Stepan Alexandrov, N. Bogachev, A. Egorov, A. Vesnin
New upper bounds for the volumes of right-angled polyhedra in hyperbolic space $mathbb{H}^3$ are obtained in the following three cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary; for compact polyhedra with only finite vertices; and for finite-volume polyhedra with vertices of both types. Bibliography: 23 titles.
{"title":"On volumes of hyperbolic right-angled polyhedra","authors":"Stepan Alexandrov, N. Bogachev, A. Egorov, A. Vesnin","doi":"10.4213/sm9740e","DOIUrl":"https://doi.org/10.4213/sm9740e","url":null,"abstract":"New upper bounds for the volumes of right-angled polyhedra in hyperbolic space $mathbb{H}^3$ are obtained in the following three cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary; for compact polyhedra with only finite vertices; and for finite-volume polyhedra with vertices of both types.\u0000Bibliography: 23 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81235079","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}
Pub Date : 2021-07-09DOI: 10.26522/jiste.v25i1.3690
Karen Bjerg Petersen
About this issue: 25.1
关于这个问题:25.1
{"title":"From the editors of this issue","authors":"Karen Bjerg Petersen","doi":"10.26522/jiste.v25i1.3690","DOIUrl":"https://doi.org/10.26522/jiste.v25i1.3690","url":null,"abstract":"About this issue: 25.1","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90618127","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}
We study canonical central extensions of the general linear group over the ring of adeles on a smooth projective algebraic surface X by means of the group of integers. By these central extensions and adelic transition matrices of a rank n locally free sheaf of O X -modules we obtain the local (adelic) decomposition for the difference of Euler characteristics of this sheaf and the sheaf O nX . Two various calculations of this difference lead to the Riemann-Roch theorem on X (without the Noether formula).
利用整数群研究了光滑射影代数曲面X上阿德尔环上一般线性群的正则中心扩展。通过这些中心扩展和O X -模的n阶局部自由层的阿德利转移矩阵，我们得到了该层与O nX层欧拉特性差异的局部(阿德利)分解。对这种差异的两种不同的计算得出了关于X的黎曼-洛克定理(没有诺特公式)。
{"title":"Central extensions and Riemann-Roch theorem on algebraic surfaces","authors":"D. Osipov","doi":"10.1070/SM9623","DOIUrl":"https://doi.org/10.1070/SM9623","url":null,"abstract":"We study canonical central extensions of the general linear group over the ring of adeles on a smooth projective algebraic surface X by means of the group of integers. By these central extensions and adelic transition matrices of a rank n locally free sheaf of O X -modules we obtain the local (adelic) decomposition for the difference of Euler characteristics of this sheaf and the sheaf O nX . Two various calculations of this difference lead to the Riemann-Roch theorem on X (without the Noether formula).","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74078679","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 time minimization problem with admissible control in a half-disc is considered on the group of motions of a plane. The control system under study provides a model of a car on the plane that can move forwards or rotate in place. Optimal trajectories of such a system are used to detect salient curves in image analysis. In particular, in medical image analysis such trajectories are used for tracking vessels in retinal images. The problem is of independent interest in geometric control theory: it provides a model example when the set of values of the control parameters contains zero at the boundary. The problem of controllability and existence of optimal trajectories is studied. By analysing the Hamiltonian system of the Pontryagin maximum principle the explicit form of extremal controls and trajectories is found. Optimality of the extremals is partially investigated. The structure of the optimal synthesis is described. Bibliography: 33 titles.
