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Almost Convergent 0-1-Sequences and Primes 几乎收敛的0-1序列与素数
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060174
N. N. Avdeev
{"title":"Almost Convergent 0-1-Sequences and Primes","authors":"N. N. Avdeev","doi":"10.1134/s0037446623060174","DOIUrl":"https://doi.org/10.1134/s0037446623060174","url":null,"abstract":"<p>We study 0-1-sequences and establish the connection\u0000between the values of the upper and lower Sucheston functional\u0000on such sequence and the set of all possible divisors\u0000of the elements in the sequence support.\u0000If the union of the sets of all simple divisors\u0000of the elements in a 0-1-sequence support is finite then the\u0000sequence is almost convergent to zero. We study the 0-1-sequences\u0000whose support consists exactly of the multiples of\u0000the elements in a given set, and establish some\u0000necessary and sufficient conditions for the upper Sucheston\u0000functional to be equal to 1 on such sequence. We prove that there are\u0000infinitely many sequences at which the lower Sucheston functional\u0000is 1, and the lower Sucheston functional never vanishes at any of\u0000such sequences.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507157","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
Openness and Discreteness of Mappings of Finite Distortion on Carnot Groups 卡诺群上有限畸变映射的开性和离散性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060046
S. G. Basalaev, S. K. Vodopyanov
{"title":"Openness and Discreteness of Mappings of Finite Distortion on Carnot Groups","authors":"S. G. Basalaev, S. K. Vodopyanov","doi":"10.1134/s0037446623060046","DOIUrl":"https://doi.org/10.1134/s0037446623060046","url":null,"abstract":"<p>We prove that a mapping of finite distortion\u0000<span>( f:Omegato 𝔾 )</span> in a domain <span>( Omega )</span>\u0000of an <span>( H )</span>-type Carnot group <span>( 𝔾 )</span>\u0000is continuous, open, and discrete provided that\u0000the distortion function <span>( K(x) )</span> of <span>( f )</span> belongs to <span>( L_{p,operatorname{loc}}(Omega) )</span>\u0000for some <span>( p&gt;nu-1 )</span>.\u0000In fact, the proof is suitable for each Carnot group\u0000provided it has a <span>( nu )</span>-harmonic function of the\u0000form <span>( logrho )</span>, where the homogeneous norm\u0000<span>( rho )</span> is <span>( C^{2} )</span>-smooth.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543746","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
The Minimal Number of Generating Involutions Whose Product Is 1 for the Groups  $ PSL_{3}(2^{m}) $ and  $ PSU_{3}(q^{2}) $ 群$ PSL_{3}(2^{m}) $和$ PSU_{3}(q^{2}) $积为1的最小生成对合数
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060058
R. I. Gvozdev, Ya. N. Nuzhin
{"title":"The Minimal Number of Generating Involutions Whose Product Is 1 for the Groups  $ PSL_{3}(2^{m}) $ and  $ PSU_{3}(q^{2}) $","authors":"R. I. Gvozdev, Ya. N. Nuzhin","doi":"10.1134/s0037446623060058","DOIUrl":"https://doi.org/10.1134/s0037446623060058","url":null,"abstract":"<p>Considering the groups <span>( PSL_{3}(2^{m}) )</span> and <span>( PSU_{3}(q^{2}) )</span>, we find the minimal number of generating\u0000involutions whose product is 1. This number is 7 for <span>( PSU_{3}(3^{2}) )</span> and 5 or 6\u0000in the remaining cases.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507160","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
$ E $ -Rings and Quotient Divisible Abelian Groups $ E $ -环与商可除阿贝尔群
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s003744662306006x
M. N. Zonov, E. A. Timoshenko
{"title":"$ E $ -Rings and Quotient Divisible Abelian Groups","authors":"M. N. Zonov, E. A. Timoshenko","doi":"10.1134/s003744662306006x","DOIUrl":"https://doi.org/10.1134/s003744662306006x","url":null,"abstract":"<p>Under study are the relations between <span>( E )</span>-rings and quotient divisible abelian groups.\u0000We obtain a criterion for the quotient divisibility of the additive group\u0000of an <span>( E )</span>-ring and give a negative solution to the Bowshell and Schultz problem\u0000about the quasidecompositions of <span>( E )</span>-rings.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507191","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
Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads 拟亚纯映射的图形极限与四分体特征的畸变
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060034
V. V. Aseev
{"title":"Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads","authors":"V. V. Aseev","doi":"10.1134/s0037446623060034","DOIUrl":"https://doi.org/10.1134/s0037446623060034","url":null,"abstract":"<p>We fully describe\u0000the form of\u0000the graphical limit of a sequence of <span>( K )</span>-quasimeromorphic mappings\u0000of a domain <span>( D )</span>\u0000in <span>( overline{R^{n}} )</span>\u0000which take each of its values\u0000at <span>( N )</span>\u0000distinct points at most.\u0000For the family of all <span>( K )</span>-quasimeromorphic mappings of <span>( overline{R^{n}} )</span>\u0000onto itself\u0000taking each value at <span>( N )</span> points at most\u0000we establish the presence of a common estimate for the distortion of\u0000the Ptolemaic characteristic of generalized tetrads\u0000(quadruples of disjoint compact sets).</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533180","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
The Myshkis 3/2 Theorem and Its Generalizations Myshkis 3/2定理及其推广
