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A note on ideal C $$^*$$ -completions and amenability 关于理想 C $$^*$$ -补全和可亲和性的说明
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-10 DOI: 10.1007/s00010-024-01077-x
Tomasz Kochanek
{"title":"A note on ideal C $$^*$$ -completions and amenability","authors":"Tomasz Kochanek","doi":"10.1007/s00010-024-01077-x","DOIUrl":"https://doi.org/10.1007/s00010-024-01077-x","url":null,"abstract":"<p>For a discrete group <i>G</i>, we consider certain ideals <span>(mathcal {I}subset c_0(G))</span> of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C<span>(^*)</span>-algebra of <i>G</i> and the C<span>(^*)</span>-completion <span>(textrm{C}^*_{mathcal {I}}(G))</span> in the sense of Brown and Guentner (Bull. London Math. Soc. 45:1181–1193, 2013) implies that <i>G</i> is amenable.\u0000</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"156 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942333","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 double Roman domination problem for several graph classes 关于几类图的双罗马支配问题
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-08 DOI: 10.1007/s00010-024-01071-3
Tatjana Zec, Dragan Matić, Marko Djukanović
{"title":"On double Roman domination problem for several graph classes","authors":"Tatjana Zec, Dragan Matić, Marko Djukanović","doi":"10.1007/s00010-024-01071-3","DOIUrl":"https://doi.org/10.1007/s00010-024-01071-3","url":null,"abstract":"<p><i>A double Roman domination function</i> (DRDF) on a graph <span>(G=(V,E))</span> is a mapping <span>(f :Vrightarrow {0,1,2,3})</span> satisfying the conditions: (<i>i</i>) each vertex with 0 assigned is adjacent to a vertex with 3 assigned or at least two vertices with 2 assigned and (<i>ii</i>) each vertex with 1 assigned is adjacent to at least one vertex with 2 or 3 assigned. The weight of a DRDF <i>f</i> is defined as the sum <span>(sum _{vin V}f(v))</span>. The minimum weight of a DRDF on a graph <i>G</i> is called the <i>double Roman domination number</i> (DRDN) of <i>G</i>. This study establishes the values on DRDN for several graph classes. The exact values of DRDN are proved for Kneser graphs <span>(K_{n,k},nge k(k+2))</span>, Johnson graphs <span>(J_{n,2})</span>, for a few classes of convex polytopes, and the flower snarks. Moreover, tight lower and upper bounds on SRDN are proved for some convex polytopes. For the generalized Petersen graphs <span>(P_{n,3}, n not equiv 0,(mathrm {mod 4}))</span>, we make a further improvement on the best known upper bound from the literature.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925658","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
Gromov hyperbolicity of Johnson and Kneser graphs 约翰逊和克奈瑟图的格罗莫夫双曲性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-08 DOI: 10.1007/s00010-024-01076-y
Jesús Méndez, Rosalio Reyes, José M. Rodríguez, José M. Sigarreta
{"title":"Gromov hyperbolicity of Johnson and Kneser graphs","authors":"Jesús Méndez,&nbsp;Rosalio Reyes,&nbsp;José M. Rodríguez,&nbsp;José M. Sigarreta","doi":"10.1007/s00010-024-01076-y","DOIUrl":"10.1007/s00010-024-01076-y","url":null,"abstract":"<div><p>The concept of Gromov hyperbolicity is a geometric concept that leads to a rich general theory. Johnson and Kneser graphs are interesting combinatorial graphs defined from systems of sets. In this work we compute the precise value of the hyperbolicity constant of every Johnson graph. Also, we obtain good bounds on the hyperbolicity constant of every Kneser graph, and in many cases, we even compute its precise value.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"661 - 686"},"PeriodicalIF":0.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01076-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925581","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
Probabilistic Stirling numbers and applications 概率斯特林数及其应用
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-08 DOI: 10.1007/s00010-024-01073-1
José A. Adell, Beáta Bényi
