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Metric symmetry and distance distribution functions on graphs 图上的度量对称和距离分布函数
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-10 DOI: 10.1007/s00010-024-01145-2
J. M. Calabuig, E. A. Sánchez Pérez, S. Sanjuan
{"title":"Metric symmetry and distance distribution functions on graphs","authors":"J. M. Calabuig,&nbsp;E. A. Sánchez Pérez,&nbsp;S. Sanjuan","doi":"10.1007/s00010-024-01145-2","DOIUrl":"10.1007/s00010-024-01145-2","url":null,"abstract":"<div><p>After reviewing various notions of symmetry in graph theory, which are typically defined by the connections between vertices, we demonstrate that traditional concepts of symmetry, such as vertex transitivity, can be too restrictive for certain applications. For instance, in some areas of graph analysis, symmetry based on metric properties (such as average distances between vertices) may be more appropriate, particularly in social network analysis or economic fraud detection. This paper focuses on developing metric-based symmetry concepts by introducing mathematical analysis tools, all related to the central idea of the distance distribution function, to group vertices according to their distance-related properties within the graph. In particular, we prove several results that show, under certain compactness properties for the set of distribution functions of all the vertices in an infinite graph, that it is always possible to group these vertices into a finite number of classes with the desired accuracy based on distances.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1675 - 1704"},"PeriodicalIF":0.7,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01145-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110493","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
Note on the variance of generalized random polygons 注意广义随机多边形的方差
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-10 DOI: 10.1007/s00010-024-01147-0
Ferenc Fodor, Balázs Grünfelder
{"title":"Note on the variance of generalized random polygons","authors":"Ferenc Fodor,&nbsp;Balázs Grünfelder","doi":"10.1007/s00010-024-01147-0","DOIUrl":"10.1007/s00010-024-01147-0","url":null,"abstract":"<div><p>We consider a probability model in which the hull of a sample of i.i.d. uniform random points from a convex disc <i>K</i> is formed by the intersection of all translates of another suitable fixed convex disc <i>L</i> that contain the sample. Such an object is called a random <i>L</i>-polygon in <i>K</i>. We assume that both <i>K</i> and <i>L</i> have <span>(C^2_+)</span> smooth boundaries, and we prove upper bounds on the variance of the number of vertices and missed area of random <i>L</i>-polygons assuming different curvature conditions. We also transfer some of our result to a circumscribed variant of this model.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"869 - 882"},"PeriodicalIF":0.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01147-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073844","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
Coincidence theory for lower semicontinuous type maps with decomposable values 具有可分解值的下半连续型映射的符合理论
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-10 DOI: 10.1007/s00010-024-01149-y
Donal O’Regan
{"title":"Coincidence theory for lower semicontinuous type maps with decomposable values","authors":"Donal O’Regan","doi":"10.1007/s00010-024-01149-y","DOIUrl":"10.1007/s00010-024-01149-y","url":null,"abstract":"<div><p>In this paper we present some coincidence results between lower semicontinuous type maps, one of which has decomposable values. Our argument relies on fixed point theory combined with continuous (or upper semicontinuous) selection theory.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1385 - 1402"},"PeriodicalIF":0.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073915","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 generalization of a theorem of von Neumann 冯·诺伊曼定理的推广
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-06 DOI: 10.1007/s00010-024-01141-6
Ali Bayati Eshkaftaki
