Pub Date : 2020-10-12DOI: 10.17398/2605-5686.37.2.223
Sachindranath Jayaraman, Y. Prajapaty, S. Sridharan
The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic points of a nonnegative matrix to products of finitely many nonnegative matrices associated to a word and later to products of nonnegative matrices associated to a word, possibly of infinite length.
{"title":"Dynamics of products of nonnegative matrices","authors":"Sachindranath Jayaraman, Y. Prajapaty, S. Sridharan","doi":"10.17398/2605-5686.37.2.223","DOIUrl":"https://doi.org/10.17398/2605-5686.37.2.223","url":null,"abstract":"The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic points of a nonnegative matrix to products of finitely many nonnegative matrices associated to a word and later to products of nonnegative matrices associated to a word, possibly of infinite length.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42512014","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 : 2020-07-02DOI: 10.17398/2605-5686.38.1.27
T. Chtioui, S. Mabrouk, A. Makhlouf
The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.
{"title":"Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras","authors":"T. Chtioui, S. Mabrouk, A. Makhlouf","doi":"10.17398/2605-5686.38.1.27","DOIUrl":"https://doi.org/10.17398/2605-5686.38.1.27","url":null,"abstract":"The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42112800","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 : 2020-05-14DOI: 10.17398/2605-5686.35.1.1
M. Garayev, F. Bouzeffour, M. Gürdal, C. M. Yangoz
In this article, we use Kantorovich and Kantorovich type inequalities in order to prove some new Berezin number inequalities. Also, by using a refinement of the classical Schwarz inequality, we prove Berezin number inequalities for powers of f(A), where A is self-adjoint operator on the Hardy space H2 (D) and f is a positive continuous function. Some related questions are also discussed.
{"title":"Refinements of Kantorovich type, Schwarz and Berezin number inequalities","authors":"M. Garayev, F. Bouzeffour, M. Gürdal, C. M. Yangoz","doi":"10.17398/2605-5686.35.1.1","DOIUrl":"https://doi.org/10.17398/2605-5686.35.1.1","url":null,"abstract":"In this article, we use Kantorovich and Kantorovich type inequalities in order to prove some \u0000new Berezin number inequalities. Also, by using a refinement of the classical Schwarz inequality, we \u0000prove Berezin number inequalities for powers of f(A), where A is self-adjoint operator on the Hardy \u0000space H2 \u0000(D) and f is a positive continuous function. Some related questions are also discussed.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46392000","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 : 2020-05-14DOI: 10.17398/2605-5686.35.1.35
D. V. Krishna, D. Shalini
The objective of this paper is to obtain an upper bound to Hankel determinant of third order for any function f, when it belongs to certain subclass of analytic functions, defined on the open unit disc in the complex plane.
{"title":"On H3 (1) Hankel determinant for certain subclass of analytic functions","authors":"D. V. Krishna, D. Shalini","doi":"10.17398/2605-5686.35.1.35","DOIUrl":"https://doi.org/10.17398/2605-5686.35.1.35","url":null,"abstract":"The objective of this paper is to obtain an upper bound to Hankel determinant of third order for any function f, when it belongs to certain subclass of analytic functions, defined on the open unit disc in the complex plane.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46929243","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 : 2019-08-23DOI: 10.17398/2605-5686.36.1.1
Sylvain Attan
This paper is mainly devoted to a structure study of Hom-alternative algebras. Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are provided. Moreover some results about Hom-alternative bimodule are found.
{"title":"Structure and bimodules of simple Hom-alternative algebras","authors":"Sylvain Attan","doi":"10.17398/2605-5686.36.1.1","DOIUrl":"https://doi.org/10.17398/2605-5686.36.1.1","url":null,"abstract":"This paper is mainly devoted to a structure study of Hom-alternative algebras. Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are provided. Moreover some results about Hom-alternative bimodule are found.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42653130","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 : 2019-05-29DOI: 10.17398/2605-5686.35.1.99
S. Mabrouk, A. Makhlouf, S. Massoud
The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology theory and study semi-direct products. We provide a key construction, various examples and computation of 2-cocycles of the new cohomology. Also, we give a connection between a split abelian extension of a 3-Hom-Lie algebra and a generalized semidirect product 3-Hom-Lie algebra.
{"title":"Generalized representations of 3-Hom-Lie algebras","authors":"S. Mabrouk, A. Makhlouf, S. Massoud","doi":"10.17398/2605-5686.35.1.99","DOIUrl":"https://doi.org/10.17398/2605-5686.35.1.99","url":null,"abstract":"The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology theory and study semi-direct products. We provide a key construction, various examples and computation of 2-cocycles of the new cohomology. Also, we give a connection between a split abelian extension of a 3-Hom-Lie algebra and a generalized semidirect product 3-Hom-Lie algebra.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48476603","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 : 2017-01-26DOI: 10.17398/2605-5686.35.1.55
A. Tarizadeh
In this paper, the projectivity of a finitely generated flat module of a commutative ring is studied through its exterior powers and invariant factors and then various new results are obtained. Specially, the related results of Endo, Vasconcelos, Wiegand, Cox-Rush and Puninski-Rothmaler on the projectivity of finitely generated flat modules are generalized.
{"title":"On the projectivity of finitely generated flat modules","authors":"A. Tarizadeh","doi":"10.17398/2605-5686.35.1.55","DOIUrl":"https://doi.org/10.17398/2605-5686.35.1.55","url":null,"abstract":"In this paper, the projectivity of a finitely generated flat module of a commutative ring is studied through its exterior powers and invariant factors and then various new results are obtained. Specially, the related results of Endo, Vasconcelos, Wiegand, Cox-Rush and Puninski-Rothmaler on the projectivity of finitely generated flat modules are generalized.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46289892","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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