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Maps to virtual braids and braid representations 映射到虚拟辫子和辫子表示
4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10087e
Vassily Olegovich Manturov, Igor Mikhailovich Nikonov
{"title":"Maps to virtual braids and braid representations","authors":"Vassily Olegovich Manturov, Igor Mikhailovich Nikonov","doi":"10.4213/rm10087e","DOIUrl":"https://doi.org/10.4213/rm10087e","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136368151","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 integrability of the deformed Ruijsenaars-Schneider system 变形rujsenaars - schneider系统的可积性
4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10105e
Anton Vladimirovich Zabrodin
{"title":"On integrability of the deformed Ruijsenaars-Schneider system","authors":"Anton Vladimirovich Zabrodin","doi":"10.4213/rm10105e","DOIUrl":"https://doi.org/10.4213/rm10105e","url":null,"abstract":"We find integrals of motion for the recently introduced deformed Ruijsenaars-Schneider many-body system, which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint of type B. Our method is based on the fact that the equations of motion for this system coincide with those for pairs of Ruijsenaars-Schneider particles which stick together preserving a special fixed distance between the particles. We also obtain Bäcklund transformations and integrable time discretization of the deformed Ruijsenaars-Schneider system, which is shown to be the dynamical system for poles of elliptic solutions to the fully discrete Kadomtsev-Petviashvili equation of type B. In additon, we propose a field analogue of the deformed Ruijsenaars-Schneider system on a space-time lattice. Bibliography: 35 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"45-46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136368180","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 number of components of the Pell-Abel equations with primitive solutions of given degree 具有给定阶元解的Pell-Abel方程的分量数
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10082e
A. Bogatyrev, Q. Gendron
{"title":"The number of components of the Pell-Abel equations with primitive solutions of given degree","authors":"A. Bogatyrev, Q. Gendron","doi":"10.4213/rm10082e","DOIUrl":"https://doi.org/10.4213/rm10082e","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70328908","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
Index of minimal surfaces in the 3-sphere 球面上最小曲面的指数
4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10094e
Egor Aleksandrovich Morozov, Alexei Viktorovich Penskoi
{"title":"Index of minimal surfaces in the 3-sphere","authors":"Egor Aleksandrovich Morozov, Alexei Viktorovich Penskoi","doi":"10.4213/rm10094e","DOIUrl":"https://doi.org/10.4213/rm10094e","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136368166","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
Geometry of Diophantine exponents 丢番图指数几何
4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10089e
Oleg Nikolaevich German
{"title":"Geometry of Diophantine exponents","authors":"Oleg Nikolaevich German","doi":"10.4213/rm10089e","DOIUrl":"https://doi.org/10.4213/rm10089e","url":null,"abstract":"Diophantine exponents are some of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of Diophantine approximation that studies Diophantine exponents and relations they satisfy. We discuss classical Diophantine exponents arising in the problem of approximating zero with the set of the values of several linear forms at integer points, their analogues in Diophantine approximation with weights, multiplicative Diophantine exponents, and Diophantine exponents of lattices. We pay special attention to the transference principle. Bibliography: 99 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136368159","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
Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions 椭圆函数可积李群上的左不变最优控制问题
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10063e
Y. Sachkov
{"title":"Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions","authors":"Y. Sachkov","doi":"10.4213/rm10063e","DOIUrl":"https://doi.org/10.4213/rm10063e","url":null,"abstract":"Left-invariant optimal control problems on Lie groups are an important class of problems with a large symmetry group. They are theoretically interesting because they can often be investigated in full and general laws can be studied by using these model problems. In particular, problems on nilpotent Lie groups provide a fundamental nilpotent approximation to general problems. Also, left-invariant problems often arise in applications such as classical and quantum mechanics, geometry, robotics, visual perception models, and image processing. The aim of this paper is to present a survey of the main concepts, methods, and results pertaining to left-invariant optimal control problems on Lie groups that can be integrated by elliptic functions. The focus is on describing extremal trajectories and their optimality, the cut time and cut locus, and optimal synthesis. Bibliography: 162 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70328887","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
Cyclic Frobenius algebras 循环Frobenius代数
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10096e
V. Buchstaber, A. Mikhailov
