Pub Date : 2021-04-27DOI: 10.33048/semi.2021.18.032
V. Golubyatnikov, L. S. Minushkina
{"title":"On uniqueness and stability of a cycle in one gene network","authors":"V. Golubyatnikov, L. S. Minushkina","doi":"10.33048/semi.2021.18.032","DOIUrl":"https://doi.org/10.33048/semi.2021.18.032","url":null,"abstract":"","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42050848","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}
Pub Date : 2021-04-23DOI: 10.33048/semi.2022.19.012
A. J. O. Andrade, Gabriela C. Moraes, R. N. Ferreira, B. Ferreira
Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA cdot e = 0$ implies $x = 0$ and $xA cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.
{"title":"Nonlinear *-Jordan-type derivations on alternative *-algebras","authors":"A. J. O. Andrade, Gabriela C. Moraes, R. N. Ferreira, B. Ferreira","doi":"10.33048/semi.2022.19.012","DOIUrl":"https://doi.org/10.33048/semi.2022.19.012","url":null,"abstract":"Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA cdot e = 0$ implies $x = 0$ and $xA cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45077929","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}
Pub Date : 2021-04-22DOI: 10.33048/semi.2021.18.031
T. Batueva, O. Borodin, A. Ivanova, D. Nikiforov
{"title":"All tight descriptions of major $3$-paths in $3$-polytopes without $3$-vertices","authors":"T. Batueva, O. Borodin, A. Ivanova, D. Nikiforov","doi":"10.33048/semi.2021.18.031","DOIUrl":"https://doi.org/10.33048/semi.2021.18.031","url":null,"abstract":"","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45587748","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}
Pub Date : 2021-04-20DOI: 10.33048/semi.2021.18.030
A. Yeshkeyev, M. T. Kassymetova, O. I. Ulbrikht
{"title":"Independence and simplicity in Jonsson theories with abstract geometry","authors":"A. Yeshkeyev, M. T. Kassymetova, O. I. Ulbrikht","doi":"10.33048/semi.2021.18.030","DOIUrl":"https://doi.org/10.33048/semi.2021.18.030","url":null,"abstract":"","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42848882","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}
Pub Date : 2021-04-18DOI: 10.33048/semi.2021.18.029
M. V. Tryamkin
We consider the class of mappings generalizing qusiregular mappings. Every mapping from this class is de ned in a domain of Euclidean n-space and possesses the following properties: it is open, continuous, and discrete, it belongs locally to the Sobolev classW 1 q , it has nite distortion and nonnegative Jacobian, and its function of weighted (p, q)-distortion is integrable to a certian power depending on p and q, where n − 1 < q 6 p < ∞. We obtain an analog of Schwarz's lemma for such mappings provided that p > n. The technique used is based on the spherical symmetrization procedure and the notion of Gr otzsch condenser.
{"title":"A version of Schwarz's lemma for mappings with weighted bounded distortion","authors":"M. V. Tryamkin","doi":"10.33048/semi.2021.18.029","DOIUrl":"https://doi.org/10.33048/semi.2021.18.029","url":null,"abstract":"We consider the class of mappings generalizing qusiregular mappings. Every mapping from this class is de ned in a domain of Euclidean n-space and possesses the following properties: it is open, continuous, and discrete, it belongs locally to the Sobolev classW 1 q , it has nite distortion and nonnegative Jacobian, and its function of weighted (p, q)-distortion is integrable to a certian power depending on p and q, where n − 1 < q 6 p < ∞. We obtain an analog of Schwarz's lemma for such mappings provided that p > n. The technique used is based on the spherical symmetrization procedure and the notion of Gr otzsch condenser.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46042980","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}
Pub Date : 2021-04-16DOI: 10.33048/semi.2021.18.028
M. G. Lee, L. P. Zhang, Z. C. Li, A. Kazakov
The dual techniques have been widely used in many engineering papers, to deal with singularity and ill-conditioning of the boundary element method (BEM). In this paper, we consider Laplace's equation with circular domains with one circular hole. The explicit algebraic equations of the rst and second kinds of the null eld method (NFM) are provided for applications. Traditionally, the rst and the second kinds of the NFM are used for the Dirichlet and the Neumann problems, respectively. To bypass the degenerate scales of Dirichlet problems, however, the second and the rst kinds of the NFM are used for the exterior and the interior boundaries, simultaneously, called the dual NFM (DNFM) in this paper. The excellent stability and the optimal convergence rates are explored in this paper. By using the simple Gaussian elimination or the iteration methods, numerical solutions can be easily obtained. Recently, the study on degenerate scales is active, many removal techniques are proposed, where the advanced solution methods may be needed, such as the truncated singular value decomposition (TSVD) and the overdetermined systems. In contrast, the solution methods of the DNFM in this paper are much simpler, with a little risk of the algorithm singularity from degenerate scales.
