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SITT-ring properties in bi-amalgamated rings along ideals 沿理想双杂化环的sitt环性质
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1382
A. Aruldoss, C. Selvaraj
{"title":"SITT-ring properties in bi-amalgamated rings along ideals","authors":"A. Aruldoss, C. Selvaraj","doi":"10.56947/gjom.v15i1.1382","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1382","url":null,"abstract":"Let f: A → B and g: A → C be two ring homomorphisms and let J and J' be two ideals of B and C, respectively, such that f-1(J) = g-1(J'). In this paper, we give a characterization for the amalgamation of A with B along J with respect to f (denoted by A ⋈f J) to be a SITT-ring and also we give a characterization for the bi-amalgamation of A with (B, C) along (J, J') with respect to (f, g) (denoted by A ⋈f,g (J, J')) to be a SITT-ring. We also give some characterizations for strong weakly SIT-rings.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"15 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":"132174095","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
Evolution algebras satisfying train identity of degree 2 and exponent 3 满足2次和3次列恒等式的演化代数
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1387
Joseph Tenkodogo, Souleymane Savadogo, André Conseibo, Abdoulaye Dembega
{"title":"Evolution algebras satisfying train identity of degree 2 and exponent 3","authors":"Joseph Tenkodogo, Souleymane Savadogo, André Conseibo, Abdoulaye Dembega","doi":"10.56947/gjom.v15i1.1387","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1387","url":null,"abstract":"In this paper, we give the necessary and sufficient conditions for an evolution algebra to satisfy a train identity of degree 2 and exponent 3. We show that this class of algebras is a subclass of the Bernstein algebras of order 2. Then, we study the relations existing between these algebras and the Bernstein algebras as well as the power associative algebras. Moreover we give a classification in dimension ≤ 4 of evolution algebras satisfying strictly a train identity of degree 2 and exponent 3. Finally, we describe the derivations and automorphisms of these algebras.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"55 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":"128080380","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
Algebraic structure of plenary train algebras of rank 4 4阶全列代数的代数结构
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1386
Joseph Bayara, S. Coulibaly
{"title":"Algebraic structure of plenary train algebras of rank 4","authors":"Joseph Bayara, S. Coulibaly","doi":"10.56947/gjom.v15i1.1386","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1386","url":null,"abstract":"In this paper, we study plenary train algebras of rank 4 admitting an idempotent. We obtain the Peirce decomposition of these algebras relative to an idempotent and the product of the associated Peirce components. The effect of changing an idempotent is discussed under the e-stability hypothesis. We show that a back-crossing algebra is a plenary train algebra of rank 4 if and only if it is a principal train algebra of rank 4. Finally, we study the particular case of monogenic back-crossing train algebras.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"1 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":"131006952","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
Lucas generalized numbers in Narayana's cows sequence Lucas推广了Narayana奶牛序列中的数
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1381
Salifou Nikiema, Japhet Odjoumani
{"title":"Lucas generalized numbers in Narayana's cows sequence","authors":"Salifou Nikiema, Japhet Odjoumani","doi":"10.56947/gjom.v15i1.1381","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1381","url":null,"abstract":"Let {Nn}n≥0 be the Narayana's cows sequence given by N0 = 0, N1 = N2 = 1 and \u0000Nn+3 = Nn+2 + Nn, for integers n ≥ 0 \u0000and let {Un}n ≥ 0 be the generalized Lucas sequence with parameters integers a ≥1, b =±1 given by U0 = 0, U1 = 1 and \u0000Un+2 = aUn+1 + bUn, for integers n ≥ 0. \u0000In this paper we give effective bounds for the Diophantine equation Nm =Un, in positive unknowns m and n. We then solve explicitly that equation with Fibonacci, Pell and Balancing sequences cases.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"150 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":"134484057","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
Some questions on the distribution of prime gaps and some formulas involving prime gaps 关于素数间隙分布的几个问题及涉及素数间隙的一些公式
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1380
R. Jakimczuk
{"title":"Some questions on the distribution of prime gaps and some formulas involving prime gaps","authors":"R. Jakimczuk","doi":"10.56947/gjom.v15i1.1380","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1380","url":null,"abstract":"In this article we present some questions on the distribution of prime gaps. Apparently the solutions of these questions are very difficult. We also obtain some formulas involving prime gaps. Our results are valid for more general integer sequences.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"545 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":"124363434","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
