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Arabian Journal of Mathematics最新文献

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Equilibrium problems when the equilibrium condition is missing 缺少平衡条件时的平衡问题
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-04-21 DOI: 10.1007/s40065-023-00428-x
Mircea Balaj, Dan Florin Serac
{"title":"Equilibrium problems when the equilibrium condition is missing","authors":"Mircea Balaj,&nbsp;Dan Florin Serac","doi":"10.1007/s40065-023-00428-x","DOIUrl":"10.1007/s40065-023-00428-x","url":null,"abstract":"<div><p>Given a nonempty convex subset <i>X</i> of a topological vector space and a real bifunction <i>f</i> defined on <span>(X times X)</span>, the associated equilibrium problem consists in finding a point <span>(x_0 in X)</span> such that <span>(f(x_0, y) ge 0)</span>, for all <span>(y in X)</span>. A standard condition in equilibrium problems is that the values of <i>f</i> to be nonnegative on the diagonal of <span>(X times X)</span>. In this paper, we deal with equilibrium problems in which this condition is missing. For this purpose, we will need to consider, besides the function <i>f</i>, another one <span>(g: X times X rightarrow mathbb {R})</span>, the two bifunctions being linked by a certain compatibility condition. Applications to variational inequality problems, quasiequilibrium problems and vector equilibrium problems are given.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 2","pages":"331 - 340"},"PeriodicalIF":1.2,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00428-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50501160","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
Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems 柔性导弹的稳定性和四阶边值问题特征值的渐近性
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-04-15 DOI: 10.1007/s40065-023-00427-y
Bertin Zinsou
{"title":"Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems","authors":"Bertin Zinsou","doi":"10.1007/s40065-023-00427-y","DOIUrl":"10.1007/s40065-023-00427-y","url":null,"abstract":"<div><p>Fourth order problems with the differential equation <span>(y^{(4)}-(gy')'=lambda ^2y)</span>, where <span>(gin C^1[0,a])</span> and <span>(a&gt;0)</span>, occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation <span>(y^{(4)}-(gy')'=lambda ^2y)</span> and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non-self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"711 - 732"},"PeriodicalIF":1.2,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00427-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50482551","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
Primes and G-primes in (mathbb {Z})-nearalgebras （mathbb｛Z｝）-近代数中的素数和G-素数
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-04-01 DOI: 10.1007/s40065-023-00426-z
Shalini Chandel, Ram Parkash Sharma
{"title":"Primes and G-primes in (mathbb {Z})-nearalgebras","authors":"Shalini Chandel,&nbsp;Ram Parkash Sharma","doi":"10.1007/s40065-023-00426-z","DOIUrl":"10.1007/s40065-023-00426-z","url":null,"abstract":"<div><p>Let <i>N</i> be a <span>(mathbb {Z})</span>-nearalgebra; that is, a left nearring with identity satisfying <span>( k(nn^{prime })=(kn)n^{prime }=n(kn^{prime }))</span> for all <span>(kin mathbb {Z})</span>, <span>(n,n^{prime }in N)</span> and <i>G</i> be a finite group acting on <i>N</i>. Then the skew group nearring <span>(N*G)</span> of the group <i>G</i> over <i>N</i> is formed. If <i>N</i> is 3-prime (<span>(aNb=0)</span> implies <span>(a=0)</span> or <span>(b=0)</span>), then a nearring of quotients <span>( Q_{0}(N))</span> is constructed using semigroup ideals <span>(A_{i})</span> (a multiplicative closed set <span>(A_{i}subseteq N)</span> such that <span>(A_{i}Nsubseteq A_{i}supseteq NA_{i})</span>) of <i>N</i> and the maps <span>(f_{i}:A_{i}rightarrow N)</span> satisfying <span>( (na)f_{i}=n(af_{i}))</span>, <span>(nin N)</span> and <span>(ain A_{i})</span>. Through <span>(Q_{0}(N))</span>, we discuss the relationships between invariant prime subnearrings (<i>I</i>-primes) of <span>(N*G)</span> and <i>G</i>-invariant prime subnearrings (<i>GI</i>-primes) of <i>N</i>. Particularly we describe all the <i>I</i>-primes <span>(P_{i})</span> of <span>(N*G)</span> such that each <span>( P_{i}cap N={0})</span>, a <i>GI</i>-prime of <i>N</i>. As an application, we settle Incomparability and Going Down Problem for <i>N</i> and <span>(N*G)</span> in this situation.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"685 - 695"},"PeriodicalIF":1.2,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00426-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50428281","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: 1