{"title":"Dual null field method for Dirichlet problems of Laplace's equation in circular domains with circular holes","authors":"M. G. Lee, L. P. Zhang, Z. C. Li, A. Kazakov","doi":"10.33048/semi.2021.18.028","DOIUrl":"https://doi.org/10.33048/semi.2021.18.028","url":null,"abstract":"The dual techniques have been widely used in many engineering papers, to deal with singularity and ill-conditioning of the boundary element method (BEM). In this paper, we consider Laplace's equation with circular domains with one circular hole. The explicit algebraic equations of the rst and second kinds of the null eld method (NFM) are provided for applications. Traditionally, the rst and the second kinds of the NFM are used for the Dirichlet and the Neumann problems, respectively. To bypass the degenerate scales of Dirichlet problems, however, the second and the rst kinds of the NFM are used for the exterior and the interior boundaries, simultaneously, called the dual NFM (DNFM) in this paper. The excellent stability and the optimal convergence rates are explored in this paper. By using the simple Gaussian elimination or the iteration methods, numerical solutions can be easily obtained. Recently, the study on degenerate scales is active, many removal techniques are proposed, where the advanced solution methods may be needed, such as the truncated singular value decomposition (TSVD) and the overdetermined systems. In contrast, the solution methods of the DNFM in this paper are much simpler, with a little risk of the algorithm singularity from degenerate scales.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42662308","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}
Pub Date : 2021-04-13DOI: 10.33048/semi.2021.18.027
R. A. Kornev
{"title":"Computable metrics above the standard real metric","authors":"R. A. Kornev","doi":"10.33048/semi.2021.18.027","DOIUrl":"https://doi.org/10.33048/semi.2021.18.027","url":null,"abstract":"","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42065794","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}
Pub Date : 2021-04-08DOI: 10.33048/semi.2021.18.062
V. Gubarev
We extend the correspondence between double Lie algebras and skew-symmetric Rota—Baxter operators of weight 0 on the matrix algebra for the infinitedimensional case. We give the first example of simple double Lie algebra.
{"title":"An example of a simple double Lie algebra","authors":"V. Gubarev","doi":"10.33048/semi.2021.18.062","DOIUrl":"https://doi.org/10.33048/semi.2021.18.062","url":null,"abstract":"We extend the correspondence between double Lie algebras and skew-symmetric Rota—Baxter operators of weight 0 on the matrix algebra for the infinitedimensional case. We give the first example of simple double Lie algebra.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46465744","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}
Pub Date : 2021-04-02DOI: 10.33048/semi.2021.18.024
T. I. Fedoryaeva
A property of graphs from a class under consideration is typical if almost all graphs from this class have the given property. Typical properties of the class of n-vertex graphs of a xed diameter k are studied. A family of embedded classes of typical n-vertex graphs of a given diameter k ≥ 3, which possess a number of established metric properties, is constructed. Based on the typical properties of metric balls contained in the graph, the radius of almost all n-vertex graphs from the investigated classes is found. It is proved that for every xed integer k ≥ 3 almost all n-vertex graphs of diameter k have radius d k 2 e, while the radius of almost all graphs of diameter k = 1, 2 is equal to the diameter. All found typical properties of n-vertex graphs of a xed diameter k ≥ 2 are also typical for connected graphs of diameter at least k, as well as for graphs (not necessarily connected) containing the shortest path of length at least k.
{"title":"On radius and typical properties of $n$-vertex graphs of given diameter","authors":"T. I. Fedoryaeva","doi":"10.33048/semi.2021.18.024","DOIUrl":"https://doi.org/10.33048/semi.2021.18.024","url":null,"abstract":"A property of graphs from a class under consideration is typical if almost all graphs from this class have the given property. Typical properties of the class of n-vertex graphs of a xed diameter k are studied. A family of embedded classes of typical n-vertex graphs of a given diameter k ≥ 3, which possess a number of established metric properties, is constructed. Based on the typical properties of metric balls contained in the graph, the radius of almost all n-vertex graphs from the investigated classes is found. It is proved that for every xed integer k ≥ 3 almost all n-vertex graphs of diameter k have radius d k 2 e, while the radius of almost all graphs of diameter k = 1, 2 is equal to the diameter. All found typical properties of n-vertex graphs of a xed diameter k ≥ 2 are also typical for connected graphs of diameter at least k, as well as for graphs (not necessarily connected) containing the shortest path of length at least k.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43622780","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}
Pub Date : 2021-03-31DOI: 10.33048/semi.2021.18.023
M. Mustafa, D. Suragan
{"title":"A note on Hardy type inequalities for quaternion-valued functions","authors":"M. Mustafa, D. Suragan","doi":"10.33048/semi.2021.18.023","DOIUrl":"https://doi.org/10.33048/semi.2021.18.023","url":null,"abstract":"","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45733780","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}
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