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Afrika Matematika最新文献

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Admissible wave packets and frame decompositions on the Heisenberg group 海森堡群上的容许波包和帧分解
IF 0.7
Afrika Matematika Pub Date : 2026-03-17 DOI: 10.1007/s13370-026-01461-7
Ishtaq Ahmad, Dowlath Fathima
{"title":"Admissible wave packets and frame decompositions on the Heisenberg group","authors":"Ishtaq Ahmad,&nbsp;Dowlath Fathima","doi":"10.1007/s13370-026-01461-7","DOIUrl":"10.1007/s13370-026-01461-7","url":null,"abstract":"<div><p>This paper presents a detailed study of wave packets on the Heisenberg group <span>({mathbb {H}}^n,)</span> a fundamental non-commutative Lie group arising naturally in harmonic analysis and quantum mechanics. We develop the theory of wave packet transforms adapted to the intrinsic geometry and representation theory of <span>({mathbb {H}}^n.)</span> Key contributions include the characterization of admissible wave packets, the construction of continuous frames generated by dilations, modulations, and translations on <span>({mathbb {H}}^n,)</span> and explicit inversion formulas using dual frames. We provide explicit examples of admissible wave packets arising from Gaussian-type functions and heat kernels, emphasizing their localization and spectral properties. The results establish a robust framework for time-frequency analysis on <span>({mathbb {H}}^n)</span> and open pathways for applications in signal processing and partial differential equations on non-commutative groups.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559669","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 generalization of the cosine-sine functional equation on a semigroup 余弦-正弦泛函方程在半群上的推广
IF 0.7
Afrika Matematika Pub Date : 2026-03-14 DOI: 10.1007/s13370-026-01458-2
Omar Ajebbar, Elhoucien Elqorachi
{"title":"A generalization of the cosine-sine functional equation on a semigroup","authors":"Omar Ajebbar,&nbsp;Elhoucien Elqorachi","doi":"10.1007/s13370-026-01458-2","DOIUrl":"10.1007/s13370-026-01458-2","url":null,"abstract":"<div><p>Given a semigroup <i>S</i> equipped with an involutive automorphism <span>(sigma )</span>, we determine the complex-valued solutions <i>f</i>, <i>g</i>, <i>h</i> of the functional equation </p><div><div><span>$$begin{aligned}f(xsigma (y))=f(x)g(y)+g(x)f(y)+h(x)h(y),,,x,yin S,end{aligned}$$</span></div></div><p>in terms of multiplicative functions and solutions of the special cases of sine and cosine–sine functional equations </p><div><div><span>$$begin{aligned} varphi (xy)=varphi (x)chi (y)+chi (x)varphi (y), x,yin S end{aligned}$$</span></div></div><p>and </p><div><div><span>$$begin{aligned} psi (xy)=psi (x)chi (y)+chi (x)psi (y)+varphi (x)varphi (y), x,yin S end{aligned}$$</span></div></div><p>where <span>(chi :Srightarrow mathbb {C})</span> is a multiplicative function.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441720","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
Continuous biframes in Hilbert spaces 希尔伯特空间中的连续双框
IF 0.7
Afrika Matematika Pub Date : 2026-03-13 DOI: 10.1007/s13370-026-01453-7
Hafida Massit, Roumaissae Eljazzar, Mohamed Rossafi
{"title":"Continuous biframes in Hilbert spaces","authors":"Hafida Massit,&nbsp;Roumaissae Eljazzar,&nbsp;Mohamed Rossafi","doi":"10.1007/s13370-026-01453-7","DOIUrl":"10.1007/s13370-026-01453-7","url":null,"abstract":"<div><p>In this paper, we present the concept of continuous biframes in a Hilbert space. We examine the essential properties of biframes with an emphasis on the biframe operator. Moreover, we introduce a new type of Riesz bases, referred to as continuous biframe-Riesz bases.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441455","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
Second Hankel determinant for a certain subclass of analytic functions defined by close-to-convex functions and the Salagean derivative operator 一类由近凸函数和Salagean导数算子定义的解析函数的二阶Hankel行列式
IF 0.7
Afrika Matematika Pub Date : 2026-03-11 DOI: 10.1007/s13370-026-01449-3
Halit Orhan, Hava Arıkan, Ebru Başıbüyük
