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Afrika Matematika最新文献

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Structural and spectral analysis of Fibonacci graphs and their zagreb indices 斐波那契图的结构和谱分析及其萨格勒布指数
IF 0.7
Afrika Matematika Pub Date : 2025-09-02 DOI: 10.1007/s13370-025-01373-y
Yasir Bashir, Bilal A. Chat
{"title":"Structural and spectral analysis of Fibonacci graphs and their zagreb indices","authors":"Yasir Bashir,&nbsp;Bilal A. Chat","doi":"10.1007/s13370-025-01373-y","DOIUrl":"10.1007/s13370-025-01373-y","url":null,"abstract":"<div><p>This study explores the relationship between a specific type of graph and the Fibonacci sequence by introducing and analyzing the Fibonacci numbers graph, denoted as <span>(G_{f_n})</span>. We delve into the structural properties of <span>(G_{f_n})</span> and establish new bounds for the first Zagreb index <span>(M_1(G_{f_n}))</span>, relating it to the number of vertices <i>n</i>, the number of edges <i>m</i>, the maximum vertex degree <span>(Delta)</span>, the minimum vertex degree <span>(delta)</span>, and the clique number <span>(omega)</span>. Additionally, we investigate the domination number specific to Fibonacci graphs. Furthermore, we introduce two matrices: the equi-degree Laplacian matrix and the equi-degree signless Laplacian matrix, and examine their spectral characteristics to gain deeper insights into the eigenvalues of these matrices associated with connected graphs corresponding to Fibonacci numbers. This research not only broadens the theoretical understanding of Fibonacci graphs but also contributes to the field of algebraic graph theory by examining these new matrices.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144927065","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
Denjoy-Wolff like set for rational semigroups 有理半群的Denjoy-Wolff类集
IF 0.7
Afrika Matematika Pub Date : 2025-09-02 DOI: 10.1007/s13370-025-01370-1
Subham Chatterjee, Gorachand Chakraborty, Tarun Kumar Chakra
{"title":"Denjoy-Wolff like set for rational semigroups","authors":"Subham Chatterjee,&nbsp;Gorachand Chakraborty,&nbsp;Tarun Kumar Chakra","doi":"10.1007/s13370-025-01370-1","DOIUrl":"10.1007/s13370-025-01370-1","url":null,"abstract":"<div><p>In this paper, we introduce the concept of Denjoy-Wolff set in rational semigroups. We show that for finitely generated Abelian rational semigroups, the Denjoy-Wolff like set is countable. Some results concerning the Denjoy-Wolff like set and the Julia set are also discussed. Then we consider a special class of rational semigroups and discuss various properties of the Denjoy-Wolff like set for this class. We use the concept of Denjoy-Wolff like set to classify the class into three sub-classes. We also show that for any semigroup in this class, the semigroup can be partitioned into <i>k</i> partitions where <i>k</i> is the cardinality of the Denjoy-Wolff like set.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144927067","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
Radii for sections of functions convex in one direction 在一个方向上凸的函数的截面的半径
IF 0.7
Afrika Matematika Pub Date : 2025-09-02 DOI: 10.1007/s13370-025-01372-z
Prachi Prajna Dash, Jugal Kishore Prajapat, Naveen Kumari
{"title":"Radii for sections of functions convex in one direction","authors":"Prachi Prajna Dash,&nbsp;Jugal Kishore Prajapat,&nbsp;Naveen Kumari","doi":"10.1007/s13370-025-01372-z","DOIUrl":"10.1007/s13370-025-01372-z","url":null,"abstract":"<div><p>Let <span>({mathcal {G}}(alpha ))</span> denote the family of functions <i>f</i>(<i>z</i>) in the open unit disk <span>({mathbb {D}} :={zin {mathbb {C}}: |z|&lt;1})</span> that satisfy <span>(f(0)=0=f'(0)=1)</span> and </p><div><div><span>$$begin{aligned} Re left( 1+ dfrac{zf''(z)}{f'(z)}right) &lt;1+dfrac{alpha }{2} , quad zin {mathbb {D}}. end{aligned}$$</span></div></div><p>We determine the disks <span>(|z|&lt;rho _n)</span> in which sections <span>(s_n(z;f))</span> of <i>f</i>(<i>z</i>) are convex, starlike, and close-to-convex of order <span>(beta ;(0le beta &lt; 1))</span>. Further, we obtain certain inequalities of sections in the considered class of functions.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144927066","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
Decision-making algorithm based on the scored-energy of neutrosophic soft sets 基于中性软集得分能量的决策算法
IF 0.7