General rotational surfaces in Euclidean 4-space with generalized 1-type Gauss map 欧几里得4空间中具有广义1型高斯映射的一般旋转曲面
Gulf Journal of Mathematics Pub Date : 2023-08-22 DOI: 10.56947/gjom.v15i1.1383
M. Sagdic, N. Turgay, E. Kiliç
{"title":"General rotational surfaces in Euclidean 4-space with generalized 1-type Gauss map","authors":"M. Sagdic, N. Turgay, E. Kiliç","doi":"10.56947/gjom.v15i1.1383","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1383","url":null,"abstract":"In this paper, we consider rotational surfaces in the Euclidean 4-space E4 with the profile curve contained in a 2-plane. We obtain some classification results of such surfaces in terms of having generalized 1-type Gauss map.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"48 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":"122924632","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 the base locus of linear systems of general double points 一般双点线性系统的基轨迹
Gulf Journal of Mathematics Pub Date : 2023-08-19 DOI: 10.56947/gjom.v15i1.1256
E. Ballico
{"title":"On the base locus of linear systems of general double points","authors":"E. Ballico","doi":"10.56947/gjom.v15i1.1256","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1256","url":null,"abstract":"Fix integers n ≥ 1, d ≥ 4 and  x>0 such that (n+1)(x-1) +Bin(n+2, 2) ≤ Bin(n+d, n). Take a general S ⊂ Pn such that #S=x and let B denote the scheme-theoretic base locus of |I2s(d)|, where 2S is the union of the double points with S as their reduction. Then 2S is the union of the connected components of B containing at least one point of S. We prove this theorem proving that a general union of x-1 double points and one triple point has no higher cohomology in degree d.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122175613","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
Totally (m, n)-paranormal operators 全(m, n)-超算子
Gulf Journal of Mathematics Pub Date : 2023-08-18 DOI: 10.56947/gjom.v15i1.1248
S. Ram, P. Dharmarha
{"title":"Totally (m, n)-paranormal operators","authors":"S. Ram, P. Dharmarha","doi":"10.56947/gjom.v15i1.1248","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1248","url":null,"abstract":"In this paper, we investigate the class of totally (m, n)-paranormal operators on Hilbert space and prove some additional properties of totally (m, n)-paranormal operators on Hilbert space. Also, we show that Weyl's theorem holds for operators in this class. Moreover, we also show that for totally (m, n)-paranormal operators, the Weyl spectrum satisfies the spectral mapping theorem.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123574719","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 open neighborhood energy of graphs 图的开邻域能
Gulf Journal of Mathematics Pub Date : 2023-08-18 DOI: 10.56947/gjom.v15i1.1122
H. K. A, Manilal K
{"title":"On open neighborhood energy of graphs","authors":"H. K. A, Manilal K","doi":"10.56947/gjom.v15i1.1122","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1122","url":null,"abstract":"The open neighborhood of a vertex u denoted by N(u) in a simple connected graph G is the collection of all vertices other than u and adjacent to u. In this paper, we introduce a square matrix of order n, called the open neighborhood matrix, ONM(G) of a graph G whose (i, j)th entry is |N(vi) ∩ N(vj)|/(di+dj) whenever vi~vj,  i≠ j; and zero otherwise, where di and dj, are the degrees of vi and vj respectively. We then establish the relationship between the connectedness of the graph G and the multiplicity of the eigenvalue zero of the matrix ONM(G), if it exists. Furthermore, we found the bounds for the largest open neighbourhood eigenvalue and open neighbourhood energy of graphs. \u0000 ","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128797538","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
Series involving Dirichlet Eta function 包含狄利克雷函数的级数
Gulf Journal of Mathematics Pub Date : 2023-08-18 DOI: 10.56947/gjom.v15i1.1135
Vuk Stojiljković
{"title":"Series involving Dirichlet Eta function","authors":"Vuk Stojiljković","doi":"10.56947/gjom.v15i1.1135","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1135","url":null,"abstract":"In this article, we obtain an integral representation for a remainder sum of the Dirichlet Eta function. We then obtain numerous generating functions and series concerning the usage of the obtained integral representation. Alternating Fibonacci sum of the partial sum of the Dirichlet Eta function has been obtained, as well as the squared version Fibonacci series concerning the sum. A generalized representation of the product of polynomials concerning the partial sum of the Dirichlet Eta function has been obtained. Numerous examples have been provided to showcase the derived results.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131775598","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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