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Aequationes Mathematicae最新文献

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Analytical aspects of a q, r-analogue of poly-Stirling numbers of both kinds
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-02-22 DOI: 10.1007/s00010-024-01135-4
Takao Komatsu, Eli Bagno, David Garber
{"title":"Analytical aspects of a q, r-analogue of poly-Stirling numbers of both kinds","authors":"Takao Komatsu,&nbsp;Eli Bagno,&nbsp;David Garber","doi":"10.1007/s00010-024-01135-4","DOIUrl":"10.1007/s00010-024-01135-4","url":null,"abstract":"<div><p>The Stirling numbers of type <i>B</i> of the second kind count signed set partitions. In this paper, we provide new combinatorial and analytical identities regarding these numbers as well as Broder’s <i>r</i>-version of these numbers. Among these identities one can find recursions, explicit formulas based on the inclusion–exclusion principle, and also exponential generating functions. These Stirling numbers can be considered as members of a wider family of triangles of numbers that are characterized using results of Comtet and Lancaster. We generalize these theorems, which present equivalent conditions for a triangle of numbers to be a triangle of generalized Stirling numbers, to the case of the <i>q</i>, <i>r</i>-poly Stirling numbers, which are <i>q</i>-analogues of the restricted Stirling numbers defined by Broder and having a polynomial value appearing in their defining recursion. There are two ways to do this and these ways are related by a nice identity.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"287 - 320"},"PeriodicalIF":0.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871400","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 composition and Right Distributive Law for formal power series of multiple variables
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-23 DOI: 10.1007/s00010-024-01152-3
Dariusz Bugajewski, Alessia Galimberti, Piotr Maćkowiak
{"title":"On composition and Right Distributive Law for formal power series of multiple variables","authors":"Dariusz Bugajewski,&nbsp;Alessia Galimberti,&nbsp;Piotr Maćkowiak","doi":"10.1007/s00010-024-01152-3","DOIUrl":"10.1007/s00010-024-01152-3","url":null,"abstract":"<div><p>In the first part of the paper we prove a necessary and sufficient condition for the existence of the composition of formal power series in the case when the outer series is a series of one variable while the inner one is a series of multiple variables. The aim of the second part is to remove ambiguities connected with the Right Distributive Law for formal power series of one variable as well as to provide analogues of that law in the multivariable case.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"21 - 35"},"PeriodicalIF":0.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554185","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
Correction to: On the solvability of the (SSIE) with operator ({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} ), involving the fine spectrum of an operator
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-15 DOI: 10.1007/s00010-024-01142-5
Bruno de Malafosse, Eberhard Malkowsky, Vladinir Rakočević
{"title":"Correction to: On the solvability of the (SSIE) with operator ({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} ), involving the fine spectrum of an operator","authors":"Bruno de Malafosse,&nbsp;Eberhard Malkowsky,&nbsp;Vladinir Rakočević","doi":"10.1007/s00010-024-01142-5","DOIUrl":"10.1007/s00010-024-01142-5","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"823 - 824"},"PeriodicalIF":0.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871356","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
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
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
Sparse groups need not be semisparse
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
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
Homomorphisms from Functional Equations: The Goldie Equation, II
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-11-11 DOI: 10.1007/s00010-024-01130-9
N. H. Bingham, A. J. Ostaszewski
{"title":"Homomorphisms from Functional Equations: The Goldie Equation, II","authors":"N. H. Bingham,&nbsp;A. J. Ostaszewski","doi":"10.1007/s00010-024-01130-9","DOIUrl":"10.1007/s00010-024-01130-9","url":null,"abstract":"<div><p>This first of three sequels to <i>Homomorphisms from Functional equations: The Goldie equation</i> (Ostaszewski in Aequationes Math 90:427–448, 2016) by the second author—the second of the resulting quartet—starts from the Goldie functional equation arising in the general regular variation of our joint paper (Bingham et al. in J Math Anal Appl 483:123610, 2020). We extend the work there in two directions. First, we algebraicize the theory, by systematic use of certain groups—the <i>Popa groups</i> arising in earlier work by Popa, and their relatives the <i>Javor groups </i>. Secondly, we extend from the original context on the real line to multi-dimensional (or infinite-dimensional) settings.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"1 - 19"},"PeriodicalIF":0.9,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01130-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554162","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 simple proof of the rationality of Takagi-like functions 高木类函数合理性的简单证明
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-11-04 DOI: 10.1007/s00010-024-01134-5
Yangyang Chen, Nankun Hong, Hongyuan Yu
{"title":"A simple proof of the rationality of Takagi-like functions","authors":"Yangyang Chen,&nbsp;Nankun Hong,&nbsp;Hongyuan Yu","doi":"10.1007/s00010-024-01134-5","DOIUrl":"10.1007/s00010-024-01134-5","url":null,"abstract":"<div><p>Takagi function is a well-known continuous but nowhere differentiable function defined over real numbers. The Takagi function maps rational numbers to themselves. In this note, by applying Euler’s theorem, we give a simple proof of this property for Takagi-like functions, a slight generalization of the Takagi function.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"433 - 437"},"PeriodicalIF":0.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871145","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 strongly m-convex stochastic processes
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-10-30 DOI: 10.1007/s00010-024-01128-3
Jaya Bisht, Rohan Mishra, Abdelouahed Hamdi
{"title":"On strongly m-convex stochastic processes","authors":"Jaya Bisht,&nbsp;Rohan Mishra,&nbsp;Abdelouahed Hamdi","doi":"10.1007/s00010-024-01128-3","DOIUrl":"10.1007/s00010-024-01128-3","url":null,"abstract":"<div><p>In this paper, we introduce the concept of strongly <i>m</i>-convex stochastic processes and present some basic properties of these stochastic processes. We derive Hermite-Hadamard type inequalities for stochastic processes whose first derivatives in absolute values are strongly <i>m</i>-convex. The results presented in this paper are a generalization and extension of previously known results.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"655 - 667"},"PeriodicalIF":0.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01128-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871394","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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