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Looped fundamental group of weighted graphs 加权图的环基群
IF 0.7
Afrika Matematika Pub Date : 2025-09-16 DOI: 10.1007/s13370-025-01376-9
Sahawat Wongkhunen, Pongdate Montagantirud
{"title":"Looped fundamental group of weighted graphs","authors":"Sahawat Wongkhunen,&nbsp;Pongdate Montagantirud","doi":"10.1007/s13370-025-01376-9","DOIUrl":"10.1007/s13370-025-01376-9","url":null,"abstract":"<div><p>In recent years, the notions of discrete homotopy for graphs, such as <i>A</i>-homotopy and <span>(times)</span>-homotopy fundamental groupoid for graphs, have been introduced. This paper develops the notion of a looped fundamental groupoid for graphs to the isotropy group of the vertex <i>v</i> in the fundamental groupoid. We show that it is similar to the classical fundamental group of a topological space and the <i>A</i>-theory of graphs in some sense. Then, we generalize the concept of this theory to the looped fundamental group of weighted reflexive graphs and investigate some properties for the classification of weighted reflexive graphs in various situations. Moreover, we show that it satisfies the Seifert–Van Kampen property, with analogous results similar to the classical theory. Finally, we discuss the conclusion, its applications in the real world, and future works.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145062213","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
Multiplication operators on Cesàro function spaces on rooted trees 扎根树上Cesàro函数空间上的乘法运算符
IF 0.7
Afrika Matematika Pub Date : 2025-09-08 DOI: 10.1007/s13370-025-01369-8
Vivek Kumar, M. Mursaleen, Ajay K. Sharma
{"title":"Multiplication operators on Cesàro function spaces on rooted trees","authors":"Vivek Kumar,&nbsp;M. Mursaleen,&nbsp;Ajay K. Sharma","doi":"10.1007/s13370-025-01369-8","DOIUrl":"10.1007/s13370-025-01369-8","url":null,"abstract":"<div><p>This paper aims to study some topological properties of Cesàro function spaces on rooted trees. We also characterize bounded, compact, invertible and Fredhlom multiplication operators on these spaces.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011760","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
Bounds on the embedding co-dimension of analytic pseudo-Riemannian spacetimes 解析伪黎曼时空的嵌入协维的界
IF 0.7
Afrika Matematika Pub Date : 2025-09-08 DOI: 10.1007/s13370-025-01363-0
Simphiwe Mathenjwa, Gareth Amery
{"title":"Bounds on the embedding co-dimension of analytic pseudo-Riemannian spacetimes","authors":"Simphiwe Mathenjwa,&nbsp;Gareth Amery","doi":"10.1007/s13370-025-01363-0","DOIUrl":"10.1007/s13370-025-01363-0","url":null,"abstract":"<div><p>We provide a new theorem which asserts that any analytic n-dimensional pseudo-Riemannian manifold can be locally and isometrically embedded into (n+2)-dimensional pseudo-Euclidean spacetimes with at least two possible signatures <span>(mathbb {E}^{n+1,1})</span> and <span>(mathbb {E}^{n,2})</span>. Hence, such manifolds are at most of embedding class two. This theorem may be viewed as a direct consequence of the Dahia–Romero embedding theorem for embeddings into (n+1)-dimension pseudo-Riemannian space, in the context of vacuum and constant non-zero curvature. As consequence of this embedding theorem, we note that it resolves the open problem concerning the embedding class of the Gödel metric. We recapitulate the known Euclidean embedding results for FLRW geometries into pseudo-Euclidean spaces, and make some corrections to the possible signature. We also provide an explicit example demonstrating this.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01363-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on vague near algebra 关于模糊近似代数的注解
IF 0.7
Afrika Matematika Pub Date : 2025-09-08 DOI: 10.1007/s13370-025-01375-w
L. Bhaskar
{"title":"A note on vague near algebra","authors":"L. Bhaskar","doi":"10.1007/s13370-025-01375-w","DOIUrl":"10.1007/s13370-025-01375-w","url":null,"abstract":"<div><p>In this paper, we introduce the notion of a vague near-algebra over a vague field. We also define the concepts of the image and pre-image of a vague near-algebra. Based on these foundations, we analyse several properties and results that contribute to the development of the theory of vague near-algebras. Illustrative examples are provided to support and clarify the theoretical results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011761","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