{"title":"A generalization of a theorem of von Neumann","authors":"Ali Bayati Eshkaftaki","doi":"10.1007/s00010-024-01141-6","DOIUrl":"10.1007/s00010-024-01141-6","url":null,"abstract":"<div><p>In 1953 von Neumann proved that every <span>(ntimes n)</span> doubly substochastic matrix <i>A</i> can be <i>increased</i> to a doubly stochastic matrix, i.e., there is an <span>(ntimes n)</span> doubly stochastic matrix <i>D</i> for which <span>(Ale D.)</span> In this paper, we will discuss this result for a class of <span>(Itimes I)</span> doubly substochastic matrices. In fact, by a constructive method, we find an equivalent condition for the existence of a doubly stochastic matrix <i>D</i> which satisfies <span>(Ale D,)</span> for all <span>(Ain {mathcal {A}},)</span> where <span>({mathcal { A}})</span> is assumed to be a class of (finite or infinite) doubly substochastic matrices. Such a matrix <i>D</i> is called a cover of <span>(mathcal {A}.)</span> The uniqueness of the cover will also be discussed. Then we obtain an application of this concept to a system of (infinite) linear equations and inequalities.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"61 - 70"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554141","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
Pexider invariance equation for embeddable mean-type mappings 可嵌入均值型映射的Pexider不变性方程
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-03 DOI: 10.1007/s00010-024-01139-0
Paweł Pasteczka
{"title":"Pexider invariance equation for embeddable mean-type mappings","authors":"Paweł Pasteczka","doi":"10.1007/s00010-024-01139-0","DOIUrl":"10.1007/s00010-024-01139-0","url":null,"abstract":"<div><p>We prove that whenever <span>(M_1,dots ,M_n:I^k rightarrow I)</span>, (<span>(n,k in mathbb {N})</span>) are symmetric, continuous means on the interval <i>I</i> and <span>(S_1,dots ,S_m:I^k rightarrow I)</span> (<span>(m &lt; n)</span>) satisfy a sort of embeddability assumptions then for every continuous function <span>(mu :I^n rightarrow mathbb {R})</span> which is strictly monotone in each coordinate, the functional equation </p><div><div><span>$$ mu (S_1(v),dots ,S_m(v),underbrace{F(v),dots ,F(v)}_{(n-m)text { times}})=mu (M_1(v),dots ,M_n(v)) $$</span></div></div><p>has the unique solution <span>(F=F_mu :I^k rightarrow I)</span> which is a mean. We deliver some sufficient conditions so that <span>(F_mu )</span> is well-defined (in particular uniquely determined) and study its properties. The aim of this research is to provide a broad overview of the family of Beta-type means introduced in (Himmel and Matkowski, 2018).</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"611 - 622"},"PeriodicalIF":0.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01139-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871198","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
A generalization of the Kannappan-sine addition law on semigroups 半群上Kannappan-sine加法律的推广
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-12-26 DOI: 10.1007/s00010-024-01138-1
Ahmed Jafar, Omar Ajebbar, Elhoucien Elqorachi
{"title":"A generalization of the Kannappan-sine addition law on semigroups","authors":"Ahmed Jafar,&nbsp;Omar Ajebbar,&nbsp;Elhoucien Elqorachi","doi":"10.1007/s00010-024-01138-1","DOIUrl":"10.1007/s00010-024-01138-1","url":null,"abstract":"<div><p>Given a semigroup <i>S</i> equipped with an involutive automorphic <span>(sigma :S rightarrow S)</span>, we determine the complex-valued solutions of the following generalization of the Kannappan-sine addition law </p><div><div><span>$$f(xsigma (y)z_0)=f(x)g(y)+f(y)g(x),; x,y in S. $$</span></div></div><p>As an application we obtain the solutions of the following functional equation </p><div><div><span>$$f(xsigma (y)z_0)=f(x)f(z_1y)+f(z_1x)f(y),; x,y in S, $$</span></div></div><p>where <span>(z_0, z_1)</span> are two fixed elements in <i>S</i> such that <span>(z_0ne z_1)</span>. The continuous solutions on topological semigroups are given. We illustrate the main result with two examples.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1403 - 1420"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074194","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
The Goldie Equation: III. Homomorphisms from functional equations 戈尔迪方程：泛函方程的同态
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-12-09 DOI: 10.1007/s00010-024-01133-6
N. H. Bingham, A. J. Ostaszewski
{"title":"The Goldie Equation: III. Homomorphisms from functional equations","authors":"N. H. Bingham,&nbsp;A. J. Ostaszewski","doi":"10.1007/s00010-024-01133-6","DOIUrl":"10.1007/s00010-024-01133-6","url":null,"abstract":"<div><p>This is the second of three sequels to (Ostaszewski in Aequat Math 90:427–448, 2016)—the third of the resulting quartet—concerning the real-valued continuous solutions of the multivariate Goldie functional equation (<i>GFE</i>) below of Levi–Civita type. Following on from the preceding paper (Bingham and Ostaszewski in Homomorphisms from Functional Equations: II. The Goldie Equation, arXiv:1910.05816), in which these solutions are described explicitly, here we characterize (<i>GFE</i>) as expressing homomorphy (in all but some