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$SU$-linear operations in complex cobordism and the $c_1$-spherical bordism theory 复共体中的线性运算和球面共体理论
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9334e
Taras Evgenievich Panov, George Chernykh
{"title":"$SU$-linear operations in complex cobordism and the $c_1$-spherical bordism theory","authors":"Taras Evgenievich Panov, George Chernykh","doi":"10.4213/im9334e","DOIUrl":"https://doi.org/10.4213/im9334e","url":null,"abstract":"We study the $SU$-linear operations in complex cobordism and prove that they are generated by the well-known geometric operations $partial_i$. For the theory $W$ of $c_1$-spherical bordism, we describe all $SU$-linear multiplications on $W$ and projections $MU to W$. We also analyse complex orientations on $W$ and the corresponding formal group laws $F_W$. The relationship between the formal group laws $F_W$ and the coefficient ring $W_*$ of the $W$-theory was studied by Buchstaber in 1972. We extend his results by showing that for any $SU$-linear multiplication and orientation on $W$, the coefficients of the corresponding formal group law $F_W$ do not generate the ring $W_*$, unlike the situation with complex bordism.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"23 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":"135007538","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
Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces 非对称半线性空间中集值映射的连续选择与逼近
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9331e
Igor' Germanovich Tsar'kov
{"title":"Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces","authors":"Igor' Germanovich Tsar'kov","doi":"10.4213/im9331e","DOIUrl":"https://doi.org/10.4213/im9331e","url":null,"abstract":"The Michael selection theorem is extended to the case of set-valued mappings with not necessarily convex values. Classical approximation problems on cone-spaces with symmetric and asymmetric seminorms are considered. In particular, conditions for existence of continuous selections for convex subsets of asymmetric spaces are studied. The problem of existence of a Chebyshev centre for a bounded set is solved in a semilinear space consisting of bounded convex sets with Hausdorff semimetric.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"2 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":"135007551","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
The boundary behavior of $mathcal Q_{p,q}$-homeomorphisms $数学Q_{p,q}$-同胚的边界行为
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9376e
Sergei Konstantinovich Vodopyanov, Anastasia Molchanova
{"title":"The boundary behavior of $mathcal Q_{p,q}$-homeomorphisms","authors":"Sergei Konstantinovich Vodopyanov, Anastasia Molchanova","doi":"10.4213/im9376e","DOIUrl":"https://doi.org/10.4213/im9376e","url":null,"abstract":"This article studies systematically the boundary correspondence problem for $mathcal Q_{p,q}$-homeomorphisms. The presented example demonstrates a deformation of the Euclidean boundary with the weight function degenerating on the boundary.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"144 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":"135009175","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 detailed structure of quantum control landscape for fast single qubit phase-shift gate generation 快速单量子位相移门生成的量子控制景观的详细结构
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9364e
Boris Olegovich Volkov, Alexander Nikolaevich Pechen
{"title":"On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation","authors":"Boris Olegovich Volkov, Alexander Nikolaevich Pechen","doi":"10.4213/im9364e","DOIUrl":"https://doi.org/10.4213/im9364e","url":null,"abstract":"In this work, we study the detailed structure of quantum control landscape for the problem of single-qubit phase shift gate generation on the fast time scale. In previous works, the absence of traps for this problem was proved on various time scales. A special critical point which was known to exist in quantum control landscapes was shown to be either a saddle or a global extremum, depending on the parameters of the control system. However, in case of a saddle, the numbers of negative and positive eigenvalues of the Hessian at this point and their magnitudes have not been studied. At the same time, these numbers and magnitudes determine the relative ease or difficulty for practical optimization in a vicinity of the critical point. In this work, we compute the numbers of negative and positive eigenvalues of the Hessian at this saddle point and, moreover, give estimates on magnitude of these eigenvalues. We also significantly simplify our previous proof of the theorem about this saddle point of the Hessian (Theorem 3 in [22]).","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"27 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":"135661671","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: 3
Symmetries and conservation laws of the Liouville equation 刘维尔方程的对称性和守恒定律
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9356e
Viktor Viktorovich Zharinov
{"title":"Symmetries and conservation laws of the Liouville equation","authors":"Viktor Viktorovich Zharinov","doi":"10.4213/im9356e","DOIUrl":"https://doi.org/10.4213/im9356e","url":null,"abstract":"Symmetries and conservation laws of the Liouville equation are studied in the frames of the algebra-geometrical approach to partial differential equations.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"48 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":"135661676","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
Rational points of algebraic varieties: a homotopical approach 代数变量的有理点:一种同调方法
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9315e
Yuri Ivanovich Manin