{"title":"Probabilistic Stirling numbers and applications","authors":"José A. Adell,&nbsp;Beáta Bényi","doi":"10.1007/s00010-024-01073-1","DOIUrl":"10.1007/s00010-024-01073-1","url":null,"abstract":"<div><p>We introduce probabilistic Stirling numbers of the first kind <span>(s_Y(n,k))</span> associated with a complex-valued random variable <i>Y</i> satisfying appropriate integrability conditions, thus completing the notion of probabilistic Stirling numbers of the second kind <span>(S_Y(n,k))</span> previously considered by the first author. Combinatorial interpretations, recursion formulas, and connections between <span>(s_Y(n,k))</span> and <span>(S_Y(n,k))</span> are given. We show that such numbers describe a large subset of potential polynomials, on the one hand, and the moments of sums of i. i. d. random variables, on the other, establishing their precise asymptotic behavior without appealing to the central limit theorem. We explicitly compute these numbers when <i>Y</i> has a certain familiar distribution, providing at the same time their combinatorial meaning.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1627 - 1646"},"PeriodicalIF":0.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01073-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925650","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
Distance signless Laplacian spectral radius for the existence of path-factors in graphs 图中路径因子存在的无符号拉普拉斯谱半径距离
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-06 DOI: 10.1007/s00010-024-01075-z
Sizhong Zhou, Zhiren Sun, Hongxia Liu
{"title":"Distance signless Laplacian spectral radius for the existence of path-factors in graphs","authors":"Sizhong Zhou,&nbsp;Zhiren Sun,&nbsp;Hongxia Liu","doi":"10.1007/s00010-024-01075-z","DOIUrl":"10.1007/s00010-024-01075-z","url":null,"abstract":"<div><p>Let <i>G</i> be a connected graph of order <i>n</i>, where <i>n</i> is a positive integer. A spanning subgraph <i>F</i> of <i>G</i> is called a path-factor if every component of <i>F</i> is a path of order at least 2. A <span>(P_{ge k})</span>-factor means a path-factor in which every component admits order at least <i>k</i> (<span>(kge 2)</span>). The distance matrix <span>({mathcal {D}}(G))</span> of <i>G</i> is an <span>(ntimes n)</span> real symmetric matrix whose (<i>i</i>, <i>j</i>)-entry is the distance between the vertices <span>(v_i)</span> and <span>(v_j)</span>. The distance signless Laplacian matrix <span>({mathcal {Q}}(G))</span> of <i>G</i> is defined by <span>({mathcal {Q}}(G)=Tr(G)+{mathcal {D}}(G))</span>, where <i>Tr</i>(<i>G</i>) is the diagonal matrix of the vertex transmissions in <i>G</i>. The largest eigenvalue <span>(eta _1(G))</span> of <span>({mathcal {Q}}(G))</span> is called the distance signless Laplacian spectral radius of <i>G</i>. In this paper, we aim to present a distance signless Laplacian spectral radius condition to guarantee the existence of a <span>(P_{ge 2})</span>-factor in a graph and claim that the following statements are true: (i) <i>G</i> admits a <span>(P_{ge 2})</span>-factor for <span>(nge 4)</span> and <span>(nne 7)</span> if <span>(eta _1(G)&lt;theta (n))</span>, where <span>(theta (n))</span> is the largest root of the equation <span>(x^{3}-(5n-3)x^{2}+(8n^{2}-23n+48)x-4n^{3}+22n^{2}-74n+80=0)</span>; (ii) <i>G</i> admits a <span>(P_{ge 2})</span>-factor for <span>(n=7)</span> if <span>(eta _1(G)&lt;frac{25+sqrt{161}}{2})</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"727 - 737"},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889513","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 explicit example of an iteration group in the ring of formal power series 形式幂级数环中迭代群的一个显式实例
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-06 DOI: 10.1007/s00010-024-01070-4
Wojciech Jabłoński
{"title":"An explicit example of an iteration group in the ring of formal power series","authors":"Wojciech Jabłoński","doi":"10.1007/s00010-024-01070-4","DOIUrl":"10.1007/s00010-024-01070-4","url":null,"abstract":"<div><p>We give an example of some iteration group in a ring of formal power series over a field of characteristic 0. It allows us to obtain an explicit formula for some one-parameter group of (truncated) formal power series under an additional condition. Consequently, we are able to show some non-commutative groups of solutions of the third Aczél-Jabotinsky differential equation in the ring of truncated formal power series.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"837 - 850"},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01070-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885006","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
Skew Dyck paths with air pockets 带气孔的斜戴克路径
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-03 DOI: 10.1007/s00010-024-01065-1
Jean-Luc Baril, Rémi Maréchal, Helmut Prodinger
