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A note on weakly g(x)-invo clean rings 弱g(x)-绕净环的注释
IF 0.7
Afrika Matematika Pub Date : 2026-03-07 DOI: 10.1007/s13370-026-01431-z
Kanchan Jangra, Dinesh Udar
{"title":"A note on weakly g(x)-invo clean rings","authors":"Kanchan Jangra,&nbsp;Dinesh Udar","doi":"10.1007/s13370-026-01431-z","DOIUrl":"10.1007/s13370-026-01431-z","url":null,"abstract":"<div><p>Let <i>Z</i>(<i>R</i>) be the center of a ring <i>R</i> and <span>(g(x))</span> be a fixed polynomial in <i>Z</i>(<i>R</i>)[<i>x</i>]. In this paper, we continue the study of weakly <span>(g(x))</span>-invo clean rings. A ring <i>R</i> is called weakly <span>(g(x))</span>-invo clean if each element of <i>R</i> is a sum or difference of an involution and a root of $g(x)$. We determine the necessary and sufficient conditions for the skew Hurwitz series ring <span>((HR,alpha ))</span> to be weakly <span>(g(x))</span>-invo clean, where <span>(alpha)</span> is an endomorphism of <i>R</i>. We also prove that the ring of the skew Hurwitz series <span>((HR,alpha ))</span> is weakly invo-clean if and only if <i>R</i> is weakly invo-clean.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362813","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
Computational automation for solving Pocklington’s integro-differential equation based on Fredholm integral equations and (gamma )-spline interpolants 基于Fredholm积分方程和(gamma )样条插值的Pocklington积分微分方程求解自动化
IF 0.7
Afrika Matematika Pub Date : 2026-03-07 DOI: 10.1007/s13370-026-01446-6
Mohamed Addam, Imad El Barkani
{"title":"Computational automation for solving Pocklington’s integro-differential equation based on Fredholm integral equations and (gamma )-spline interpolants","authors":"Mohamed Addam,&nbsp;Imad El Barkani","doi":"10.1007/s13370-026-01446-6","DOIUrl":"10.1007/s13370-026-01446-6","url":null,"abstract":"<div><p>To solve all types of Fredholm integro-differential equations, we develop a computational automation based on the collocation method. <span>(gamma )</span>-spline basis functions are employed to compute an approximate solution of these linear integral equations. In addition, Pocklington’s integro-differential equation is studied in this work. Accordingly, the signal reconstruction in the wire antennas is treated using these equations. Several techniques based on quadrature computational automation methods are involved to determine the computed solutions of the considered integro-differential equations. Moreover, the <span>(gamma )</span>-spline interpolation function is proposed to solve the Fredholm equation. Some examples are presented to indicate the numerical convergence orders <span>(mathcal {O}(h^{gamma +1}))</span>, accuracy, effectiveness, and robustness of the method.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440908","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 continuity properties of the joint (k, p)-numerical radii of operators （k, p）关节的连续性——算子的数值半径
IF 0.7
Afrika Matematika Pub Date : 2026-03-07 DOI: 10.1007/s13370-026-01428-8
Elif Otkun Çevik, Zameddin I. Ismailov, Fuad Kittaneh, Ali Zamani
{"title":"On the continuity properties of the joint (k, p)-numerical radii of operators","authors":"Elif Otkun Çevik,&nbsp;Zameddin I. Ismailov,&nbsp;Fuad Kittaneh,&nbsp;Ali Zamani","doi":"10.1007/s13370-026-01428-8","DOIUrl":"10.1007/s13370-026-01428-8","url":null,"abstract":"<div><p>In this paper, firstly, for one operator, later for multiple operators, the continuity properties of the joint (<i>k</i>, <i>p</i>)-numerical radii and the joint (<i>k</i>, <i>p</i>)-Crawford numbers of operators are investigated.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362812","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
Diametral designs from strongly regular graphs with given parameter sets 具有给定参数集的强正则图的直径设计
IF 0.7
Afrika Matematika Pub Date : 2026-03-07 DOI: 10.1007/s13370-026-01444-8
Medha Itagi Huilgol, Sreepriya Asok
{"title":"Diametral designs from strongly regular graphs with given parameter sets","authors":"Medha Itagi Huilgol,&nbsp;Sreepriya Asok","doi":"10.1007/s13370-026-01444-8","DOIUrl":"10.1007/s13370-026-01444-8","url":null,"abstract":"<div><p>Construction of partially balanced incomplete block (PBIB)-designs from a strongly regular graph with given set of parameters is a difficult problem. In literature only three such constructions are available. In this paper, we address this nearly impossible case by constructing PBIB-designs arising from strongly regular graphs with given parameter set for orders from 51 to 100, viz., Sims–Gewirtz graph, <span>(text {M}_{22})</span> or Mesner graph, Brouwer’s graph, Brouwer and Haemer’s graph, Higman–Sims graph, Hall–Janko graph, Paley graphs—<span>(P_{53},~P_{61},~P_{73},~P_{81},~P_{89},~P_{97})</span> and Hamming graphs <i>H</i>(2, 8) and <i>H</i>(2, 10) using vertices of diametral paths as blocks. In each case we provide the composition of blocks. All these designs are constant block sum designs.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362814","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
