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LRDP: an R package implementing a new class of decompositions for orthogonal matrices LRDP：一个R包，实现了正交矩阵的一类新的分解
IF 0.9
Afrika Matematika Pub Date : 2025-04-07 DOI: 10.1007/s13370-025-01283-z
Luca Bagnato, Antonio Punzo
{"title":"LRDP: an R package implementing a new class of decompositions for orthogonal matrices","authors":"Luca Bagnato,&nbsp;Antonio Punzo","doi":"10.1007/s13370-025-01283-z","DOIUrl":"10.1007/s13370-025-01283-z","url":null,"abstract":"<div><p>Decompositions of an orthogonal matrix <span>(varvec{Q})</span> are valuable on their own and play a crucial role in statistics by simplifying the often challenging estimation of <span>(varvec{Q})</span> when it is part of a model or method. It’s important to note that, in some cases, any orthogonal matrix generated by permuting and/or flipping the signs of the columns of <span>(varvec{Q})</span> is sufficient; principal component analysis (PCA) is one such example. With this in mind, we propose a decomposition of <span>(varvec{Q})</span>, called LRDP, which allows control over the order and the sign of the columns. Due to its structure, our proposal enables the definition of simplified decompositions that can reproduce <span>(varvec{Q})</span> up to a permutation of the columns (LRD decomposition), up to a sign flip of the columns (LRP decomposition), or up to both (LR decomposition). Additionally, we introduce <b>LRDP</b>, an <span>R</span> package provided as supplementary material, specifically designed to implement our decomposition. We illustrate its functionality using a benchmark dataset from the PCA literature.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01283-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793067","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
Nested n-radical fuzzy general hyperideals 嵌套n根模糊一般超群
IF 0.9
Afrika Matematika Pub Date : 2025-04-07 DOI: 10.1007/s13370-025-01293-x
Mohammad Hamidi
{"title":"Nested n-radical fuzzy general hyperideals","authors":"Mohammad Hamidi","doi":"10.1007/s13370-025-01293-x","DOIUrl":"10.1007/s13370-025-01293-x","url":null,"abstract":"<div><p>The purpose of this paper is to introduce the notion of nested (additive)<i>n</i>-radical fuzzy subsets in general Krasner hyperrings and to analyze some conditions such as fuzzy general Krasner hyperideals in general Krasner hyperrings. To realize the article’s goals, we introduce a concept of (additive)<i>n</i>-radical subsets and show how to be a general Krasner hyperideal in general Krasner hyperrings. The main method, in this research, is based on level subsets that are related between <i>n</i>-radical general Krasner hyperideals and <i>n</i>-radical fuzzy general Krasner hyperideals. As a result of the research, is construction of nested <i>n</i>-radical fuzzy general Krasner hyperideals via the power of fuzzy Krasner hyperideals based on the hyperproduct of fuzzy general Krasner hyperideals. The paper includes implications for the development of prime fuzzy general Krasner hyperideals, such that extends prime fuzzy general Krasner hyperideals to the concept of radical fuzzy general Krasner hyperideals. The new conception of nested <i>n</i>-radical fuzzy general Krasner hyperideals was given for the first time in this paper. Also, we find a method that can compute the <i>n</i>-radical fuzzy general Krasner hyperideals via the maximum triangular conorm and fuzzy values, for simplicity.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793058","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
Generalized almost periodic functions with values in ordered Banach spaces 有序巴拿赫空间中具有值的广义概周期函数
IF 0.9
Afrika Matematika Pub Date : 2025-04-07 DOI: 10.1007/s13370-025-01298-6
M. Kostić
