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Arabian Journal of Mathematics最新文献

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On some new arithmetic properties of certain restricted color partition functions 论某些受限颜色分割函数的一些新算术特性
IF 0.9
Arabian Journal of Mathematics Pub Date : 2024-03-29 DOI: 10.1007/s40065-024-00458-z
Ranganatha Dasappa,  Channabasavayya, Gedela Kavya Keerthana
{"title":"On some new arithmetic properties of certain restricted color partition functions","authors":"Ranganatha Dasappa,&nbsp; Channabasavayya,&nbsp;Gedela Kavya Keerthana","doi":"10.1007/s40065-024-00458-z","DOIUrl":"10.1007/s40065-024-00458-z","url":null,"abstract":"<div><p>Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely <span>(P^{*}(n), M(n), T^{*}(n), L(n), K(n), A(n))</span>, and <i>B</i>(<i>n</i>), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo <span>(2^acdot 5^ell )</span> for <span>(P^{*}(n))</span>, modulo <span>(2^3)</span> for <i>M</i>(<i>n</i>) and <span>(T^*(n))</span>, where <span>(a=3, 4)</span> and <span>(ell ge 1)</span>. For instance, we prove that for <span>(nge 0)</span>, </p><div><div><span>$$begin{aligned} P^{*}(5^ell (4n+3)+5^ell -1)&amp;equiv 0pmod {2^3cdot 5^{ell }}. end{aligned}$$</span></div></div><p>In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: </p><div><div><span>$$begin{aligned} M(5n+4)equiv 0pmod {5},quad T^{*}(5n+3)equiv 0pmod {5}. end{aligned}$$</span></div></div></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 2","pages":"275 - 289"},"PeriodicalIF":0.9,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00458-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140322341","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
On the convergence of the trajectories of the dynamical Moudafi’s viscosity approximation system 论动态穆达菲粘度近似系统轨迹的收敛性
IF 0.9
Arabian Journal of Mathematics Pub Date : 2024-03-22 DOI: 10.1007/s40065-024-00457-0
Ramzi May
{"title":"On the convergence of the trajectories of the dynamical Moudafi’s viscosity approximation system","authors":"Ramzi May","doi":"10.1007/s40065-024-00457-0","DOIUrl":"10.1007/s40065-024-00457-0","url":null,"abstract":"<div><p>We study the asymptotic behavior of trajectories of the continuous dynamical system(CDS) associated with the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi (J Math Anal Appl 241:46–55, 2000). We establish that the trajectories <i>x</i>(<i>t</i>) of the continuous dynamical system (CDS) has an asymptotic behavior similar to the behavior of the sequences <span>((x_{n}))</span> generated by the discrete viscosity approximation (DDS)</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 2","pages":"319 - 331"},"PeriodicalIF":0.9,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00457-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197999","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
Fixed points of Suzuki-generalized nonexpansive mappings in (CAT_p(0)) metric spaces CAT_p(0)$$度量空间中铃木广义非展开映射的定点
IF 0.9
Arabian Journal of Mathematics Pub Date : 2024-02-22 DOI: 10.1007/s40065-024-00455-2
Alia Abu Darweesh, Sami Shukri
{"title":"Fixed points of Suzuki-generalized nonexpansive mappings in (CAT_p(0)) metric spaces","authors":"Alia Abu Darweesh,&nbsp;Sami Shukri","doi":"10.1007/s40065-024-00455-2","DOIUrl":"10.1007/s40065-024-00455-2","url":null,"abstract":"<div><p>In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete <span>(CAT_p(0))</span> metric spaces for <span>(pge 2)</span>. Our results extend and improve many results in the literature.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"227 - 236"},"PeriodicalIF":0.9,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00455-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139922673","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
Correction to: On the inter-critical inhomogeneous generalized Hartree equation 更正：关于临界间非均质广义哈特里方程
IF 0.9
Arabian Journal of Mathematics Pub Date : 2024-02-21 DOI: 10.1007/s40065-024-00456-1
Tarek Saanouni, Talal Alharbi
