Russian Mathematical Surveys最新文献_第10页

Theory of homotopes with applications to mutually unbiased bases, harmonic analysis on graphs, and perverse sheaves 同伦理论及其在互无偏基上的应用，图上的调和分析，和反常束

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-31 DOI: 10.1070/RM9983

A. Bondal, I. Zhdanovskiy

引用次数: 3

The Dickman–Goncharov distribution Dickman-Goncharov分布

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-01 DOI: 10.1070/RM9976

S. Molchanov, V. Panov

{"title":"The Dickman–Goncharov distribution","authors":"S. Molchanov, V. Panov","doi":"10.1070/RM9976","DOIUrl":"https://doi.org/10.1070/RM9976","url":null,"abstract":"In the 1930s and 40s, one and the same delay differential equation appeared in papers by two mathematicians, Karl Dickman and Vasily Leonidovich Goncharov, who dealt with completely different problems. Dickman investigated the limit value of the number of natural numbers free of large prime factors, while Goncharov examined the asymptotics of the maximum cycle length in decompositions of random permutations. The equation obtained in these papers defines, under a certain initial condition, the density of a probability distribution now called the Dickman–Goncharov distribution (this term was first proposed by Vershik in 1986). Recently, a number of completely new applications of the Dickman–Goncharov distribution have appeared in mathematics (random walks on solvable groups, random graph theory, and so on) and also in biology (models of growth and evolution of unicellular populations), finance (theory of extreme phenomena in finance and insurance), physics (the model of random energy levels), and other fields. Despite the extensive scope of applications of this distribution and of more general but related models, all the mathematical aspects of this topic (for example, infinite divisibility and absolute continuity) are little known even to specialists in limit theorems. The present survey is intended to fill this gap. Both known and new results are given. Bibliography: 62 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"75 1","pages":"1089 - 1132"},"PeriodicalIF":0.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41688728","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: 4

Spinning tops and magnetic orbits 旋转陀螺和磁轨道

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-01 DOI: 10.1070/RM9977

S. Novikov

引用次数: 1

Bifurcations in spatially distributed chains of two-dimensional systems of equations 二维方程组空间分布链中的分岔

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-01 DOI: 10.1070/RM9986

S. Kaschenko

引用次数: 4

Mikhail Aleksandrovich Shubin Mikhail Aleksandrovich Shubin

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-01 DOI: 10.1070/RM9968

M. Braverman, V. Buchstaber, M. Gromov, V. Ivrii, Y. Kordyukov, P. Kuchment, V. Maz'ya, S. Novikov, T. Sunada, L. Friedlander, A. Khovanskii

{"title":"Mikhail Aleksandrovich Shubin","authors":"M. Braverman, V. Buchstaber, M. Gromov, V. Ivrii, Y. Kordyukov, P. Kuchment, V. Maz'ya, S. Novikov, T. Sunada, L. Friedlander, A. Khovanskii","doi":"10.1070/RM9968","DOIUrl":"https://doi.org/10.1070/RM9968","url":null,"abstract":"The prominent mathematician Mikhail Aleksandrovich Shubin passed away after a long illness on 13 May 2020. He was born on 19 December 1944 in Kuibyshev (now Samara) and raised by his mother and grandmother. His mother, Maria Arkadievna, was an engineer at the State Bearing Factory, where she was hired in 1941 after graduating from the Faculty of Mechanics and Mathematics at the Moscow State University. At that time the factory was evacuated from Moscow to Kuibyshev. She worked at the factory for many years as the Head of the Physics of Metals Laboratory. Later, she defended her Ph.D. thesis and moved to Kuibyshev Polytechnical Institute, where she worked as an associate professor. In his school years Shubin was mainly interested in music. He had absolute pitch. After finishing music school, he seriously considered entering a conservatory. However, in high school he developed an interest to mathematics, was successful in olympiads, and eventually decided to apply to the Faculty of Mechanics and Mathematics at the Moscow State University. He was admitted there in 1961. When the time came to choose an adviser, he became a student of M. I. Vishik. After graduating, he began postgraduate work there, and in 1969 defended his Ph.D. thesis. In the thesis he derived formulae for the index of matrix-valued Wiener–Hopf operators. In particular, for the study of families of such operators, he had to generalize a theorem of Birkhoff stating that a continuous matrix-valued function M(z) defined on the unit circle |z| = 1 can be factored as M(z) = A+(z)D(z)A−(z), where A+(z) and A−(z) are continuous and have analytic continuations to the interior of the unit circle and its exterior (infinity included), respectively, and D(z) is a diagonal matrix with entries zj on the diagonal, with integer nj . Shubin considered the problem of what happens when the matrix M depends continuously on an additional parameter t. The Birkhoff factorization cannot be made continuous","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"75 1","pages":"1143 - 1152"},"PeriodicalIF":0.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46819886","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

Valerii Vasil’evich Kozlov 瓦西里·瓦西里维奇·科兹洛夫

IF 0.9 4区数学

Russian Mathematical Surveys Pub Date : 2020-12-01 DOI: 10.1070/RM9949

S. Bolotin, A. V. Borisov, A. Karapetyan, B. Kashin, E. I. Kugushev, Anatolii Iserovich Neishtadt, Dmitri Orlov, D. Treschev

