Pub Date : 2023-10-21DOI: 10.1142/s1793557123502212
Hanen Damak, Mohamed Ali Hammami, Khouloud Maaloul
This paper deals with the practical feedback stabilization of a class of evolution equations in Hilbert spaces. By using the Lyapunov function method, we give sufficient conditions for the global uniform practical convergence of the closed-loop system. Based on the global null-controllability, we construct an output feedback controller that guarantees global uniform practical stability of uncertain systems. A numerical application is given to show the applicability of our theoretical results.
{"title":"On the asymptotic stabilization of the non-autonomous evolution equations in Hilbert spaces","authors":"Hanen Damak, Mohamed Ali Hammami, Khouloud Maaloul","doi":"10.1142/s1793557123502212","DOIUrl":"https://doi.org/10.1142/s1793557123502212","url":null,"abstract":"This paper deals with the practical feedback stabilization of a class of evolution equations in Hilbert spaces. By using the Lyapunov function method, we give sufficient conditions for the global uniform practical convergence of the closed-loop system. Based on the global null-controllability, we construct an output feedback controller that guarantees global uniform practical stability of uncertain systems. A numerical application is given to show the applicability of our theoretical results.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135463228","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 : 2023-10-21DOI: 10.1142/s1793557123502200
Alanka Thomas, P.G. Romeo
Classical Maschke’s theorem gives a condition for the semisimplicity of group algebras over a field. As group algebras are a particular case of twisted group rings, we extend Maschke’s theorem to twisted group rings over division rings by proving that if the characteristic of a division ring [Formula: see text] does not divide the order of a finite group [Formula: see text], twisted group ring [Formula: see text] is semisimple. Then we prove the converse of this theorem for twisted group rings arising from split extensions of [Formula: see text] by [Formula: see text]. As there is a one-to-one correspondence between twisted group rings and group lattices over division rings, we conclude with the consequence of the semisimplicity of twisted group rings on group lattices.
{"title":"On the semisimplicity of twisted group rings and generalized maschke's theorem","authors":"Alanka Thomas, P.G. Romeo","doi":"10.1142/s1793557123502200","DOIUrl":"https://doi.org/10.1142/s1793557123502200","url":null,"abstract":"Classical Maschke’s theorem gives a condition for the semisimplicity of group algebras over a field. As group algebras are a particular case of twisted group rings, we extend Maschke’s theorem to twisted group rings over division rings by proving that if the characteristic of a division ring [Formula: see text] does not divide the order of a finite group [Formula: see text], twisted group ring [Formula: see text] is semisimple. Then we prove the converse of this theorem for twisted group rings arising from split extensions of [Formula: see text] by [Formula: see text]. As there is a one-to-one correspondence between twisted group rings and group lattices over division rings, we conclude with the consequence of the semisimplicity of twisted group rings on group lattices.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135463226","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 : 2023-10-20DOI: 10.1142/s1793557123502145
H. Aharssi, H. El Mir, A. Mamouni
This paper aims to investigate the commutativity of prime rings with involution ∗ of the second kind in which endomorphisms satisfy some algebraic identities involving hermitian and skew-hermitian elements. We will also provide some classifications of these endomorphisms. Finally, we give some examples to prove that the imposed hypotheses are necessary.
{"title":"Commutativity with algebraic identities involving hermetian and skew-hermetian elements","authors":"H. Aharssi, H. El Mir, A. Mamouni","doi":"10.1142/s1793557123502145","DOIUrl":"https://doi.org/10.1142/s1793557123502145","url":null,"abstract":"This paper aims to investigate the commutativity of prime rings with involution ∗ of the second kind in which endomorphisms satisfy some algebraic identities involving hermitian and skew-hermitian elements. We will also provide some classifications of these endomorphisms. Finally, we give some examples to prove that the imposed hypotheses are necessary.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"77 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514410","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 : 2023-10-20DOI: 10.1142/s1793557123502169
Duong Quoc Huy, Doan Thi Thuy Van
In this paper we propose some Heinz-type inequalities for convex functions which provide a very simple proof of the main results of Kittaneh, Moslehian and Sababheh showed in the paper (F. Kittaneh, M. S. Moslehian and M. Sababheh, Quadratic interpolation of the Heinz means, Math. Inequal. Appl. 21(3) (2018) 739–757). We apply these inequalities to infer new inequalities for power means. As an application, we also give operator versions of Heinz-type inequalities for power and Heinz means.
本文提出了凸函数的一些Heinz型不等式，这些不等式非常简单地证明了Kittaneh, Moslehian和Sababheh在论文(F. Kittaneh, M. S. Moslehian和M. Sababheh, Heinz均值的二次插值，数学)中给出的主要结果。不平等的。苹果21(3)(2018)739-757)。我们应用这些不等式来推断新的幂均值不等式。作为应用，我们也给出了幂和均值的Heinz型不等式的算子版本。
{"title":"Some inequalities for convex functions and applications to operator inequalities","authors":"Duong Quoc Huy, Doan Thi Thuy Van","doi":"10.1142/s1793557123502169","DOIUrl":"https://doi.org/10.1142/s1793557123502169","url":null,"abstract":"In this paper we propose some Heinz-type inequalities for convex functions which provide a very simple proof of the main results of Kittaneh, Moslehian and Sababheh showed in the paper (F. Kittaneh, M. S. Moslehian and M. Sababheh, Quadratic interpolation of the Heinz means, Math. Inequal. Appl. 21(3) (2018) 739–757). We apply these inequalities to infer new inequalities for power means. As an application, we also give operator versions of Heinz-type inequalities for power and Heinz means.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"11 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514279","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 : 2023-10-20DOI: 10.1142/s1793557123502157
S. Visweswaran
Let [Formula: see text] be a nonzero commutative ring with identity. Let [Formula: see text] be a positive integer. Let [Formula: see text] ([Formula: see text] times). The total dot product graph of [Formula: see text] denoted by [Formula: see text] is an undirected graph with vertex set which equals [Formula: see text] and distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text], where [Formula: see text] is the normal dot product of [Formula: see text] and [Formula: see text]. Let [Formula: see text] denote the set of all zero-divisors of [Formula: see text] and let us denote [Formula: see text] by [Formula: see text]. The zero-divisor dot product graph of [Formula: see text], denoted by [Formula: see text] is the subgraph of [Formula: see text] induced by [Formula: see text]. The graph [Formula: see text] (respectively, [Formula: see text]) was introduced and investigated by Badawi [Commun. Algebra 43(1) (2015) 43–50]. In this paper, we characterize [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) is connected and determine the diameter and the radius of [Formula: see text] (respectively, [Formula: see text]) whenever it is connected. Moreover, if [Formula: see text] (respectively, [Formula: see text]) is connected, then we characterize [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) admits a cut vertex.