exceptional “improper” cases) between multivariate Popa groups, defined and characterized earlier in the sequence. The group operation involves a form of affine addition (with local scalar acceleration) similar to the circle operation of ring theory. We show the affine action in <span>((GFE) )</span>may be replaced by a general continuous acceleration yielding a functional equation (<i>GGE</i>) which it emerges has the same solution structure as (<i>GFE</i>). The final member of the sequence (Bingham and Ostaszewski, The Gołąb–Schinzel and Goldie functional equations in Banach algebras, arXiv:2105.07794) considers the richer framework of a Banach algebra which allows vectorial acceleration, giving the closest possible similarity to the circle operation.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1085 - 1123"},"PeriodicalIF":0.9,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01133-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073981","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
Sparse groups need not be semisparse 稀疏组不必是半解析的
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-11-26 DOI: 10.1007/s00010-024-01136-3
Isabel Hubard, Micael Toledo
{"title":"Sparse groups need not be semisparse","authors":"Isabel Hubard,&nbsp;Micael Toledo","doi":"10.1007/s00010-024-01136-3","DOIUrl":"10.1007/s00010-024-01136-3","url":null,"abstract":"<div><p>In 1999 Michael Hartley showed that any abstract polytope can be constructed as a double coset poset, by means of a C-group <span>(mathcal {W})</span> and a subgroup <span>(N le mathcal {W})</span>. Subgroups <span>(N le mathcal {W})</span> that give rise to abstract polytopes through such a construction are called <i> sparse</i>. If, further, the stabilizer of a base flag of the poset is precisely <i>N</i>, then <i>N</i> is said to be <i> semisparse</i>. In [4, Conjecture 5.2] Hartely conjectures that sparse groups are always semisparse. In this paper, we show that this conjecture is in fact false: there exist sparse groups that are not semisparse. In particular, we show that such groups are always obtained from non-faithful maniplexes that give rise to polytopes. Using this, we show that Hartely’s conjecture holds for rank 3, but we construct examples to disprove the conjecture for all ranks <span>(nge 4)</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"37 - 60"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01136-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553899","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
On some operator functional equations related to evaluation functionals and weighted composition operators on function spaces 函数空间上与求值泛函和加权复合算子相关的算子泛函方程
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-11-21 DOI: 10.1007/s00010-024-01137-2
Francesco Altomare
{"title":"On some operator functional equations related to evaluation functionals and weighted composition operators on function spaces","authors":"Francesco Altomare","doi":"10.1007/s00010-024-01137-2","DOIUrl":"10.1007/s00010-024-01137-2","url":null,"abstract":"<div><p>The paper is concerned with some operator functional equations which have been recently considered in several papers in developing some extensions and generalizations of Korovkin-type convergence theorems. It is shown that such operator functional equations although arising from different contexts, have a common root. Starting from an unifying setting, it is shown that the solutions of such operator functional equations are necessarily evaluation functionals and weighted composition operators, respectively. Several special cases are discussed in detail, including the one which concerns spaces of <span>(2pi -)</span>periodic functions on the real line.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1371 - 1384"},"PeriodicalIF":0.9,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074032","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
The 60th International Symposium on Functional Equations, Hotel Rewita, Kościelisko (Poland), June 9–15, 2024 第60届泛函方程国际研讨会，Hotel Rewita, Kościelisko（波兰），2024年6月9-15日
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-11-13 DOI: 10.1007/s00010-024-01126-5
{"title":"The 60th International Symposium on Functional Equations, Hotel Rewita, Kościelisko (Poland), June 9–15, 2024","authors":"","doi":"10.1007/s00010-024-01126-5","DOIUrl":"10.1007/s00010-024-01126-5","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1689 - 1712"},"PeriodicalIF":0.9,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142762033","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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