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On characterization of being a generalized Fibonacci Q-matrix of linear combinations of two generalized Fibonacci Q-matrices 两个广义Fibonacci q矩阵的线性组合的广义Fibonacci q矩阵的表征
IF 1.1
Afrika Matematika Pub Date : 2023-11-29 DOI: 10.1007/s13370-023-01140-x
A. Öndül, T. Demirkol, H. Özdemir
{"title":"On characterization of being a generalized Fibonacci Q-matrix of linear combinations of two generalized Fibonacci Q-matrices","authors":"A. Öndül,&nbsp;T. Demirkol,&nbsp;H. Özdemir","doi":"10.1007/s13370-023-01140-x","DOIUrl":"10.1007/s13370-023-01140-x","url":null,"abstract":"<div><p>It is given a characterization of being a matrix <span>(Q_{g({a_3},{b_3})}^{(k)})</span> of linear combination of a matrix <span>(Q_{g({a_1},{b_1})}^{(n)})</span> and a matrix <span>(Q_{g({a_2},{b_2})}^{(m)})</span>, where <span>(a_{i}, b_{i} in mathbb {R}^{*})</span>, <span>(i=1, 2, 3)</span>, <span>(m, n, k in mathbb {Z})</span>, and <span>(Q_{g({a},{b})}^{(l)})</span> denotes an (<i>a</i>, <i>b</i>)-generalized Fibonacci <i>Q</i>-matrix with <span>(lin mathbb {Z})</span>. In addition, some examples are presented illustrating the main result. Finally, some applications of the main result obtained are given.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138454617","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 periodic solution of a second order linear equation 二阶线性方程的周期解
IF 1.1
Afrika Matematika Pub Date : 2023-11-28 DOI: 10.1007/s13370-023-01142-9
Ni Hua
{"title":"The periodic solution of a second order linear equation","authors":"Ni Hua","doi":"10.1007/s13370-023-01142-9","DOIUrl":"10.1007/s13370-023-01142-9","url":null,"abstract":"<div><p>This paper deals with a class of second-order linear differential equations with periodic coefficients. By viable transformation, we put the second-order linear differential equation into Riccati’s equation. By means of two periodic solutions of Riccati’s equation and variable transformation, we obtain the existence and uniqueness of the periodic solution of the nonhomogeneous second-order linear differential equation, some new results are obtained.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138449153","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
Algebraic points on the curve of affine equation (y^2 =x(x-3)(x-4)(x-6)(x-7)) 仿射方程曲线上的代数点 (y^2 =x(x-3)(x-4)(x-6)(x-7))
IF 1.1
Afrika Matematika Pub Date : 2023-11-28 DOI: 10.1007/s13370-023-01128-7
Boubacar Sidy Balde, Oumar Sall
{"title":"Algebraic points on the curve of affine equation (y^2 =x(x-3)(x-4)(x-6)(x-7))","authors":"Boubacar Sidy Balde,&nbsp;Oumar Sall","doi":"10.1007/s13370-023-01128-7","DOIUrl":"10.1007/s13370-023-01128-7","url":null,"abstract":"<div><p>In this work, we use the finiteness of the Mordell–Weil group of the Jacobian variety of the curve <span>(mathcal {C}:y^2 =x(x-3)(x-4)(x-6)(x-7))</span> and the Riemann Roch spaces to determine explicitly the set of algebraic points of given degree <i>l</i> over <span>(mathbb {Q})</span> on the curve <span>(mathcal {C})</span>. The results obtained extend the work of Gordon and Grant, who determined the Mordell–Weil group <span>(J(mathbb {Q}))</span> and the set of rational points on the same curve.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138449078","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
Fractional maximal operator in the local Morrey–Lorentz spaces and some applications 局部Morrey-Lorentz空间中的分数极大算子及其应用
IF 1.1
Afrika Matematika Pub Date : 2023-11-27 DOI: 10.1007/s13370-023-01145-6
V. S. Guliyev, C. Aykol, A. Kucukaslan, A. Serbetci
{"title":"Fractional maximal operator in the local Morrey–Lorentz spaces and some applications","authors":"V. S. Guliyev,&nbsp;C. Aykol,&nbsp;A. Kucukaslan,&nbsp;A. Serbetci","doi":"10.1007/s13370-023-01145-6","DOIUrl":"10.1007/s13370-023-01145-6","url":null,"abstract":"<div><p>In this study, we obtain the necessary and sufficient conditions for the boundedness of the fractional maximal operator <span>(M_{alpha })</span> in the local Morrey–Lorentz spaces <span>(M_{p,q;lambda }^{loc}({mathbb {R}}^n))</span>. We use sharp rearrangement inequalities while proving our result. We apply this result to the Schrödinger operator <span>(-Delta + V)</span> on <span>({mathbb {R}}^n)</span>, where the nonnegative potential <i>V</i> belongs to the reverse Hölder class <span>(B_{infty }({mathbb {R}}^n))</span>. The local Morrey–Lorentz <span>(M_{p,r;lambda }^{loc}({mathbb {R}}^n) rightarrow M_{q,s;lambda }^{loc}({mathbb {R}}^n))</span> estimates for the Schrödinger type operators <span>(V^{gamma } (-Delta +V)^{-beta })</span> and <span>(V^{gamma } nabla (-Delta +V)^{-beta })</span> are obtained.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138449079","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