{"title":"Cyclic Frobenius algebras","authors":"V. Buchstaber, A. Mikhailov","doi":"10.4213/rm10096e","DOIUrl":"https://doi.org/10.4213/rm10096e","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70328957","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
Extremal problems in geometric function theory 几何函数理论中的极值问题
4区 数学
Russian Mathematical Surveys Pub Date : 2023-01-01 DOI: 10.4213/rm10076e
Farit Gabidinovich Avkhadiev, Ilgiz Rifatovich Kayumov, Semen Rafailovich Nasyrov
{"title":"Extremal problems in geometric function theory","authors":"Farit Gabidinovich Avkhadiev, Ilgiz Rifatovich Kayumov, Semen Rafailovich Nasyrov","doi":"10.4213/rm10076e","DOIUrl":"https://doi.org/10.4213/rm10076e","url":null,"abstract":"This survey is devoted to a number of achievements in the theory of extremal problems in geometric function theory. The approaches to the solution of problems under consideration and the methods used are based on conformal isomorphisms and on the theory of univalent functions developed since the beginning of the 20th century. Results on integral means of conformal mappings of a disc are presented and, in particular, Dolzenko's inequality for rational functions is extended to arbitrary domains with rectifiable boundaries. Investigations in the field of Bohr-type inequalities are described. An emphasis is made on integral inequalities of Hardy and Rellich type, in which the analytic properties of inequalities are intertwined with geometric characteristics of the boundaries of domains. Results related to the solution of the Vuorinen problem on the behaviour of conformal moduli under unlimited dilations of the plane are presented. Formulae for the variation of Robin capacity are obtained. One-parameter families of rational and elliptic functions whose critical values vary in accordance with a prescribed law are characterized. The last results on Smale's conjecture and Smale's dual conjecture are described. Bibliography: 149 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"186 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136368164","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
Neurobehavioral and Biochemical Evidences in Support of Protective Effect of Marrubiin (Furan Labdane Diterpene) from Marrubium vulgare Linn. and Its Extracts after Traumatic Brain Injury in Experimental Mice. 实验小鼠脑外伤后神经行为和生化证据支持 Marrubiin（呋喃拉巴旦二萜）及其提取物的保护作用
4区 数学
Russian Mathematical Surveys Pub Date : 2022-05-24 eCollection Date: 2022-01-01 DOI: 10.1155/2022/4457973
Nidhi, Govind Singh, Rekha Valecha, Govind Shukla, Deepak Kaushik, Mohammad Akhlaquer Rahman, Rupesh K Gautam, Kumud Madan, Vineet Mittal, Rajeev K Singla
{"title":"Neurobehavioral and Biochemical Evidences in Support of Protective Effect of Marrubiin (Furan Labdane Diterpene) from <i>Marrubium vulgare</i> Linn. and Its Extracts after Traumatic Brain Injury in Experimental Mice.","authors":"Nidhi, Govind Singh, Rekha Valecha, Govind Shukla, Deepak Kaushik, Mohammad Akhlaquer Rahman, Rupesh K Gautam, Kumud Madan, Vineet Mittal, Rajeev K Singla","doi":"10.1155/2022/4457973","DOIUrl":"10.1155/2022/4457973","url":null,"abstract":"<p><p>Traumatic brain injuries due to sudden accidents cause major physical and mental health problems and are one of the main reasons behind the mortality and disability of patients. Research on alternate natural sources could be a boon for the rehabilitation of poor TBI patients. The literature indicates the <i>Marrubium vulgare</i> Linn. and its secondary metabolite marrubiin (furan labdane diterpene) possess various pharmacological properties such as vasorelaxant, calcium channel blocker, antioxidant, and antiedematogenic activities. Hence, in the present research, both marrubiin and hydroalcoholic extracts of the plant were evaluated for their neuroprotective effect after TBI. The neurological severity score and oxidative stress parameters are significantly altered by the test samples. Moreover, the neurotransmitter analysis indicated a significant change in GABA and glutamate. The histopathological study also supported the observed results. The improved neuroprotective potential of the extract could be attributed to the presence of a large number of secondary metabolites including marrubiin.</p>","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"44 1","pages":"4457973"},"PeriodicalIF":0.0,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9155918/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80710636","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 normal derivative lemma and surrounding issues 正规导数引理及其相关问题
IF 0.9 4区 数学
Russian Mathematical Surveys Pub Date : 2022-04-01 DOI: 10.1070/RM10049
D. Apushkinskaya, A. Nazarov
{"title":"The normal derivative lemma and surrounding issues","authors":"D. Apushkinskaya, A. Nazarov","doi":"10.1070/RM10049","DOIUrl":"https://doi.org/10.1070/RM10049","url":null,"abstract":"In this survey we describe the history and current state of one of the key areas in the qualitative theory of elliptic partial differential equations related to the strong maximum principle and the boundary point principle (normal derivative lemma). Bibliography: 234 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"189 - 249"},"PeriodicalIF":0.9,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47121450","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: 10
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