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A note on Wedderburn and Hasse theorems 关于韦德伯恩和哈塞定理的说明
Gulf Journal of Mathematics Pub Date : 2024-02-25 DOI: 10.56947/gjom.v16i1.1419
Ilias Elmouki, S. Abdelalim
{"title":"A note on Wedderburn and Hasse theorems","authors":"Ilias Elmouki, S. Abdelalim","doi":"10.56947/gjom.v16i1.1419","DOIUrl":"https://doi.org/10.56947/gjom.v16i1.1419","url":null,"abstract":"Wedderburn and Hasse theorems have always fascinated many algebraists as there are just very few versions of their proofs and that are somehow not easy to follow because they contain other results inside. In this note, we aim to look at their proofs again but nowwith more simplified versions that include sufficient details in order to let them be understandable for most readers in the subjects of finite fields and elliptic curves. In the proof of Wedderburn’s theorem, we succeed to show how it is equivalent to define either a stabilizer or centralizer of non-central elements and that helps to consider the equation on the order of group by using interchangeably the index of its subgroup and the order of the orbit. As for Hasse’s theorem, we provide a short proof in just two paragraphs with a recall of the most important results that have been used, and then, we state three of its version with an explanation of how this all leads in the end to the need of an algorithm like the one of René Schoof in 1985.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"33 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140433310","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}
引用次数: 0
Global existence of a pair of coupled Cahn-Hilliard equations with nondegenerate mobility and logarithmic potential 具有非enerate流动性和对数势能的一对耦合卡恩-希利亚德方程的全局存在性
Gulf Journal of Mathematics Pub Date : 2024-02-25 DOI: 10.56947/gjom.v16i1.1368
A. Harfash, Ghufran A. Al-Musawi
{"title":"Global existence of a pair of coupled Cahn-Hilliard equations with nondegenerate mobility and logarithmic potential","authors":"A. Harfash, Ghufran A. Al-Musawi","doi":"10.56947/gjom.v16i1.1368","DOIUrl":"https://doi.org/10.56947/gjom.v16i1.1368","url":null,"abstract":"We conducted a mathematical investigation on a system of interconnected Cahn-Hilliard equations featuring a logarithmic potential, nondegenerate mobility, and homogeneous Neumann boundary conditions. This system emerges from a model depicting the phase separation of a binary liquid mixture in a thin film. Assuming certain conditions on the initial data, we successfully established the existence, uniqueness, and stability estimates for the weak solution. Our approach involved initially replacing the logarithmic potential with a smooth counterpart, resulting in the regularization of the original problem (Q) into a regularized problem (Qε). Utilizing the Faedo-Galerkin method and compactness arguments, we demonstrated the existence and uniqueness of a solution for (Qε). Subsequently, by letting ε approach zero, we attained the existence of a solution for the original problem (Q). Additionally, we addressed higher regularity aspects of the weak solutions for both (Q) and (Qε). Employing the standard regularity theory for elliptic problems and introducing additional assumptions regarding the domain's boundary and the initial data, we established that the weak solutions belong to higher-order Sobolev spaces.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"20 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140432224","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}
引用次数: 0
Common properties of the operator equations in ultrametric specrtal theory 超对称规范理论中算子方程的共同特性
Gulf Journal of Mathematics Pub Date : 2024-02-25 DOI: 10.56947/gjom.v16i1.1432
J. Ettayb
{"title":"Common properties of the operator equations in ultrametric specrtal theory","authors":"J. Ettayb","doi":"10.56947/gjom.v16i1.1432","DOIUrl":"https://doi.org/10.56947/gjom.v16i1.1432","url":null,"abstract":"Let X and Y be two ultrametric Banach spaces over K. Let A,D ∈ B(X,Y) and B,C ∈ B(Y,X) such that ABA=ACA (resp. ACD=DBD and DBA=ACA). In this paper, the operator equation ABA=ACA is studied, and the common operator properties of AC-IY and BA-IX are described. In particular, it is proved that N(IY-AC) is complemented in Y if and only if N(IX-BA) is complemented in X. Moreover, the approach is generalized (i.e., CD=DBD and DBA=ACA) for considering relationships between the properties IY-AC and IX-BD. Finally, several illustrative examples are provided.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"27 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140433149","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}
引用次数: 0
Core of a convex mixture set and convex functions 凸混合集的核心和凸函数
Gulf Journal of Mathematics Pub Date : 2023-11-12 DOI: 10.56947/gjom.v15i2.1415
Ismat Beg
{"title":"Core of a convex mixture set and convex functions","authors":"Ismat Beg","doi":"10.56947/gjom.v15i2.1415","DOIUrl":"https://doi.org/10.56947/gjom.v15i2.1415","url":null,"abstract":"We broach the notions of face, core and convex function of a convex mixture set. A version of famous Karush-Kuhn-Tucker theorem is proved. Several examples to illustrate are also given.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139279304","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}
引用次数: 0
A convexity in R^2 with river metric R^2 中的凸性与河流度量
Gulf Journal of Mathematics Pub Date : 2023-11-12 DOI: 10.56947/gjom.v15i2.1226
A. Rekic-Vukovic, N. Okičić