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060113
V. V. Malygina
{"title":"The Myshkis 3/2 Theorem and Its Generalizations","authors":"V. V. Malygina","doi":"10.1134/s0037446623060113","DOIUrl":"https://doi.org/10.1134/s0037446623060113","url":null,"abstract":"<p>We discuss the well-known Myshkis result on the stability of nonautonomous first-order delay differential equations,\u0000providing an extension to the general differential equations with aftereffect,\u0000and make comparison with available results.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533184","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
$ BV $ -Spaces and the Bounded Composition Operators of $ BV $ -Functions on Carnot Groups 卡诺群上的$ BV $ -空间与$ BV $ -函数的有界复合算子
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060149
D. A. Sboev
{"title":"$ BV $ -Spaces and the Bounded Composition Operators of $ BV $ -Functions on Carnot Groups","authors":"D. A. Sboev","doi":"10.1134/s0037446623060149","DOIUrl":"https://doi.org/10.1134/s0037446623060149","url":null,"abstract":"<p>Under study are the homeomorphisms that induce the bounded composition operators of <span>( BV )</span>-functions\u0000on Carnot groups.\u0000We characterize continuous\u0000<span>( BV_{operatorname{loc}} )</span>-mappings\u0000on Carnot groups\u0000in terms of the variation on integral lines\u0000and estimate the variation of the\u0000<span>( BV )</span>-derivative of the composition of a <span>( C^{1} )</span>-function\u0000and a continuous\u0000<span>( BV_{operatorname{loc}} )</span>-mapping.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533181","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 Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space 欧几里得$ d $ -空间中两个规定边长仿射等价框架的存在性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060022
V. A. Alexandrov
{"title":"On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space","authors":"V. A. Alexandrov","doi":"10.1134/s0037446623060022","DOIUrl":"https://doi.org/10.1134/s0037446623060022","url":null,"abstract":"<p>We study the existence of the two affine-equivalent bar-and-joint\u0000frameworks in Euclidean <span>( d )</span>-space which have some prescribed combinatorial\u0000structure and edge lengths.\u0000We show that the existence problem is always solvable theoretically and\u0000explain why to propose a practical algorithm for solving the problem is impossible.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543236","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 Irreducible Carpets of Additive Subgroups of Type  $ F_{4} $ $ F_{4} $型可加子群的不可约地毯
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060198
A. O. Likhacheva
{"title":"On the Irreducible Carpets of Additive Subgroups of Type  $ F_{4} $","authors":"A. O. Likhacheva","doi":"10.1134/s0037446623060198","DOIUrl":"https://doi.org/10.1134/s0037446623060198","url":null,"abstract":"<p>We consider the irreducible carpets\u0000<span>( mathfrak{A}={mathfrak{A}_{r}: rinPhi} )</span>\u0000of type <span>( F_{4} )</span> over an algebraical extension\u0000<span>( K )</span> of a field <span>( R )</span> such that all additive subgroups\u0000<span>( mathfrak{A}_{r} )</span> are <span>( R )</span>-modules.\u0000The carpets, parametrized by a pair of additive subgroups,\u0000appear only in characteristic 2.\u0000This pair of additive subgroups presents (possibly different) fields\u0000up to conjugation by a diagonal element in the corresponding\u0000Chevalley group.\u0000Moreover, we establish\u0000that such carpets <span>( mathfrak{A} )</span> are closed.\u0000Using Levchuk’s description of the\u0000irreducible carpets of Lie type of rank greater than 1 over <span>( K )</span>,\u0000we show that\u0000all additive subgroups of the carpets coincide with an\u0000intermediate subfield between <span>( R )</span> and <span>( K )</span>\u0000of the carpets of types <span>( B_{l} )</span>, <span>( C_{l} )</span>, and <span>( F_{4} )</span>\u0000in case of the characteristic of <span>( K )</span> is not 0 and 2\u0000whereas it is neither 0, 2, nor 3 for type <span>( G_{2} )</span>\u0000up to conjugation by a diagonal element.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533182","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
Classes of Noncontact Mappings of Carnot Groups and Metric Properties 卡诺群的非接触映射类及度量性质
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060083
M. B. Karmanova
{"title":"Classes of Noncontact Mappings of Carnot Groups and Metric Properties","authors":"M. B. Karmanova","doi":"10.1134/s0037446623060083","DOIUrl":"https://doi.org/10.1134/s0037446623060083","url":null,"abstract":"<p>We study the metric properties of level surfaces\u0000for classes of smooth noncontact mappings\u0000from arbitrary Carnot groups into two-step ones\u0000with some constraints on the dimensions of horizontal subbundles\u0000and the subbundles corresponding to degree 2 fields.\u0000We calculate the Hausdorff dimension of the level surfaces\u0000with respect to the sub-Riemannian quasimetric\u0000and derive an analytical relation between the Hausdorff measures\u0000for the sub-Riemannian quasimetric and the Riemannian metric.\u0000As application,\u0000we establish a new form of coarea formula, also proving that\u0000the new coarea factor is well defined.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533196","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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