{"title":"Valerii Vasil’evich Kozlov","authors":"S. Bolotin, A. V. Borisov, A. Karapetyan, B. Kashin, E. I. Kugushev, Anatolii Iserovich Neishtadt, Dmitri Orlov, D. Treschev","doi":"10.1070/RM9949","DOIUrl":"https://doi.org/10.1070/RM9949","url":null,"abstract":"On 1 January 2020 the prominent researcher and academician of the Russian Academy of Sciences Valerii Vasil’evich Kozlov observed his 70th birthday. Kozlov has made fundamental contributions to diverse areas of mathematics and mechanics: the theory of Hamiltonian systems, stability theory, the mechanics of non-holonomic systems, statistical mechanics. He has published about 300 papers on mathematics and mechanics and 8 monographs which are now classical. In this one article it is impossible to give even a brief account of all the directions of his research. Kozlov was born on 1 January 1950 in the village of Kostyli, in the Mikhailovskoe District of the Ryazan Oblast. His mother Ol’ga Arkhipovna was a teacher of mathematics, and his father Vasilii Nestorovich was a train-driver, and a veteran of World War II, from the first days when the Soviet Union was attacked until Victory Day. Valerii started his early school education in his native small village (where nobody lives now). There was only a primary school there, with one female teacher, who gave simultaneous lessons to grades I and III in the morning and to grades II and IV in the afternoon. As an 8-year boy, Kozlov moved with his parents to Lyublino-Dachnaya, close to Moscow. When the Moscow Ring Road was built (in 1961) this settlement, like many others, found itself inside the expanding Moscow. In this way Kozlov became a Moscow resident. During his last two years in secondary school he became deeply interested in mathematics and physics. Three times a week he travelled to lessons at a volunteer physics-mathematics evening school under the auspices of the Bauman Moscow State Technical School (now Technical University). This proved to be a remarkable school! (It was founded in 1962 and still exists.) Most teachers were students","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"75 1","pages":"1165 - 1180"},"PeriodicalIF":0.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49615312","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

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":"75 1","pages":"995 - 1066"},"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

Different conformational responses of the β₂-adrenergic receptor-Gs complex upon binding of the partial agonist salbutamol or the full agonist isoprenaline. 结合部分激动剂沙丁胺醇或完全激动剂异丙肾上腺素时，β2-肾上腺素能受体-Gs 复合物的不同构象反应。

IF 16.3 4区数学

Russian Mathematical Surveys Pub Date : 2020-11-24 eCollection Date: 2021-09-01 DOI: 10.1093/nsr/nwaa284

Fan Yang, Shenglong Ling, Yingxin Zhou, Yanan Zhang, Pei Lv, Sanling Liu, Wei Fang, Wenjing Sun, Liaoyuan A Hu, Longhua Zhang, Pan Shi, Changlin Tian

{"title":"Different conformational responses of the β2-adrenergic receptor-Gs complex upon binding of the partial agonist salbutamol or the full agonist isoprenaline.","authors":"Fan Yang, Shenglong Ling, Yingxin Zhou, Yanan Zhang, Pei Lv, Sanling Liu, Wei Fang, Wenjing Sun, Liaoyuan A Hu, Longhua Zhang, Pan Shi, Changlin Tian","doi":"10.1093/nsr/nwaa284","DOIUrl":"10.1093/nsr/nwaa284","url":null,"abstract":"G protein-coupled receptors (GPCRs) are responsible for most cytoplasmic signaling in response to extracellular ligands with different efficacy profiles. Various spectroscopic techniques have identified that agonists exhibiting varying efficacies can selectively stabilize a specific conformation of the receptor. However, the structural basis for activation of the GPCR-G protein complex by ligands with different efficacies is incompletely understood. To better understand the structural basis underlying the mechanisms by which ligands with varying efficacies differentially regulate the conformations of receptors and G proteins, we determined the structures of β2AR-Gαs[Formula: see text]γ bound with partial agonist salbutamol or bound with full agonist isoprenaline using single-particle cryo-electron microscopy at resolutions of 3.26 Å and 3.80 Å, respectively. Structural comparisons between the β2AR-Gs-salbutamol and β2AR-Gs-isoprenaline complexes demonstrated that the decreased binding affinity and efficacy of salbutamol compared with those of isoprenaline might be attributed to weakened hydrogen bonding interactions, attenuated hydrophobic interactions in the orthosteric binding pocket and different conformational changes in the rotamer toggle switch in TM6. Moreover, the observed stronger interactions between the intracellular loop 2 or 3 (ICL2 or ICL3) of β2AR and Gαs with binding of salbutamol versus isoprenaline might decrease phosphorylation in the salbutamol-activated β2AR-Gs complex. From the observed structural differences between these complexes of β2AR, a mechanism of β2AR activation by partial and full agonists is proposed to provide structural insights into β2AR desensitization.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"52 1","pages":"nwaa284"},"PeriodicalIF":16.3,"publicationDate":"2020-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11261663/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80828902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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