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Aequationes Mathematicae最新文献

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Path factors in bipartite graphs from size or spectral radius 从大小或谱半径看二方形图中的路径因子
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-18 DOI: 10.1007/s00010-024-01107-8
Yifang Hao, Shuchao Li
{"title":"Path factors in bipartite graphs from size or spectral radius","authors":"Yifang Hao,&nbsp;Shuchao Li","doi":"10.1007/s00010-024-01107-8","DOIUrl":"10.1007/s00010-024-01107-8","url":null,"abstract":"<div><p>Let <i>G</i> be a graph and let <span>(P_n)</span> be a path on <i>n</i> vertices. A spanning subgraph <i>H</i> of <i>G</i> is called a <span>({P_{3},P_{4},P_{5}})</span>-factor if every component of <i>H</i> is one of <span>(P_3,, P_4)</span> and <span>(P_5)</span>. In 1994, Wang (J Graph Theory 18(2):161–167, 1994) gave a sufficient and necessary condition to ensure that a bipartite graph contains a <span>({P_{3},P_{4},P_{5}})</span>-factor. In this paper, we use an equivalent form of Wang-type condition to establish two sufficient conditions to ensure that there exists a <span>({P_{3},P_{4},P_{5}})</span>-factor in a connected bipartite graph, in which one is based on the size, the other is based on the spectral radius of the bipartite graph.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 5","pages":"1177 - 1210"},"PeriodicalIF":0.9,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solutions of the functional difference Toda equation from centered Darboux transformation 从居中的达尔布变换求函数差分户田方程的解
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-09 DOI: 10.1007/s00010-024-01097-7
Pierre Gaillard
{"title":"Solutions of the functional difference Toda equation from centered Darboux transformation","authors":"Pierre Gaillard","doi":"10.1007/s00010-024-01097-7","DOIUrl":"https://doi.org/10.1007/s00010-024-01097-7","url":null,"abstract":"<p>By using a particular Darboux transformation which we can call centered Darboux transformation, we construct solutions of the functional difference Toda lattice equation in terms of Casorati determinants. We give a complete description of the method and the corresponding proofs. We construct some explicit solutions for the first orders.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"369 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-posedness for a class of pseudo-differential hyperbolic equations on the torus 环面上一类伪差分双曲方程的好求解性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-06 DOI: 10.1007/s00010-024-01093-x
Duván Cardona, Julio Delgado, Michael Ruzhansky
{"title":"Well-posedness for a class of pseudo-differential hyperbolic equations on the torus","authors":"Duván Cardona,&nbsp;Julio Delgado,&nbsp;Michael Ruzhansky","doi":"10.1007/s00010-024-01093-x","DOIUrl":"10.1007/s00010-024-01093-x","url":null,"abstract":"<div><p>In this paper we establish the well-posedness of the Cauchy problem for a class of pseudo-differential hyperbolic equations on the torus. The class considered here includes a space-like fractional order Laplacians. By applying the toroidal pseudo-differential calculus we establish regularity estimates, existence and uniqueness in the scale of the standard Sobolev spaces on the torus.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"1019 - 1038"},"PeriodicalIF":0.9,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01093-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Balanced Stirling numbers 平衡的斯特林数字
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-05 DOI: 10.1007/s00010-024-01087-9
Michael Maltenfort
{"title":"Balanced Stirling numbers","authors":"Michael Maltenfort","doi":"10.1007/s00010-024-01087-9","DOIUrl":"https://doi.org/10.1007/s00010-024-01087-9","url":null,"abstract":"<p>Hsu and Shiue (Adv Appl Math 20(3):366–384, 1998. https://doi.org/10.1006/aama.1998.0586) defined generalized Stirling numbers, which include as special cases a wide variety of combinatorial quantities. We prove that the two kinds of central factorial numbers are fundamentally different new special cases. Our approach also yields a previously unrecognized connection between the two kinds of central factorial numbers. In order to prove our main results, we introduce balanced Stirling numbers, which specialize the generalized Stirling numbers and can be further specialized into either kind of central factorial numbers.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"51 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Kannappan-sine addition law on semigroups 半群上的 Kannappan 正弦加法法则
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-04 DOI: 10.1007/s00010-024-01104-x
Jafar Ahmed, Ajebbar Omar, Elqorachi Elhoucien
{"title":"A Kannappan-sine addition law on semigroups","authors":"Jafar Ahmed,&nbsp;Ajebbar Omar,&nbsp;Elqorachi Elhoucien","doi":"10.1007/s00010-024-01104-x","DOIUrl":"10.1007/s00010-024-01104-x","url":null,"abstract":"<div><p>Let <i>S</i> be a semigroup and <span>(z_{0})</span> a fixed element in <i>S</i>. We determine the complex-valued solutions of the following Kannappan-sine addition law <span>(f(xyz_{0})=f(x)g(y)+f(y)g(x),x,yin S.)</span></p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"1001 - 1017"},"PeriodicalIF":0.9,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Set-valued dynamics related to convex-valued m-mappings 与凸值 m 映射相关的集值动力学
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-03 DOI: 10.1007/s00010-024-01103-y
Hamid Khodaei
