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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":"29 1","pages":""},"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
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":"31 1","pages":""},"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":"54 1","pages":""},"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":"2018 1","pages":""},"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":"73 1","pages":""},"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":"58 1","pages":""},"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":"77 1","pages":""},"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
Maximum Estimates for Solutions to Elliptic and Parabolic Equations on a Book-Type Stratified Set 书式分层集上椭圆和抛物方程解的最大估计值
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-01 DOI: 10.1134/S0037446623060125
F. D. Mironenko
{"title":"Maximum Estimates for Solutions to Elliptic and Parabolic Equations on a Book-Type Stratified Set","authors":"F. D. Mironenko","doi":"10.1134/S0037446623060125","DOIUrl":"https://doi.org/10.1134/S0037446623060125","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"5 1","pages":"1385-1398"},"PeriodicalIF":0.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139292201","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
Periodic Frobenius Groups 周期弗罗贝尼斯群
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-01 DOI: 10.1134/S0037446623060095
D. Lytkina, V. Mazurov
{"title":"Periodic Frobenius Groups","authors":"D. Lytkina, V. Mazurov","doi":"10.1134/S0037446623060095","DOIUrl":"https://doi.org/10.1134/S0037446623060095","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"20 1","pages":"1351-1355"},"PeriodicalIF":0.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139305204","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 Distribution of a Random Power Series on the Dyadic Half-Line 论随机幂级数在二元半线上的分布
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-01 DOI: 10.1134/S0037446623060071
M. A. Karapetyants
{"title":"On the Distribution of a Random Power Series on the Dyadic Half-Line","authors":"M. A. Karapetyants","doi":"10.1134/S0037446623060071","DOIUrl":"https://doi.org/10.1134/S0037446623060071","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"33 1","pages":"1319 - 1329"},"PeriodicalIF":0.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139303469","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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