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Estimates for the Norm of the Hardy Operator in Operator Ideals 算子理想中的哈代算子规范的估计值
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020083
E. N. Lomakina, M. G. Nasyrova
{"title":"Estimates for the Norm of the Hardy Operator in Operator Ideals","authors":"E. N. Lomakina, M. G. Nasyrova","doi":"10.1134/s0037446624020083","DOIUrl":"https://doi.org/10.1134/s0037446624020083","url":null,"abstract":"<p>We find the conditions for a compact Hardy operator in Lorentz spaces\u0000to belong to the operator ideals generated by sequences of <span>( s )</span>-numbers.\u0000We obtain some estimates of the norms of the Hardy operator in these ideals in terms of integral\u0000expressions depending on the weight functions of the operator.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"17 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299821","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
A Family with a Single Minimal but Not Least Numbering 编号最少但不单一的家庭
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020125
M. Kh. Faizrahmanov
{"title":"A Family with a Single Minimal but Not Least Numbering","authors":"M. Kh. Faizrahmanov","doi":"10.1134/s0037446624020125","DOIUrl":"https://doi.org/10.1134/s0037446624020125","url":null,"abstract":"<p>We prove the existence of a family of computably enumerable sets that,\u0000up to equivalence,\u0000has a unique computable minimal but not least numbering.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299651","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
Craig’s Interpolation Property in Pretabular Logics 预表逻辑中的克雷格插值特性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020095
L. L. Maksimova, V. F. Yun
{"title":"Craig’s Interpolation Property in Pretabular Logics","authors":"L. L. Maksimova, V. F. Yun","doi":"10.1134/s0037446624020095","DOIUrl":"https://doi.org/10.1134/s0037446624020095","url":null,"abstract":"<p>All pretabular extensions of the minimal logic were described and\u0000the tabularity problem was solved earlier. As turned out, in total, there are seven\u0000pretabular logics over the minimal logic. It was proved that four of them have\u0000Craig’s interpolation property (CIP) and two do not. In the present article,\u0000we solve the problem of CIP in the seventh logic. We prove that\u0000it has Craig’s interpolation property.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"23 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299652","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 the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum 论从函数谱的近似信息中优化恢复一类函数上的一个算子族
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020010
E. V. Abramova, E. O. Sivkova
{"title":"On the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum","authors":"E. V. Abramova, E. O. Sivkova","doi":"10.1134/s0037446624020010","DOIUrl":"https://doi.org/10.1134/s0037446624020010","url":null,"abstract":"<p>We find explicit expressions for optimal recovery methods in the problem\u0000of recovering the values of continuous linear operators on a Sobolev function class\u0000from the following information: The Fourier transform of functions is known approximately\u0000on some measurable subset of the finite-dimensional space on which the functions are\u0000defined. As corollaries, we obtain optimal methods for recovering the solution to the heat\u0000equation and solving the Dirichlet problem for a half-space.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297694","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
Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral Teichmüller 的模态和狄利克特积分的变化
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020058
V. N. Dubinin
{"title":"Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral","authors":"V. N. Dubinin","doi":"10.1134/s0037446624020058","DOIUrl":"https://doi.org/10.1134/s0037446624020058","url":null,"abstract":"<p>We show that\u0000changing the level curve of a harmonic function\u0000with the classical Hadamard variation with a small parameter\u0000entails a change in the Dirichlet integral of the function\u0000which is quadratic in the parameter.\u0000As a corollary,\u0000we supplement the well-known theorem of Teichmüller\u0000about the sum of moduli of doubly connected domains\u0000into which an annulus is subdivided\u0000by a continuum that differs little from a concentric circle.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299537","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
Novikov $ ��_{2} $ -Graded Algebras with an Associative 0-Component 具有关联0分量的诺维科夫级代数
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020150
A. S. Panasenko, V. N. Zhelyabin
{"title":"Novikov $ ��_{2} $ -Graded Algebras with an Associative 0-Component","authors":"A. S. Panasenko, V. N. Zhelyabin","doi":"10.1134/s0037446624020150","DOIUrl":"https://doi.org/10.1134/s0037446624020150","url":null,"abstract":"<p>In 1974 Kharchenko proved that if a <span>( 0 )</span>-component of an <span>( n )</span>-graded associative algebra is PI then this algebra is PI.\u0000In the Novikov algebras of characteristic 0 the existence of a polynomial identity is equivalent to the solvability of the commutator ideal.\u0000We study a <span>( 𝕑_{2} )</span>-graded Novikov algebra <span>( N=A+M )</span> and prove that if the characteristic of the basic field is not 2 or 3\u0000and its 0-component <span>( A )</span> is associative or Lie-nilpotent of index 3 then\u0000the commutator ideal <span>( [N,N] )</span> is solvable.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299572","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
Birman–Hilden Bundles. II 比尔曼-希尔登包。二
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020101
A. V. Malyutin
