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Arabian Journal of Mathematics最新文献

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Three equivalent conditions for spectral decomposable linear relations 谱可分解线性关系的三个等价条件
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-03-13 DOI: 10.1007/s40065-025-00503-5
Yosra Barkaoui, Maher Mnif
{"title":"Three equivalent conditions for spectral decomposable linear relations","authors":"Yosra Barkaoui,&nbsp;Maher Mnif","doi":"10.1007/s40065-025-00503-5","DOIUrl":"10.1007/s40065-025-00503-5","url":null,"abstract":"<div><p>The spectral decomposability of a closed linear relation <i>T</i> on a complex Banach space is demonstrated through three new characterisations: The first two are expressed in terms of the extended Bishop and decomposition properties while the third one is given by means of the coinduced operator of <i>T</i> and its local spectral subspaces. This has been achieved through the intensive study of the properties of the last mentioned subspaces as well as the ER-SVEP.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"15 - 27"},"PeriodicalIF":0.9,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865459","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
Extension of the Tricomi problem for a third-order loaded parabolic-hyperbolic equation 一类三阶负载抛物-双曲型方程Tricomi问题的推广
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-03-08 DOI: 10.1007/s40065-025-00506-2
Umida Baltaeva, Marjona Sh. Kosimova, Hamrobek Hayitbayev
{"title":"Extension of the Tricomi problem for a third-order loaded parabolic-hyperbolic equation","authors":"Umida Baltaeva,&nbsp;Marjona Sh. Kosimova,&nbsp;Hamrobek Hayitbayev","doi":"10.1007/s40065-025-00506-2","DOIUrl":"10.1007/s40065-025-00506-2","url":null,"abstract":"<div><p>In this paper, we investigate the unique solvability of a generalized Tricomi problem with an integral condition for a loaded equation involving a fractional operator. By analyzing the problem for a third-order equation with a telegraph operator, we extend the results to a generalized operator with small parameters. Furthermore, the integral condition in the parabolic region enables the generalization of local problems associated with second- and third-order equations.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"1 - 13"},"PeriodicalIF":0.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865427","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
Convergence of the modified Newton-type iteration method for the generalized absolute value equation 广义绝对值方程修正牛顿迭代法的收敛性
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-24 DOI: 10.1007/s40065-025-00500-8
Ximing Fang, Minhai Huang
{"title":"Convergence of the modified Newton-type iteration method for the generalized absolute value equation","authors":"Ximing Fang,&nbsp;Minhai Huang","doi":"10.1007/s40065-025-00500-8","DOIUrl":"10.1007/s40065-025-00500-8","url":null,"abstract":"<div><p>For the modified Newton-type (MN) iteration method for solving the GAVE, the convergence conditions and the quasi-optimal parameter matrix are discussed. The sufficient conditions are supplied to ensure that the GAVE has a unique solution. Besides, the numerical experiments are illustrated to show some of the presented results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"29 - 37"},"PeriodicalIF":0.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865397","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
Relative versions of depth, Ischebeck, and Chouinard formulas with respect to a semidualizing module 相对版本的深度，Ischebeck，和Chouinard公式关于半虚化模块
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-18 DOI: 10.1007/s40065-025-00498-z
Maryam Salimi, Elham Tavasoli
{"title":"Relative versions of depth, Ischebeck, and Chouinard formulas with respect to a semidualizing module","authors":"Maryam Salimi,&nbsp;Elham Tavasoli","doi":"10.1007/s40065-025-00498-z","DOIUrl":"10.1007/s40065-025-00498-z","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative Noetherian ring, and let <i>C</i> be a semidualizing <i>R</i>-module. The present paper aims at studying some properties of <span>({textrm{Hom}_{textrm{R}}}(C, M))</span> and <span>(C otimes _{R} M)</span> where <i>M</i> is a non-zero finitely generated <i>R</i>-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to <i>C</i>. Finally, we establish relative versions of Ischebeck and Chouinard formulas for <i>R</i>-modules of finite relative homological dimensions with respect to <i>C</i>.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"171 - 181"},"PeriodicalIF":0.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865424","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
