Afrika Matematika最新文献

{"title":"Process capability indices for Marshall–Olkin inverse log-logistic distribution","authors":"Olubisi Lawrence Aako,&nbsp;Kayode Samuel Adekeye,&nbsp;Johnson Ademola Adewara,&nbsp;Jean-Claude Malela-Majika","doi":"10.1007/s13370-025-01353-2","DOIUrl":"10.1007/s13370-025-01353-2","url":null,"abstract":"<div><p>Process capability analysis is a vital tool in quality management that enables organizations to evaluate and enhance their processes. Real-world data are mostly non-normal, they often deviate from the assumption of normality. The estimators of process capability indices (PCIs) for normal processes are not sufficient to characterize non-normal processes and can give misleading results. The Marshall-Olkin inverse log-logistic (MO-ILL) distribution is a flexible distribution that can effectively model data exhibiting positive skewness, asymmetry and heavy tails. In this paper, we derived the process capability indices (PCIs) based on the MO-ILL distribution when the process is assumed to be in a state of statistical control. Two PCIs based on MO-ILL mean and variance, and MO-ILL quantiles are proposed. The proposed PCIs were compared with the traditional PCIs and percentile-based PCIs using two real life data and data generated from MO-ILL distribution. Moreover, the effect of the sample size and parameters of the MO-ILL distribution on the PCI measures is also investigated. The results showed that PCIs values based on the proposed MO-ILL mean and variance, and MO-ILL quantiles are respectively lower and better than the traditional PCIs and percentile-based PCIs. This is an indication that MO-ILL distribution-based methods developed have narrow margin of error and are more appropriate in assessing the performance of a skewed process.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01353-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880935","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}

{"title":"On the family of elliptic curves (y^2=x^3-5pqx)","authors":"Arkabrata Ghosh","doi":"10.1007/s13370-025-01352-3","DOIUrl":"10.1007/s13370-025-01352-3","url":null,"abstract":"<div><p>This article considers the family of elliptic curves given by <span>(E_{pq}: y^2=x^3-5pqx)</span> and certain conditions on odd primes <i>p</i> and <i>q</i>. More specifically, we have shown that if <span>(p equiv 33 pmod {40})</span> and <span>(q equiv 7 pmod {40})</span>, then the rank of <span>(E_{pq})</span> is zero over both <span>(mathbb {Q})</span> and <span>(mathbb {Q}(i))</span>. Furthermore, if the primes <i>p</i> and <i>q</i> are of the form <span>(40k + 33)</span> and <span>(40,l + 27)</span>, where <span>(k,l in mathbb {Z})</span> such that <span>((25k+ 5,l +21))</span> is a perfect square, then the given family of elliptic curves has rank one over <span>(mathbb {Q})</span> and rank two over <span>(mathbb {Q}(i))</span>. Finally, we have shown that the torsion of <span>(E_{pq})</span> over <span>(mathbb {Q})</span> is isomorphic to <span>(mathbb {Z}/ 2mathbb {Z})</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163656","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}

{"title":"Modules whose fully invariant ec-closed submodules are direct summands","authors":"Enas Mustafa Kamil,&nbsp;Haneen Siraj Ibrahim","doi":"10.1007/s13370-025-01356-z","DOIUrl":"10.1007/s13370-025-01356-z","url":null,"abstract":"<div><p>In this article, we define a module <i>H</i> to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of <i>H</i> is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163657","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}

{"title":"Hamilton-type gradient estimates for Yamabe-type equations on Finsler manifolds","authors":"Shansong Huang,&nbsp;Xiang Liu,&nbsp;Bin Shen,&nbsp;Yuhan Zhu","doi":"10.1007/s13370-025-01355-0","DOIUrl":"10.1007/s13370-025-01355-0","url":null,"abstract":"<div><p>In this paper, we study the positive solution to the Finslerian Yamabe-type equation </p><div><div><span>$$u_t=Delta ^{nabla u} u+au+bu^alpha .$$</span></div></div><p>We give the Hamilton-type gradient estimate on compact Finsler metric measure spaces with the celebrated <span>(CD(-K,N))</span> condition. Besides, on forward complete noncompact Finsler metric measure spaces with the mixed weighted Ricci curvature bounded below, the new comparison theorem established by the third author (Shen in Operators on nonlinear metric measure spaces I: A new Laplacian comparison theorem on Finsler manifolds and a traditional approach to gradient estimates of Finslerian Schrödinger equation arXiv:2312.06617v2 [math.DG], 2024) allows us to give the gradient estimate under the assumption of certain bounded non-Riemannian tensors. Finally, we prove the Liouville-type theorem and the Harnack inequality for such solutions as applications.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163658","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}