The (p, q, r)-generations of the Chevalley group (G_{2}(3)) Chevalley群的（p, q, r）代 (G_{2}(3))
IF 0.7
Afrika Matematika Pub Date : 2026-03-04 DOI: 10.1007/s13370-026-01448-4
A. B. M. Basheer, M. J. Motalane, M. G. Sehoana, T. T. Seretlo
{"title":"The (p, q, r)-generations of the Chevalley group (G_{2}(3))","authors":"A. B. M. Basheer,&nbsp;M. J. Motalane,&nbsp;M. G. Sehoana,&nbsp;T. T. Seretlo","doi":"10.1007/s13370-026-01448-4","DOIUrl":"10.1007/s13370-026-01448-4","url":null,"abstract":"<div><p>A finite group <i>G</i> is called (<i>l</i>, <i>m</i>, <i>n</i>)<i>-generated</i>, if it is a quotient group of the triangle group <span>(T(l,m, n) = left&lt;x, y, z|x^{l} = y^{m} = z^{n} = xyz = 1right&gt;.)</span> In [23], Moori posed the question of finding all the (<i>p</i>, <i>q</i>, <i>r</i>) triples, where <span>(p, q)</span> and <i>r</i> are prime numbers, such that a non-abelian finite simple group <i>G</i> is a (<i>p</i>, <i>q</i>, <i>r</i>)-generated. In answering this question, we establish all the (<i>p</i>, <i>q</i>, <i>r</i>)-generations for the group <span>(G_{2}(3).)</span> We mainly used the structure constant method together with other results to establish the generation and non-generation of the <span>(G_{2}(3))</span> by the triples (<i>p</i>, <i>q</i>, <i>r</i>). The Groups, Algorithms and Programming, GAP [21] and the Atlas of finite group representations [27] are used in our computations.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-026-01448-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352807","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
Bohr phenomenon for K-Quasiconformal harmonic mappings and logarithmic power series k -拟共形调和映射的玻尔现象与对数幂级数
IF 0.7
Afrika Matematika Pub Date : 2026-03-01 DOI: 10.1007/s13370-026-01447-5
Kamaljeet Gangania, Shivani Sharma
{"title":"Bohr phenomenon for K-Quasiconformal harmonic mappings and logarithmic power series","authors":"Kamaljeet Gangania,&nbsp;Shivani Sharma","doi":"10.1007/s13370-026-01447-5","DOIUrl":"10.1007/s13370-026-01447-5","url":null,"abstract":"<div><p>In this article, we establish the Bohr inequalities for the sense-preserving <i>K</i>-quasiconformal harmonic mappings defined in the unit disk <span>(mathbb {D})</span> associated with the subclasses of Ma-Minda starlike and convex univalent functions denoted by <span>(mathcal {S}^*(psi ))</span> and <span>(mathcal {C}(psi ))</span> respectively, and for <span>(log (f(z)/z))</span> where <i>f</i> belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate the Logarithmic coefficient’s bounds for the functions in the subclass <span>(mathcal {C}(psi ))</span> when <span>(psi (mathbb {D}))</span> is convex, which complement the result for starlike functions.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336197","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 estimates for the q-analogue of Dunkl transform in the weighted space (L^{2}_{q,alpha }(mathbb {R}_{q})) 加权空间中Dunkl变换q-模拟的估计 (L^{2}_{q,alpha }(mathbb {R}_{q}))
IF 0.7
Afrika Matematika Pub Date : 2026-02-28 DOI: 10.1007/s13370-026-01436-8
Radouan Daher, Othman Tyr
{"title":"On estimates for the q-analogue of Dunkl transform in the weighted space (L^{2}_{q,alpha }(mathbb {R}_{q}))","authors":"Radouan Daher,&nbsp;Othman Tyr","doi":"10.1007/s13370-026-01436-8","DOIUrl":"10.1007/s13370-026-01436-8","url":null,"abstract":"<div><p>In this paper, using some elements of the q-harmonic analysis associated to the q-Dunkl operator introduced in [3], for fixed <span>(0&lt;q&lt;1)</span>, some new estimates useful in applications are proved for the generalized q-Dunkl transform in the space <span>(L^{2}_{q,alpha }(mathbb {R}_{q}))</span> as applied to some classes of functions characterized by a generalized modulus of continuity.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342789","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
Sakaguchi type functions defined by q-Bernoulli numbers 由q-伯努利数定义的Sakaguchi型函数
IF 0.7
Afrika Matematika Pub Date : 2026-02-26 DOI: 10.1007/s13370-026-01442-w
S. Bulut, G. Saravanan, S. Baskaran
