Pub Date : 2021-04-13DOI: 10.1108/AJMS-09-2020-0060
G. Shanker, Ankit Yadav
PurposeThe purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.Design/methodology/approachThe paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.FindingsThe geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.Originality/valueAll results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.
{"title":"An investigation on the existence of warped product irrotational screen-real lightlike submanifolds of metallic semi-Riemannian manifolds","authors":"G. Shanker, Ankit Yadav","doi":"10.1108/AJMS-09-2020-0060","DOIUrl":"https://doi.org/10.1108/AJMS-09-2020-0060","url":null,"abstract":"PurposeThe purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.Design/methodology/approachThe paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.FindingsThe geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.Originality/valueAll results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"ahead-of-print 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43016830","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 : 2021-04-06DOI: 10.1108/AJMS-12-2020-0127
S. Chaubey, U. De
PurposeThe authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold.Design/methodology/approachThe authors have used the tensorial approach to achieve the goal.FindingsA second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.Originality/valueThe authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.
{"title":"Three-dimensional trans-Sasakian manifolds and solitons","authors":"S. Chaubey, U. De","doi":"10.1108/AJMS-12-2020-0127","DOIUrl":"https://doi.org/10.1108/AJMS-12-2020-0127","url":null,"abstract":"PurposeThe authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold.Design/methodology/approachThe authors have used the tensorial approach to achieve the goal.FindingsA second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.Originality/valueThe authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49007610","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 : 2021-04-05DOI: 10.1108/AJMS-10-2020-0097
S. Ssekajja
PurposeThe author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1.Design/methodology/approachThe autho
Pub Date : 2021-03-30DOI: 10.1108/AJMS-09-2020-0058
H. Debela
PurposeThe purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.Design/methodology/approachThis study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.FindingsThe stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.Originality/valueIn this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.
{"title":"Robust numerical method for singularly perturbed differential equations having both large and small delay","authors":"H. Debela","doi":"10.1108/AJMS-09-2020-0058","DOIUrl":"https://doi.org/10.1108/AJMS-09-2020-0058","url":null,"abstract":"PurposeThe purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.Design/methodology/approachThis study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.FindingsThe stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.Originality/valueIn this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48066505","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 : 2021-03-26DOI: 10.1108/AJMS-10-2020-0085
H. Manjunatha, S. Narasimhamurthy, Z. Nekouee
PurposeThe purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.Design/methodology/approachThis paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.FindingsThe Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.Originality/valueThe findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.
{"title":"Geometric properties of the Bertotti–Kasner space-time","authors":"H. Manjunatha, S. Narasimhamurthy, Z. Nekouee","doi":"10.1108/AJMS-10-2020-0085","DOIUrl":"https://doi.org/10.1108/AJMS-10-2020-0085","url":null,"abstract":"PurposeThe purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.Design/methodology/approachThis paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.FindingsThe Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.Originality/valueThe findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48320780","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 : 2021-03-09DOI: 10.1108/AJMS-08-2020-0042
A. Sarkar
The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain.,For positive and bounded initial data, the authors study the initial zero-boundary value problem.,The findings of this study showed the complete extinction of a continuous weak solution at a finite time.,The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.
{"title":"Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type","authors":"A. Sarkar","doi":"10.1108/AJMS-08-2020-0042","DOIUrl":"https://doi.org/10.1108/AJMS-08-2020-0042","url":null,"abstract":"The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain.,For positive and bounded initial data, the authors study the initial zero-boundary value problem.,The findings of this study showed the complete extinction of a continuous weak solution at a finite time.,The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44069103","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 : 2021-03-05DOI: 10.1108/AJMS-08-2020-0044
J. Srivastava
PurposeIn this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.Design/methodology/approachThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.FindingsShowed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.Originality/valueThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.
{"title":"Introduction of new Picard–S hybrid iteration with application and some results for nonexpansive mappings","authors":"J. Srivastava","doi":"10.1108/AJMS-08-2020-0044","DOIUrl":"https://doi.org/10.1108/AJMS-08-2020-0044","url":null,"abstract":"PurposeIn this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.Design/methodology/approachThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.FindingsShowed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.Originality/valueThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44473483","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 : 2021-03-02DOI: 10.1108/AJMS-10-2020-0086
S. Ramdane, A. Guezane-Lakoud
PurposeThe paper deals with the existence of positive solutions for a coupled system of nonlinear fractional differential equations with p-Laplacian operator and involving both right Riemann–Liouville and left Caputo-type fractional derivatives. The existence results are obtained by the help of Guo–Krasnosel'skii fixed-point theorem on a cone in the sublinear case. In addition, an example is included to illustrate the main results.Design/methodology/approachFixed-point theorems.FindingsNo finding.Originality/valueThe obtained results are original.
{"title":"Existence of positive solutions for p-Laplacian systems involving left and right fractional derivatives","authors":"S. Ramdane, A. Guezane-Lakoud","doi":"10.1108/AJMS-10-2020-0086","DOIUrl":"https://doi.org/10.1108/AJMS-10-2020-0086","url":null,"abstract":"PurposeThe paper deals with the existence of positive solutions for a coupled system of nonlinear fractional differential equations with p-Laplacian operator and involving both right Riemann–Liouville and left Caputo-type fractional derivatives. The existence results are obtained by the help of Guo–Krasnosel'skii fixed-point theorem on a cone in the sublinear case. In addition, an example is included to illustrate the main results.Design/methodology/approachFixed-point theorems.FindingsNo finding.Originality/valueThe obtained results are original.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43175401","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 : 2021-02-25DOI: 10.1108/AJMS-08-2020-0039
Bikash Barman, Kukil Kalpa Rajkhowa
PurposeThe authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R.Design/methodology/approachThe method is theoretical.FindingsThe authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found.Originality/valueThe paper is original.
{"title":"Nonessential sum graph of an Artinian ring","authors":"Bikash Barman, Kukil Kalpa Rajkhowa","doi":"10.1108/AJMS-08-2020-0039","DOIUrl":"https://doi.org/10.1108/AJMS-08-2020-0039","url":null,"abstract":"PurposeThe authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R.Design/methodology/approachThe method is theoretical.FindingsThe authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found.Originality/valueThe paper is original.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62021580","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 : 2021-02-16DOI: 10.1108/AJMS-10-2020-0088
Rimah Amami, M. Pontier, Hani Abidi
PurposeThe purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.Design/methodology/approachThe main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.FindingsIn this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.Originality/valueIn this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.
{"title":"Infinite horizon impulse control problem with jumps and continuous switching costs","authors":"Rimah Amami, M. Pontier, Hani Abidi","doi":"10.1108/AJMS-10-2020-0088","DOIUrl":"https://doi.org/10.1108/AJMS-10-2020-0088","url":null,"abstract":"PurposeThe purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.Design/methodology/approachThe main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.FindingsIn this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.Originality/valueIn this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42213560","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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