Afrika Matematika Pub Date : 2025-08-29 DOI: 10.1007/s13370-025-01366-x
Nenad Stojanović, Nemanja Vučićević, Orhan Dalkılıç
{"title":"Decision-making algorithm based on the scored-energy of neutrosophic soft sets","authors":"Nenad Stojanović,&nbsp;Nemanja Vučićević,&nbsp;Orhan Dalkılıç","doi":"10.1007/s13370-025-01366-x","DOIUrl":"10.1007/s13370-025-01366-x","url":null,"abstract":"<div><p>Neutrosophic soft sets are a potent tool for data modeling and have therefore been the focus of extensive research, both in practical applications and from a theoretical mathematical perspective. This study aims to determine a numerical characteristic of neutrosophic soft sets that parallels the concept of energy found in graph theory and fuzzy soft set theory. This study aims to develop a decision-making algorithm that surpasses the efficiency of existing algorithms. The energy of graphs and fuzzy soft sets is determined using the singular values of a matrix, with the sum of these values representing a norm function, known as the nuclear norm in optimization problems. This concept inspires the introduction of neutrosophic soft set energy and an exploration of its potential applications. The created algorithm has been compared with a large number of existing algorithms, and in all these comparisons, the advantages of the energy-based algorithm have been highlighted.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914563","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 Solow-Swan framework for economic growth with memory effect 具有记忆效应的经济增长的索洛-斯旺框架
IF 0.7
Afrika Matematika Pub Date : 2025-08-28 DOI: 10.1007/s13370-025-01365-y
M. O. Aibinu, K. J. Duffy, S. Moyo
{"title":"A Solow-Swan framework for economic growth with memory effect","authors":"M. O. Aibinu,&nbsp;K. J. Duffy,&nbsp;S. Moyo","doi":"10.1007/s13370-025-01365-y","DOIUrl":"10.1007/s13370-025-01365-y","url":null,"abstract":"<div><p>The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing a formulation based on the Caputo fractional derivative. A comparative analysis is conducted between the integer-order and fractional-order versions of the model to examine the influence of fractional dynamics on capital accumulation. The findings reveal that the inclusion of a fractional-order derivative significantly affects the trajectory and long-term stability of capital, offering a more flexible and comprehensive framework for modeling economic growth processes.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01365-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909758","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 number of dominating sets in d-ary trees d元树中支配集的数目
IF 0.7
Afrika Matematika Pub Date : 2025-08-20 DOI: 10.1007/s13370-025-01360-3
Opeyemi Oyewumi, Adriana Roux, Stephan Wagner
{"title":"The number of dominating sets in d-ary trees","authors":"Opeyemi Oyewumi,&nbsp;Adriana Roux,&nbsp;Stephan Wagner","doi":"10.1007/s13370-025-01360-3","DOIUrl":"10.1007/s13370-025-01360-3","url":null,"abstract":"<div><p>An (unrooted) <i>d</i>-<i>ary tree</i> is a tree in which every internal vertex has degree <span>(d+1)</span>. In this paper, we show for every fixed <span>(dge 2)</span> that <i>d</i>-ary caterpillars have the minimum number of dominating sets among <i>d</i>-ary trees of a given order. We also determine the maximum number of dominating sets in binary trees (the special case <span>(d=2)</span>) and classify the extremal trees, which are also unique.</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/s13370-025-01360-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880727","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 Lie symmetry approach to migration and gene frequency 迁移和基因频率的李氏对称方法
IF 0.7
Afrika Matematika Pub Date : 2025-08-20 DOI: 10.1007/s13370-025-01357-y
Sameerah Jamal
{"title":"A Lie symmetry approach to migration and gene frequency","authors":"Sameerah Jamal","doi":"10.1007/s13370-025-01357-y","DOIUrl":"10.1007/s13370-025-01357-y","url":null,"abstract":"<div><p>This paper examines a genetic frequency model, governed by a second-order differential equation that includes a migration mean and variance parameters. Such a model is critical for understanding how gene flow affects genetic variation across migrating populations. We prove how to reduce the equation to a solvable expression, and thereafter apply Lie symmetries to obtain exact solutions. Finally, a case study of the CCR5-<span>(triangle)</span>32 mutant gene which provides resistance to HIV, is discussed.</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/s13370-025-01357-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880934","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
