. In this paper, we consider a one-dimensional Lord-Shulman ther-moelastic system [4] with porous damping and distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well-posedness of the system by using semigroup theory and we show that the dissipations due to thermal effects with porous damping are strong enough to stabilise the system exponentially, independently of the wave speeds of the system.
{"title":"Exponential stability of Lord Shulman thermoelastic system with porous damping and distributed delay term","authors":"Lamine Bouzettouta, Chaima Boulkheloua, Houssem Eddine Khochemane, Widad Karek","doi":"10.1142/s179355712350225x","DOIUrl":"https://doi.org/10.1142/s179355712350225x","url":null,"abstract":". In this paper, we consider a one-dimensional Lord-Shulman ther-moelastic system [4] with porous damping and distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well-posedness of the system by using semigroup theory and we show that the dissipations due to thermal effects with porous damping are strong enough to stabilise the system exponentially, independently of the wave speeds of the system.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"16 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":"135854424","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 : 2023-10-06DOI: 10.1142/s1793557123502108
Devia Narrania, Kuldip Raj
In this paper, we introduce the notions of product measurable convergence, deferred Cesàro statistical product measurable convergence and deferred Cesàro statistical Lebesgue product measurable convergence for sequences of measurable functions on product measure spaces. We establish some fundamental relations among these convergences and also give several explanatory examples in support of our definitions and results. Finally, as an application, we prove a new version of Korovkin-type approximation theorems for sequences of measurable functions on product measure spaces by using the notion of deferred Cesàro statistical Lebesgue product measurable convergence.
{"title":"Applications of deferred lebesgue product measurable convergence to approximation theorems","authors":"Devia Narrania, Kuldip Raj","doi":"10.1142/s1793557123502108","DOIUrl":"https://doi.org/10.1142/s1793557123502108","url":null,"abstract":"In this paper, we introduce the notions of product measurable convergence, deferred Cesàro statistical product measurable convergence and deferred Cesàro statistical Lebesgue product measurable convergence for sequences of measurable functions on product measure spaces. We establish some fundamental relations among these convergences and also give several explanatory examples in support of our definitions and results. Finally, as an application, we prove a new version of Korovkin-type approximation theorems for sequences of measurable functions on product measure spaces by using the notion of deferred Cesàro statistical Lebesgue product measurable convergence.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302742","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 : 2023-10-05DOI: 10.1142/s1793557123502029
Diksha Upadhyay, Harish Chandra, Suchi Bhatt
Let [Formula: see text] be a group, [Formula: see text] be a finite field with a positive characteristic [Formula: see text], then [Formula: see text] is the group algebra of a group [Formula: see text] over [Formula: see text] with a positive characteristic [Formula: see text]. In this paper, the normal complement problem on semisimple group algebra [Formula: see text] is examined. The normal complement problem of groups of order up to 16 in their corresponding unit groups [Formula: see text] has already been discussed. We have proved that up to isomorphism all the three non-abelian groups of order 18 and up to isomorphism all three non-abelian groups of order 20 do not have normal complement in their corresponding unit groups [Formula: see text].