{"title":"Time minimization problem on the group of motions of a plane with admissible control in a half-disc","authors":"Alexey Pavlovich Mashtakov","doi":"10.1070/SM9609","DOIUrl":"https://doi.org/10.1070/SM9609","url":null,"abstract":"The time minimization problem with admissible control in a half-disc is considered on the group of motions of a plane. The control system under study provides a model of a car on the plane that can move forwards or rotate in place. Optimal trajectories of such a system are used to detect salient curves in image analysis. In particular, in medical image analysis such trajectories are used for tracking vessels in retinal images. The problem is of independent interest in geometric control theory: it provides a model example when the set of values of the control parameters contains zero at the boundary. The problem of controllability and existence of optimal trajectories is studied. By analysing the Hamiltonian system of the Pontryagin maximum principle the explicit form of extremal controls and trajectories is found. Optimality of the extremals is partially investigated. The structure of the optimal synthesis is described. Bibliography: 33 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72951841","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}
Let and be formal power series at the origin and infinity, and , , be the rational function that simultaneously interpolates at the origin with order and at infinity with order . When germs and represent multi-valued functions with finitely many branch points, it was shown by Buslaev that there exists a unique compact set in the complement of which the approximants converge in capacity to the approximated functions. The set may or may not separate the plane. We study uniform convergence of the approximants for the geometrically simplest sets that do separate the plane. Bibliography: 26 titles.
{"title":"Convergence of two-point Padé approximants to piecewise holomorphic functions","authors":"M. Yattselev","doi":"10.1070/SM9024","DOIUrl":"https://doi.org/10.1070/SM9024","url":null,"abstract":"Let and be formal power series at the origin and infinity, and , , be the rational function that simultaneously interpolates at the origin with order and at infinity with order . When germs and represent multi-valued functions with finitely many branch points, it was shown by Buslaev that there exists a unique compact set in the complement of which the approximants converge in capacity to the approximated functions. The set may or may not separate the plane. We study uniform convergence of the approximants for the geometrically simplest sets that do separate the plane. Bibliography: 26 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78913341","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}
One of Erdős’s conjectures states that every triangle-free graph on vertices has an induced subgraph on vertices with at most edges. We report several partial results towards this conjecture. In particular, we establish the new bound on the number of edges in the general case. We completely prove the conjecture for graphs of girth , for graphs with independence number and for strongly regular graphs. Each of these three classes includes both known (conjectured) extremal configurations, the 5-cycle and the Petersen graph. Bibliography: 21 titles.
{"title":"More about sparse halves in triangle-free graphs","authors":"A. Razborov","doi":"10.1070/SM9615","DOIUrl":"https://doi.org/10.1070/SM9615","url":null,"abstract":"One of Erdős’s conjectures states that every triangle-free graph on vertices has an induced subgraph on vertices with at most edges. We report several partial results towards this conjecture. In particular, we establish the new bound on the number of edges in the general case. We completely prove the conjecture for graphs of girth , for graphs with independence number and for strongly regular graphs. Each of these three classes includes both known (conjectured) extremal configurations, the 5-cycle and the Petersen graph. Bibliography: 21 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75488587","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}
We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it to del Pezzo surfaces and coverings of projective spaces of index . For coverings of degree greater than the log Calabi-Yau compactification is singular; moreover, no smooth projective log Calabi-Yau compactification exists. We also prove, in the cases under consideration, the conjecture that the number of components of the fibre over infinity is equal to the dimension of an anticanonical system of the Fano variety. Bibliography: 46 titles.
{"title":"On singular log Calabi-Yau compactifications of Landau-Ginzburg models","authors":"V. Przyjalkowski","doi":"10.1070/SM9510","DOIUrl":"https://doi.org/10.1070/SM9510","url":null,"abstract":"We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it to del Pezzo surfaces and coverings of projective spaces of index . For coverings of degree greater than the log Calabi-Yau compactification is singular; moreover, no smooth projective log Calabi-Yau compactification exists. We also prove, in the cases under consideration, the conjecture that the number of components of the fibre over infinity is equal to the dimension of an anticanonical system of the Fano variety. Bibliography: 46 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91075763","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}
Let be a field of formal Laurent series with coefficients in a finite field of characteristic , the maximal quotient of the Galois group of of period and nilpotency class and the filtration by ramification subgroups in the upper numbering. Let be the identification of nilpotent Artin-Schreier theory: here is the group obtained from a suitable profinite Lie -algebra via the Campbell-Hausdorff composition law. We develop a new technique for describing the ideals such that and constructing their generators explicitly. Given , we construct an epimorphism of Lie algebras and an action of the formal group of order , , , on . Suppose , where , and is the ideal of generated by the elements of . The main result in the paper states that . In the last sections we relate this result to the explicit construction of generators of obtained previously by the author, develop a more efficient version of it and apply it to recover the whole ramification filtration of from the set of its jumps. Bibliography: 13 titles.