{"title":"Set-valued dynamics related to convex-valued m-mappings","authors":"Hamid Khodaei","doi":"10.1007/s00010-024-01103-y","DOIUrl":"https://doi.org/10.1007/s00010-024-01103-y","url":null,"abstract":"<p>In this article, we study the set-valued dynamics related to some Euler-Lagrange type functional equations of convex-valued <i>m</i>-mappings. We deal with perturbations of these equations. In order to do this, we use the Banach contraction principle and the Hausdorff distance. Several outcomes on approximate solutions of a few important classic equations are discussed and some applications are given.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"83 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic expansions of the Archimedean compounds 阿基米德化合物的渐近展开
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-01 DOI: 10.1007/s00010-024-01102-z
Tomislav Burić, Neven Elezović, Lenka Mihoković
{"title":"Asymptotic expansions of the Archimedean compounds","authors":"Tomislav Burić,&nbsp;Neven Elezović,&nbsp;Lenka Mihoković","doi":"10.1007/s00010-024-01102-z","DOIUrl":"10.1007/s00010-024-01102-z","url":null,"abstract":"<div><p>In this paper we present a complete asymptotic expansion of the Archimedean compound of two symmetric homogeneous means and derive recursive algorithms for coefficients in this expansion. We also show some examples and obtain explicit expansions for the Archimedean compounds of the arithmetic, geometric and harmonic means.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"979 - 999"},"PeriodicalIF":0.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On surface of Apollonius of two ellipsoids 关于两个椭圆体的阿波罗尼奥斯曲面
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-27 DOI: 10.1007/s00010-024-01101-0
Attila Végh
{"title":"On surface of Apollonius of two ellipsoids","authors":"Attila Végh","doi":"10.1007/s00010-024-01101-0","DOIUrl":"10.1007/s00010-024-01101-0","url":null,"abstract":"<div><p>Apollonius defined the circle as the set of points that have a given ratio <span>(mu )</span> of distances from two given points, where the ratio is not equal to one. In a more general sense, consider two 0-symmetric, bounded, convex bodies <i>K</i> and <span>(K')</span>, which define two norms. Their unit balls are <i>K</i> and <span>(K')</span>. The surface of Apollonius is defined as the set of points equidistant from the centres of bodies <i>K</i> and <span>(K')</span> with respect to the aforementioned norms. In this paper we demonstrate that the surface of Apollonius of two ellipsoids is a quadratic surface. We also examine the circumstances under which this surface becomes a sphere.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 5","pages":"1333 - 1349"},"PeriodicalIF":0.9,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01101-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical models of functional extreme leaning machins: operator-algebraic and free-probabilistic approaches 功能极端倾斜机数学模型：算子代数和自由概率方法
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-24 DOI: 10.1007/s00010-024-01096-8
Ilwoo Cho, Palle E. T. Jorgensen
{"title":"Mathematical models of functional extreme leaning machins: operator-algebraic and free-probabilistic approaches","authors":"Ilwoo Cho, Palle E. T. Jorgensen","doi":"10.1007/s00010-024-01096-8","DOIUrl":"https://doi.org/10.1007/s00010-024-01096-8","url":null,"abstract":"<p>In this paper, we establish mathematical models for an arbitrarily fixed functional extreme learning machine (FELM). From a FELM <span>({mathfrak {M}})</span>, we construct a direct graph <i>G</i> induced by <span>({mathfrak {M}})</span>, and then define the graph groupoid <span>({mathbb {G}})</span> of <i>G</i>. Then the graph-groupoid <span>(C^{*})</span>-algebra <span>(M_{G})</span> of <i>G</i> generated by <span>({mathbb {G}})</span> is well-determined. This <span>(C^{*})</span>-algebra <span>(M_{G})</span> is realized on a certain Hilbert space <span>(H_{G})</span> up to a canonical representation. It means that the FELM <span>({mathfrak {M}})</span> is analyzed in a representation-depending structure in terms of operator algebra theory. By defining a natural free probability on <span>(M_{G})</span>, one can have an assessment tool of the operator algebra on <span>(M_{G})</span>, too.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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 generalized notion of metrics 关于广义度量概念
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-23 DOI: 10.1007/s00010-024-01092-y
Wolf-Jürgen Beyn
{"title":"On a generalized notion of metrics","authors":"Wolf-Jürgen Beyn","doi":"10.1007/s00010-024-01092-y","DOIUrl":"10.1007/s00010-024-01092-y","url":null,"abstract":"<div><p>In these notes we generalize the notion of a (pseudo) metric measuring the distance of two points, to a (pseudo) <i>n</i>-metric which assigns a value to a tuple of <span>(n ge 2)</span> points. Some elementary properties of pseudo <i>n</i>-metrics are provided and their construction via exterior products is investigated. We discuss some examples from the geometry of Euclidean vector spaces leading to pseudo <i>n</i>-metrics on the unit sphere, on the Stiefel manifold, and on the Grassmann manifold. Further, we construct a pseudo <i>n</i>-metric on hypergraphs and discuss the problem of generalizing the Hausdorff metric for closed sets to a pseudo <i>n</i>-metric.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"953 - 977"},"PeriodicalIF":0.9,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01092-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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