{"title":"On the Normal Complement Problem of Finite Group Algebra","authors":"Diksha Upadhyay, Harish Chandra, Suchi Bhatt","doi":"10.1142/s1793557123502029","DOIUrl":"https://doi.org/10.1142/s1793557123502029","url":null,"abstract":"Let [Formula: see text] be a group, [Formula: see text] be a finite field with a positive characteristic [Formula: see text], then [Formula: see text] is the group algebra of a group [Formula: see text] over [Formula: see text] with a positive characteristic [Formula: see text]. In this paper, the normal complement problem on semisimple group algebra [Formula: see text] is examined. The normal complement problem of groups of order up to 16 in their corresponding unit groups [Formula: see text] has already been discussed. We have proved that up to isomorphism all the three non-abelian groups of order 18 and up to isomorphism all three non-abelian groups of order 20 do not have normal complement in their corresponding unit groups [Formula: see text].","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134948044","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 : 2023-10-04DOI: 10.1142/s179355712350211x
Clement Johnson Rayer, Ravi Sankar Jeyaraj
Let [Formula: see text] be commutative ring and [Formula: see text] be the set of all non-zero zero divisors of [Formula: see text]. Then [Formula: see text] is said to be the zero divisor graph if and only if [Formula: see text] where [Formula: see text] and [Formula: see text]. Graph energy [Formula: see text] is defined as the sum of the absolute eigenvalues of the adjacency matrix [Formula: see text], then [Formula: see text]. Wiener index [Formula: see text] is defined as the sum of all distance between pairs of vertices [Formula: see text] and [Formula: see text], then [Formula: see text]. In this paper, we compute the graph energy from the adjacency matrix of the zero divisor graph and the Wiener index from the zero divisor graph associated with commutative rings.
{"title":"Wiener Index and Graph Energy of Zero Divisor Graph for Commutative Rings","authors":"Clement Johnson Rayer, Ravi Sankar Jeyaraj","doi":"10.1142/s179355712350211x","DOIUrl":"https://doi.org/10.1142/s179355712350211x","url":null,"abstract":"Let [Formula: see text] be commutative ring and [Formula: see text] be the set of all non-zero zero divisors of [Formula: see text]. Then [Formula: see text] is said to be the zero divisor graph if and only if [Formula: see text] where [Formula: see text] and [Formula: see text]. Graph energy [Formula: see text] is defined as the sum of the absolute eigenvalues of the adjacency matrix [Formula: see text], then [Formula: see text]. Wiener index [Formula: see text] is defined as the sum of all distance between pairs of vertices [Formula: see text] and [Formula: see text], then [Formula: see text]. In this paper, we compute the graph energy from the adjacency matrix of the zero divisor graph and the Wiener index from the zero divisor graph associated with commutative rings.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135548632","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 : 2023-09-30DOI: 10.1142/s1793557123502042
Thodsaporn Kumduang, Songpon Sriwongsa
For fixed integers [Formula: see text] and [Formula: see text], we study the faithful representation of superassociative algebras by two kinds of functions of the arity [Formula: see text], the so called [Formula: see text]-commutative and [Formula: see text]-commutative. The automorphism on the algebra of all [Formula: see text]-commutative functions is determined. In general, an isomorphism from a superassociative system which consists of a family of nonempty sets and a family of operations satisfying the axiom of superassociativity to a system of full multiplace functions is discussed. Particularly, we also provide necessary and sufficient conditions under which a superassociative system and a system of [Formula: see text]-commutative functions are isomorphic. With these results, a close connection with the theory of terms and tree languages is described.
{"title":"Representations of superassociative algebras by commutative functions with different types","authors":"Thodsaporn Kumduang, Songpon Sriwongsa","doi":"10.1142/s1793557123502042","DOIUrl":"https://doi.org/10.1142/s1793557123502042","url":null,"abstract":"For fixed integers [Formula: see text] and [Formula: see text], we study the faithful representation of superassociative algebras by two kinds of functions of the arity [Formula: see text], the so called [Formula: see text]-commutative and [Formula: see text]-commutative. The automorphism on the algebra of all [Formula: see text]-commutative functions is determined. In general, an isomorphism from a superassociative system which consists of a family of nonempty sets and a family of operations satisfying the axiom of superassociativity to a system of full multiplace functions is discussed. Particularly, we also provide necessary and sufficient conditions under which a superassociative system and a system of [Formula: see text]-commutative functions are isomorphic. With these results, a close connection with the theory of terms and tree languages is described.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136272104","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 : 2023-09-30DOI: 10.1142/s179355712350208x
Manseob Lee, Jumi Oh
In this paper, we extend the expansivity, pseudo trajectory tracing property and hyperbolicity of linear dynamical systems for the random view point. We show that to a random linear cocycle [Formula: see text] it is expansive if and only if it has the generalized pseudo trajectory tracing property. Moreover, we show that [Formula: see text] is topologically stable if and only if it is structurally stable.