{"title":"Some results on the complement of the dot product graph of a commutative ring","authors":"S. Visweswaran","doi":"10.1142/s1793557123502157","DOIUrl":"https://doi.org/10.1142/s1793557123502157","url":null,"abstract":"Let [Formula: see text] be a nonzero commutative ring with identity. Let [Formula: see text] be a positive integer. Let [Formula: see text] ([Formula: see text] times). The total dot product graph of [Formula: see text] denoted by [Formula: see text] is an undirected graph with vertex set which equals [Formula: see text] and distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text], where [Formula: see text] is the normal dot product of [Formula: see text] and [Formula: see text]. Let [Formula: see text] denote the set of all zero-divisors of [Formula: see text] and let us denote [Formula: see text] by [Formula: see text]. The zero-divisor dot product graph of [Formula: see text], denoted by [Formula: see text] is the subgraph of [Formula: see text] induced by [Formula: see text]. The graph [Formula: see text] (respectively, [Formula: see text]) was introduced and investigated by Badawi [Commun. Algebra 43(1) (2015) 43–50]. In this paper, we characterize [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) is connected and determine the diameter and the radius of [Formula: see text] (respectively, [Formula: see text]) whenever it is connected. Moreover, if [Formula: see text] (respectively, [Formula: see text]) is connected, then we characterize [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) admits a cut vertex.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"91 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514409","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 : 2023-10-17DOI: 10.1142/s1793557123502133
Rupali S. Jain, B. Surendranath Reddy, Wajid M. Shaikh
In this paper, we consider the unit graph [Formula: see text], where [Formula: see text] and [Formula: see text] are distinct primes. For any prime [Formula: see text], we construct [Formula: see text]-ary linear codes from the incidence matrix of the unit graph [Formula: see text] with their parameters. We also prove that the dual of the constructed codes have minimum distance either three or four. Lastly, we stated two conjectures on diameter of unit graph [Formula: see text] and linear codes constructed from the incidence matrix of the unit graph [Formula: see text] for any integer [Formula: see text].
{"title":"Construction of Linear Codes from the Unit Graph <i>G</i>(ℤ<sub><i>n</i></sub>)","authors":"Rupali S. Jain, B. Surendranath Reddy, Wajid M. Shaikh","doi":"10.1142/s1793557123502133","DOIUrl":"https://doi.org/10.1142/s1793557123502133","url":null,"abstract":"In this paper, we consider the unit graph [Formula: see text], where [Formula: see text] and [Formula: see text] are distinct primes. For any prime [Formula: see text], we construct [Formula: see text]-ary linear codes from the incidence matrix of the unit graph [Formula: see text] with their parameters. We also prove that the dual of the constructed codes have minimum distance either three or four. Lastly, we stated two conjectures on diameter of unit graph [Formula: see text] and linear codes constructed from the incidence matrix of the unit graph [Formula: see text] for any integer [Formula: see text].","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135945129","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 : 2023-10-14DOI: 10.1142/s1793557123502091
Laszlo Horvath
In this paper, we examine the relationship between a recent new discrete majorization-type inequality and classical majorization-type inequalities. The multiplicative analog of the studied new inequality is also given, which is a wide generalization of Weyl’s inequality. As an application, we give a parametric refinement of Popoviciu’s version of the Petrović inequality.
{"title":"Discrete majorization type inequalities, comparison of classic results with a recent result","authors":"Laszlo Horvath","doi":"10.1142/s1793557123502091","DOIUrl":"https://doi.org/10.1142/s1793557123502091","url":null,"abstract":"In this paper, we examine the relationship between a recent new discrete majorization-type inequality and classical majorization-type inequalities. The multiplicative analog of the studied new inequality is also given, which is a wide generalization of Weyl’s inequality. As an application, we give a parametric refinement of Popoviciu’s version of the Petrović inequality.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767368","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 : 2023-10-13DOI: 10.1142/s1793557123502261
Randa Chalekh, El Amir Djeffal
{"title":"New smoothing function for solving absolute value equations","authors":"Randa Chalekh, El Amir Djeffal","doi":"10.1142/s1793557123502261","DOIUrl":"https://doi.org/10.1142/s1793557123502261","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853583","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 : 2023-10-13DOI: 10.1142/s1793557123502297
Alexander Balandin
{"title":"Inverse scattering problem for the tensor fields in a coordinate-free representation","authors":"Alexander Balandin","doi":"10.1142/s1793557123502297","DOIUrl":"https://doi.org/10.1142/s1793557123502297","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854934","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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