V. Buslaev, V. Buchstaber, A. Dranishnikov, Vitalii Mendelevich Kliatskin, S. A. Melikhov, L. Montejano, S. Novikov, P. Semenov
{"title":"Evgenii Vital'evich Shchepin (on his seventieth birthday)","authors":"V. Buslaev, V. Buchstaber, A. Dranishnikov, Vitalii Mendelevich Kliatskin, S. A. Melikhov, L. Montejano, S. Novikov, P. Semenov","doi":"10.1070/rm10043","DOIUrl":"https://doi.org/10.1070/rm10043","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":"59013431","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}
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
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,
{"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}
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
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
著名科学家和教育家、动力系统和遍历理论专家阿纳托利·米哈伊洛维奇·斯捷平于2020年11月7日逝世。他的去世对他的家人、学生、同事和数学家来说都是一个痛苦的损失。他于1940年7月20日出生于莫斯科。战争期间，他和母亲一起被疏散到车里雅宾斯克，而他的父亲是一名化学工程师，在一家国防工厂工作。战争结束后，他们一家回到了莫斯科。阿纳托利毕业于莫斯科第一中学。他打算追随父亲的脚步，进入莫斯科动力工程学院热物理系学习。当时，以研究偏微分方程而闻名的M. I. Vishik在该研究所学习数学课程。这位才华横溢的学生对这些讲座很感兴趣，在动力工程学院读了三年后，他决定转到莫斯科国立大学力学和数学学院。在解决了转学的棘手问题后，Stepin成为了函数理论与泛函分析系的一名学生，并选择了F.A. Berezin作为他的科学顾问。除了别列津的研究研讨会，斯捷平也
{"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}
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
{"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}
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}
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.
{"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}
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.
{"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}
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.
Q的重要性主要是由于它为两个稳定矩阵M = - diag(1,2，…)定义了一个公共Lyapunov函数。， N)和A + BC，其中对于i = 1, Aei =−iei+1，…， N, B = e1，且C =−(1/2)B * Q。这里是ei, i = 1，…， N，构成R和eN+1 = 0的标准基。[6]中证明了Q是一个偶数矩阵，即Qij∈2Z，并推测了矩阵的所有元素都可以被N(N + 1)整除。[6]中的证明是基于考虑正交多项式的。这里我们用类似的方法证明了这个猜想。
{"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}
{"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}
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：