In this paper, we establish some inequalities for a more general class of polynomials P(S(z)), where P(z) = ∑ ajzj and S(z) = ∑ bjzj of degree n and m respectively. These results not only generalize the results due to Dubinin [ J. Math. Sci., 143 (2007), 3069-3076] but also refine a result due to Shah and Liman [ NFAA, 9(2004), 223-232].
{"title":"Inequalities for a class of composite polynomials","authors":"Mohd Yousf Mir, W. M. Shah","doi":"10.56947/gjom.v14i1.946","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.946","url":null,"abstract":"In this paper, we establish some inequalities for a more general class of polynomials P(S(z)), where P(z) = ∑ ajzj and S(z) = ∑ bjzj of degree n and m respectively. These results not only generalize the results due to Dubinin [ J. Math. Sci., 143 (2007), 3069-3076] but also refine a result due to Shah and Liman [ NFAA, 9(2004), 223-232].","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115225272","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}
Let T be a strongly Laskerian domain containing a field K as a subring. Let I be a non-zero proper ideal of T. Let D be a subring of K. The aim of this article is to determine necessary and sufficient conditions in order that (D + I, K + I) to be an S-Laskerian pair.
设T是包含域K作为子域的强拉斯克定义域。设I是t的非零固有理想，设D是K的子理想，本文的目的是确定(D + I, K + I)是S-Laskerian对的充分必要条件。
{"title":"When is (D + I, K +I) an S-Laskerian pair?","authors":"S. Visweswaran","doi":"10.56947/gjom.v14i1.992","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.992","url":null,"abstract":"Let T be a strongly Laskerian domain containing a field K as a subring. Let I be a non-zero proper ideal of T. Let D be a subring of K. The aim of this article is to determine necessary and sufficient conditions in order that (D + I, K + I) to be an S-Laskerian pair.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115619282","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}
Z. Mitrović, Gunaseelan Mani, A. Gnanaprakasam, R. George
In this manuscript, owing to the concept of bicomplex b-metric spaces, we prove common fixed point theorem in bicomplex b-metric spaces. In order to strengthen our main results, a suitable example is presented. More over, the results we obtained is supplement and improve on previous research findings. A fruitful application is also supplied to endorse our outcomes
{"title":"The existence of a solution of a nonlinear Fredholm integral equations over bicomplex b-metric spaces","authors":"Z. Mitrović, Gunaseelan Mani, A. Gnanaprakasam, R. George","doi":"10.56947/gjom.v14i1.984","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.984","url":null,"abstract":"In this manuscript, owing to the concept of bicomplex b-metric spaces, we prove common fixed point theorem in bicomplex b-metric spaces. In order to strengthen our main results, a suitable example is presented. More over, the results we obtained is supplement and improve on previous research findings. A fruitful application is also supplied to endorse our outcomes","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130716241","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}
Let F⊂ P2× P2v be the 3-dimensional flag. Let π1 F→ P2 and π2 F→ P2v be the projections. For all u,v ∈N{(0,0)} let M(u,v) denote the set of all curves π1-1(F) ∪ π2-1(E) such that π1-1(F) ∩ π2-1(E)=∅, #F=v and #E=u. Any A∈ M(u,v) has u+v connected components, all of them smooth and rational and embedded as lines by the Segre embedding of F⊂ P2× P2v. In this paper we study the bigraded Hilbert function H0(IA(a,b)), (a,b)∈N2, for a general A∈M(u,v). We also give geometric properties of IA(a,b) (spannedness and a uniqueness result for non-general A∈ M(u,v)).
{"title":"The bigraded Hilbert function of unions of lines in the 3-dimensional flag variety","authors":"E. Ballico","doi":"10.56947/gjom.v14i1.883","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.883","url":null,"abstract":"Let F⊂ P2× P2v be the 3-dimensional flag. Let π1 F→ P2 and π2 F→ P2v be the projections. For all u,v ∈N{(0,0)} let M(u,v) denote the set of all curves π1-1(F) ∪ π2-1(E) such that π1-1(F) ∩ π2-1(E)=∅, #F=v and #E=u. Any A∈ M(u,v) has u+v connected components, all of them smooth and rational and embedded as lines by the Segre embedding of F⊂ P2× P2v. In this paper we study the bigraded Hilbert function H0(IA(a,b)), (a,b)∈N2, for a general A∈M(u,v). We also give geometric properties of IA(a,b) (spannedness and a uniqueness result for non-general A∈ M(u,v)).","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114334070","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}
In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied and given some properties. An example is constructed for an invariant submanifold of a generalized Kenmotsu manifold. In addition, integrabilities of invariant distribution is investigated, and some theorems are given related to curvature tensor and the second fundamental form in invariant submanifolds of a generalized Kenmotsu manifold. Moreover, semi-parallel and 2-semi-parallel invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on semi-parallel and 2-semi-parallel invariant submanifolds of a generalized Kenmotsu manifold to be totally geodesic.