O-metrics: new metric-types, polygon inequalities and fixed point theorems from binary operations o -度量：新的度量类型，多边形不等式和由二元运算得出的不动点定理
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-14 DOI: 10.1007/s40065-025-00493-4
Hallowed Oluwadara Olaoluwa, Aminat Olawunmi Ige, Johnson Olajire Olaleru
{"title":"O-metrics: new metric-types, polygon inequalities and fixed point theorems from binary operations","authors":"Hallowed Oluwadara Olaoluwa,&nbsp;Aminat Olawunmi Ige,&nbsp;Johnson Olajire Olaleru","doi":"10.1007/s40065-025-00493-4","DOIUrl":"10.1007/s40065-025-00493-4","url":null,"abstract":"<div><p>The class of O-metric spaces generalizes several existing metric-type spaces in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and establish in the setting, fixed point theorems for contractions and generalized contractions. The proofs of the theorems rely heavily on polygon <span>({{textbf {o}}})</span>-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the notion of <span>({{textbf {o}}})</span>-series following a pattern of functions. As application, conditions for the existence of solutions of initial value problems are discussed and a generalization of Lebesgue spaces is introduced.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"121 - 154"},"PeriodicalIF":0.9,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865460","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
Decoupled matrix Riccati differential equations approach for robust boundary data completion in time-fractional diffusion problems 时间分数扩散问题鲁棒边界数据补全的解耦矩阵Riccati微分方程方法
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-11 DOI: 10.1007/s40065-025-00497-0
Fadhel Jday, Ridha Mdimagh, Haithem Omri
{"title":"Decoupled matrix Riccati differential equations approach for robust boundary data completion in time-fractional diffusion problems","authors":"Fadhel Jday,&nbsp;Ridha Mdimagh,&nbsp;Haithem Omri","doi":"10.1007/s40065-025-00497-0","DOIUrl":"10.1007/s40065-025-00497-0","url":null,"abstract":"<div><p>This research introduces an innovative algorithmic framework tailored to solve the inverse boundary data completion problem for time-fractional diffusion equations in a bounded domain, especially under partially specified Neumann and Dirichlet conditions. This issue is notoriously ill-posed in the Hadamard sense, which demands a sophisticated and nuanced approach. Our method innovatively transforms this problem into a system of first-order differential equations linked with Matrix Riccati Differential Equations. Moving beyond traditional methods, our framework integrates a state-of-the-art decoupling algorithm, which effectively blends the strategic depth of optimal control theory with the precision of the Golden Section Search algorithm. This integration determines the optimal regularization parameter essential for ensuring the stability and the reliability of the solution. The robustness and effectiveness of our approach have been rigorously verified through extensive numerical experiments, proving its resilience even in conditions marked by significant noise levels.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"85 - 105"},"PeriodicalIF":0.9,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865457","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
Finite-dimensional nilpotent Lie superalgebras of class two and skew-supersymmetric bilinear maps 有限维二阶幂零李超代数与斜超对称双线性映射
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-04 DOI: 10.1007/s40065-025-00496-1
Ibrahem Yakzan Hasan, Rudra Narayan Padhan
{"title":"Finite-dimensional nilpotent Lie superalgebras of class two and skew-supersymmetric bilinear maps","authors":"Ibrahem Yakzan Hasan,&nbsp;Rudra Narayan Padhan","doi":"10.1007/s40065-025-00496-1","DOIUrl":"10.1007/s40065-025-00496-1","url":null,"abstract":"<div><p>In this article, we discuss the category <span>(mathcal{S}mathcal{N}_2)</span> where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category <span>(mathcal {SSKE})</span> where the objects are skew-supersymmetric bilinear maps. We establish a relation between <span>(mathcal{S}mathcal{N}_2)</span> and <span>(mathcal {SSKE})</span>. As a result, we discuss the capability of nilpotent Lie superalgebras of class two.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"39 - 51"},"PeriodicalIF":0.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865421","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 study on the finite time stability and controllability of time delay fractional model 时滞分数阶模型的有限时间稳定性和可控性研究
