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On the Metric Dimension of Circulant Graphs 关于循环图的度量维数
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-28 DOI: 10.4153/s0008439523000759
Rui Gao, Yingqing Xiao, Zhanqi Zhang
{"title":"On the Metric Dimension of Circulant Graphs","authors":"Rui Gao, Yingqing Xiao, Zhanqi Zhang","doi":"10.4153/s0008439523000759","DOIUrl":"https://doi.org/10.4153/s0008439523000759","url":null,"abstract":"Abstract In this note, we bound the metric dimension of the circulant graphs $C_n(1,2,ldots ,t)$ . We shall prove that if $n=2tk+t$ and if t is odd, then $dim (C_n(1,2,ldots ,t))=t+1$ , which confirms Conjecture 4.1.1 in Chau and Gosselin (2017, Opuscula Mathematica 37, 509–534). In Vetrík (2017, Canadian Mathematical Bulletin 60, 206–216; 2020, Discussiones Mathematicae. Graph Theory 40, 67–76), the author has shown that $dim (C_n(1,2,ldots ,t))leq t+left lceil frac {p}{2}right rceil $ for $n=2tk+t+p$ , where $tgeq 4$ is even, $1leq pleq t+1$ , and $kgeq 1$ . Inspired by his work, we show that $dim (C_n(1,2,ldots ,t))leq t+left lfloor frac {p}{2}right rfloor $ for $n=2tk+t+p$ , where $tgeq 5$ is odd, $2leq pleq t+1$ , and $kgeq 2$ .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135344649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors 区间上的分段收缩映射:Hausdorff维数、熵和吸引子
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-21 DOI: 10.4153/s0008439523000747
Alfredo E. Calderón, Edgardo Villar-Sepúlveda
{"title":"Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors","authors":"Alfredo E. Calderón, Edgardo Villar-Sepúlveda","doi":"10.4153/s0008439523000747","DOIUrl":"https://doi.org/10.4153/s0008439523000747","url":null,"abstract":"Abstract We consider the attractor $Lambda $ of a piecewise contracting map f defined on a compact interval. If f is injective, we show that it is possible to estimate the topological entropy of f (according to Bowen’s formula) and the Hausdorff dimension of $Lambda $ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 UNIVERSAL INEQUALITY FOR NEUMANN EIGENVALUES OF THE LAPLACIAN ON A CONVEX DOMAIN IN EUCLIDEAN SPACE 欧几里德空间凸域上拉普拉斯算子的诺伊曼特征值的一个普遍不等式
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-19 DOI: 10.4153/s0008439523000735
KEI FUNANO
{"title":"A UNIVERSAL INEQUALITY FOR NEUMANN EIGENVALUES OF THE LAPLACIAN ON A CONVEX DOMAIN IN EUCLIDEAN SPACE","authors":"KEI FUNANO","doi":"10.4153/s0008439523000735","DOIUrl":"https://doi.org/10.4153/s0008439523000735","url":null,"abstract":"Abstract We obtain a new upper bound for Neumann eigenvalues of the Laplacian on a bounded convex domain in Euclidean space. As an application of the upper bound, we derive universal inequalities for Neumann eigenvalues of the Laplacian.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135015937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Theorems of Fermat, Wilson and Gegenbauer 论费马、威尔逊和格根鲍尔的定理
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-12 DOI: 10.4153/s0008439523000723
Heng Huat Chan, Song Heng Chan, Teoh Guan Chua, Cheng Yeaw Ku
{"title":"On Theorems of Fermat, Wilson and Gegenbauer","authors":"Heng Huat Chan, Song Heng Chan, Teoh Guan Chua, Cheng Yeaw Ku","doi":"10.4153/s0008439523000723","DOIUrl":"https://doi.org/10.4153/s0008439523000723","url":null,"abstract":"Abstract In this article, we give generalizations of the well-known Fermat’s Little Theorem, Wilson’s theorem, and the little-known Gegenbauer’s theorem.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135831385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations 高速公路的进出弧线:它们在变分法中的精确计算
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-12 DOI: 10.4153/s000843952300070x
L. Bayón, P. Fortuny Ayuso, J.M. Grau, M.M. Ruiz
{"title":"Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations","authors":"L. Bayón, P. Fortuny Ayuso, J.M. Grau, M.M. Ruiz","doi":"10.4153/s000843952300070x","DOIUrl":"https://doi.org/10.4153/s000843952300070x","url":null,"abstract":"Abstract We settle the question of how to compute the entry and leaving arcs for turnpikes in autonomous variational problems, in the one-dimensional case using the phase space of the vector field associated with the Euler equation, and the initial/final and/or the transversality condition. The results hinge on the realization that extremals are the contours of a well-known function and that the transversality condition is (generically) a curve. An approximation algorithm is presented, and an example is included for completeness.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135879285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ideals with approximate unit in semicrossed products 半交叉产品中近似单位的理想
