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Mediterranean Journal of Mathematics最新文献

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Quantum Annular Homology and Bigger Burnside Categories 量子环同构与更大的伯恩赛德范畴
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-07-01 DOI: 10.1007/s00009-024-02693-2
Federico Cantero Morán, Sergio García-Rodrigo, Marithania Silvero
{"title":"Quantum Annular Homology and Bigger Burnside Categories","authors":"Federico Cantero Morán, Sergio García-Rodrigo, Marithania Silvero","doi":"10.1007/s00009-024-02693-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02693-2","url":null,"abstract":"<p>As part of their construction of the Khovanov spectrum, Lawson, Lipshitz and Sarkar assigned to each cube in the Burnside category of finite sets and finite correspondences, a finite cellular spectrum. In this paper, we extend this assignment to cubes in Burnside categories of infinite sets. This is later applied to the work of Akhmechet, Krushkal and Willis on the quantum annular Khovanov spectrum with an action of a finite cyclic group: we obtain a quantum annular Khovanov spectrum with an action of the infinite cyclic group.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519917","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 Birkhoff–Kellogg Type Theorem for Discontinuous Operators with Applications 不连续算子的伯克霍夫-凯洛格类型定理及其应用
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-07-01 DOI: 10.1007/s00009-024-02692-3
Alessandro Calamai, Gennaro Infante, Jorge Rodríguez-López
{"title":"A Birkhoff–Kellogg Type Theorem for Discontinuous Operators with Applications","authors":"Alessandro Calamai, Gennaro Infante, Jorge Rodríguez-López","doi":"10.1007/s00009-024-02692-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02692-3","url":null,"abstract":"<p>By means of fixed point index theory for multivalued maps, we provide an analogue of the classical Birkhoff–Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general and can be applied, for example, to eigenvalues and parameter problems for ordinary differential equations with discontinuities. We illustrate in detail this fact for a class of second-order boundary value problem with deviated arguments and discontinuous terms. In a specific example, we explicitly compute the terms that occur in our theory.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"27 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507668","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
Isolation of Regular Graphs and k-Chromatic Graphs 正则图和 k 色度图的隔离
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-27 DOI: 10.1007/s00009-024-02680-7
Peter Borg
{"title":"Isolation of Regular Graphs and k-Chromatic Graphs","authors":"Peter Borg","doi":"10.1007/s00009-024-02680-7","DOIUrl":"https://doi.org/10.1007/s00009-024-02680-7","url":null,"abstract":"<p>Given a set <span>({mathcal {F}})</span> of graphs, we call a copy of a graph in <span>({mathcal {F}})</span> an <span>({mathcal {F}})</span>-graph. The <span>({mathcal {F}})</span>-isolation number of a graph <i>G</i>, denoted by <span>(iota (G,{mathcal {F}}))</span>, is the size of a smallest set <i>D</i> of vertices of <i>G</i> such that the closed neighborhood of <i>D</i> intersects the vertex sets of the <span>({mathcal {F}})</span>-graphs contained by <i>G</i> (equivalently, <span>(G - N[D])</span> contains no <span>({mathcal {F}})</span>-graph). Thus, <span>(iota (G,{K_1}))</span> is the domination number of <i>G</i>. For any integer <span>(k ge 1)</span>, let <span>({mathcal {F}}_{1,k})</span> be the set of regular graphs of degree at least <span>(k-1)</span>, let <span>({mathcal {F}}_{2,k})</span> be the set of graphs whose chromatic number is at least <i>k</i>, and let <span>({mathcal {F}}_{3,k})</span> be the union of <span>({mathcal {F}}_{1,k})</span> and <span>({mathcal {F}}_{2,k})</span>. Thus, <i>k</i>-cliques are members of both <span>({mathcal {F}}_{1,k})</span> and <span>({mathcal {F}}_{2,k})</span>. We prove that for each <span>(i in {1, 2, 3})</span>, <span>(frac{m+1}{{k atopwithdelims ()2} + 2})</span> is a best possible upper bound on <span>(iota (G, {mathcal {F}}_{i,k}))</span> for connected <i>m</i>-edge graphs <i>G</i> that are not <i>k</i>-cliques. The bound is attained by infinitely many (non-isomorphic) graphs. The proof of the bound depends on determining the graphs attaining the bound. This appears to be a new feature in the literature on isolation. Among the result’s consequences are a sharp bound of Fenech, Kaemawichanurat, and the present author on the <i>k</i>-clique isolation number and a sharp bound on the cycle isolation number.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"184 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507669","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 the Depth of Generalized Binomial Edge Ideals 论广义二项式边理想的深度
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-26 DOI: 10.1007/s00009-024-02685-2
J. Anuvinda, Ranjana Mehta, Kamalesh Saha
{"title":"On the Depth of Generalized Binomial Edge Ideals","authors":"J. Anuvinda, Ranjana Mehta, Kamalesh Saha","doi":"10.1007/s00009-024-02685-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02685-2","url":null,"abstract":"<p>This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of <i>d</i>-compatible map and use it to give a combinatorial lower bound for the depth of generalized binomial edge ideals. Subsequently, we determine an upper bound for the depth of generalized binomial edge ideals in terms of the vertex-connectivity of graphs. We demonstrate that the difference between the upper and lower bounds can be arbitrarily large, even in cases when one of the bounds is sharp. In addition, we calculate the depth of generalized binomial edge ideals of certain classes of graphs, including cycles and graphs with Cohen-Macaulay binomial edge ideals.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529670","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
An Adaptive Difference Method for Variable-Order Diffusion Equations 变阶扩散方程的自适应差分法
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-25 DOI: 10.1007/s00009-024-02681-6
Joaquín Quintana-Murillo, Santos Bravo Yuste