Positive semigroups and maximum principle for the Heckman-Opdam-Jacobi operator Heckman-Opdam-Jacobi算子的正半群与极大原理
IF 0.7
Afrika Matematika Pub Date : 2025-08-20 DOI: 10.1007/s13370-025-01359-w
Fida Bahba, Rabiaa Ghabi
{"title":"Positive semigroups and maximum principle for the Heckman-Opdam-Jacobi operator","authors":"Fida Bahba,&nbsp;Rabiaa Ghabi","doi":"10.1007/s13370-025-01359-w","DOIUrl":"10.1007/s13370-025-01359-w","url":null,"abstract":"<div><p>In this paper, we study the generalized heat equation associated with the Heckman-Opdam-Jacobi operator <span>(Delta _{textrm{HJ}})</span> on <span>({mathbb {R}}^{d+1})</span>. Specifically, we show that the extension of this operator on the space of continuous functions on <span>({mathbb {R}}^{d+1})</span> and which tend towards 0 to infinity, is the generator of a positive strongly continuous contraction semi group. This is ensured by a maximum principle for the Heckman-Opdam-Jacobi operator <span>(Delta _{textrm{HJ}})</span>. The explicit solution to the corresponding Cauchy problem incorporates a generalized heat kernel <span>(h_t)</span>, which is demonstrated to be nonnegative for real arguments.</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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880936","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
Kirillov–Lipsman orbit method of a class of Gelfand pairs: part I 一类Gelfand对的Kirillov-Lipsman轨道方法：第1部分
IF 0.7
Afrika Matematika Pub Date : 2025-08-20 DOI: 10.1007/s13370-025-01354-1
Aymen Rahali, Ibtissem Ben Chenni
{"title":"Kirillov–Lipsman orbit method of a class of Gelfand pairs: part I","authors":"Aymen Rahali,&nbsp;Ibtissem Ben Chenni","doi":"10.1007/s13370-025-01354-1","DOIUrl":"10.1007/s13370-025-01354-1","url":null,"abstract":"<div><p>Let <span>(G:=Kltimes N)</span> be the semidirect product with Lie algebra <span>(mathfrak {g},)</span> where <i>N</i> is a simply connected nilpotent Lie group, and <i>K</i> is a subgroup of the automorphisms group, <i>Aut</i>(<i>N</i>),  of <i>N</i>. We say that the pair (<i>K</i>, <i>N</i>) is a nilpotent Gelfand pair when the set <span>(L_K^1(N))</span> of integrable <i>K</i>-invariant functions on <i>N</i> forms an abelian algebra under convolution. According to Lipsman, the unitary dual <span>(widehat{G})</span> of <i>G</i> is in one-to-one correspondence with the space of admissible coadjoint orbits <span>(mathfrak {g}^ddag /G)</span> of <i>G</i>. Under some assumptions on the pair (<i>K</i>, <i>N</i>) we will show in this paper and its sequel (part II), that the Kirillov–Lipsman bijection </p><div><div><span>$$widehat{G}simeq mathfrak {g}^ddagger /G$$</span></div></div><p>is a homeomorphism for a class of Lie groups associated with the nilpotent Gelfand pairs (<i>K</i>, <i>N</i>). Part I (this paper) concerns generalities and the study of the convergence in the quotient space <span>(mathfrak {g}^ddag /G.)</span> More precisely, we give a necessary and sufficient conditions when a sequence of admissible coadjoint orbits converges in <span>(mathfrak {g}^ddag /G.)</span></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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880930","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
Discrete Sturm–Liouville problems with transmission conditions 具有传输条件的离散Sturm-Liouville问题
IF 0.7
Afrika Matematika Pub Date : 2025-08-20 DOI: 10.1007/s13370-025-01367-w
Bilender P. Allahverdiev, Hüseyin Tuna
{"title":"Discrete Sturm–Liouville problems with transmission conditions","authors":"Bilender P. Allahverdiev,&nbsp;Hüseyin Tuna","doi":"10.1007/s13370-025-01367-w","DOIUrl":"10.1007/s13370-025-01367-w","url":null,"abstract":"<div><p>In this paper, we consider regular discrete Sturm–Liouville problems with transmission conditions. Some fundamental properties are studied concerning self-adjointness, orthogonality of eigenfunctions, and eigenfunction expansions.</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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880933","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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