Equivariant homotopy equivalence of homotopy colimits of (G)-functors （G）-函子的同胚共线的等变同胚等价
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-03-25 DOI: 10.1007/s40065-023-00424-1
Rafael Villarroel-Flores
{"title":"Equivariant homotopy equivalence of homotopy colimits of (G)-functors","authors":"Rafael Villarroel-Flores","doi":"10.1007/s40065-023-00424-1","DOIUrl":"10.1007/s40065-023-00424-1","url":null,"abstract":"<div><p>Given a group <i>G</i> and a <i>G</i>-category <span>({textbf{C}})</span>, we give a condition on a diagram of simplicial sets indexed by <span>({textbf{C}})</span> that allows us to define a natural action of <i>G</i> on its homotopy colimit, and some other simplicial sets defined in terms of the diagram. Well-known theorems on homeomorphisms and homotopy equivalences are generalized to equivariant versions.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"703 - 710"},"PeriodicalIF":1.2,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00424-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50513251","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 effective monoids of some blow-ups of Hirzebruch surfaces Hirzebruch曲面某些爆破的有效拟群
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-03-13 DOI: 10.1007/s40065-023-00425-0
G. Andablo-Reyes, B. L. De La Rosa-Navarro, M. Lahyane
{"title":"The effective monoids of some blow-ups of Hirzebruch surfaces","authors":"G. Andablo-Reyes,&nbsp;B. L. De La Rosa-Navarro,&nbsp;M. Lahyane","doi":"10.1007/s40065-023-00425-0","DOIUrl":"10.1007/s40065-023-00425-0","url":null,"abstract":"<div><p>We mainly give a numerical condition to ensure the finite generation of the effective monoids of some smooth projective rational surfaces. These surfaces are constructed from the blow-up of any fixed Hirzebruch surface at some special configurations of ordinary points. Under this numerical condition, we determine explicitly the list of all <span>((-1))</span> and <span>((-2))</span>-curves. In particular, we complete a result obtained by Harbourne (Duke Math J 52(1):129–148, 1985) and another result obtained by the third author (C R Math 338(11):873–878, 2004). Moreover, the Cox rings of these surfaces are finitely generated. Our ground field is assumed to be algebraically closed of any characteristic.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"601 - 612"},"PeriodicalIF":1.2,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00425-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50477667","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 unified analysis for reaction–diffusion models with application to the spiral waves dynamics of the Barkley model 反应-扩散模型的统一分析及其在Barkley模型螺旋波动力学中的应用
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-02-27 DOI: 10.1007/s40065-023-00423-2
Yahya Alnashri, Hasan Alzubaidi
{"title":"A unified analysis for reaction–diffusion models with application to the spiral waves dynamics of the Barkley model","authors":"Yahya Alnashri,&nbsp;Hasan Alzubaidi","doi":"10.1007/s40065-023-00423-2","DOIUrl":"10.1007/s40065-023-00423-2","url":null,"abstract":"<div><p>Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for nonlinear equations called the reaction–diffusion model. Using only three properties, this analysis provides convergence results for several conforming and non-conforming numerical schemes that align with the GDM. As an application of this analysis, the hybrid mimetic mixed (HMM) method for the reaction–diffusion model is designed, and its convergence is established. Numerical experiments using the HMM method are presented to facilitate the study of the creation of spiral waves in the Barkley model and the ways in which the waves behave when interacting with the boundaries of their generating medium.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"445 - 465"},"PeriodicalIF":1.2,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00423-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50517450","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 dual of the sequence spaces with mixed norms (l^{(p, infty )}) 具有混合范数的序列空间的对偶（l^｛（p，infty）｝）
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-02-25 DOI: 10.1007/s40065-023-00421-4
J. Lang, O. Méndez