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-04 DOI: 10.1007/s40065-025-00492-5
P. K. Lakshmi Priya, K. Kaliraj
{"title":"A study on the finite time stability and controllability of time delay fractional model","authors":"P. K. Lakshmi Priya,&nbsp;K. Kaliraj","doi":"10.1007/s40065-025-00492-5","DOIUrl":"10.1007/s40065-025-00492-5","url":null,"abstract":"<div><p>The mainspring of this analytical study is to implement the idea of delayed argument cosine and sine conformable matrices to interpret the stability bounds of conformable type fractional operator over finite time period using modified integral form of Gronwall’s inequality. Further, we establish the conformable Grammian matrices in-terms of sine function to analyze the controllability results. The main inception is to first consider the linear controllability result of our defined system and to a greater extent, fixed point techniques along with the properties of Bochner-integral and inner product spaces are implemented to verify the controllability results of the nonlinear system. The theoretical study is graphically visualized using matlab software.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"155 - 170"},"PeriodicalIF":0.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865422","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
Approximation and shape preserving properties by nonlinear Lupaş type Bernstein operators of max-product kind 最大积类非线性lupaku型Bernstein算子的逼近和保形性质
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-02-04 DOI: 10.1007/s40065-025-00494-3
Mohd Shanawaz Mansoori, Asif Khan, Khursheed J. Ansari
{"title":"Approximation and shape preserving properties by nonlinear Lupaş type Bernstein operators of max-product kind","authors":"Mohd Shanawaz Mansoori,&nbsp;Asif Khan,&nbsp;Khursheed J. Ansari","doi":"10.1007/s40065-025-00494-3","DOIUrl":"10.1007/s40065-025-00494-3","url":null,"abstract":"<div><p>A new analogue of the nonlinear Lupaş type Bernstein operators using max-product algebra and <i>q</i>-integers, which possess the endpoint interpolation property, is constructed. Quasi-convexity, monotonicity, and shape-preserving properties are studied. The graphs have also been added to support the theoretical results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"107 - 120"},"PeriodicalIF":0.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865420","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 class of relaxed-inertial derivative-free projection method beyond monotonicity with application 一类超越单调性的松弛惯性无导数投影法及其应用
IF 0.9
Arabian Journal of Mathematics Pub Date : 2025-01-24 DOI: 10.1007/s40065-024-00491-y
Abdulkarim Hassan Ibrahim, Mohammed Alshahrani, Suliman Al-Homidan
{"title":"A class of relaxed-inertial derivative-free projection method beyond monotonicity with application","authors":"Abdulkarim Hassan Ibrahim,&nbsp;Mohammed Alshahrani,&nbsp;Suliman Al-Homidan","doi":"10.1007/s40065-024-00491-y","DOIUrl":"10.1007/s40065-024-00491-y","url":null,"abstract":"<div><p>Recent advances have introduced derivative-free projection methods incorporating a relaxed-inertial technique to solve large-scale systems of nonlinear equations (LSoNE). These methods are often studied under restrictive assumptions such as monotonicity and Lipschitz continuity assumptions. In this paper, we propose a new class of derivative-free projection method with a relaxed inertial technique for solving LSoNE. Unlike existing approaches that rely on monotonicity and Lipschitz continuity assumptions, our method extends beyond these limitations, broadening the applicability of projection methods to more general problem classes. This enhances both the theoretical framework and the practical efficiency in large-scale applications. Moreover, we establish global convergence without the need for a summability condition on the inertial extrapolation step length. To demonstrate the effectiveness of the method, we present numerical experiments to solve LSoNE and regularized decentralized logistic regression, a key problem in machine learning applications.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"53 - 84"},"PeriodicalIF":0.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865524","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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