{"title":"Skew Dyck paths with air pockets","authors":"Jean-Luc Baril,&nbsp;Rémi Maréchal,&nbsp;Helmut Prodinger","doi":"10.1007/s00010-024-01065-1","DOIUrl":"10.1007/s00010-024-01065-1","url":null,"abstract":"<div><p>We yield bivariate generating function for the number of <i>n</i>-length partial skew Dyck paths with air pockets (DAPs) ending at a given ordinate. We also give an asymptotic approximation for the average ordinate of the endpoint in all partial skew DAPs of a given length. Similar studies are made for two subclasses of skew DAPs, namely valley-avoiding and zigzagging, valley-avoiding skew DAPs. We express these results as Riordan arrays. Finally, we present two one-to-one correspondences with binary words avoiding the patterns 00 and 0110, and palindromic compositions with parts in <span>({2,1,3,5,7,ldots })</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"257 - 274"},"PeriodicalIF":0.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885005","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
Equalities for mixed operations of Moore–Penrose and group inverses of a matrix 摩尔-彭罗斯混合运算和矩阵的群逆运算的等式
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-03 DOI: 10.1007/s00010-024-01072-2
Yongge Tian
{"title":"Equalities for mixed operations of Moore–Penrose and group inverses of a matrix","authors":"Yongge Tian","doi":"10.1007/s00010-024-01072-2","DOIUrl":"10.1007/s00010-024-01072-2","url":null,"abstract":"<div><p>This article shows how to establish expansion formulas for calculating the nested operations <span>((A^{dag })^{#})</span>, <span>((A^{#})^{dag })</span>, <span>(((A^{dag })^{#})^{dag })</span>, <span>(((A^{#})^{dag })^{#})</span>, <span>(ldots )</span> of generalized inverses, where <span>((cdot )^{dag })</span> denotes the Moore–Penrose inverse of a matrix and <span>((cdot )^{#})</span> denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above nested operations, and derives necessary and sufficient conditions for them to hold.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"175 - 197"},"PeriodicalIF":0.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885072","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
Rotations on the triangular grid: angles of changes of the neighborhood motion map 三角形网格的旋转：邻域运动图的变化角度
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-02 DOI: 10.1007/s00010-024-01062-4
Müge Saadetoğlu, Benedek Nagy, Aydın Avkan
{"title":"Rotations on the triangular grid: angles of changes of the neighborhood motion map","authors":"Müge Saadetoğlu,&nbsp;Benedek Nagy,&nbsp;Aydın Avkan","doi":"10.1007/s00010-024-01062-4","DOIUrl":"10.1007/s00010-024-01062-4","url":null,"abstract":"<div><p>Digital image processing is a well-known field that applies various mathematical methods. Among other parts of image processing the study of digital rotations is an important field that is applied in our everyday life. Digital images are understood in a discrete domain, usually on a periodic grid. On the triangular grid, the digitized rotations of a main triangle pixel (trixel) together with its side neighbors are considered. Given a main triangle pixel lying anywhere on the plane, and the centre of rotation taken to be the midpoint of any triangle pixel, we calculate the rotation angles where the neighborhood motion map (NMM) changes. This occurs when the respective locations of the side neighbor trixels change. An algorithm to compute angles for the following neighborhood motion map changes is also given.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"1053 - 1070"},"PeriodicalIF":0.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839754","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
All solutions to a Schröder type functional equation 施罗德函数式方程的所有解
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-27 DOI: 10.1007/s00010-024-01069-x
Raymond Mortini, Rudolf Rupp
{"title":"All solutions to a Schröder type functional equation","authors":"Raymond Mortini,&nbsp;Rudolf Rupp","doi":"10.1007/s00010-024-01069-x","DOIUrl":"10.1007/s00010-024-01069-x","url":null,"abstract":"<div><p>We determine the solutions on various intervals in <span>([0,infty [)</span> to the functional equation <span>(f(x^m)=r f(x))</span> for real <i>r</i> and positive <i>m</i>. Explicit formulas, involving periodic functions, are given for the set <span>({mathcal {S}})</span> of all solutions. The formulas for <span>(r&lt;0)</span> are more complicated. An approach to <span>({mathcal {S}})</span> with the help of the axiom of choice is also given. A special attention is laid on solutions that are continuous on <span>([0,infty [)</span> or on various open subintervals. We also describe solutions satisfying some asymptotic properties at the boundary of these intervals.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1503 - 1525"},"PeriodicalIF":0.9,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799833","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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