Fixed point theory for F-set-contraction multimaps and application to a system of integral inclusions f集收缩多映射的不动点理论及其在整包含系统上的应用
IF 1.1
Afrika Matematika Pub Date : 2023-11-25 DOI: 10.1007/s13370-023-01146-5
Maha Belhadj, Mohamed Boumaiza
{"title":"Fixed point theory for F-set-contraction multimaps and application to a system of integral inclusions","authors":"Maha Belhadj,&nbsp;Mohamed Boumaiza","doi":"10.1007/s13370-023-01146-5","DOIUrl":"10.1007/s13370-023-01146-5","url":null,"abstract":"<div><p>In this paper, we prove some generalizations of Darbo’s fixed point theorem for multivalued mappings by considering a measure of noncompactness which does not necessarily have the maximum property. Moreover, we prove some coupled fixed point theorems for multivalued mappings. Our results generalize, prove and extend well-known results in the subject. An application to solve a nonlinear system of integral inclusions is given.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138449070","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 rejoinder model for the population dynamics of the spread of two interacting pieces of information 两个相互作用的信息块传播的种群动态响应模型
IF 1.1
Afrika Matematika Pub Date : 2023-11-24 DOI: 10.1007/s13370-023-01134-9
Emmanuel Jesuyon Dansu, Hiromi Seno
{"title":"A rejoinder model for the population dynamics of the spread of two interacting pieces of information","authors":"Emmanuel Jesuyon Dansu,&nbsp;Hiromi Seno","doi":"10.1007/s13370-023-01134-9","DOIUrl":"10.1007/s13370-023-01134-9","url":null,"abstract":"<div><p>Information warfare requires more attention as competing interests get escalated by the spread of information on various Internet-based social media platforms in recent times. In this work, we construct and analyze a mathematical model with a system of ordinary differential equations to consider how two interacting pieces of information, where the first one is incomplete and misleading while the second one is corrective of the first, evolve with time in an online population. The counter and correctional information is the rejoinder. Human psychological and sociological attributes like disbelief in the rejoinder and increased tendency to keep spreading the misleading information even after knowing the correct one are factored into our model. We find that in correcting a misleading piece of information that is already spreading within a population, the rejoinder has to be released early enough within a certain time range. The findings can help us appreciate the impact of misinformation on the society and promote information literacy at optimal cost.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138437166","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 codes over ({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3} ) and their applications in secret sharing schemes ({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3} )上的一些代码及其在秘密共享方案中的应用
IF 1.1
Afrika Matematika Pub Date : 2023-11-23 DOI: 10.1007/s13370-023-01143-8
Karima Chatouh
{"title":"Some codes over ({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3} ) and their applications in secret sharing schemes","authors":"Karima Chatouh","doi":"10.1007/s13370-023-01143-8","DOIUrl":"10.1007/s13370-023-01143-8","url":null,"abstract":"<div><p>Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring <span>({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3})</span>. We have introduced a novel family of linear codes over <span>({mathbb {F}}_{p})</span>. These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. <span>({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3})</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138431612","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 a group extension involving the Suzuki group Sz(8) 关于铃木集团Sz(8)的群延
