Pub Date : 2024-07-10DOI: 10.56947/gjom.v17i1.2098
Youssef Fadil, Said Ait Temghart, C. Allalou, Mohamed Oukessou
This paper investigates the existence of weak solutions for (p,q)-Laplacian problems where p and q depend on the unknown solution. We focus on the case where p and q are local quantities. By means of a singular perturbation technique, we prove the existence of weak solutions for certain Dirichlet problem.
本文研究了 p 和 q 取决于未知解的（p,q）-拉普拉斯问题的弱解的存在性。我们重点研究 p 和 q 是局部量的情况。通过奇异扰动技术，我们证明了某些 Dirichlet 问题的弱解的存在性。
{"title":"Existence of weak solutions for a class of (p(u),q(u))-Laplacian problems","authors":"Youssef Fadil, Said Ait Temghart, C. Allalou, Mohamed Oukessou","doi":"10.56947/gjom.v17i1.2098","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2098","url":null,"abstract":"This paper investigates the existence of weak solutions for (p,q)-Laplacian problems where p and q depend on the unknown solution. We focus on the case where p and q are local quantities. By means of a singular perturbation technique, we prove the existence of weak solutions for certain Dirichlet problem.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"11 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141660894","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 : 2024-07-05DOI: 10.56947/gjom.v17i1.2000
I. Qaralleh, F. Mukhamedov
In this paper, we thoroughly investigate the local and 2-local derivations of a flow of quantumgenetic Lotka-Volterra algebras on M2(C) (FQGLV-A). The analysis is mainly geared towards understanding how specific parameter values influence the properties of these derivations. Our findings elucidate the structural intricacies of FQGLV-A algebras and bridge gaps in the current understanding of local and 2-local derivations. We prove that any local derivation is indeed a derivation. Furthermore, the set of2-local deviations coincide with the set of deviations.
{"title":"Local derivations and Rota-Baxter operators of quantum Lotka-Volterra algebras on M_2(C)","authors":"I. Qaralleh, F. Mukhamedov","doi":"10.56947/gjom.v17i1.2000","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2000","url":null,"abstract":"In this paper, we thoroughly investigate the local and 2-local derivations of a flow of quantumgenetic Lotka-Volterra algebras on M2(C) (FQGLV-A). The analysis is mainly geared towards understanding how specific parameter values influence the properties of these derivations. Our findings elucidate the structural intricacies of FQGLV-A algebras and bridge gaps in the current understanding of local and 2-local derivations. We prove that any local derivation is indeed a derivation. Furthermore, the set of2-local deviations coincide with the set of deviations.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674098","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 : 2024-07-01DOI: 10.56947/gjom.v17i1.2081
Mahmoud El Ahmadi, Mohamed Bouabdallah, A. Lamaizi
Our focus in this study revolves around investigating a Kirchhoff problem involving the fractional p(x)-Laplacian operator. The purpose is to study the existence and multiplicity of weak solutions for the above problem under appropriate hypotheses on functions f and m. By using the Mountain Pass Theorem with Cerami condition, we show the existence of non-trivial weak solution for the problem without assuming the Ambrosetti-Rabinowitz condition. Furthermore, our second purpose is to determine the precise positive interval of λ for which the above problem admits at least two nontrivial weak solutions. It should be noted that the existence of infinitely many weak solutions is proved by employing the Fountain Theorem.
本研究的重点是研究涉及分数 p(x)-Laplacian 算子的基尔霍夫问题。目的是研究在函数 f 和 m 的适当假设条件下，上述问题弱解的存在性和多重性。通过使用带有 Cerami 条件的山口定理，我们证明了在不假设 Ambrosetti-Rabinowitz 条件的情况下，该问题存在非三值弱解。此外，我们的第二个目的是确定λ 的精确正区间，对于该区间，上述问题至少有两个非难弱解。需要注意的是，无穷多个弱解的存在是通过福泉定理来证明的。
{"title":"Existence and multiplicity results for Kirchhoff-type superlinear problems involving the fractional p(x)-Laplacian satisfying (C)-condition","authors":"Mahmoud El Ahmadi, Mohamed Bouabdallah, A. Lamaizi","doi":"10.56947/gjom.v17i1.2081","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2081","url":null,"abstract":"Our focus in this study revolves around investigating a Kirchhoff problem involving the fractional p(x)-Laplacian operator. The purpose is to study the existence and multiplicity of weak solutions for the above problem under appropriate hypotheses on functions f and m. By using the Mountain Pass Theorem with Cerami condition, we show the existence of non-trivial weak solution for the problem without assuming the Ambrosetti-Rabinowitz condition. Furthermore, our second purpose is to determine the precise positive interval of λ for which the above problem admits at least two nontrivial weak solutions. It should be noted that the existence of infinitely many weak solutions is proved by employing the Fountain Theorem.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"20 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141703945","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 : 2024-07-01DOI: 10.56947/gjom.v17i1.2078
C. Darsana, P. Sini
In this paper, we study the properties of the lattice of c-structures. We define the concept of simple expansion and examine some of its properties. Additionally, we determine the automorphism group of the lattice of c-structures and explore the fixed points of the group of automorphisms.