{"title":"Generalized almost periodic functions with values in ordered Banach spaces","authors":"M. Kostić","doi":"10.1007/s13370-025-01298-6","DOIUrl":"10.1007/s13370-025-01298-6","url":null,"abstract":"<div><p>In this paper, we analyze some classes of generalized almost periodic functions with values in ordered Banach spaces. The main structural characterizations for the introduced classes of almost periodic functions are established. We also present some applications of our results to the abstract Volterra integro-differential equations in ordered Banach spaces.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793066","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 best constants in some new sharp bounds for sinc function 在sinc函数的新边界上的最佳常数
IF 0.9
Afrika Matematika Pub Date : 2025-04-07 DOI: 10.1007/s13370-025-01288-8
Branko Malešević, Miloš Mićović, Bojana Mihailović, Tatjana Lutovac, Vesna Šešum-Čavić
{"title":"The best constants in some new sharp bounds for sinc function","authors":"Branko Malešević,&nbsp;Miloš Mićović,&nbsp;Bojana Mihailović,&nbsp;Tatjana Lutovac,&nbsp;Vesna Šešum-Čavić","doi":"10.1007/s13370-025-01288-8","DOIUrl":"10.1007/s13370-025-01288-8","url":null,"abstract":"<div><p>In this paper, some bounds of the <span>(text {sinc})</span> function from Huy et al. (Afr Mat 35:1–13, 2024) are generalised by introducing real parameters. These generalisations are based on the concept of stratification. Additionally, the best real values of the introduced parameters for which the corresponding inequalities hold are determined.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793059","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
Solution of a Fredholm integral equation on (C^star )-algebra-valued partial b-metric spaces (C^star ) -代数值偏b-度量空间上Fredholm积分方程的解
IF 0.9
Afrika Matematika Pub Date : 2025-04-07 DOI: 10.1007/s13370-025-01297-7
Gunaseelan Mani, Arul Joseph Gnanaprakasam, Choonkil Park
{"title":"Solution of a Fredholm integral equation on (C^star )-algebra-valued partial b-metric spaces","authors":"Gunaseelan Mani,&nbsp;Arul Joseph Gnanaprakasam,&nbsp;Choonkil Park","doi":"10.1007/s13370-025-01297-7","DOIUrl":"10.1007/s13370-025-01297-7","url":null,"abstract":"<div><p>In this paper, we prove fixed point theorems for generalized contraction on complete <span>(C^star )</span>-algebra-valued partial <i>b</i>-metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is presented. We also explore some of applications of our key results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793063","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
Subdiagonal and superdiagonal partitions 亚对角和超对角分区
IF 0.9
Afrika Matematika Pub Date : 2025-04-07 DOI: 10.1007/s13370-025-01282-0
M. Archibald, A. Blecher, Sergi Elizalde, A. Knopfmacher
{"title":"Subdiagonal and superdiagonal partitions","authors":"M. Archibald,&nbsp;A. Blecher,&nbsp;Sergi Elizalde,&nbsp;A. Knopfmacher","doi":"10.1007/s13370-025-01282-0","DOIUrl":"10.1007/s13370-025-01282-0","url":null,"abstract":"<div><p>In this paper we consider weakly monotonic sequences of positive integers <span>(lambda _1,lambda _2,dots ,lambda _k)</span> such that either <span>(lambda _ile i)</span> for all <i>i</i> (subdiagonal partitions) or <span>(lambda _ige i)</span> for all <i>i</i> (superdiagonal partitions). We provide generating functions for these partitions with respect to size and number of parts, using various approaches involving multivariate generating functions, functional equations, area statistics on lattice paths, and bijections.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01282-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793197","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 large family of third degree semiclassical forms of class three 第三类的一个三次半经典形式的大族
IF 0.9
Afrika Matematika Pub Date : 2025-04-01 DOI: 10.1007/s13370-025-01294-w
Mohamed Khalfallah