{"title":"A convexity in R^2 with river metric","authors":"A. Rekic-Vukovic, N. Okičić","doi":"10.56947/gjom.v15i2.1226","DOIUrl":"https://doi.org/10.56947/gjom.v15i2.1226","url":null,"abstract":"In this paper we consider the space R2 with the river metric d* and different types of convexity of this space. We define W-convex structure in (R2, d*) and we give the complete characterization of the convex sets in this space. We consider some measures of noncompactness and we give the moduli of noncompactness for considered measures on this space.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"103 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139279520","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}
引用次数: 0
A problem with periodic boundary conditions for the non-Fourier heat equation 非傅里叶热方程的周期性边界条件问题
Gulf Journal of Mathematics Pub Date : 2023-11-12 DOI: 10.56947/gjom.v15i2.1373
Jozil Takhirov
{"title":"A problem with periodic boundary conditions for the non-Fourier heat equation","authors":"Jozil Takhirov","doi":"10.56947/gjom.v15i2.1373","DOIUrl":"https://doi.org/10.56947/gjom.v15i2.1373","url":null,"abstract":"All diffusion equations are based on the infinite velocity of potential fields, which leads to well-known paradoxes. Consequently, in non-stationary processes, the evolution of these quantities do not completely obey the above equations due to the lack of parameters in them that take into account the finite rate of potential growth.In the heat conduction theory, numerous generalizations of the Fourier law are used as a remedy for these issues. The article gives a brief overview of generalizations of the Fourier law. Some mathematical issues of well-posed boundary value problems for the Guyer-Krumhansl model are discussed. As an application, a boundary value problem for a general quasilinear equation with periodic boundary conditions is considered. Schauder-type a priori estimates are established and the uniqueness of the solution is proved.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"62 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139279571","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}
引用次数: 0
Differentiable Ostrowski type tensorial norm inequality for continuous functions of selfadjoint operators in Hilbert spaces 希尔伯特空间中自相关算子连续函数的可微奥斯特洛夫斯基式张量规范不等式
Gulf Journal of Mathematics Pub Date : 2023-11-12 DOI: 10.56947/gjom.v15i2.1247
Vuk Stojiljković, S. Dragomir
{"title":"Differentiable Ostrowski type tensorial norm inequality for continuous functions of selfadjoint operators in Hilbert spaces","authors":"Vuk Stojiljković, S. Dragomir","doi":"10.56947/gjom.v15i2.1247","DOIUrl":"https://doi.org/10.56947/gjom.v15i2.1247","url":null,"abstract":"In this paper several tensorial norm inequalities of Ostrowski type for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities are obtained with variations due to the convexity properties of the mapping f.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"26 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139279314","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}
引用次数: 0
On ideal convergence of double sequences in neutrosophic normed spaces 论中性规范空间中双序列的理想收敛性
Gulf Journal of Mathematics Pub Date : 2023-11-12 DOI: 10.56947/gjom.v15i2.1394
C. Choudhury, Carlos Granados
{"title":"On ideal convergence of double sequences in neutrosophic normed spaces","authors":"C. Choudhury, Carlos Granados","doi":"10.56947/gjom.v15i2.1394","DOIUrl":"https://doi.org/10.56947/gjom.v15i2.1394","url":null,"abstract":"In this paper, we introduce the notion of I2 and I∗2−convergence of double sequences in neutrosophic normed spaces mainly as a generalization of statistical convergence of double sequences. We investigate a few fundamental properties and study the relationship between the two notions. We also introduce and investigate the concept of I2 and I∗2−Cauchy sequence of double sequences and show that the condition (AP2) plays a crucial role to study the interrelationship between them.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"13 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139279325","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}
引用次数: 0
Bi-amalgamations subject to j-clean and weakly j-clean properties 符合 j-清洁和弱 j-清洁特性的双汞齐化
Gulf Journal of Mathematics Pub Date : 2023-11-12 DOI: 10.56947/gjom.v15i2.1439
Khalid Adarbeh, Mohammad Adarbeh
{"title":"Bi-amalgamations subject to j-clean and weakly j-clean properties","authors":"Khalid Adarbeh, Mohammad Adarbeh","doi":"10.56947/gjom.v15i2.1439","DOIUrl":"https://doi.org/10.56947/gjom.v15i2.1439","url":null,"abstract":"This paper establishes the necessary and sufficient conditions for a bi-amalgamation to inherit the J-clean and weakly J-clean properties in the commutative setting. The new results recover previous works carried on these rings in amalgamations and trivial extensions, also, they are used to provide new examples and counterexamples of J-clean and weakly J-clean rings arise as bi-amalgamations.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"39 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139279679","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}
引用次数: 0
On Lie-Rinehart-Poisson algebras structures 关于Lie-Rinehart-Poisson代数结构
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1384
N. M. Moukala, B. G. R. Bossoto
{"title":"On Lie-Rinehart-Poisson algebras structures","authors":"N. M. Moukala, B. G. R. Bossoto","doi":"10.56947/gjom.v15i1.1384","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1384","url":null,"abstract":"We define the Schouten-Nijenhuis bracket on the algebra of the module of Kahler differentials. We give the main features of Poisson manifolds by using the universal property of derivation. We prove the equivalence between a Lie-Rinehart algebra structure and a Poisson structure and we recover Lichnerowicz's notion of Poisson manifold. We show that a symplectic Lie-Rinehart algebra structure induce a nondegenerate Poisson structure and conversely.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125177436","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}
引用次数: 0
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