{"title":"Rational points of algebraic varieties: a homotopical approach","authors":"Yuri Ivanovich Manin","doi":"10.4213/im9315e","DOIUrl":"https://doi.org/10.4213/im9315e","url":null,"abstract":"This article, dedicated to the 100 th anniversary of I. R. Shafarevich, is a survey of techniques of homotopical algebra, applied to the problem of distribution of rational points on algebraic varieties. We due to I. R. Shafarevich, jointly with J. Tate, one of the breakthrough discoveries in this domain: construction of the so-called Shafarevich-Tate groups and the related obstructions to the existence of rational points. Later it evolved into the theory of Brauer-Manin obstructions. Here we focus on some facets of the later developments in Diophantine geometry: the study of the distribution of rational points on them. More precisely, we show how the definition of accumulating subvarieties, based upon counting the number of points whose height is bounded by varying $H$, can be encoded by a special class of categories in such a way that the arithmetical invariants of varieties are translated into homotopical invariants of objects and morphisms of these categories. The central role in this study is played by the structure of an assembler (I. Zakharevich) in general, and a very particular case of it, an assembler on the family of unions of half-open intervals $(a,b]$ with rational ends.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"17 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":"135440254","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
Isogeny classes and endomorphism algebras of abelian varieties over finite fields 有限域上阿贝尔变异的同胚类和自同态代数
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9332e
Yuri Gennad'evich Zarhin
{"title":"Isogeny classes and endomorphism algebras of abelian varieties over finite fields","authors":"Yuri Gennad'evich Zarhin","doi":"10.4213/im9332e","DOIUrl":"https://doi.org/10.4213/im9332e","url":null,"abstract":"We construct nonisogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"30 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":"135440263","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
Multiple positive solutions for a Schrödinger-Poisson system with critical and supercritical growths 临界和超临界生长Schrödinger-Poisson系统的多个正解
3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9244e
Jun Lei, Hong-Min Suo
{"title":"Multiple positive solutions for a Schrödinger-Poisson system with critical and supercritical growths","authors":"Jun Lei, Hong-Min Suo","doi":"10.4213/im9244e","DOIUrl":"https://doi.org/10.4213/im9244e","url":null,"abstract":"In this paper, we are concerned with the following Schrödinger-Poisson system $$ begin{cases} -Delta u+u+lambdaphi u= Q(x)|u|^{4}u+mu dfrac{|x|^beta}{1+|x|^beta}|u|^{q-2}u&amp;amp;in mathbb{R}^3, -Delta phi=u^{2} &amp;amp;in mathbb{R}^3, end{cases} $$ where $0< beta<3$, $6<q<6+2beta$, $Q(x)$ is a positive continuous function on $mathbb{R}^3$, $lambda,mu>0$ are real parameters. By the variational method and the Nehari method, we obtain that the system has $k$ positive solutions.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"141 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":"136079306","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
"Far-field interaction" of concentrated masses in two-dimensional Neumann and Dirichlet problems 二维Neumann和Dirichlet问题中集中质量的“远场相互作用”
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9262e
S. Nazarov
{"title":"\"Far-field interaction\" of concentrated masses in two-dimensional Neumann and Dirichlet problems","authors":"S. Nazarov","doi":"10.4213/im9262e","DOIUrl":"https://doi.org/10.4213/im9262e","url":null,"abstract":"We study the eigenvalues of the Neumann and Dirichlet boundary-value problems in a two-dimensional domain containing several small, of diameter $O(varepsilon)$, inclusions of large \"density\" $O(varepsilon^{-gamma})$, $gammageq2$, that is, the \"mass\" $O(varepsilon^{2-gamma})$ of each of them is comparable ($gamma=2$) or much bigger ($gamma>2$) than that of the embracing material. We construct a model of such spectral problems on concentrated masses which (the model) provides an asymptotic expansions of the eigenvalues with remainders of power-law smallness order $O(varepsilon^{vartheta})$ as $varepsilonto+0$ and $varthetain(0,1)$. Besides, the correction terms are real analytic functions of the parameter $|{ln varepsilon}|^{-1}$. A \"far-field interaction\" of the inclusions is observed at the levels $|{ln varepsilon}|^{-1}$ or $|{ln varepsilon}|^{-2}$. The results are obtained with the help of the machinery of weighted spaces with detached asymptotics and also by using weighted estimates of solutions to limit problems in a bounded punctured domain and in the intact plane.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70326946","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
Multivariate tile $mathrm{B}$-splines 多元平铺$ mathm {B}$-样条
IF 0.8 3区 数学
Izvestiya Mathematics Pub Date : 2023-01-01 DOI: 10.4213/im9296e
T. Zaitseva
{"title":"Multivariate tile $mathrm{B}$-splines","authors":"T. Zaitseva","doi":"10.4213/im9296e","DOIUrl":"https://doi.org/10.4213/im9296e","url":null,"abstract":"Tile $mathrm{B}$-splines in $mathbb R^d$ are defined as autoconvolutions of indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $mathbb R^d$. These functions are not piecewise-polynomial, however, being direct generalizations of the classical $mathrm{B}$-splines, they enjoy many of their properties and have some advantages. In particular, exact values of the Hölder exponents of tile $mathrm{B}$-splines are evaluated and are shown, in some cases, to exceed those of the classical $mathrm{B}$-splines. Orthonormal systems of wavelets based on tile B-splines are constructed, and estimates of their exponential decay are obtained. Efficiency in applications of tile $mathrm{B}$-splines is demonstrated on an example of subdivision schemes of surfaces. This efficiency is achieved due to high regularity, fast convergence, and small number of coefficients in the corresponding refinement equation.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70326993","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
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