本文研究了 c 结构晶格的性质。我们定义了简单展开的概念，并研究了它的一些性质。此外，我们还确定了 c 结构网格的自变群，并探讨了自变群的定点。
{"title":"Lattice of c-structures","authors":"C. Darsana, P. Sini","doi":"10.56947/gjom.v17i1.2078","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2078","url":null,"abstract":"In this paper, we study the properties of the lattice of c-structures. We define the concept of simple expansion and examine some of its properties. Additionally, we determine the automorphism group of the lattice of c-structures and explore the fixed points of the group of automorphisms.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"24 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141703039","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 : 2024-07-01DOI: 10.56947/gjom.v17i1.2082
Prasanta Malik, Saikat Das
In this paper we introduce the notion of ℑ-convergence of sequences of k-dimensional subspaces of an inner product space, where ℑ is an ideal of subsets of ℕ, the set of all natural numbers and k⊂ℕ. We also study some basic properties of this notion.
本文介绍了内积空间 k 维子空间序列的ℑ-收敛概念，其中ℑ是所有自然数的集合ℕ的理想子集，而 k⊂ℕ是所有自然数的集合。我们还将研究这一概念的一些基本性质。
{"title":"I- Convergence of sequences of subspaces in an inner product space","authors":"Prasanta Malik, Saikat Das","doi":"10.56947/gjom.v17i1.2082","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2082","url":null,"abstract":"In this paper we introduce the notion of ℑ-convergence of sequences of k-dimensional subspaces of an inner product space, where ℑ is an ideal of subsets of ℕ, the set of all natural numbers and k⊂ℕ. We also study some basic properties of this notion.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"51 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141712721","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 : 2024-07-01DOI: 10.56947/gjom.v17i1.2079
Hiren D. Patel
The rings considered in this article are commutative with non-zero identity which are not integral domains. Let R be a ring. Let Z(R) denote the set of all zero-divisors of R and we denote Z(R){0} by Z(R)∗. In this article, we introduce and investigate the power serieswise Armendariz graph of R denoted by PA(R). It is the undirected graph whose vertex set is Z(R[[X]])∗ and distinct vertices f(X)=∑i=0∞ aiXi and g(X)=∑j=0∞ bjXj are adjacent in PA(R) if and only if ai bj = 0 for all i and j. The aim of this article is to study the interplay between the ring-theoretic properties of R and the graph-theoretic properties of PA(R). We discuss some results on diameter, clique, and girth of PA(R).
本文所考虑的环都是具有非零特征的交换环，它们都不是积分域。让 R 是一个环。让 Z(R) 表示 R 的所有零分因子的集合，我们用 Z(R)∗ 表示 Z(R){0}。本文将介绍并研究 R 的幂级数阿门达尼兹图，用 PA(R) 表示。它是无向图，其顶点集为 Z(R[[X]])∗，并且当且仅当 ai bj = 0 for all i and j 时，不同顶点 f(X)=∑i=0∞ aiXi 和 g(X)=∑j=0∞ bjXj 在 PA(R) 中相邻。我们讨论了 PA(R) 的直径、簇和周长的一些结果。
{"title":"The power serieswise Armendariz graph of a commutative ring","authors":"Hiren D. Patel","doi":"10.56947/gjom.v17i1.2079","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2079","url":null,"abstract":"The rings considered in this article are commutative with non-zero identity which are not integral domains. Let R be a ring. Let Z(R) denote the set of all zero-divisors of R and we denote Z(R){0} by Z(R)∗. In this article, we introduce and investigate the power serieswise Armendariz graph of R denoted by PA(R). It is the undirected graph whose vertex set is Z(R[[X]])∗ and distinct vertices f(X)=∑i=0∞ aiXi and g(X)=∑j=0∞ bjXj are adjacent in PA(R) if and only if ai bj = 0 for all i and j. The aim of this article is to study the interplay between the ring-theoretic properties of R and the graph-theoretic properties of PA(R). We discuss some results on diameter, clique, and girth of PA(R).","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"23 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141690303","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 : 2024-07-01DOI: 10.56947/gjom.v17i1.2076
Gideon Effiong, Temitope Gbolahan Jaiyeola, Martin Chucks Obi, L. S. Akinola
A loop (Q,∙) is called a Basarab loop if the identities: (x ∙ yxρ)∙(xz)=x ∙ yz and (yx) ∙ (xλ z∙x)=yz ∙ x hold. The holomorphy of a Basarab loop Q was investigated with respect to a group A(Q)$ of automorphisms of the loop. Some necessary and sufficient conditions for an A(Q)-holomorph of a loop Q to be a left (right) Basarab loop or Basarab loop were established. Specifically, the A(Q)-holomorph of a loop Q was shown to be a left (right) Basarab loop if and only if Q is a left (right) Basarab loop and every element of A(Q) is left (right) regular. The A(Q)-holomorph of a loop Q was shown to be a Basarab loop if and only if Q is a Basarab loop, every element of A(Q) is both left and right nuclear and the A(Q)-generalized inner mappings of Q take some particular forms. These results were expressed in form of commutative diagrams. In any left (right) Basarab loop or Basarab loop Q, it was shown that the set of α ∈ A(Q) with four autotopic characterizations actually form normal subgroups of A(Q).
