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Nikolay Nikolayevich Konstantinov (obituary) 尼古拉·尼古拉耶维奇·康斯坦蒂诺夫（讣告）
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/rm10052
V. Arlazarov, Aleksei Yakovlevich Kanel-Belov, V. Bugaenko, V. Vassiliev, A. Gorodentsev, Sergei Aleksandrovich Dorichenko, Yulij Ilyashenko, V. Imaykin, Stanislav Igorevich Komarov, A. Kushnirenko, Yurii P. Lysov, Aleksei Lvovich Semenov, V. Tikhomirov, Aleksei Kirillovich Tolpygo, A. Khovanskii, Pavel Aleksandrovich Yakushkin, I. Yaschenko
{"title":"Nikolay Nikolayevich Konstantinov (obituary)","authors":"V. Arlazarov, Aleksei Yakovlevich Kanel-Belov, V. Bugaenko, V. Vassiliev, A. Gorodentsev, Sergei Aleksandrovich Dorichenko, Yulij Ilyashenko, V. Imaykin, Stanislav Igorevich Komarov, A. Kushnirenko, Yurii P. Lysov, Aleksei Lvovich Semenov, V. Tikhomirov, Aleksei Kirillovich Tolpygo, A. Khovanskii, Pavel Aleksandrovich Yakushkin, I. Yaschenko","doi":"10.1070/rm10052","DOIUrl":"https://doi.org/10.1070/rm10052","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"806 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59014027","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
Victor Nikolaevich Latyshev 维克托·尼古拉耶维奇·拉蒂舍夫
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/RM9996
V. Artamonov, L. Bokut, V. V. Borisenko, E. Bunina, V. Buchstaber, A. Guterman, Y. Ershov, M. Zaitsev, A. Kanel-Belov, A. R. Kemer, A. Mikhalev, S. Mishchenko, S. Novikov, A. Ol’shanskii, Yuri Prokhorov, Yu. P. Razmyslov, A. I. Shafarevich, I. Shestakov
{"title":"Victor Nikolaevich Latyshev","authors":"V. Artamonov, L. Bokut, V. V. Borisenko, E. Bunina, V. Buchstaber, A. Guterman, Y. Ershov, M. Zaitsev, A. Kanel-Belov, A. R. Kemer, A. Mikhalev, S. Mishchenko, S. Novikov, A. Ol’shanskii, Yuri Prokhorov, Yu. P. Razmyslov, A. I. Shafarevich, I. Shestakov","doi":"10.1070/RM9996","DOIUrl":"https://doi.org/10.1070/RM9996","url":null,"abstract":"The prominent Soviet and Russian mathematician, outstanding teacher, Professor of the Department of Higher Algebra of the Faculty of Mechanics and Mathematics at Moscow State University Victor Nikolaevich Latyshev passed away on 13 April 2020. Latyshev was born in Moscow on 9 February 1934. He spent his childhood in the town of Pushkino near Moscow, where he graduated from school with a gold medal. Almost the entire life of Victor Nikolaevich was connected with the Lomonosov Moscow State University (MSU) and specifically with the Department of Higher Algebra of the Faculty of Mechanics and Mathematics (Mech-Mat). He enrolled at Mech-Mat in 1953, graduated from it in 1958 to become a PhD student at the Department of Algebra, and started working at this Department in 1961. The outstanding algebraist Anatolii Illarionovich Shirshov was his research advisor. Experts in the theory of associative and Lie rings are well aware of the results of Shirshov,","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"165 - 170"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59006451","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
Anatolii Mikhailovich Stepin Anatoly Mikhailovich Stepin
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/RM10053
O. Ageev, Yaroslav Vorobets, B. Weiss, R. Grigorchuk, V. Grines, B. Gurevich, L. S. Efremova, A. Y. Zhirov, E. Zhuzhoma, B. Kashin, V. Kolokoltsov, A. Kochergin, L. Lerman, I. Mykytyuk, V. Oseledets, A. Plakhov, O. Pochinka, V. Ryzhikov, V. Sakbaev, A. Sergeev, Y. Sinai, A. T. Tagi-zade, S. Tikhonov, J. Thouvenot, A. Helemskiĭ, A. Shafarevich
{"title":"Anatolii Mikhailovich Stepin","authors":"O. Ageev, Yaroslav Vorobets, B. Weiss, R. Grigorchuk, V. Grines, B. Gurevich, L. S. Efremova, A. Y. Zhirov, E. Zhuzhoma, B. Kashin, V. Kolokoltsov, A. Kochergin, L. Lerman, I. Mykytyuk, V. Oseledets, A. Plakhov, O. Pochinka, V. Ryzhikov, V. Sakbaev, A. Sergeev, Y. Sinai, A. T. Tagi-zade, S. Tikhonov, J. Thouvenot, A. Helemskiĭ, A. Shafarevich","doi":"10.1070/RM10053","DOIUrl":"https://doi.org/10.1070/RM10053","url":null,"abstract":"Anatolii Mikhailovich Stepin, a prominent scientist and educator, expert in dynamical systems and ergodic theory, passed away on 7 November 2020. His death was a bitter loss for his family, students, colleagues, and mathematicians at large. He was born in Moscow on 