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Aequationes Mathematicae最新文献

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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
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
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
On the minimality of the Winterbottom shape 论温特巴顿形状的最小性
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-17 DOI: 10.1007/s00010-024-01122-9
Shokhrukh Yu. Kholmatov
{"title":"On the minimality of the Winterbottom shape","authors":"Shokhrukh Yu. Kholmatov","doi":"10.1007/s00010-024-01122-9","DOIUrl":"https://doi.org/10.1007/s00010-024-01122-9","url":null,"abstract":"<p>In this short note we prove that the Winterbottom shape (Winterbottom in Acta Metallurgica 15:303-310, 1967) is a volume-constraint minimizer of the corresponding anisotropic capillary functional.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266631","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
Two-sided delay-difference equations and evolution maps 双侧延迟差分方程和演化图
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-14 DOI: 10.1007/s00010-024-01121-w
Luís Barreira, Claudia Valls
{"title":"Two-sided delay-difference equations and evolution maps","authors":"Luís Barreira, Claudia Valls","doi":"10.1007/s00010-024-01121-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01121-w","url":null,"abstract":"<p>We establish the equivalence of hyperbolicity and of two other properties for a two-sided linear delay-difference equation and its evolution map. These two properties are the admissibility with respect to various pairs of spaces, and the Ulam–Hyers stability of the equation, again with respect to various spaces. This gives characterizations of important properties of a linear dynamical system in terms of corresponding properties of the autonomous dynamical system determined by the associated evolution map.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"21 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266632","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
Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime 广义立方分区和以质数为模数的过分区的算术性质
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-10 DOI: 10.1007/s00010-024-01116-7
Tewodros Amdeberhan, James A. Sellers, Ajit Singh
{"title":"Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime","authors":"Tewodros Amdeberhan, James A. Sellers, Ajit Singh","doi":"10.1007/s00010-024-01116-7","DOIUrl":"https://doi.org/10.1007/s00010-024-01116-7","url":null,"abstract":"<p>A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We emphasize two methods of proofs, one elementary (relying significantly on functional equations) and the other based on modular forms. We close by proving analogous results for generalized overcubic partitions.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194427","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
Min-phase-isometries on the unit sphere of (mathcal {L}^infty (Gamma ))-type spaces $$mathcal {L}^infty (Gamma )$$ 型空间单位球上的最小相位等分线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-10 DOI: 10.1007/s00010-024-01119-4
Dongni Tan, Lu Yuan, Peng Yang
{"title":"Min-phase-isometries on the unit sphere of (mathcal {L}^infty (Gamma ))-type spaces","authors":"Dongni Tan,&nbsp;Lu Yuan,&nbsp;Peng Yang","doi":"10.1007/s00010-024-01119-4","DOIUrl":"10.1007/s00010-024-01119-4","url":null,"abstract":"<div><p>We show that every surjective mapping <i>f</i> between the unit spheres of two real <span>(mathcal {L}^infty (Gamma ))</span>-type spaces satisfies </p><div><div><span>$$begin{aligned} min {Vert f(x)+f(y)Vert ,Vert f(x)-f(y)Vert }=min {Vert x+yVert ,Vert x-yVert }quad (x,yin S_X) end{aligned}$$</span></div></div><p>if and only if <i>f</i> is phase-equivalent to an isometry, i.e., there is a phase-function <span>(varepsilon )</span> from the unit sphere of the <span>(mathcal {L}^infty (Gamma ))</span>-type space onto <span>({-1,1})</span> such that <span>(varepsilon cdot f)</span> is a surjective isometry between the unit spheres of two real <span>(mathcal {L}^infty (Gamma ))</span>-type spaces, and furthermore, this isometry can be extended to a linear isometry on the whole space <span>(mathcal {L}^infty (Gamma ))</span>. We also give an example to show that these are not true if “min” is replaced by “max”.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1475 - 1487"},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194428","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
Multivariable generalizations of bivariate means via invariance 通过不变性对二元均值进行多变量概括
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-09 DOI: 10.1007/s00010-024-01113-w
Paweł Pasteczka
{"title":"Multivariable generalizations of bivariate means via invariance","authors":"Paweł Pasteczka","doi":"10.1007/s00010-024-01113-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01113-w","url":null,"abstract":"<p>For a given <i>p</i>-variable mean <span>(M :I^p rightarrow I)</span> (<i>I</i> is a subinterval of <span>({mathbb {R}})</span>), following (Horwitz in J Math Anal Appl 270(2):499–518, 2002) and (Lawson and Lim in Colloq Math 113(2):191–221, 2008), we can define (under certain assumptions) its <span>((p+1))</span>-variable <span>(beta )</span>-invariant extension as the unique solution <span>(K :I^{p+1} rightarrow I)</span> of the functional equation </p><span>$$begin{aligned}&amp;Kbig (M(x_2,dots ,x_{p+1}),M(x_1,x_3,dots ,x_{p+1}),dots ,M(x_1,dots ,x_p)big )&amp;quad =K(x_1,dots ,x_{p+1}), text { for all }x_1,dots ,x_{p+1} in I end{aligned}$$</span><p>in the family of means. Applying this procedure iteratively we can obtain a mean which is defined for vectors of arbitrary lengths starting from the bivariate one. The aim of this paper is to study the properties of such extensions.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"69 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194426","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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