{"title":"Birman–Hilden Bundles. II","authors":"A. V. Malyutin","doi":"10.1134/s0037446624020101","DOIUrl":"https://doi.org/10.1134/s0037446624020101","url":null,"abstract":"<p>We study the structure of self-homeomorphism groups of fibered manifolds.\u0000A fibered topological space\u0000is a Birman–Hilden space\u0000whenever in each isotopic pair of its fiber-preserving\u0000(taking each fiber to a fiber)\u0000self-homeomorphisms\u0000the homeomorphisms are also fiber-isotopic\u0000(isotopic through fiber-preserving homeomorphisms).\u0000We prove in particular that\u0000the Birman–Hilden class contains\u0000all compact connected locally trivial surface bundles over the circle,\u0000including nonorientable ones and those with nonempty boundary,\u0000as well as all closed orientable Haken 3-manifold bundles over the circle,\u0000including nonorientable ones.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"31 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299759","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 the Qualitative Properties of a Solution to a System of Infinite Nonlinear Algebraic Equations 论无穷非线性代数方程解的定性特性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020186
M. H. Avetisyan, Kh. A. Khachatryan
{"title":"On the Qualitative Properties of a Solution to a System of Infinite Nonlinear Algebraic Equations","authors":"M. H. Avetisyan, Kh. A. Khachatryan","doi":"10.1134/s0037446624020186","DOIUrl":"https://doi.org/10.1134/s0037446624020186","url":null,"abstract":"<p>We study and solve some class of infinite systems of\u0000algebraic equations with monotone nonlinearity and Toeplitz-type matrices.\u0000Such systems\u0000for the specific representations of nonlinearities arise in the discrete problems of\u0000dynamic theory of clopen <span>( p )</span>-adic strings for a scalar field of tachyons,\u0000the mathematical theory of spatio-temporal spread of an epidemic, radiation transfer theory\u0000in inhomogeneous media, and the kinetic theory of gases in the framework of the modified Bhatnagar–Gross–Krook\u0000model. The noncompactness of the corresponding operator in the bounded sequence space\u0000and the criticality property (the presence of trivial nonphysical\u0000solutions) is a distinctive feature of these systems.\u0000For these reasons, the use of the well-known classical principles of existence\u0000of fixed points for such equations do not lead to the desired results.\u0000Constructing some invariant cone segments for the corresponding\u0000nonlinear operator, we prove the existence and uniqueness of a nontrivial\u0000nonnegative solution in the bounded sequence space.\u0000Also, we study the asymptotic behavior of the solution at <span>( pminfty )</span>.\u0000In particular, we prove that the limit at <span>( pminfty )</span> of a solution is finite.\u0000Also, we show that the difference between\u0000this limit and a solution belongs to <span>( l_{1} )</span>.\u0000By way of illustration, we provide some special applied examples.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"22 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297587","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
Homogenization of the Scalar Boundary Value Problem in a Thin Periodically Broken Cylinder 薄周期性断裂圆柱体中的标量边界值问题的均质化
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020113
S. A. Nazarov, A. S. Slutskii
{"title":"Homogenization of the Scalar Boundary Value Problem in a Thin Periodically Broken Cylinder","authors":"S. A. Nazarov, A. S. Slutskii","doi":"10.1134/s0037446624020113","DOIUrl":"https://doi.org/10.1134/s0037446624020113","url":null,"abstract":"<p>Homogenization of the Neumann problem for a differential equation\u0000in a periodically broken multidimensional cylinder\u0000leads to a second-order ordinary differential equation.\u0000We study asymptotics for the coefficient of the averaged operator\u0000in the case of small transverse cross-sections.\u0000The main asymptotic term depends on\u0000the “area” of cross-sections of the links,\u0000their lengths,\u0000and the coefficient matrix of the original operator.\u0000We find the characteristics of kink zones which affect correction terms,\u0000while the asymptotic remainder becomes exponentially small.\u0000The justification of the asymptotics\u0000is based on Friedrichs’s inequality\u0000with a coefficient independent of both small parameters:\u0000the period of fractures and the relative diameter of cross-sections.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"73 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299754","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
Light 3-Paths in 3-Polytopes without Adjacent Triangles 无相邻三角形的 3 多面体中的光 3 路径
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020022
O. V. Borodin, A. O. Ivanova
{"title":"Light 3-Paths in 3-Polytopes without Adjacent Triangles","authors":"O. V. Borodin, A. O. Ivanova","doi":"10.1134/s0037446624020022","DOIUrl":"https://doi.org/10.1134/s0037446624020022","url":null,"abstract":"<p>Let <span>( w_{k} )</span> be the maximum of the minimum degree-sum (weight) of vertices in <span>( k )</span>-vertex paths (<span>( k )</span>-paths) in 3-polytopes.\u0000Trivially, each 3-polytope has a vertex of degree at most 5, and so <span>( w_{1}leq 5 )</span>.\u0000Back in 1955, Kotzig proved that <span>( w_{2}leq 13 )</span> (so there is an edge of weight at most 13), which is sharp.\u0000In 1993, Ando, Iwasaki, and Kaneko proved that <span>( w_{3}leq 21 )</span>, which is also sharp\u0000due to a construction by Jendrol’ of 1997.\u0000In 1997, Borodin refined this by proving that <span>( w_{3}leq 18 )</span> for 3-polytopes with <span>( w_{2}geq 7 )</span>,\u0000while <span>( w_{3}leq 17 )</span> holds for 3-polytopes\u0000with <span>( w_{2}geq 8 )</span>, where the sharpness of 18 was confirmed by Borodin et al. in 2013,\u0000and that of 17 was known long ago.\u0000Over the last three decades, much research has been devoted to structural and coloring problems\u0000on the plane graphs that are sparse in this or that sense.\u0000In this paper we deal with 3-polytopes without adjacent 3-cycles that is without chordal 4-cycle\u0000(in other words, without <span>( K_{4}-e )</span>).\u0000It is known that such 3-polytopes satisfy <span>( w_{1}leq 4 )</span>; and, moreover, <span>( w_{2}leq 9 )</span> holds, where\u0000both bounds are sharp (Borodin, 1992).\u0000We prove now that each 3-polytope without chordal 4-cycles\u0000has a 3-path of weight at most 15; and so <span>( w_{3}leq 15 )</span>, which is sharp.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"32 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300061","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
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