20 July 1940. During the war he was evacuated to Chelyabinsk together with his mother, while his father, a chemical engineer, worked at a defense factory. After the war their family returned to Moscow. Anatolii graduated from Moscow School no. 434 with a gold medal and, intending to follow in his father’s footsteps, enrolled at the Moscow Power Engineering Institute, the Division of Thermal Physics. At that time M. I. Vishik, who was well known for his work on partial differential equations, read mathematics courses at the Institute. The talented student became interested in these lectures, and after his 3rd year at Power Engineering Institute, he decided to transfer to the Faculty of Mechanics and Mathematics at Moscow State University. After solving the tricky problem of being transferred to another university, Stepin became a student at the Department of Theory of Functions and Functional Analysis, and chose F.A. Berezin to be his scientific advisor. In addition to Berezin’s research seminar, Stepin was also","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"361 - 367"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013642","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
Feynman checkers: towards algorithmic quantum theory 费曼跳棋:走向算法量子理论
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/rm10025
Mihail Borisovich Skopenkov, A. Ustinov
{"title":"Feynman checkers: towards algorithmic quantum theory","authors":"Mihail Borisovich Skopenkov, A. Ustinov","doi":"10.1070/rm10025","DOIUrl":"https://doi.org/10.1070/rm10025","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59012672","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
An observation on the Gram matrices of systems of uniformly bounded functions and a problem of Olevskii 一致有界函数系统的Gram矩阵的观察及一个Olevskii问题
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/RM10045
B. Kashin
{"title":"An observation on the Gram matrices of systems of uniformly bounded functions and a problem of Olevskii","authors":"B. Kashin","doi":"10.1070/RM10045","DOIUrl":"https://doi.org/10.1070/RM10045","url":null,"abstract":"In what follows ⟨ · , · ⟩ and | · | denote the scalar product and Euclidean norm in R , SN−1 = {x ∈ R : |x| = 1}, and μN−1 is the normalized Lebesgue measure on SN−1, N = 2, 3, . . . . For an N × N matrix G, we let ∥G∥op denote the norm of G as an operator in (R , | · |). We also use the following notation: ( · , · ) is the inner product in the function space L and ∥ · ∥∞ is the norm in L∞(0, 1). Given a system of vectors Z = {zj}j=1 ⊂ R , consider the Gram matrix GZ = {⟨zj , zk⟩}, 1 ⩽ j, k ⩽ N . The problem of finding a system of functions F = {fj}j=1 ⊂ L∞(0, 1) with uniform norms as small as possible and such that","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"171 - 173"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013534","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
Viktor Stepanovich Kulikov (on his seventieth birthday) 维克托·斯捷潘诺维奇·库利科夫(庆祝70岁生日)
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/rm10060
F. Bogomolov, S. Gorchinskiy, A. Zheglov, V. Nikulin, Dmitri Orlov, D. Osipov, A. N. Parshin, V. Popov, V. Przyjalkowski, Yuri Prokhorov, M. Reid, A. Sergeev, D. Treschev, A. K. Tsikh, I. Cheltsov, E. Chirka
{"title":"Viktor Stepanovich Kulikov (on his seventieth birthday)","authors":"F. Bogomolov, S. Gorchinskiy, A. Zheglov, V. Nikulin, Dmitri Orlov, D. Osipov, A. N. Parshin, V. Popov, V. Przyjalkowski, Yuri Prokhorov, M. Reid, A. Sergeev, D. Treschev, A. K. Tsikh, I. Cheltsov, E. Chirka","doi":"10.1070/rm10060","DOIUrl":"https://doi.org/10.1070/rm10060","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59014924","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
Spectrum of the Laplace operator on closed surfaces 闭曲面上拉普拉斯算子的谱
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/RM9916
D. A. Popov