{"title":"Holomorphy of Basarab Loops","authors":"Gideon Effiong, Temitope Gbolahan Jaiyeola, Martin Chucks Obi, L. S. Akinola","doi":"10.56947/gjom.v17i1.2076","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2076","url":null,"abstract":"A loop (Q,∙) is called a Basarab loop if the identities: (x ∙ yxρ)∙(xz)=x ∙ yz and (yx) ∙ (xλ z∙x)=yz ∙ x hold. The holomorphy of a Basarab loop Q was investigated with respect to a group A(Q)$ of automorphisms of the loop. Some necessary and sufficient conditions for an A(Q)-holomorph of a loop Q to be a left (right) Basarab loop or Basarab loop were established. Specifically, the A(Q)-holomorph of a loop Q was shown to be a left (right) Basarab loop if and only if Q is a left (right) Basarab loop and every element of A(Q) is left (right) regular. The A(Q)-holomorph of a loop Q was shown to be a Basarab loop if and only if Q is a Basarab loop, every element of A(Q) is both left and right nuclear and the A(Q)-generalized inner mappings of Q take some particular forms. These results were expressed in form of commutative diagrams. In any left (right) Basarab loop or Basarab loop Q, it was shown that the set of α ∈ A(Q) with four autotopic characterizations actually form normal subgroups of A(Q).","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"2001 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141707595","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 : 2024-07-01DOI: 10.56947/gjom.v17i1.2080
Hassan Khaider, Fatima Ouidirne, Achraf Azanzal, C. Allalou
In this paper, we first establish the existence and uniqueness of solutions of the stochastic incompressible Hall-magnetohydrodynamic system in the deterministic case in Fourier-Besov-Morrey critical spaces. In the second part, we show the existence and uniqueness of solutions in the stochastic case.
{"title":"Well-posedness for the stochastic incompressible Hall-magnetohydrodynamic system","authors":"Hassan Khaider, Fatima Ouidirne, Achraf Azanzal, C. Allalou","doi":"10.56947/gjom.v17i1.2080","DOIUrl":"https://doi.org/10.56947/gjom.v17i1.2080","url":null,"abstract":"In this paper, we first establish the existence and uniqueness of solutions of the stochastic incompressible Hall-magnetohydrodynamic system in the deterministic case in Fourier-Besov-Morrey critical spaces. In the second part, we show the existence and uniqueness of solutions in the stochastic case.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141705643","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 : 2024-02-25DOI: 10.56947/gjom.v16i1.1430
Rene Erín Castillo, Juan E. Nápoles Valdés, Héctor Chaparro
In this paper, we introduce the Ω-derivative, which generalizes the classical concept of derivative. Main properties of this new derivative are revised. We also study Ω-differential equations and some of its applications.
{"title":"Omega derivative","authors":"Rene Erín Castillo, Juan E. Nápoles Valdés, Héctor Chaparro","doi":"10.56947/gjom.v16i1.1430","DOIUrl":"https://doi.org/10.56947/gjom.v16i1.1430","url":null,"abstract":"In this paper, we introduce the Ω-derivative, which generalizes the classical concept of derivative. Main properties of this new derivative are revised. We also study Ω-differential equations and some of its applications.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"12 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140433323","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 : 2024-02-25DOI: 10.56947/gjom.v16i1.1371
Ahmed Lahmoudi, E. Lakhel, Salah Hajji
In this paper, we study the approximate controllability of certain class of impulsive evolution stochastic functional differential equations, with variable delays, driven by a fractional Brownian motion in a separable real Hilbert space. We derive a new set of sufficient conditions for approximate controllability using a stochastic analysis of fractional Brownian motion with Hurst parameter H ∈ (1/2,1) and a Schaefer's fixed point theorem. An example is considered at the end of the paper to illustrate the obtained abstract results.
{"title":"Approximate controllability of impulsive evolution stochastic functional differential equations driven by a fractional Brownian motion","authors":"Ahmed Lahmoudi, E. Lakhel, Salah Hajji","doi":"10.56947/gjom.v16i1.1371","DOIUrl":"https://doi.org/10.56947/gjom.v16i1.1371","url":null,"abstract":"In this paper, we study the approximate controllability of certain class of impulsive evolution stochastic functional differential equations, with variable delays, driven by a fractional Brownian motion in a separable real Hilbert space. We derive a new set of sufficient conditions for approximate controllability using a stochastic analysis of fractional Brownian motion with Hurst parameter H ∈ (1/2,1) and a Schaefer's fixed point theorem. An example is considered at the end of the paper to illustrate the obtained abstract results.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"26 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140432231","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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