{"title":"Detection of degree distribution for biological networks in pearson family and its approximation","authors":"Omolola Atanda,&nbsp;Vilda Purutçuoğlu,&nbsp;Ernst Wit,&nbsp;Gerhard Wilhelm Weber","doi":"10.1007/s13370-025-01349-y","DOIUrl":"10.1007/s13370-025-01349-y","url":null,"abstract":"<div><p>The degree distribution is one of the characteristic features of the topology of networks. This distribution describes the in-degree and out-degree of nodes in systems. In genetic networks, the in-degree or arriving connectivity represents the number of links coming to a target gene, while the out-degree or departing connectivity represents the number of links leaving the target gene. For biological networks, the in-degree distribution can be modeled by the exponential distribution, whereas the power-law distribution generally models the out-degree distribution. However, truncated power-law, generalized Pareto, stretched exponential, geometric, or combinations of these distributions may serve as robust alternative out-degree models, satisfying the centrality and small-world properties even without scale-free behavior. The Pearson curve is a fundamental tool for categorizing distributions based on the characteristics of their first four moments. In this study, we aim to describe the out-degree of biological systems through an alternative approach. This approach ensures that the previously mentioned out-degree densities are treated as special cases within the Pearson curve framework. Their distributional similarities are evaluated using the three-moment Chi-square and four-moment F approximations. As a result, we assess the effectiveness of our proposed method in accurately classifying these distributions. The findings reveal that the degree distributions satisfying the scale-free property mainly fall within the Pearson Type I family, with only a few in Type VI. In contrast, clustered and hub networks do not align with Pearson distributions. The scale-free networks demonstrate the applicability of the four-moment F approximation, highlighting the robustness of Pearson curves in modeling biological networks. This study suggests that fitting a plausible distribution in the Pearson families provides realistic choices for the degree distribution in biological networks, addressing limitations in existing methodologies and opening pathways for further research on various biological network types and distribution systems.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162859","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}

{"title":"On consecutive cube-free numbers of the form (lfloor n^crfloor), (lfloor n^crfloor)+1","authors":"Pinthira Tangsupphathawat,&nbsp;Teerapat Srichan","doi":"10.1007/s13370-025-01351-4","DOIUrl":"10.1007/s13370-025-01351-4","url":null,"abstract":"<div><p>In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed <span>(1&lt;c&lt;2)</span>, there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162053","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}

{"title":"Hyers–Ulam–Rassias stability of a finite variable cubic functional equation in matrix paranormed spaces","authors":"Kandhasamy Tamilvanan,&nbsp;G. Balasubramanian,&nbsp;Choonkil Park,&nbsp;Jung Rye Lee","doi":"10.1007/s13370-025-01350-5","DOIUrl":"10.1007/s13370-025-01350-5","url":null,"abstract":"<div><p>We introduce the finite variable cubic functional equation of the form </p><div><div><span>$$begin{aligned} sum _{a=1}^{m}phi left( -t_{a}+sum _{b=1;a ne b}^{m}t_{b}right) -sum _{a=1}^{m}phi left( 2t_{a}right) =left( m-6right) sum _{1 le a&lt; b&lt; c le m}phi left( t_{a}+t_{b}+t_{c}right) +left( -m^{2}+9m-14right) sum _{1le a&lt;ble m}phi left( t_{a}+t_{b}right) +left( frac{m^{3}-11 m^{2}+28 m-36}{2}right) sum _{a=1}^{m}phi left( t_{a}right) end{aligned}$$</span></div></div><p>where <span>(m ge 4)</span> is a fixed integer, and we establish the Hyers–Ulam–Rassias stability results in paranormed spaces and matrix paranormed spaces.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160806","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}

{"title":"Anisotropic stellar objects cast in isotropic coordinates","authors":"Suntharalingam Thirukkanesh,&nbsp;Megandhren Govender,&nbsp;Anand Kaisavelu","doi":"10.1007/s13370-025-01345-2","DOIUrl":"10.1007/s13370-025-01345-2","url":null,"abstract":"<div><p>In this work we model a compact star in simultaneosuly comoving and isotropic coordinates. Using a transformation first developed by Kustaanheimo and Qvist [republished: Gen Relat Grav <b>30</b>, 663 (1998)] we recast the Einstein field equations into a simple, albeit, nonlinear system. We further impose a linear equation of state of the form, <span>({p_{r}} = alpha rho -beta)</span>, which we integrate in general. We reduce the problem of finding exact solutions of the Einstein field equations to quadratures relating the metric functions. We complete the gravitational description of the model by choosing one of the metric functions by appealing to physics. A complete physical analysis of our model is carried out to test its robustness as a viable description of compact objects within the framework of general relativity.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01345-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164485","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}

{"title":"On integral operator generated by a symmetric difference expression","authors":"Ibtisam Aldawish,&nbsp;Rabha W. Ibrahim,&nbsp;Praveen Agarwal","doi":"10.1007/s13370-025-01344-3","DOIUrl":"10.1007/s13370-025-01344-3","url":null,"abstract":"<div><p>Using the concept of the symmetric difference formula of the Dunkl operator, a new fractional integral iteration of symmetric Schur functions is constructed in the open unit disk. That will be referred to as the fractional Schur–Dunkl operator. When applying the fractional Schur–Dunkl operator to the normalized class of holomorphic functions in the open unit disk, we take it into consideration. Some geometric criteria for the convexity and starlikeness of the envisaged operator are investigated. Furthermore, we declare a series of requirements for the fractional Schur–Dunkl operator to be in the domains of Symmetric Piatetski–Shapiro. Using Mathematica 13.3, figures are shown for the proposed fractional Schur–Dunkl operator.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163478","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}

{"title":"Correction: On a minimization problem involving fractional Sobolev spaces on Nehari manifold","authors":"S. H. Rasouli","doi":"10.1007/s13370-025-01337-2","DOIUrl":"10.1007/s13370-025-01337-2","url":null,"abstract":"","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163486","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}