{"title":"A large family of third degree semiclassical forms of class three","authors":"Mohamed Khalfallah","doi":"10.1007/s13370-025-01294-w","DOIUrl":"10.1007/s13370-025-01294-w","url":null,"abstract":"<div><p>The aim of this contribution is to study several characterizations of a large family of symmetric semiclassical linear forms of class three which are of third degree. In fact, by using the Stieltjes function and the moments of those forms, we give necessary and sufficient conditions for a regular form to be at the same time of strict third degree (resp. second degree), symmetric and semiclassical of class three under conditions <span>(Phi (x)=x(x^4-1))</span> and <span>(Psi (0)in {0, 2})</span>. Thus, we focus our attention on the link between these forms and the Jacobi forms <span>(mathcal {V}_{q}^{k, l}:=mathcal {J}(k+q/3,l-q/3), k+lge -1, k, l in mathbb {Z}, qin {1,2})</span> (resp. <span>(mathcal {T}_{p,q}:=mathcal {J}(p-1/2,q-1/2), p+qge 0, p, q in mathbb {Z})</span>). All of them are rational transformations of the Jacobi form <span>(mathcal {V}:= mathcal {J} left( -2/3, -1/3 right) )</span> (resp. the Tchebychev form of first kind <span>(mathcal {T}:= mathcal {J} left( -1/2, -1/2 right) )</span>).</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740851","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
Curves of constant breadth in Galilean 4-space (mathbb {G}_4) 伽利略4空间中的等宽曲线 (mathbb {G}_4)
IF 0.9
Afrika Matematika Pub Date : 2025-04-01 DOI: 10.1007/s13370-025-01296-8
Adama Thiandoum
{"title":"Curves of constant breadth in Galilean 4-space (mathbb {G}_4)","authors":"Adama Thiandoum","doi":"10.1007/s13370-025-01296-8","DOIUrl":"10.1007/s13370-025-01296-8","url":null,"abstract":"<div><p>In this paper, we study curves of constant breadth according to Serret-Frenet frame on 4-dimensional Galilean space <span>(mathbb {G}_4)</span> and characterize these curves in terms of torsion and curvature functions. We give an example of curves of constant breadth to illustrate main results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740854","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 Toeplitz-like operator with rational matrix symbol having poles on the unit circle: matrix representation and spectral analysis 在单位圆上具有极点的有理矩阵符号的类toeplitz算子：矩阵表示和谱分析
IF 0.9
Afrika Matematika Pub Date : 2025-03-31 DOI: 10.1007/s13370-025-01291-z
Gilbert J. Groenewald, Sanne ter Horst, Jacob J. Jaftha, André C. M. Ran
{"title":"A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: matrix representation and spectral analysis","authors":"Gilbert J. Groenewald,&nbsp;Sanne ter Horst,&nbsp;Jacob J. Jaftha,&nbsp;André C. M. Ran","doi":"10.1007/s13370-025-01291-z","DOIUrl":"10.1007/s13370-025-01291-z","url":null,"abstract":"<div><p>In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in Groenewald et al. (J Math Anal Appl 532, Paper no. 127925, 2024) of this class of operators, to study the connection with semi-infinite Toeplitz matrices and to determine the essential spectrum and resolvent set.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01291-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740878","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
(Delta _h)-Appell versions of U-Bernoulli and U-Euler polynomials: properties, zero distribution patterns, and the monomiality principle (Delta _h)-阿佩尔版的u -伯努利和u -欧拉多项式：性质，零分布模式，和单项式原理
IF 0.9
Afrika Matematika Pub Date : 2025-03-28 DOI: 10.1007/s13370-025-01286-w
William Ramírez, Stiven Díaz, Alejandro Urieles, Clemente Cesarano, Shahid Ahmad Wani
{"title":"(Delta _h)-Appell versions of U-Bernoulli and U-Euler polynomials: properties, zero distribution patterns, and the monomiality principle","authors":"William Ramírez,&nbsp;Stiven Díaz,&nbsp;Alejandro Urieles,&nbsp;Clemente Cesarano,&nbsp;Shahid Ahmad Wani","doi":"10.1007/s13370-025-01286-w","DOIUrl":"10.1007/s13370-025-01286-w","url":null,"abstract":"<div><p>This paper explores the properties, generating functions, recurrence relations, and summation formulas of a novel class of polynomials, referred to as <span>(Delta _h)</span>-type <i>U</i>-Bernoulli and <span>(Delta _h)</span>-type <i>U</i>-Euler polynomials. We delve into the characterization of these polynomials, including the monomiality principle, and derive the corresponding derivative and multiplicative operators. Additionally, we provide computational values in tables and visually appealing representations of the zeros of these polynomials in figures, offering a comprehensive understanding of their behavior.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716892","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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