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Subharmonic Functions with Separated Variables and Their Connection with Generalized Convex Functions 带分离变量的次谐函数及其与广义凸函数的联系
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700439
R. R. Muryasov
{"title":"Subharmonic Functions with Separated Variables and Their Connection with Generalized Convex Functions","authors":"R. R. Muryasov","doi":"10.3103/s1066369x24700439","DOIUrl":"https://doi.org/10.3103/s1066369x24700439","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider the necessary and sufficient conditions for the subharmonicity of functions of two variables representable as a product of two functions of one variable in the Cartesian coordinate system or in the polar coordinate system in domains on the plane. We establish a connection of such functions with functions that are convex with respect to solutions of second-order linear differential equations, that is, convex with respect to two functions.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Best Approximation of Functions Analytic in the Disk in the Weighted Bergman Space $${{mathcal{B}}_{{2,mu }}}$$ 论加权伯格曼空间 $${{mathcal{B}}_{{2,mu }}$ 盘中解析函数的最佳近似值
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700415
M. R. Langarshoev
{"title":"On the Best Approximation of Functions Analytic in the Disk in the Weighted Bergman Space $${{mathcal{B}}_{{2,mu }}}$$","authors":"M. R. Langarshoev","doi":"10.3103/s1066369x24700415","DOIUrl":"https://doi.org/10.3103/s1066369x24700415","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Sharp inequalities between the best approximations of functions analytic in the unit disk are obtained using algebraic polynomials and the moduli of continuity of higher-order derivatives in the Bergman space <span>({{mathcal{B}}_{{2,mu }}})</span> Based on these inequalities, the exact values of some known <span>(n)</span>-widths of classes of functions analytic in the unit disk are calculated.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Simultaneous Approximation of Certain Classes of Functions in the Bergman Space B2 论伯格曼空间 B2 中若干类函数的同时逼近
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700452
M. Sh. Shabozov, A. A. Shabozova
{"title":"On Simultaneous Approximation of Certain Classes of Functions in the Bergman Space B2","authors":"M. Sh. Shabozov, A. A. Shabozova","doi":"10.3103/s1066369x24700452","DOIUrl":"https://doi.org/10.3103/s1066369x24700452","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem of finding the supremums of the best simultaneous polynomial approximations of some classes of functions analytic in the unit disk and belonging to the Bergman space <span>({{B}_{2}})</span> is considered. The indicated function classes are defined by the averaged values of the <span>(m)</span>th-order moduli of continuity of the highest derivative bounded from above by some majorant <span>(Phi )</span>.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Problem with Analogue of the Frankl and Mixing Conditions for the Gellerstedt Equation with Singular Coefficient 具有奇异系数的盖勒斯特方程的弗兰克尔和混合条件的类似问题
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700427
D. M. Mirsaburova
{"title":"A Problem with Analogue of the Frankl and Mixing Conditions for the Gellerstedt Equation with Singular Coefficient","authors":"D. M. Mirsaburova","doi":"10.3103/s1066369x24700427","DOIUrl":"https://doi.org/10.3103/s1066369x24700427","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>For the equation <span>((operatorname{sgn} y){{left| y right|}^{m}}{{u}_{{xx}}} + {{u}_{{yy}}} + {{alpha }_{0}}{{left| y right|}^{{(m - 2)/2}}}{{u}_{x}} + ({{beta }_{0}}{text{/}}y){{u}_{y}} = 0,)</span> considered in some unbounded mixed domain, uniqueness and existence theorems are proved for a solution to the problem with the missing shift condition on the boundary characteristics and an analogue of the Frankl-type condition on the interval of degeneracy of the equation.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inequalities for the Differences of Averages on H1 Spaces H1 空间上的均值差不等式
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700403
S. Demir
{"title":"Inequalities for the Differences of Averages on H1 Spaces","authors":"S. Demir","doi":"10.3103/s1066369x24700403","DOIUrl":"https://doi.org/10.3103/s1066369x24700403","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Let <span>(({{x}_{n}}))</span> be a sequence and <span>({ {{c}_{k}}} in {{ell }^{infty }}(mathbb{Z}))</span> such that <span>({{left| {{{c}_{k}}} right|}_{{{{ell }^{infty }}}}} leqslant 1)</span>. Define <span>(mathcal{G}({{x}_{n}}) = mathop {sup }limits_j left| {sumlimits_{k = 0}^j ,{{c}_{k}}left( {{{x}_{{{{n}_{{k + 1}}}}}} - {{x}_{{{{n}_{k}}}}}} right)} right|.)</span> Let now <span>((X,beta ,mu ,tau ))</span> be an ergodic, measure preserving dynamical system with <span>((X,beta ,mu ))</span> a totally <span>(sigma )</span>-finite measure space. Suppose that the sequence <span>(({{n}_{k}}))</span> is lacunary. Then we prove the following results: 1. Define <span>({{phi }_{n}}(x) = frac{1}{n}{{chi }_{{[0,n]}}}(x))</span> on <span>(mathbb{R})</span>. Then there exists a constant <span>(C &gt; 0)</span> such that <span>({{left| {mathcal{G}({{phi }_{n}} * f)} right|}_{{{{L}^{1}}(mathbb{R})}}} leqslant C{{left| f right|}_{{{{H}^{1}}(mathbb{R})}}},)</span> for all <span>(f in {{H}^{1}}(mathbb{R}))</span>. 2. Let <span>({{A}_{n}}f(x) = frac{1}{n}sumlimits_{k = 0}^{n - 1} ,f({{tau }^{k}}x),)</span> be the usual ergodic averages in ergodic theory. Then <span>({{left| {mathcal{G}({{A}_{n}}f)} right|}_{{{{L}^{1}}(X)}}} leqslant C{{left| f right|}_{{{{H}^{1}}(X)}}},)</span> for all <span>(f in {{H}^{1}}(X))</span>. 3. If <span>({{[f(x)log (x)]}^{ + }})</span> is integrable, then <span>(mathcal{G}({{A}_{n}}f))</span> is integrable.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Logical Specifications of Effectively Separable Data Models 有效可分离数据模型的逻辑规范