(lambda)-Symmetries of the Painlevé–Ince equation (lambda)- painlev<s:1> - ince方程的对称性
IF 0.7
Afrika Matematika Pub Date : 2025-09-08 DOI: 10.1007/s13370-025-01361-2
Slungile Tshibase, Keshlan S. Govinder
{"title":"(lambda)-Symmetries of the Painlevé–Ince equation","authors":"Slungile Tshibase,&nbsp;Keshlan S. Govinder","doi":"10.1007/s13370-025-01361-2","DOIUrl":"10.1007/s13370-025-01361-2","url":null,"abstract":"<div><p>Lie symmetries play a central role in the analysis and solution of differential equations, offering systematic techniques for order reduction and integration. However, many differential equations do not admit classical Lie point symmetries, limiting the applicability of this approach. To address this limitation, various generalisations have been developed, among which the notion of <span>(lambda)</span>-symmetries (also known as <span>(C^{infty })</span>-symmetries) has proven particularly effective. These <span>(lambda)</span>-symmetries extend the symmetry framework, enabling the reduction of order and the derivation of first integrals even in the absence of classical symmetries. In this paper, we investigate the Painlevé–Ince equation within the context of <span>(lambda)</span>-symmetries for the first time. We identify the conditions under which the equation admits such symmetries and employ them to obtain a novel reduction of order. This analysis yields new insights into the structural properties and integrability of the equation.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01361-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coefficient estimates for certain class of bi-Bazilevič bounded functions with complex of order 一类复阶bi- bazileviv有界函数的系数估计
IF 0.7
Afrika Matematika Pub Date : 2025-09-03 DOI: 10.1007/s13370-025-01364-z
Tamer M. Seoudy
{"title":"Coefficient estimates for certain class of bi-Bazilevič bounded functions with complex of order","authors":"Tamer M. Seoudy","doi":"10.1007/s13370-025-01364-z","DOIUrl":"10.1007/s13370-025-01364-z","url":null,"abstract":"<div><p>In this paper, we introduce a new class of Bazilevič bi-univalent functions with complex order, defined in the open unit disk by employing bounded analytic functions. We establish precise bounds for the second and third Taylor–Maclaurin coefficients of functions in this class. Our results generalize several known coefficient estimates in geometric function theory. Furthermore, we examine important special cases that demonstrate the practical implications of our findings.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01364-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On (r)-({mathcal {I}}) limit set of a fuzzy number sequence 关于(r) - ({mathcal {I}})一个模糊数列的极限集
IF 0.7
Afrika Matematika Pub Date : 2025-09-03 DOI: 10.1007/s13370-025-01371-0
Debjani Rakshit
{"title":"On (r)-({mathcal {I}}) limit set of a fuzzy number sequence","authors":"Debjani Rakshit","doi":"10.1007/s13370-025-01371-0","DOIUrl":"10.1007/s13370-025-01371-0","url":null,"abstract":"<div><p>This paper is motivated by the emerging framework of rough ideal convergence which provides a tolerance parameter that allows sequences to converge within a certain margin and is studied in the context of fuzzy sequences. We introduce detailed notations for rough ideal convergence of fuzzy sequences and define the corresponding rough ideal limit sets. We then explore their fundamental properties and relationships, and present counterexamples to illustrate the concepts more clearly.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929406","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
Lacunary euler sequence spaces over n-normed spaces defined by Musielak–Orlicz function via matrix transformation of order ((alpha ,beta )) 通过序矩阵变换得到由Musielak-Orlicz函数定义的n赋范空间上的缺欧拉序列空间 ((alpha ,beta ))
IF 0.7
Afrika Matematika Pub Date : 2025-09-03 DOI: 10.1007/s13370-025-01368-9