IF 1.1
Afrika Matematika Pub Date : 2023-11-17 DOI: 10.1007/s13370-023-01130-z
Ayoub B. M. Basheer
{"title":"On a group extension involving the Suzuki group Sz(8)","authors":"Ayoub B. M. Basheer","doi":"10.1007/s13370-023-01130-z","DOIUrl":"10.1007/s13370-023-01130-z","url":null,"abstract":"<div><p>The Suzuki simple group <i>Sz</i>(8) has an automorphism group 3. Using the electronic Atlas [22], the group <i>Sz</i>(8) : 3 has an absolutely irreducible module of dimension 12 over <span>({mathbb {F}}_{2}.)</span> Therefore a split extension group of the form <span>(2^{12}{:}(Sz(8){:}3):= {overline{G}})</span> exists. In this paper we study this group, where we determine its conjugacy classes and character table using the coset analysis technique together with Clifford-Fischer Theory. We determined the inertia factor groups of <span>({overline{G}})</span> by analysing the maximal subgroups of <i>Sz</i>(8) : 3 and maximal of the maximal subgroups of <i>Sz</i>(8) : 3 together with various other information. It turns out that the character table of <span>({overline{G}})</span> is a <span>(43 times 43)</span> complex valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 7.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-023-01130-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138138504","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
Canal surfaces generated by special curves and quaternions 运河表面由特殊曲线和四元数生成
IF 1.1
Afrika Matematika Pub Date : 2023-11-17 DOI: 10.1007/s13370-023-01138-5
Abdussamet Çalışkan
{"title":"Canal surfaces generated by special curves and quaternions","authors":"Abdussamet Çalışkan","doi":"10.1007/s13370-023-01138-5","DOIUrl":"10.1007/s13370-023-01138-5","url":null,"abstract":"<div><p>In this paper, we show that canal and tubular surfaces can be obtained by special curves. Also, we give the equations of the canal and tubular surfaces given by the different frames. Besides, these surfaces are obtained by quaternion and homothetic motion.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138138535","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
Causal structure of spacetime and Scott topology 时空因果结构与斯科特拓扑学
IF 1.1
Afrika Matematika Pub Date : 2023-11-17 DOI: 10.1007/s13370-023-01122-z
Langelihle Mazibuko, Dharmanand Baboolal, Rituparno Goswami
{"title":"Causal structure of spacetime and Scott topology","authors":"Langelihle Mazibuko,&nbsp;Dharmanand Baboolal,&nbsp;Rituparno Goswami","doi":"10.1007/s13370-023-01122-z","DOIUrl":"10.1007/s13370-023-01122-z","url":null,"abstract":"<div><p>In this paper we establish the spacetime manifold as a partially ordered set via the casual structure. We show that these partially ordered sets are naturally continuous as a suitable way below relation can be established via the chronological order. We further consider those classes of spacetimes on which a lattice structure can be endowed by physically defining the joins and meets. By considering the physical properties of null geodesics on the spacetime manifold we show that these lattices are necessarily distributive. These lattices are then continuous as a result of the equivalence between the way below relation and chronology. This enables us to define the Scott topology on the spacetime manifold and describe it on an equal footing as any other continuous lattice. We further show that the Scott topology is a proper subset of Alexandroff topology, which must be the manifold topology for the strongly causal spacetimes, (and hence a coarser topology than Alexandroff). In the process we find some interesting results on the sobriety of these manifolds. We prove that they are necessarily not sober under the Scott topology but regain their sobriety under Alexandroff topology. We also define a dual Scott topology on these manifolds by endowing them with bicontinuous poset structure and show that the join of the Scott topology with the dual is the Alexandroff topology. We also discuss the previous works done in this topic and how the present work generalises those results to some extent.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-023-01122-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878375","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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