{"title":"Sakaguchi type functions defined by q-Bernoulli numbers","authors":"S. Bulut,&nbsp;G. Saravanan,&nbsp;S. Baskaran","doi":"10.1007/s13370-026-01442-w","DOIUrl":"10.1007/s13370-026-01442-w","url":null,"abstract":"<div><p>This study uses a <i>q</i>-derivative operator and <i>q</i>-Bernoulli numbers to establish the subclass <span>({mathcal {S}}mathfrak {B}_{q,lambda }^{s,b}left( mathcal {F}_{0}right) )</span> of Sakaguchi type functions. We obtained constraints for the initial coefficients <span>(vert a_2 vert )</span> and <span>(vert a_3 vert )</span> through our analysis, providing insight into the characteristics and behavior of functions in this subclass. Furthermore, we derive the Fekete-Szegö inequality that is peculiar to this class, along with a number of corollaries that expand on our results and enhance our comprehension of their implications.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342160","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
Uniqueness and reciprocity in multi-phase-lag thermoviscoelastic diffusion models 多相滞后热粘弹性扩散模型的唯一性和互易性
IF 0.7
Afrika Matematika Pub Date : 2026-02-24 DOI: 10.1007/s13370-026-01441-x
Saurav Sharma, Sangeeta Devi, Rajneesh Kumar
{"title":"Uniqueness and reciprocity in multi-phase-lag thermoviscoelastic diffusion models","authors":"Saurav Sharma,&nbsp;Sangeeta Devi,&nbsp;Rajneesh Kumar","doi":"10.1007/s13370-026-01441-x","DOIUrl":"10.1007/s13370-026-01441-x","url":null,"abstract":"<div><p>A new model involving the equations of isotropic thermoviscoelastic diffusion under a multi-phase-lags medium (ITDM) has been proposed in this study. The model is developed by modifying the classical Fourier’s (Theorie Analytique de la Chaleur. Oeuvres de Fourier, Paris, 1822) and Fick’s (Ann Phys 94:59–86, 1855) laws to incorporate higher-order time derivatives of the heat flux vector and the mass flux, along with gradients of temperature and chemical potential. These modifications enable the model to more accurately capture memory and non-local effects in heat and mass transport. The governing equations are employed to establish uniqueness and reciprocity theorems, which are essential for validating the well-posedness and symmetric properties of the system. The <i>reciprocity theorem</i> is applied to cases involving instantaneous and moving sources of heat, mass, and body forces, demonstrating how system responses are influenced by parameter variations and the sensitivity of field variables. The methodology adopted in this work allows for the derivation of generalized theoretical results and their validation through special and limiting cases, offering a sturdy theoretical framework for further study. Several unique cases are also derived and shown to correlate well with previously established results, thereby confirming the reliability of the proposed model. Although the study is theoretical, it lays the groundwork for future exploration of fundamental problems in thermoelastic continua involving multiple coupled field variables. The developed model has applications in material science, geomechanics, soil dynamics, and the electronic industry, where complex interactions between thermal, mechanical, and diffusive processes are prevalent.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341469","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
Square mean asymptotically (varkappa)-periodic solution for stochastic integro-differential equations via the degree of nondensifiability 随机积分微分方程的平方均值渐近(varkappa) -周期解的非密度度
IF 0.7
Afrika Matematika Pub Date : 2026-02-21 DOI: 10.1007/s13370-026-01411-3
Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra, Gaston N’Guérékata
{"title":"Square mean asymptotically (varkappa)-periodic solution for stochastic integro-differential equations via the degree of nondensifiability","authors":"Abdelhamid Bensalem,&nbsp;Abdelkrim Salim,&nbsp;Mouffak Benchohra,&nbsp;Gaston N’Guérékata","doi":"10.1007/s13370-026-01411-3","DOIUrl":"10.1007/s13370-026-01411-3","url":null,"abstract":"<div><p>In this paper, we explore square-mean asymptotically <span>(varkappa)</span>-periodic mild solutions from square mean <span>(varkappa)</span>-periodic limit for a stochastic integro-differential equations driven by Brownian motion, utilizing Grimmer’s resolvent and a version of Darbo’s fixed point theorem based on the degree of nondensifiability. Additionally, an example is given to illustrate our results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-026-01411-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341111","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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