{"title":"Second Hankel determinant for a certain subclass of analytic functions defined by close-to-convex functions and the Salagean derivative operator","authors":"Halit Orhan,&nbsp;Hava Arıkan,&nbsp;Ebru Başıbüyük","doi":"10.1007/s13370-026-01449-3","DOIUrl":"10.1007/s13370-026-01449-3","url":null,"abstract":"<div><p>In this investigation, we derive Fekete–Szegè inequalities and upper bounds for the second Hankel determinant for a new subclass of analytic functions in the open unit disk formed by the close-to-convex functions and the Salagean derivative operator. Additionally, there is discussion of a number of intriguing applications of the findings given here.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441877","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 establishment and philosophical implications of Hausdorff measure 豪斯多夫测度的建立及其哲学意义
IF 0.7
Afrika Matematika Pub Date : 2026-03-10 DOI: 10.1007/s13370-026-01457-3
Nan Jiang, Nana Ma
{"title":"The establishment and philosophical implications of Hausdorff measure","authors":"Nan Jiang,&nbsp;Nana Ma","doi":"10.1007/s13370-026-01457-3","DOIUrl":"10.1007/s13370-026-01457-3","url":null,"abstract":"<div><p>With the deepening of rigorous analysis in mathematics since the modern era, irregular pathological mathematical objects such as the Weierstrass function, Cantor set, and Koch curve, have been produced one after another, which result in some phenomena and problems that are difficult to explain by traditional mathematical theory. The measurement problem of the Cantor set is typical in these problems. According to the conventional mathematical theory, the measure of the Cantor set is zero. However, the zero-measure set constitutes infinite points which brings people confusion intuitively. Inspired by Fréchet’s fractional dimension, Hausdorff found the internal relationship between the fractional dimension and irregular pathological set based on Carathéodory measure and further created the Hausdorff measure, the predecessor of fractal measure, which not only solved the measurement problem of Cantor set but also paved the way of fractal theory. As the metric of nature, the fractal measure has unique and profound implications in ontology, epistemology, and methodology, in addition to accurately characterizing the magnitude of irregular objective things.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441293","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
Line graph of annihilating-ideal graph of commutative rings 交换环的湮灭-理想图的线图
IF 0.7
Afrika Matematika Pub Date : 2026-03-10 DOI: 10.1007/s13370-026-01459-1
Nadeem ur Rehman, Shabir Ahmad Mir, Mohd Nazim, Haribhau R. Bhapkar,  Nazim
{"title":"Line graph of annihilating-ideal graph of commutative rings","authors":"Nadeem ur Rehman,&nbsp;Shabir Ahmad Mir,&nbsp;Mohd Nazim,&nbsp;Haribhau R. Bhapkar,&nbsp; Nazim","doi":"10.1007/s13370-026-01459-1","DOIUrl":"10.1007/s13370-026-01459-1","url":null,"abstract":"<div><p>Let <span>(mathscr {P})</span> be a commutative ring with unity, and let <span>(A(mathscr {P}))</span> denote the set of ideals of <span>(mathscr {P})</span> having a nonzero annihilator. The annihilating-ideal graph of <span>(mathscr {P})</span>, denoted by <span>(AG(mathscr {P}))</span>, is an undirected graph whose vertex set <span>(A(mathscr {P})^*)</span> consists of all nonzero ideals in <span>(A(mathscr {P}))</span>, where two distinct vertices <i>I</i> and <i>J</i> are adjacent if and only if <span>(IJ=(0))</span>. In this paper, we investigate the structure of <span>(AG(mathscr {P}))</span> for Artinian non-local commutative rings. Our main results provide a complete characterization of all such rings for which the annihilating-ideal graph is a line graph, as well as those for which it is the complement of a line graph. In particular, we show that these graphs arise precisely for rings that decompose into specific finite direct products of fields and local rings with a unique nontrivial ideal.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441294","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 new integral representations for the generalized hypergeometric function and their applications 广义超几何函数的一些新的积分表示及其应用
IF 0.7
Afrika Matematika Pub Date : 2026-03-09 DOI: 10.1007/s13370-026-01455-5
Wathek Chammam, Mongia Khlifi, Arjun K. Rathie
