{"title":"On the Levi Class of the Quasivariety of Right-Orderable Groups","authors":"A. V. Zenkov","doi":"10.1134/s0037446624010051","DOIUrl":"https://doi.org/10.1134/s0037446624010051","url":null,"abstract":"<p>We show that the Levi class of the quasivariety of right-orderable groups strictly\u0000includes this quasivariety.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769747","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}
{"title":"Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space","authors":"A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov","doi":"10.1134/s0037446624010105","DOIUrl":"https://doi.org/10.1134/s0037446624010105","url":null,"abstract":"<p>We construct two new infinite series of irreducible components of\u0000the moduli space of semistable nonlocally free reflexive rank 2 sheaves\u0000on the three-dimensional complex projective space.\u0000In the first series\u0000the sheaves have an even first Chern class,\u0000and in the second series\u0000they have an odd one,\u0000while the second and third Chern classes\u0000can be expressed as polynomials of a special form\u0000in three integer variables.\u0000We prove the uniqueness of components in these series\u0000for the Chern classes\u0000given by those polynomials.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769748","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}
{"title":"Kolmogorov Equations for Degenerate Ornstein–Uhlenbeck Operators","authors":"V. I. Bogachev, S. V. Shaposhnikov","doi":"10.1134/s0037446624010038","DOIUrl":"https://doi.org/10.1134/s0037446624010038","url":null,"abstract":"<p>We consider Kolmogorov operators with constant diffusion matrices and linear drifts, i.e.,\u0000Ornstein–Uhlenbeck operators, and show that\u0000all solutions to the corresponding stationary Fokker–Planck–Kolmogorov equations (including signed solutions)\u0000are invariant measures for the generated semigroups. This also gives a relatively explicit description of all solutions.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769987","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}
{"title":"On the Approximative Properties of Fourier Series in Laguerre–Sobolev Polynomials","authors":"R. M. Gadzhimirzaev","doi":"10.1134/s003744662401004x","DOIUrl":"https://doi.org/10.1134/s003744662401004x","url":null,"abstract":"<p>Considering the approximation of a function <span>( f )</span> from a Sobolev space\u0000by the partial sums of Fourier series in a system of Sobolev orthogonal polynomials\u0000generated by classical Laguerre polynomials,\u0000we obtain an estimate for the convergence rate of the partial sums to <span>( f )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769752","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}
{"title":"Hilbert–Pólya Operators in Krein Spaces","authors":"V. V. Kapustin","doi":"10.1134/s0037446624010087","DOIUrl":"https://doi.org/10.1134/s0037446624010087","url":null,"abstract":"<p>We construct some class of selfadjoint operators in the Krein spaces consisting of functions on\u0000the straight line <span>( {operatorname{Re}s=frac{1}{2}} )</span>.\u0000Each of these operators is a rank-one perturbation of a selfadjoint operator\u0000in the corresponding Hilbert space\u0000and has eigenvalues complex numbers of the form <span>( frac{1}{s(1-s)} )</span>,\u0000where <span>( s )</span> ranges over the set of nontrivial zeros of the Riemann zeta-function.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769753","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}
{"title":"Admissible Inference Rules of Modal WCP-Logics","authors":"V. V. Rimatskiy","doi":"10.1134/s0037446624010142","DOIUrl":"https://doi.org/10.1134/s0037446624010142","url":null,"abstract":"<p>We study admissible rules\u0000for the extensions of the modal logics S4\u0000and GL\u0000with the weak co-covering property\u0000and describe some explicit independent basis for the admissible rules of these logics.\u0000The resulting basis consists of an infinite sequence of rules\u0000in compact and simple form.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769845","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}
{"title":"Oriented Rotatability Exponents of Solutions to Homogeneous Autonomous Linear Differential Systems","authors":"A. Kh. Stash","doi":"10.1134/s003744662401018x","DOIUrl":"https://doi.org/10.1134/s003744662401018x","url":null,"abstract":"<p>We fully study the oriented rotatability exponents of solutions to\u0000homogeneous autonomous linear differential systems and\u0000establish that the strong and weak oriented\u0000rotatability exponents coincide for each solution to an autonomous system\u0000of differential equations. We also show that the\u0000spectrum of this exponent (i.e., the set of values of nonzero\u0000solutions) is naturally determined by the number-theoretic\u0000properties of the set of imaginary parts of the eigenvalues of the\u0000matrix of a system. This set (in contrast to the oscillation\u0000and wandering exponents) can contain other than zero values and the\u0000imaginary parts of the eigenvalues of the system matrix; moreover,\u0000the power of this spectrum can be exponentially large in\u0000comparison with the dimension of the space.\u0000In demonstration we use the basics of ergodic theory,\u0000in particular, Weyl’s Theorem.\u0000We prove that the spectra of all oriented rotatability exponents\u0000of autonomous systems with a symmetrical\u0000matrix consist of a single zero value.\u0000We also establish relationships\u0000between the main values of the exponents on a set of autonomous systems.\u0000The obtained results allow us to conclude that the exponents of\u0000oriented rotatability, despite their simple and natural definitions,\u0000are not analogs of the Lyapunov exponent in oscillation theory.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769746","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}
{"title":"Birman–Hilden Bundles. I","authors":"A. V. Malyutin","doi":"10.1134/s0037446624010117","DOIUrl":"https://doi.org/10.1134/s0037446624010117","url":null,"abstract":"<p>A topological fibered space is a Birman–Hilden space\u0000whenever in each isotopic pair of its fiber-preserving\u0000(taking each fiber to a fiber) self-homeomorphisms\u0000the homeomorphisms are also fiber-isotopic\u0000(isotopic through fiber-preserving homeomorphisms).\u0000We present a series of sufficient conditions\u0000for a fiber bundle over the circle\u0000to be a Birman–Hilden space.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769805","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}
A. G. Kachurovskii, I. V. Podvigin, V. È. Todikov, A. Zh. Khakimbaev
{"title":"A Spectral Criterion for Power-Law Convergence Rate in the Ergodic Theorem for $ {��}^{d} $ and $ {��}^{d} $ Actions","authors":"A. G. Kachurovskii, I. V. Podvigin, V. È. Todikov, A. Zh. Khakimbaev","doi":"10.1134/s0037446624010099","DOIUrl":"https://doi.org/10.1134/s0037446624010099","url":null,"abstract":"<p>We prove the equivalence of the power-law convergence rate in the <span>( L_{2} )</span>-norm\u0000of ergodic averages for <span>( {}^{d} )</span> and <span>( {}^{d} )</span> actions and the same\u0000power-law estimate for the spectral measure of symmetric <span>( d )</span>-dimensional\u0000parallelepipeds: for the degrees that are roots of some special symmetric\u0000polynomial in <span>( d )</span> variables. Particularly, all possible range\u0000of power-law rates is covered for <span>( d=1 )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769745","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}
{"title":"Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5","authors":"S. V. Pchelintsev","doi":"10.1134/s0037446624010130","DOIUrl":"https://doi.org/10.1134/s0037446624010130","url":null,"abstract":"<p>We construct an additive basis for a relatively free\u0000alternative algebra of Lie-nilpotent degree 5,\u0000describe the associative center and core of this algebra, and find\u0000the T-generators of the full center.\u0000Also, we give some asymptotic estimate for the codimension\u0000of the T-ideal generated by a commutator of degree 5\u0000in a free alternative algebra, and find\u0000a finite-dimensional superalgebra that\u0000generates the variety of alternative algebras\u0000with the Lie-nilpotency of the selfadjoint operator of degree 5.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769623","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}