi.org/10.1070/RM9965","url":null,"abstract":"Anatolii Iserovish Neishtadt, a prominent researcher and outstanding expert in the theory of perturbations of dynamical systems and the theory of adiabatic invariants, observed his 70th birthday on 27 July 2020. He was born in Moscow in the family of a chemical engineer and a flight technician (his mother). As a high-school senior he attended lessons at a voluntary evening physicsmathematics school under the auspices of the Bauman Moscow State Technical School (now Technical University), from which he graduated with honours. In 1967 he graduated from Moscow school no. 358 with a gold medal and enrolled in the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University. He was a student in the Department of Theoretical Mechanics, where M. L. Lidov was his scientific advisor. Neishtadt graduated from the university with distinction and, after defending his diploma thesis, was admitted to postgraduate studies in the faculty, where in 1975 he presented, and in 1976 defended, his Ph.D. thesis “Some resonance problems in non-linear systems”, written under the supervision of Lidov. From 1975 to 1987 Neishtadt worked in the All-Union Scientific Research Institute of Medical Instrument Design, where his work involved applied programming. Apart from his duties there, he continued active research in mathematics, working on some problems posed by V. I. Arnold. In 1989 Neishtadt defended his D.Sc. thesis “Questions of perturbation theory for non-linear resonance systems” in the Faculty of Mechanics and Mathematics at Moscow State University. In 1987 he was hired on Arnold’s recommendation by the Institute of Space Research, as a researcher in G. M. Zaslavsky’s laboratory (subsequently, department). Neishtadt then worked there for a long time as head of the Laboratory of Non-Linear and Chaotic Dynamics, and is currently a leading researcher at the institute.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59004886","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

Online algorithm for aggregating experts’ predictions with unbounded quadratic loss 具有无界二次损失的专家预测在线聚合算法

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-10-01 DOI: 10.1070/RM9961

Alexander Korotin, V. V'yugin, E. Burnaev

引用次数: 1

Quantisation ideals of nonabelian integrable systems 非贝利可积系统的量子化理想

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-09-02 DOI: 10.1070/RM9966

A. Mikhailov

引用次数: 6

Fenchel–Nielsen coordinates and Goldman brackets fenhel - nielsen坐标和Goldman括号

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-08-28 DOI: 10.1070/RM9972

L. Chekhov

引用次数: 1