{"title":"Correction to: On the inter-critical inhomogeneous generalized Hartree equation","authors":"Tarek Saanouni,&nbsp;Talal Alharbi","doi":"10.1007/s40065-024-00456-1","DOIUrl":"10.1007/s40065-024-00456-1","url":null,"abstract":"","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"197 - 197"},"PeriodicalIF":0.9,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00456-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140354891","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
Classical symmetries of the Klein–Gordon–Zakharov equations with time-dependent variable coefficients 具有时变系数的克莱因-戈登-扎哈罗夫方程的经典对称性
IF 0.9
Arabian Journal of Mathematics Pub Date : 2024-01-23 DOI: 10.1007/s40065-023-00454-9
Preeti Devi, Abhishek Guleria
{"title":"Classical symmetries of the Klein–Gordon–Zakharov equations with time-dependent variable coefficients","authors":"Preeti Devi,&nbsp;Abhishek Guleria","doi":"10.1007/s40065-023-00454-9","DOIUrl":"10.1007/s40065-023-00454-9","url":null,"abstract":"<div><p>In this article, we employ the group-theoretic methods to explore the Lie symmetries of the Klein–Gordon–Zakharov equations, which include time-dependent coefficients. We obtain the Lie point symmetries admitted by the Klein–Gordon–Zakharov equations along with the forms of variable coefficients. From the resulting symmetries, we construct similarity reductions.The similarity reductions are further analyzed using the power series method/approach and furnished the series solutions. Additionally, the convergence of the series solutions has been reported.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"103 - 119"},"PeriodicalIF":0.9,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00454-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139551675","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
B. Y. Chen-Ricci inequalities for anti-invariant Riemannian submersions in Kenmotsu space forms B.Kenmotsu 空间形式中反不变黎曼潜影的里奇不等式
IF 0.9
Arabian Journal of Mathematics Pub Date : 2024-01-19 DOI: 10.1007/s40065-023-00453-w
Murat Polat
{"title":"B. Y. Chen-Ricci inequalities for anti-invariant Riemannian submersions in Kenmotsu space forms","authors":"Murat Polat","doi":"10.1007/s40065-023-00453-w","DOIUrl":"10.1007/s40065-023-00453-w","url":null,"abstract":"<div><p>The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms <span>(K_{s}(varepsilon ))</span>. We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of <span>(xi )</span>. Moreover, we acquire Chen-Ricci inequalities on the <span>(ker vartheta _{*})</span> and <span>((ker vartheta _{*})^{bot })</span> distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of <span>(xi )</span>.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"181 - 196"},"PeriodicalIF":0.9,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00453-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509232","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
On deformable fractional impulsive implicit boundary value problems with delay 关于有延迟的可变形分数脉冲隐式边界值问题
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-12-19 DOI: 10.1007/s40065-023-00450-z
Salim Krim, Abdelkrim Salim, Mouffak Benchohra
{"title":"On deformable fractional impulsive implicit boundary value problems with delay","authors":"Salim Krim,&nbsp;Abdelkrim Salim,&nbsp;Mouffak Benchohra","doi":"10.1007/s40065-023-00450-z","DOIUrl":"10.1007/s40065-023-00450-z","url":null,"abstract":"<div><p>This paper deals with some existence and uniqueness results for a class of deformable fractional differential equations. These problems encompassed nonlinear implicit fractional differential equations involving boundary conditions and various types of delays, including finite, infinite, and state-dependent delays. Our approach to proving the existence and uniqueness of solutions relied on the application of the Banach contraction principle and Schauder’s fixed-point theorem. In the last section, we provide different examples to illustrate our obtained results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"199 - 226"},"PeriodicalIF":0.9,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00450-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742977","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
General stability for a Cohen–Grossberg neural network system 科恩-格罗斯伯格神经网络系统的一般稳定性