{"title":"Ramification filtration via deformations","authors":"V. Abrashkin","doi":"10.1070/SM9322","DOIUrl":"https://doi.org/10.1070/SM9322","url":null,"abstract":"Let be a field of formal Laurent series with coefficients in a finite field of characteristic , the maximal quotient of the Galois group of of period and nilpotency class and the filtration by ramification subgroups in the upper numbering. Let be the identification of nilpotent Artin-Schreier theory: here is the group obtained from a suitable profinite Lie -algebra via the Campbell-Hausdorff composition law. We develop a new technique for describing the ideals such that and constructing their generators explicitly. Given , we construct an epimorphism of Lie algebras and an action of the formal group of order , , , on . Suppose , where , and is the ideal of generated by the elements of . The main result in the paper states that . In the last sections we relate this result to the explicit construction of generators of obtained previously by the author, develop a more efficient version of it and apply it to recover the whole ramification filtration of from the set of its jumps. Bibliography: 13 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78418772","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 norms of the images of multiplier type operators generated by an arbitrary generator are estimated in terms of the best approximations of univariate periodic functions by trigonometric polynomials in the -spaces, . As corollaries, estimates for the quality of approximation by Fourier means, an inverse theorem of approximation theory, comparison theorems, an analogue of the Marchaud inequality for generalized moduli of smoothness defined by a periodic generator, as well as some constructive sufficient conditions for generalized smoothness and Bernstein type inequalities for generalized derivatives of trigonometric polynomials are obtained. Bibliography: 49 titles.
{"title":"Multiplicator type operators and approximation of periodic functions of one variable by trigonometric polynomials","authors":"K. Runovskii","doi":"10.1070/SM9136","DOIUrl":"https://doi.org/10.1070/SM9136","url":null,"abstract":"The norms of the images of multiplier type operators generated by an arbitrary generator are estimated in terms of the best approximations of univariate periodic functions by trigonometric polynomials in the -spaces, . As corollaries, estimates for the quality of approximation by Fourier means, an inverse theorem of approximation theory, comparison theorems, an analogue of the Marchaud inequality for generalized moduli of smoothness defined by a periodic generator, as well as some constructive sufficient conditions for generalized smoothness and Bernstein type inequalities for generalized derivatives of trigonometric polynomials are obtained. Bibliography: 49 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76342848","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}
We say that a zero of a Laurent polynomial that lies on the unit circle with centre is real. We also say that a Laurent polynomial that is real on this circle is real. In contrast with ordinary polynomials, it is known that for random real Laurent polynomials of increasing degree the average proportion of real roots tends to rather than to . We show that this phenomenon of the asymptotically nonvanishing proportion of real roots also holds for systems of Laurent polynomials of several variables. The corresponding asymptotic formula is obtained in terms of the mixed volumes of certain convex compact sets determining the growth of the system of polynomials. Bibliography: 11 titles.
{"title":"How many roots of a system of random Laurent polynomials are real?","authors":"B. Kazarnovskii","doi":"10.1070/SM9559","DOIUrl":"https://doi.org/10.1070/SM9559","url":null,"abstract":"We say that a zero of a Laurent polynomial that lies on the unit circle with centre is real. We also say that a Laurent polynomial that is real on this circle is real. In contrast with ordinary polynomials, it is known that for random real Laurent polynomials of increasing degree the average proportion of real roots tends to rather than to . We show that this phenomenon of the asymptotically nonvanishing proportion of real roots also holds for systems of Laurent polynomials of several variables. The corresponding asymptotic formula is obtained in terms of the mixed volumes of certain convex compact sets determining the growth of the system of polynomials. Bibliography: 11 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73723689","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：