{"title":"Some submanifolds of generalized Kenmotsu manifolds","authors":"R. Sarı, A. Turgut Vanlı","doi":"10.56947/gjom.v14i1.908","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.908","url":null,"abstract":"In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied and given some properties. An example is constructed for an invariant submanifold of a generalized Kenmotsu manifold. In addition, integrabilities of invariant distribution is investigated, and some theorems are given related to curvature tensor and the second fundamental form in invariant submanifolds of a generalized Kenmotsu manifold. Moreover, semi-parallel and 2-semi-parallel invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on semi-parallel and 2-semi-parallel invariant submanifolds of a generalized Kenmotsu manifold to be totally geodesic.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124678747","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}
The Daftardar-Gejji Jafari Method (DGJM) has been used extensively in the recent one and a half decades to solve various non-linear equations such as algebraic equations, integral equations, partial differential equations, ordinary and fractional differential equations and so on. In this paper, we present a new time-efficient algorithm for DGJM for solving non-linear fractional foam drainage and Zakharov-Kuznetsov equations. We compare the DGJM solutions with those obtained by the Adomian decomposition method and the homotopy perturbation method. The obtained results reveal that the new algorithm of DGJM is more effective and time-efficient for predicting the solutions to such problems that too without calculating tedious calculations such as finding Adomian's polynomials and constructing homotopy function.
{"title":"Solutions of fractional foam drainage and Zakharov-Kuznetsov equations using a new algorithm","authors":"Manoj Kumar","doi":"10.56947/gjom.v14i1.884","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.884","url":null,"abstract":"The Daftardar-Gejji Jafari Method (DGJM) has been used extensively in the recent one and a half decades to solve various non-linear equations such as algebraic equations, integral equations, partial differential equations, ordinary and fractional differential equations and so on. In this paper, we present a new time-efficient algorithm for DGJM for solving non-linear fractional foam drainage and Zakharov-Kuznetsov equations. We compare the DGJM solutions with those obtained by the Adomian decomposition method and the homotopy perturbation method. The obtained results reveal that the new algorithm of DGJM is more effective and time-efficient for predicting the solutions to such problems that too without calculating tedious calculations such as finding Adomian's polynomials and constructing homotopy function.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131994869","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}
The present article is designed to deal with the existence of Finsler space’s reversible geodesics with generalized (α, β)-metric. we find the criteria for a Finsler space F defined on M to be reversible geodesics. We will investigate the various geometrical characteristics of F using reversible geodesics and shown that the Finsler metric F generates a weighted quasi-metric dF defined on M. Also, we will examine the T-tensor for this (α, β)-metric.
{"title":"Reversible geodesics of a Finsler space with generalized (α, β)-metric","authors":"Pradeep Kumar, Ajaykumar Ar","doi":"10.56947/gjom.v14i1.842","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.842","url":null,"abstract":"The present article is designed to deal with the existence of Finsler space’s reversible geodesics with generalized (α, β)-metric. we find the criteria for a Finsler space F defined on M to be reversible geodesics. We will investigate the various geometrical characteristics of F using reversible geodesics and shown that the Finsler metric F generates a weighted quasi-metric dF defined on M. Also, we will examine the T-tensor for this (α, β)-metric.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114861796","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}
In this paper, we introduce and investigate the transfer of the property of coherence to the bi-amalgamation module M⋈φ,ψ(JN, J'P). We provide necessary and sufficient conditions for M⋈φ,ψ(JN, J'P) to be a coherent module.
{"title":"Coherence properties in bi-amalgamated modules","authors":"Selvaraj Chelliah, A. Aruldoss, B. Davvaz","doi":"10.56947/gjom.v14i1.913","DOIUrl":"https://doi.org/10.56947/gjom.v14i1.913","url":null,"abstract":"In this paper, we introduce and investigate the transfer of the property of coherence to the bi-amalgamation module M⋈φ,ψ(JN, J'P). We provide necessary and sufficient conditions for M⋈φ,ψ(JN, J'P) to be a coherent module.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123236748","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}
K. S. K. Krishnamurthy, N. David, K. G. Subramanian
A dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph dominates every vertex of some color class. The dominator chromatic number of G is the minimum number of color classes in a dominator coloring of G. When operation on graphs is performed on classes of graphs result from the new class of graphs are obtained. The neighborhood corona is one such operation on graphs, having interesting applications as well. In this paper we study this operation on certain graph classes and discuss the bounds in terms of domination number and dominator chromatic number.
{"title":"Domination and dominator coloring of neighborhood corona of certain graphs","authors":"K. S. K. Krishnamurthy, N. David, K. G. Subramanian","doi":"10.56947/gjom.v13i2.811","DOIUrl":"https://doi.org/10.56947/gjom.v13i2.811","url":null,"abstract":"A dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph dominates every vertex of some color class. The dominator chromatic number of G is the minimum number of color classes in a dominator coloring of G. When operation on graphs is performed on classes of graphs result from the new class of graphs are obtained. The neighborhood corona is one such operation on graphs, having interesting applications as well. In this paper we study this operation on certain graph classes and discuss the bounds in terms of domination number and dominator chromatic number.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"534 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123067136","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}
We study zero-dimensional linearly dependent subschemes W of the Segre variety with deg(W)≤5. If W is connected and curvilinear with arbitrary degree we give a strong restriction on the number of factors of the concise Segre containing W.
{"title":"Curvilinear subschemes of Segre varieties and the cactus rank","authors":"E. Ballico","doi":"10.56947/gjom.v13i2.902","DOIUrl":"https://doi.org/10.56947/gjom.v13i2.902","url":null,"abstract":"We study zero-dimensional linearly dependent subschemes W of the Segre variety with deg(W)≤5. If W is connected and curvilinear with arbitrary degree we give a strong restriction on the number of factors of the concise Segre containing W.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115358442","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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