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-12-15 DOI: 10.1007/s40065-023-00452-x
Mohammed D. Kassim, Nasser-Eddine Tatar
{"title":"General stability for a Cohen–Grossberg neural network system","authors":"Mohammed D. Kassim,&nbsp;Nasser-Eddine Tatar","doi":"10.1007/s40065-023-00452-x","DOIUrl":"10.1007/s40065-023-00452-x","url":null,"abstract":"<div><p>Of concern is a Cohen–Grossberg neural network (<b>CGNNs</b>) system taking into account distributed and discrete delays. The class of delay kernels ensuring exponential stability existing in the previous papers is enlarged to an extended class of functions guaranteeing more general types of stability. The exponential and polynomial (or power type) type stabilities becomes particular cases of our result. This is achieved using appropriate Lyapunov-type functionals and the characteristics of the considered class.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"133 - 147"},"PeriodicalIF":0.9,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00452-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138691698","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 note on the inhomogeneous fractional nonlinear Schrödinger equation 关于非均质分数非线性薛定谔方程的说明
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-12-07 DOI: 10.1007/s40065-023-00451-y
Tarek Saanouni, Qihong Shi
{"title":"A note on the inhomogeneous fractional nonlinear Schrödinger equation","authors":"Tarek Saanouni,&nbsp;Qihong Shi","doi":"10.1007/s40065-023-00451-y","DOIUrl":"10.1007/s40065-023-00451-y","url":null,"abstract":"<div><p>This paper investigates some well-posedness issues of the fractional inhomogeneous Schrödinger equation </p><div><div><span>$$begin{aligned} idot{u}-(-Delta )^gamma u=pm |x|^rho |u|^{p-1}u, end{aligned}$$</span></div></div><p>where <span>(0&lt;gamma &lt;1)</span> and <span>(rho &lt;0)</span>. Here, one considers the inter-critical regime <span>(0&lt;s_c:=frac{N}{2}-frac{2gamma +rho }{p-1}&lt;gamma )</span>, where <span>(s_c)</span> is the energy critical exponent, which is the only one real number satisfying <span>(Vert kappa ^frac{2gamma +rho }{p-1}u_0(kappa cdot )Vert _{dot{H}^{s_c}}=Vert u_0Vert _{dot{H}^{s_c}})</span>. In order to avoid a loss of regularity in Strichartz estimates, one assumes that the datum is spherically symmetric. First, using a sharp Gagliardo–Nirenberg-type estimate, one develops a local theory in the space <span>(dot{H}^gamma cap dot{H}^{s_c})</span>. Then, one investigates the <span>(L^{frac{N(p-1)}{rho +2gamma }})</span> concentration of finite-time blow-up solutions bounded in <span>(dot{H}^{s_c})</span>. Finally, one proves the existence of non-global solutions with negative energy. Since one considers the homogeneous Sobolev space <span>(dot{H}^{s_c})</span>, the main difficulty here is to avoid the mass conservation law.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 2","pages":"389 - 407"},"PeriodicalIF":0.9,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00451-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547660","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
On the uniqueness of a meromorphic function and its higher difference operator under the purview of two shared sets 两个共享集下亚纯函数及其高差分算子的唯一性
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-12-06 DOI: 10.1007/s40065-023-00449-6
Sanjay Mallick, Pratap Basak
{"title":"On the uniqueness of a meromorphic function and its higher difference operator under the purview of two shared sets","authors":"Sanjay Mallick,&nbsp;Pratap Basak","doi":"10.1007/s40065-023-00449-6","DOIUrl":"10.1007/s40065-023-00449-6","url":null,"abstract":"<div><p>In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared set problems and thus improve a recent result of Chen–Chen (Bull Malays Math Sci Soc 35(3): 765-774, 2012) .</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"149 - 162"},"PeriodicalIF":0.9,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00449-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526194","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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