Ravi Kumar, Patchalai Anuchaivong, Vivek Kumar, Ajay K. Sharma, Sunil K. Sharma
{"title":"Lacunary euler sequence spaces over n-normed spaces defined by Musielak–Orlicz function via matrix transformation of order ((alpha ,beta ))","authors":"Ravi Kumar,&nbsp;Patchalai Anuchaivong,&nbsp;Vivek Kumar,&nbsp;Ajay K. Sharma,&nbsp;Sunil K. Sharma","doi":"10.1007/s13370-025-01368-9","DOIUrl":"10.1007/s13370-025-01368-9","url":null,"abstract":"<div><p>In this paper, we investigate the properties of a specialized class of lacunary sequences defined through the Euler transform within the framework of an <i>n</i>-normed space, employing the Musielak–Orlicz function of order <span>((alpha , beta ))</span>. By constructing these spaces through Euler and matrix transformations of order <span>((alpha , beta ))</span>, we aim to develop the structural and topological characteristics that govern the behavior of these sequences and analyse some inclusion relations. Our analysis focuses on how such transformations influence convergence behaviors, embedding new perspectives on functional interactions within <i>n</i>-normed spaces. These insights contribute to a deeper understanding of convergence and stability phenomena, broadening the applicability of Musielak–Orlicz function theory in advanced functional analysis and sequence spaces over order <span>((alpha , beta ))</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929409","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
Algorithmic solution of the power option PDE by the lie group approach 用李群方法求解功率期权PDE
IF 0.7
Afrika Matematika Pub Date : 2025-09-03 DOI: 10.1007/s13370-025-01358-x
M. O. Okelola, K. S. Govinder, J. G. O’Hara
{"title":"Algorithmic solution of the power option PDE by the lie group approach","authors":"M. O. Okelola,&nbsp;K. S. Govinder,&nbsp;J. G. O’Hara","doi":"10.1007/s13370-025-01358-x","DOIUrl":"10.1007/s13370-025-01358-x","url":null,"abstract":"<div><p>From the era of Black–Scholes, European options have dwelt on pay-offs that are a linear function of the asset price. In this paper, we will look at a special case of exotic options - power options - whose payoffs are nonlinear functions of the underlying asset price. Exotic options are derivatives which have features that makes them more complex than commonly traded products - thus finding their fair value is not an always easy task. Previous analyses of the power option partial differential equation (PDE) have only obtained closed form solutions either by guessing solutions, similarity methods or the martingale approach [8, 9, 25]. Using Lie symmetry analysis we obtain an optimal system of the Lie point symmetries of the power option PDE and demonstrate an algorithmic method for finding solutions to the equation. In addition, we find a new analytical solution to the asymmetric type of the power option.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01358-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The life and mathematics of Ismail Mohamed 伊斯梅尔·穆罕默德的生平和数学
IF 0.7
Afrika Matematika Pub Date : 2025-09-03 DOI: 10.1007/s13370-025-01362-1
Eder Kikianty, Loyiso G. Nongxa
{"title":"The life and mathematics of Ismail Mohamed","authors":"Eder Kikianty,&nbsp;Loyiso G. Nongxa","doi":"10.1007/s13370-025-01362-1","DOIUrl":"10.1007/s13370-025-01362-1","url":null,"abstract":"<div><p>Ismail Mohamed’s major contributions, which were in collaboration with Hermann Heineken, was to provide a procedure for constructing groups with prescribed characteristics. In particular, they constructed examples of non-nilpotent groups in which every subgroup is subnormal and nilpotent. These have become known as the Heineken–Mohamed groups. This construction led to settling a few questions posed, in the 1940s, by Kurosh and Cernikov in their survey of various generalisations of nilpotency. He also studied properties of series of subgroups of a group <i>G</i> that are constructed from arbitrary subgroups of automorphisms of a group.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01362-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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