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-12 DOI: 10.4153/s0008439523000711
Charalampos Magiatis
{"title":"Ideals with approximate unit in semicrossed products","authors":"Charalampos Magiatis","doi":"10.4153/s0008439523000711","DOIUrl":"https://doi.org/10.4153/s0008439523000711","url":null,"abstract":"Abstract We characterize the ideals of the semicrossed product $C_0(X)times _phi {mathbb Z}_+$ , associated with suitable sequences of closed subsets of X , with left (resp. right) approximate unit. As a consequence, we obtain a complete characterization of ideals with left (resp. right) approximate unit under the assumptions that X is metrizable and the dynamical system $(X,phi )$ contains no periodic points.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135831400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Problems for generalized Monge-Ampère equations 广义monge - ampantere方程问题
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-11 DOI: 10.4153/s0008439523000656
Cristian Enache, Giovanni Porru
{"title":"Problems for generalized Monge-Ampère equations","authors":"Cristian Enache, Giovanni Porru","doi":"10.4153/s0008439523000656","DOIUrl":"https://doi.org/10.4153/s0008439523000656","url":null,"abstract":"Abstract This paper deals with some Monge–Ampère type equations involving the gradient that are elliptic in the framework of convex functions. First, we show that such equations may be obtained by minimizing a suitable functional. Moreover, we investigate a P-function associated with the solution to a boundary value problem of our generalized Monge–Ampère equation in a bounded convex domain. It will be shown that this P-function attains its maximum value on the boundary of the underlying domain. Furthermore, we show that such a P-function is actually identically constant when the underlying domain is a ball. Therefore, our result provides a best possible maximum principles in the sense of L. E. Payne. Finally, in case of dimension 2, we prove that this P-function also attains its minimum value on the boundary of the underlying domain. As an application, we will show that the solvability of a Serrin’s type overdetermined problem for our generalized Monge–Ampère type equation forces the underlying domain to be a ball.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
EVERY SYMMETRIC KUBO-ANDO CONNECTION HAS THE ORDER-DETERMINING PROPERTY 每一个对称久保-安藤连接都具有定序性质
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-11 DOI: 10.4153/s0008439523000668
EMMANUEL CHETCUTI, CURT HEALEY
{"title":"EVERY SYMMETRIC KUBO-ANDO CONNECTION HAS THE ORDER-DETERMINING PROPERTY","authors":"EMMANUEL CHETCUTI, CURT HEALEY","doi":"10.4153/s0008439523000668","DOIUrl":"https://doi.org/10.4153/s0008439523000668","url":null,"abstract":"Abstract In this article, the question of whether the Löwner partial order on the positive cone of an operator algebra is determined by the norm of any arbitrary Kubo–Ando mean is studied. The question was affirmatively answered for certain classes of Kubo–Ando means, yet the general case was left as an open problem. We here give a complete answer to this question, by showing that the norm of every symmetric Kubo–Ando mean is order-determining, i.e., if $A,Bin mathcal B(H)^{++}$ satisfy $Vert Asigma XVert le Vert Bsigma XVert $ for every $Xin mathcal {A}^{{++}}$ , where $mathcal A$ is the C*-subalgebra generated by $B-A$ and I , then $Ale B$ .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Convexity of the radial sum of a star body and a ball 星体与球体径向和的凸性
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-04 DOI: 10.4153/s0008439523000681
S. Sakata
{"title":"Convexity of the radial sum of a star body and a ball","authors":"S. Sakata","doi":"10.4153/s0008439523000681","DOIUrl":"https://doi.org/10.4153/s0008439523000681","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46947687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
BCM volume 66 issue 3 Cover and Front matter BCM 66卷第3期封面和封面问题
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-01 DOI: 10.4153/s0008439523000632
{"title":"BCM volume 66 issue 3 Cover and Front matter","authors":"","doi":"10.4153/s0008439523000632","DOIUrl":"https://doi.org/10.4153/s0008439523000632","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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