{"title":"An Adaptive Difference Method for Variable-Order Diffusion Equations","authors":"Joaquín Quintana-Murillo, Santos Bravo Yuste","doi":"10.1007/s00009-024-02681-6","DOIUrl":"https://doi.org/10.1007/s00009-024-02681-6","url":null,"abstract":"<p>An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional-time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of these timesteps is chosen by an adaptive algorithm to keep the local error bounded around a preset value, a value that can be chosen at will. For some types of problems, this adaptive method is much faster than the corresponding usual method with fixed timesteps while keeping the local error of the numerical solution around the preset values. These findings turn out to be similar to those found for constant-order fractional diffusion equations.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519921","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
Clifford Actions Defining Klein Surfaces 定义克莱因曲面的克利福德行为
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-25 DOI: 10.1007/s00009-024-02691-4
Ewa Tyszkowska
{"title":"Clifford Actions Defining Klein Surfaces","authors":"Ewa Tyszkowska","doi":"10.1007/s00009-024-02691-4","DOIUrl":"https://doi.org/10.1007/s00009-024-02691-4","url":null,"abstract":"<p>We represent Klein surfaces as the orbit spaces of Riemann surfaces under actions of multiplicative subgroups of real Clifford algebras. We define a partial order on the set of all Klein surfaces and we prove that the defining action of any Klein surface <i>Y</i> can be obtained by induction from the defining action of a minimal element of the chain to which <i>Y</i> belongs.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"237 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519922","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
Weighted and Unweighted Composition Operators Close to Isometries 接近等距的加权和非加权合成算子
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-19 DOI: 10.1007/s00009-024-02688-z
Jatin Anand, Sneh Lata, Sachi Srivastava
{"title":"Weighted and Unweighted Composition Operators Close to Isometries","authors":"Jatin Anand, Sneh Lata, Sachi Srivastava","doi":"10.1007/s00009-024-02688-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02688-z","url":null,"abstract":"<p>In this paper, we study composition and weighted composition operators that are close to isometries on <span>({mathcal {H}}^2)</span> but not necessarily isometric. We also obtain a Wold type decomposition for such operators.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"88 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507670","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 Transference Theorem and Its Application 转移定理及其应用
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-17 DOI: 10.1007/s00009-024-02687-0
Ziyao Liu, Jiecheng Chen, Dashan Fan
{"title":"A Transference Theorem and Its Application","authors":"Ziyao Liu, Jiecheng Chen, Dashan Fan","doi":"10.1007/s00009-024-02687-0","DOIUrl":"https://doi.org/10.1007/s00009-024-02687-0","url":null,"abstract":"<p>In this article, we establish a transference between the n-dimensional Euclidean space <span>( mathbb {R} ^{n})</span> and the n-torus <span>(mathbb {T}^{n})</span> about the <span>(H^{p}-L^{p,infty })</span> boundedness of maximal multipliers. As an application, we obtain that the maximal oscillatory integral <span>(S_{alpha ,beta }^{*})</span> is bounded from <span>( H^{p}left( mathbb {R} ^{n}right) )</span> to <span>(L^{p,infty }left( mathbb {R} ^{n}right) )</span> under the sharp relation among <span>(alpha ,beta )</span> and <i>p</i>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507671","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
Bases of $$varepsilon $$ -Canonical Number Systems in Quadratic Number Fields 二次数域中的$$varepsilon$$规范数系的基数
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-16 DOI: 10.1007/s00009-024-02676-3
Borka Jadrijević
{"title":"Bases of $$varepsilon $$ -Canonical Number Systems in Quadratic Number Fields","authors":"Borka Jadrijević","doi":"10.1007/s00009-024-02676-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02676-3","url":null,"abstract":"<p>In this paper, we give an explicit characterization of all bases of <span>(varepsilon )</span>-canonical number systems (<span>(varepsilon )</span>-CNS) with finiteness property in quadratic number fields for all values <span>(varepsilon in [0,1))</span>. This result is a consequence of the recent result of Jadrijević and Miletić on the characterization of quadratic <span>(varepsilon )</span>-CNS polynomials. Our result includes the well-known characterization of all bases of classical CNS (<span>(varepsilon =0)</span>) with finiteness property in quadratic number fields. It also fits into the general framework of generalized number systems (GNS) introduced by A. Pethő and J. Thuswaldner.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507672","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 Representation Theorem for Archimedean Riesz Spaces 阿基米德里兹空间的表示定理
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-06-13 DOI: 10.1007/s00009-024-02684-3
A. W. Wickstead
{"title":"A Representation Theorem for Archimedean Riesz Spaces","authors":"A. W. Wickstead","doi":"10.1007/s00009-024-02684-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02684-3","url":null,"abstract":"<p>In previous works, Buskes and the author have made use of representations of Archimedean Riesz spaces in terms of real-valued continuous functions defined on dense open subsets of a topological space in studying tensor products. These representations may be obtained from the Ogasawara–Maeda representation by means of restriction to the set on which representing functions are real-valued, rather than infinite. In this note, we show how to obtain such a representation as a simple consequence of the Krein–Kakutani representation of an order unit space. We conclude by studying the representation of Riesz homomorphisms in this setting.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"49 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519923","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
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