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Simple solutions of the Burgers and Hopf equations Burgers和Hopf方程的简单解
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9051
V. K. Beloshapka
{"title":"Simple solutions of the Burgers and Hopf equations","authors":"V. K. Beloshapka","doi":"10.1070/IM9051","DOIUrl":"https://doi.org/10.1070/IM9051","url":null,"abstract":"We describe all solutions of the Burgers equation of analytic complexity not exceeding . It turns out that all such solutions fall into four families of dimensions not exceeding that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity is given. A similar problem is also solved for the Hopf equation. It turns out that all solutions to the Hopf equation of complexity form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"343 - 350"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58575698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 a class of Anosov diffeomorphisms on the infinite-dimensional torus 无穷维环面上的一类Anosov微分同态
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9002
S. Glyzin, A. Kolesov, N. Rozov
{"title":"On a class of Anosov diffeomorphisms on the infinite-dimensional torus","authors":"S. Glyzin, A. Kolesov, N. Rozov","doi":"10.1070/IM9002","DOIUrl":"https://doi.org/10.1070/IM9002","url":null,"abstract":"We study a quite natural class of diffeomorphisms on , where is the infinite-dimensional torus (the direct product of countably many circles endowed with the topology of uniform coordinatewise convergence). The diffeomorphisms under consideration can be represented as the sums of a linear hyperbolic map and a periodic additional term. We find some constructive sufficient conditions, which imply that any in our class is hyperbolic, that is, an Anosov diffeomorphism on . Moreover, under these conditions we prove the following properties standard in the hyperbolic theory: the existence of stable and unstable invariant foliations, the topological conjugacy to a linear hyperbolic automorphism of the torus and the structural stability of .","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"56 1","pages":"177 - 227"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58573981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Inequalities for the average exit time of a random walk from an interval 从一个区间随机游走的平均退出时间不等式
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9068
V. I. Lotov
{"title":"Inequalities for the average exit time of a random walk from an interval","authors":"V. I. Lotov","doi":"10.1070/IM9068","DOIUrl":"https://doi.org/10.1070/IM9068","url":null,"abstract":"Two-sided inequalities are obtained for the average exit time from an interval for a random walk with zero and negative drift.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"745 - 754"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Lattice of definability (of reducts) for integers with successor 具有后继整数的可定义性(约化)格
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9107
Alexei L. Semenov, S. Soprunov
{"title":"Lattice of definability (of reducts) for integers with successor","authors":"Alexei L. Semenov, S. Soprunov","doi":"10.1070/IM9107","DOIUrl":"https://doi.org/10.1070/IM9107","url":null,"abstract":"In this paper the lattice of definability for integers with a successor (the relation ) is described. The lattice, whose elements are also knows as reducts, consists of three (naturally described) infinite series of relations. The proof uses a version of the Svenonius theorem for structures of special form.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"1257 - 1269"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 issue is dedicated to the memory of Anatoliy Georgievich Vitushkin 这期特刊是为了纪念阿纳托利·格奥尔基耶维奇·维图什金
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/im9204
{"title":"The issue is dedicated to the memory of Anatoliy Georgievich Vitushkin","authors":"","doi":"10.1070/im9204","DOIUrl":"https://doi.org/10.1070/im9204","url":null,"abstract":"","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"341 - 342"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type Sobolev型模型方程Cauchy问题中临界指数“瞬时爆破”与“局部溶解度”的关系
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM8949
M. O. Korpusov, A. A. Panin, A. Shishkov
{"title":"On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type","authors":"M. O. Korpusov, A. A. Panin, A. Shishkov","doi":"10.1070/IM8949","DOIUrl":"https://doi.org/10.1070/IM8949","url":null,"abstract":"We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when 3/2$?> there is a local weak solution.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"111 - 144"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58573475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Tau functions of solutions of soliton equations 孤子方程解的函数
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9058
A. Domrin
{"title":"Tau functions of solutions of soliton equations","authors":"A. Domrin","doi":"10.1070/IM9058","DOIUrl":"https://doi.org/10.1070/IM9058","url":null,"abstract":"In the holomorphic version of the inverse scattering method, we prove that the determinant of a Toeplitz-type Fredholm operator arising in the solution of the inverse problem is an entire function of the spatial variable for all potentials whose scattering data belong to a Gevrey class strictly less than 1. As a corollary, we establish that, up to a constant factor, every local holomorphic solution of the Korteweg–de Vries equation is the second logarithmic derivative of an entire function of the spatial variable. We discuss the possible order of growth of this entire function. Analogous results are given for all soliton equations of parabolic type.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"367 - 387"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58575867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the classification problem for polynomials with a periodic continued fraction expansion of in hyperelliptic fields 超椭圆域上具有周期连分数展开的多项式的分类问题
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9098
V. Platonov, G. V. Fedorov
{"title":"On the classification problem for polynomials with a periodic continued fraction expansion of in hyperelliptic fields","authors":"V. Platonov, G. V. Fedorov","doi":"10.1070/IM9098","DOIUrl":"https://doi.org/10.1070/IM9098","url":null,"abstract":"The classical problem of the periodicity of continued fractions for elements of hyperelliptic fields has a long and deep history. This problem has up to now been far from completely solved. A surprising result was obtained in [1] for quadratic extensions defined by cubic polynomials with coefficients in the field of rational numbers: except for trivial cases there are only three (up to equivalence) cubic polynomials over whose square root has a periodic continued fraction expansion in the field of formal power series. In view of the results in [1], we completely solve the classification problem for polynomials with periodic continued fraction expansion of in elliptic fields with the field of rational numbers as the field of constants.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"972 - 1007"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Interior estimates for solutions of linear elliptic inequalities 线性椭圆不等式解的内估计
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM8989
Vladimir Stepanovich Klimov
{"title":"Interior estimates for solutions of linear elliptic inequalities","authors":"Vladimir Stepanovich Klimov","doi":"10.1070/IM8989","DOIUrl":"https://doi.org/10.1070/IM8989","url":null,"abstract":"We study the wedge of solutions of the inequality , where is a linear elliptic operator of order acting on functions of variables. We establish interior estimates of the form for the elements of this wedge, where is a compact subdomain of , is the Sobolev space, , is the Lebesgue space of integrable functions, and the constant is independent of .","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"11 1","pages":"92 - 110"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58574154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the standard conjecture for projective compactifications of Néron models of -dimensional Abelian varieties 关于n -维阿贝尔型nsamron模型射影紧化的标准猜想
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2021-01-01 DOI: 10.1070/IM9005
S. G. Tankeev
{"title":"On the standard conjecture for projective compactifications of Néron models of -dimensional Abelian varieties","authors":"S. G. Tankeev","doi":"10.1070/IM9005","DOIUrl":"https://doi.org/10.1070/IM9005","url":null,"abstract":"We prove that the Grothendieck standard conjecture of Lefschetz type holds for a smooth complex projective -dimensional variety fibred by Abelian varieties (possibly, with degeneracies) over a smooth projective curve if the endomorphism ring of the generic geometric fibre is not an order of an imaginary quadratic field. This condition holds automatically in the cases when the reduction of the generic scheme fibre at some place of the curve is semistable in the sense of Grothendieck and has odd toric rank or the generic geometric fibre is not a simple Abelian variety.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"145 - 175"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58574191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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