{"title":"The dual of the sequence spaces with mixed norms (l^{(p, infty )})","authors":"J. Lang,&nbsp;O. Méndez","doi":"10.1007/s40065-023-00421-4","DOIUrl":"10.1007/s40065-023-00421-4","url":null,"abstract":"<div><p>We identify a norm-dense subspace of the dual of the sequence space <span>(l^{(p,infty )})</span>, thus closing the existing gap in the literature. We based our approach on the notion of James orthogonality, absolutely continuous norms and on the uniform convexity and the uniform smoothness of the underlying subspaces.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 2","pages":"413 - 421"},"PeriodicalIF":1.2,"publicationDate":"2023-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00421-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50512729","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 conservation laws, Lie symmetry analysis and power series solutions of a class of third-order polynomial evolution equations 一类三阶多项式演化方程的守恒定律、李对称性分析及幂级数解
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-02-24 DOI: 10.1007/s40065-023-00417-0
B. Gwaxa, Sameerah Jamal, A. G. Johnpillai
{"title":"On the conservation laws, Lie symmetry analysis and power series solutions of a class of third-order polynomial evolution equations","authors":"B. Gwaxa,&nbsp;Sameerah Jamal,&nbsp;A. G. Johnpillai","doi":"10.1007/s40065-023-00417-0","DOIUrl":"10.1007/s40065-023-00417-0","url":null,"abstract":"<div><p>In the present paper, we consider a special class of third-order polynomial evolutionary equations. These equations, via Lie theory admit the same one-parameter point transformations which leave the equations invariant. Reductions with these invariant functions lead to highly nonlinear third-order ordinary differential equations. We use a power series to establish interesting solutions to the reduced equations, whereby recurrence relations occur and convergence of the series may be tested. Finally, the conserved vectors of the class are constructed.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"553 - 564"},"PeriodicalIF":1.2,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00417-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50509762","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: 1
New method for solving non-homogeneous periodic second-order difference equation and some applications 求解非齐次周期二阶差分方程的新方法及其应用
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-02-23 DOI: 10.1007/s40065-023-00422-3
R. Ben Taher, M. Lassri, M. Rachidi
{"title":"New method for solving non-homogeneous periodic second-order difference equation and some applications","authors":"R. Ben Taher,&nbsp;M. Lassri,&nbsp;M. Rachidi","doi":"10.1007/s40065-023-00422-3","DOIUrl":"10.1007/s40065-023-00422-3","url":null,"abstract":"<div><p>In the present study, we are interested in solving the nonhomogeneous second-order linear difference equation with periodic coefficients of period <span>( pge 2)</span>, by bringing two new approaches enabling us to provide both analytic and combinatorial solutions to this family of equations. First, we get around the problem by converting this kind of equations to an equivalent family of nonhomogeneous linear difference equations of order <i>p</i> with constant coefficients. Second, we propose new expressions of the solutions of this family of equations, using our techniques of calculating the powers of product of companion matrices and some properties of generalized Fibonacci sequences. The study of the special case <span>( p=2 )</span> is provided. And to enhance the effectiveness of our approaches, some numerical examples are discussed.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"647 - 665"},"PeriodicalIF":1.2,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00422-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50507527","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 monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space 有序Hilbert空间中的单调伪压缩算子和Krasnoselskij迭代
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-02-22 DOI: 10.1007/s40065-023-00419-y
Eduardo Daniel Jorquera Álvarez
{"title":"On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space","authors":"Eduardo Daniel Jorquera Álvarez","doi":"10.1007/s40065-023-00419-y","DOIUrl":"10.1007/s40065-023-00419-y","url":null,"abstract":"<div><p>The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state monotone versions of Theorem 12 in [F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 2.1 in [Berinde, Vasile. Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators, Annals of West University of Timisoara-Mathematics and Computer Science, vol. 56, no. 2, 2018, pp. 13–27], as well as, several related results. Further results, in Hilbert spaces without a partial order, are stated too.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 2","pages":"297 - 307"},"PeriodicalIF":1.2,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00419-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50504356","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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