{"title":"Spectrum of the Laplace operator on closed surfaces","authors":"D. A. Popov","doi":"10.1070/RM9916","DOIUrl":"https://doi.org/10.1070/RM9916","url":null,"abstract":"A survey is given of classical and relatively recent results on the distribution of the eigenvalues of the Laplace operator on closed surfaces. For various classes of metrics the dependence of the behaviour of the second term in Weyl’s formula on the geometry of the geodesic flow is considered. Various versions of trace formulae are presented, along with ensuing identities for the spectrum. The case of a compact Riemann surface with the Poincaré metric is considered separately, with the use of Selberg’s formula. A number of results on the stochastic properties of the spectrum in connection with the theory of quantum chaos and the universality conjecture are presented. Bibliography: 51 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"20 1","pages":"81 - 97"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59004530","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
Structures of non-classical discontinuities in solutions of hyperbolic systems of equations 双曲型方程组解中的非经典不连续结构
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/RM10033
A. Kulikovskii, A. P. Chugainova
{"title":"Structures of non-classical discontinuities in solutions of hyperbolic systems of equations","authors":"A. Kulikovskii, A. P. Chugainova","doi":"10.1070/RM10033","DOIUrl":"https://doi.org/10.1070/RM10033","url":null,"abstract":"Discontinuity structures in solutions of a hyperbolic system of equations are considered. The system of equations has a rather general form and, in particular, can describe the longitudinal and torsional non-linear waves in elastic rods in the simplest setting and also one-dimensional waves in unbounded elastic media. The properties of discontinuities in solutions of these equations have been investigated earlier under the assumption that only the relations following from the conservation laws for the longitudinal momentum and angular momentum about the axis of the rod and the displacement continuity condition hold on the discontinuities. The shock adiabat has been studied. This paper deals with stationary discontinuity structures under the assumption that viscosity is the main governing mechanism inside the structure. Some segments of the shock adiabat are shown to correspond to evolutionary discontinuities without structure. It is also shown that there are special discontinuities on which an additional relation must hold, which arises from the condition that a discontinuity structure exists. The additional relation depends on the processes in the structure. Special discontinuities satisfy evolutionary conditions that differ from the well-known Lax conditions. Conclusions are discussed, which can also be of interest in the case of other systems of hyperbolic equations. Bibliography: 58 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"47 - 79"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59012990","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
A number-theoretic part of control theory 控制论的数论部分
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/RM10050
Aleksandr Iosifovich Ovseevich
{"title":"A number-theoretic part of control theory","authors":"Aleksandr Iosifovich Ovseevich","doi":"10.1070/RM10050","DOIUrl":"https://doi.org/10.1070/RM10050","url":null,"abstract":"The importance of Q is primarily due to the fact that it defines a common Lyapunov function for the two stable matrices M = −diag(1, 2, . . . , N) and A + BC, where Aei = −iei+1 for i = 1, . . . , N , B = e1, and C = −(1/2)B∗Q. Here the ei, i = 1, . . . , N , form the standard basis of R and eN+1 = 0. In [6] it was shown that Q is an even integer matrix, that is, Qij ∈ 2Z, and it was conjectured that all elements of the matrix are divisible by N(N + 1). The proofs in [6] were based on considering orthogonal polynomials. Here we prove this conjecture using similar methods.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"369 - 371"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013305","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
Spectrum of a convolution operator with potential 具有势的卷积算子的谱
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-01-01 DOI: 10.1070/rm10055
A. Kupavskii, A. Sagdeev, Nóra Frankl
{"title":"Spectrum of a convolution operator with potential","authors":"A. Kupavskii, A. Sagdeev, Nóra Frankl","doi":"10.1070/rm10055","DOIUrl":"https://doi.org/10.1070/rm10055","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013709","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
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