{"title":"Some new integral representations for the generalized hypergeometric function and their applications","authors":"Wathek Chammam,&nbsp;Mongia Khlifi,&nbsp;Arjun K. Rathie","doi":"10.1007/s13370-026-01455-5","DOIUrl":"10.1007/s13370-026-01455-5","url":null,"abstract":"<div><p>In this paper, we provide some new integral representations for the generalized hypergeometric function. These results represent a generalization of formula [15.3.1, p.558] in [Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards, Applied Mathematics Series 55, 10th printing, Washington] by Abramowitz and Stegun, extending it beyond the Gauss hypergeometric function to include the generalized hypergeometric function. As applications of these results, we present several new integral representations for Catalan number and its different generalizations are established. In the end we also provide a derivative for the generalized hypergeometric function. This provides a broader framework for applying integral representations in various mathematical contexts, particularly in applied mathematics, functional analysis, and the theory of special functions.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441116","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 irreducibility of eccentricity matrix of graphs and construction of (epsilon )-equienergetic graphs 图的偏心矩阵的不可约性及(epsilon ) -等能图的构造
IF 0.7
Afrika Matematika Pub Date : 2026-03-09 DOI: 10.1007/s13370-026-01454-6
Anjitha Ashokan, Chithra A. V.
{"title":"On irreducibility of eccentricity matrix of graphs and construction of (epsilon )-equienergetic graphs","authors":"Anjitha Ashokan,&nbsp;Chithra A. V.","doi":"10.1007/s13370-026-01454-6","DOIUrl":"10.1007/s13370-026-01454-6","url":null,"abstract":"<div><p>The eccentricity matrix <span>(epsilon (G),)</span> of a connected graph <i>G</i> is obtained by retaining the maximum distance from each row and column of the distance matrix of <i>G</i>, and the other entries are assigned with 0. In this paper, we discuss the eccentricity spectrum of the subdivision vertex (edge) join of regular graphs. Also, we obtain new families of graphs having irreducible or reducible eccentricity matrix. Furthermore, we use these results to construct infinitely many <span>(epsilon )</span>-cospectral graph pairs as well as infinitely many pairs and triplets of non <span>(epsilon )</span>-cospectral <span>(epsilon )</span>-equienergetic graphs. Moreover, we present some new family of <span>(epsilon )</span>-integral graphs.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440995","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
Frames and operators on quaternionic Hilbert spaces 四元Hilbert空间上的帧和算子
IF 0.7
Afrika Matematika Pub Date : 2026-03-09 DOI: 10.1007/s13370-026-01460-8
Najib Khachiaa
{"title":"Frames and operators on quaternionic Hilbert spaces","authors":"Najib Khachiaa","doi":"10.1007/s13370-026-01460-8","DOIUrl":"10.1007/s13370-026-01460-8","url":null,"abstract":"<div><p>The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form <span>({L(u_i)}_{i in I})</span>, where <i>L</i> is a bounded right <span>(mathbb {H})</span>-linear operator and <span>({u_i}_{i in I})</span> is a frame. We also show that every bounded, positive, invertible right <span>(mathbb {H})</span>-linear operator arises as a frame operator.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441115","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
Maclaurin’s inequalities for differentiable s-convex functions 可微s-凸函数的Maclaurin不等式
IF 0.7
Afrika Matematika Pub Date : 2026-03-07 DOI: 10.1007/s13370-026-01443-9
Badreddine Meftah, Nouha Allel
{"title":"Maclaurin’s inequalities for differentiable s-convex functions","authors":"Badreddine Meftah,&nbsp;Nouha Allel","doi":"10.1007/s13370-026-01443-9","DOIUrl":"10.1007/s13370-026-01443-9","url":null,"abstract":"<div><p>In this work, we use a novel identity to show a number of new Maclaurin-type inequalities for functions whose first derivatives are <i>s</i>-convex. We also deal with cases where the first derivatives are bounded and Lipschitzian. Applications in numerical integration and inequalities utilizing special means are provided out this research.</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":"147362807","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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