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700397
N. Kh. Kasymov
{"title":"Logical Specifications of Effectively Separable Data Models","authors":"N. Kh. Kasymov","doi":"10.3103/s1066369x24700397","DOIUrl":"https://doi.org/10.3103/s1066369x24700397","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>It is established that any effectively separable many-sorted universal algebra has an enrichment that is the only (up to isomorphism) model constructed from constants for a suitable computably enumerable set of sentences.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Сurvilinear Three-Webs with Automorphisms 带自动形态的布尔线性三维网
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700464
A. M. Shelekhov
{"title":"Сurvilinear Three-Webs with Automorphisms","authors":"A. M. Shelekhov","doi":"10.3103/s1066369x24700464","DOIUrl":"https://doi.org/10.3103/s1066369x24700464","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A general form of the equation of a curvilinear three-web admitting a one-parameter family of automorphisms (<span>(AW)</span>-webs) is found. It is proved that the trajectories of automorphisms of an <span>(AW)</span>-web are geodesics of its Chern connection. All <span>(AW)</span>-webs are found for which one of the covariant derivatives of curvature is zero.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System 洛特卡-伏特拉混合系统解的终极边界性和永久性条件
IF 0.4
Russian Mathematics Pub Date : 2024-09-05 DOI: 10.3103/s1066369x24700440
A. V. Platonov
{"title":"Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System","authors":"A. V. Platonov","doi":"10.3103/s1066369x24700440","DOIUrl":"https://doi.org/10.3103/s1066369x24700440","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the paper, a generalized Lotka–Volterra-type system with switching is considered. The conditions for the ultimate boundedness of solutions and the permanence of the system are studied. With the aid of the direct Lyapunov method, the requirements for the switching law are established to guarantee the necessary dynamics of the system. An attractive compact invariant set is constructed in the phase space of the system, and a given region of attraction for this set is provided. A distinctive feature of the work is the use of a combination of two different Lyapunov functions, each of which plays its own special role in solving the problem.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Construction of First-Order Invariant Differential Operators 构建一阶不变微分算子
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700336
O. L. Kurnyavko, I. V. Shirokov
{"title":"Construction of First-Order Invariant Differential Operators","authors":"O. L. Kurnyavko, I. V. Shirokov","doi":"10.3103/s1066369x24700336","DOIUrl":"https://doi.org/10.3103/s1066369x24700336","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers the problem of constructing systems of vector fields that are invariant under the action of the local Lie group of transformations. It is shown that there exists a special class of Lie groups for which this problem can be solved elementarily.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Variation Operator of Differences of Averages over Lacunary Sequences Maps $$H_{w}^{1}(mathbb{R})$$ to $$L_{w}^{1}(mathbb{R})$$ 拉昆序列平均数差的变异算子将 $$H_{w}^{1}(mathbb{R})$$ 映射到 $$L_{w}^{1}(mathbb{R})$$
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700324
S. Demir
{"title":"The Variation Operator of Differences of Averages over Lacunary Sequences Maps $$H_{w}^{1}(mathbb{R})$$ to $$L_{w}^{1}(mathbb{R})$$","authors":"S. Demir","doi":"10.3103/s1066369x24700324","DOIUrl":"https://doi.org/10.3103/s1066369x24700324","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Let <span>(f)</span> be a locally integrable function defined on <span>(mathbb{R})</span>, and <span>(({{n}_{k}}))</span> be a lacunary sequence. Define\u0000<span>({{A}_{n}}f(x) = frac{1}{n}int_0^n f(x - t)dt,)</span>\u0000and let <span>({{mathcal{V}}_{rho }}f(x) = {{left( {sumlimits_{k = 1}^infty {{{left| {{{A}_{{{{n}_{k}}}}}f(x) - {{A}_{{{{n}_{{k - 1}}}}}}f(x)} right|}}^{rho }}} right)}^{{1/rho }}}.)</span>\u0000Suppose that <span>(w in {{A}_{p}})</span>, <span>(1 leqslant p &lt; infty )</span>, and <span>(rho geqslant 2)</span>. Then, there exists a positive constant <span>(C)</span> such that <span>({{left| {{{mathcal{V}}_{rho }}f} right|}_{{L_{w}^{1}}}} leqslant C{{left| f right|}_{{H_{w}^{1}}}})</span>\u0000for all <span>(f in H_{w}^{1}(mathbb{R}))</span>.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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