{"title":"Dynamic properties of random linear cocycles","authors":"Manseob Lee, Jumi Oh","doi":"10.1142/s179355712350208x","DOIUrl":"https://doi.org/10.1142/s179355712350208x","url":null,"abstract":"In this paper, we extend the expansivity, pseudo trajectory tracing property and hyperbolicity of linear dynamical systems for the random view point. We show that to a random linear cocycle [Formula: see text] it is expansive if and only if it has the generalized pseudo trajectory tracing property. Moreover, we show that [Formula: see text] is topologically stable if and only if it is structurally stable.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136271686","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 : 2023-09-30DOI: 10.1142/s1793557123502078
H. A. Abass, M. Aphane, M. O. Olayiwola
The Generalized mixed equilibrium problems, which includes the equilibrium and mixed equilibrium problem of monotone type mapping is considered in this paper with the fixed point of Bregman strongly nonexpansive mapping in the framework of real reflexive Banach space. We approximate the common solution of the system of generalized mixed equilibrium and fixed point problems for the finite family of Bregman strongly nonexpansive mappings using an inertial Halpern method. Using our iterative method, we prove a strong convergence result for solving the aforementioned problems. We also present some applications and numerical examples to demonstrate the performance of our iterative method. Our result improves and extends some important results presented by authors in the literature.
{"title":"An Inertial Method for Solving Systems of Generalized Mixed Equilibrium and Fixed Point Problems in Reflexive Banach Spaces","authors":"H. A. Abass, M. Aphane, M. O. Olayiwola","doi":"10.1142/s1793557123502078","DOIUrl":"https://doi.org/10.1142/s1793557123502078","url":null,"abstract":"The Generalized mixed equilibrium problems, which includes the equilibrium and mixed equilibrium problem of monotone type mapping is considered in this paper with the fixed point of Bregman strongly nonexpansive mapping in the framework of real reflexive Banach space. We approximate the common solution of the system of generalized mixed equilibrium and fixed point problems for the finite family of Bregman strongly nonexpansive mappings using an inertial Halpern method. Using our iterative method, we prove a strong convergence result for solving the aforementioned problems. We also present some applications and numerical examples to demonstrate the performance of our iterative method. Our result improves and extends some important results presented by authors in the literature.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136272101","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 : 2023-09-30DOI: 10.1142/s1793557123502030
Samir Lemita, Mohammed Ghaith Mahcene
By introducing matrices of linear bounded infinite-dimensional operators defined over some Banach spaces, and within the context of study, we make use of the definition of row strict diagonal dominance property to construct a generalization version of the Jacobi Under-Relaxation and the Successive Under-Relaxation iterative methods. The convergence analyses of the two new iterative methods are provided, and a numerical application to solve one Fredholm integral equation is presented to show the generalized methods’ effectiveness compared with their conventional opponents.
{"title":"Of a Couple of Relaxation Iterative Methods Suited for Matrices of Bounded Linear Operators Defined over Banach Spaces","authors":"Samir Lemita, Mohammed Ghaith Mahcene","doi":"10.1142/s1793557123502030","DOIUrl":"https://doi.org/10.1142/s1793557123502030","url":null,"abstract":"By introducing matrices of linear bounded infinite-dimensional operators defined over some Banach spaces, and within the context of study, we make use of the definition of row strict diagonal dominance property to construct a generalization version of the Jacobi Under-Relaxation and the Successive Under-Relaxation iterative methods. The convergence analyses of the two new iterative methods are provided, and a numerical application to solve one Fredholm integral equation is presented to show the generalized methods’ effectiveness compared with their conventional opponents.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136272096","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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