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An algebraic classification of means 手段的代数分类
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-29 DOI: 10.1007/s10474-024-01471-6
L. R. Berrone
{"title":"An algebraic classification of means","authors":"L. R. Berrone","doi":"10.1007/s10474-024-01471-6","DOIUrl":"10.1007/s10474-024-01471-6","url":null,"abstract":"<div><p>Given a real interval <span>(I)</span>, a group of homeomorphisms <span>(mathcal{G} left(M,Iright))</span> is associated to every continuous mean defined <span>(i)</span>n <span>(I)</span>. Two\u0000means <span>(M)</span>, <span>(N)</span> defined in <span>(I)</span> will belong to the same class when <span>(mathcal{G} (M, I) = mathcal{G} (N,I))</span>. The equivalence relation\u0000defined in this way in <span>(mathcal{CM}(I))</span>, the family of\u0000continuous means defined in <span>(I)</span>, gives a principle of classification based\u0000on the algebrai object <span>(mathcal{G}(M, I))</span>. Two major questions\u0000are raised by this classification: 1) the problem of computing <span>(mathcal{G} (M, I))</span> for a given mean <span>(M in mathcal{CM} (I))</span>, and 2) the determination of general properties of the means belonging to a\u0000same class. Some instances of these questions will find suitable responses\u0000in the present paper.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"209 - 233"},"PeriodicalIF":0.6,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672614","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 finite pseudorandom binary sequences: functions from a Hardy field 论有限伪随机二进制序列：来自哈代域的函数
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-22 DOI: 10.1007/s10474-024-01469-0
M. G. Madritsch, J. Rivat, R. F. Tichy
{"title":"On finite pseudorandom binary sequences: functions from a Hardy field","authors":"M. G. Madritsch,&nbsp;J. Rivat,&nbsp;R. F. Tichy","doi":"10.1007/s10474-024-01469-0","DOIUrl":"10.1007/s10474-024-01469-0","url":null,"abstract":"<div><p>We provide a construction of binary pseudorandom sequences\u0000based on Hardy fields <span>(mathcal{H})</span> as considered by Boshernitzan. In particular we give upper\u0000bounds for the well distribution measure and the correlation measure defined\u0000by Mauduit and Sárközy. Finally we show that the correlation measure of order <i>s</i>\u0000is small only if <i>s</i> is small compared to the “growth exponent” of <span>(mathcal{H})</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"121 - 137"},"PeriodicalIF":0.6,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672608","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
Every connected first countable T1-space is a continuous open image of a connected metrizable space 每个连通的第一可数 T1 空间都是一个连通的可元空间的连续开图像
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-15 DOI: 10.1007/s10474-024-01474-3
V. Smolin
{"title":"Every connected first countable T1-space is a continuous open image of a connected metrizable space","authors":"V. Smolin","doi":"10.1007/s10474-024-01474-3","DOIUrl":"10.1007/s10474-024-01474-3","url":null,"abstract":"<div><p>Answering a question posed by Vladimir Tkachuk, we prove that\u0000every connected first countable <i>T</i><sub>1</sub>-space is a continuous open image of a connected\u0000metrizable space.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"266 - 273"},"PeriodicalIF":0.6,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672664","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 sufficient and necessary condition for infinite orthogonal sets on some Moran measures 某些莫兰量纲上无限正交集的充分必要条件
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-15 DOI: 10.1007/s10474-024-01458-3
S. Chen, J.-C. Liu, J. Su, S. Wu
{"title":"A sufficient and necessary condition for infinite orthogonal sets on some Moran measures","authors":"S. Chen,&nbsp;J.-C. Liu,&nbsp;J. Su,&nbsp;S. Wu","doi":"10.1007/s10474-024-01458-3","DOIUrl":"10.1007/s10474-024-01458-3","url":null,"abstract":"<div><p>In this work we shall concentrate on fractal-harmonic analysis of a class of Moran measures. Let <span>({M_n}_{n=1}^{infty})</span> be a sequence of expanding matrix in <span>(M_2(mathbb{Z}))</span> and\u0000<span>({D_n}_{n=1}^{infty})</span> be a sequence of non-collinear integer digit sets satisfying \u0000</p><div><div><span>$$D_n= left{begin{pmatrix}00end{pmatrix},begin{pmatrix}alpha_{n1}alpha_{n2}end{pmatrix},begin{pmatrix}beta_{n1}beta_{n2}end{pmatrix},begin{pmatrix}-alpha_{n1}-beta_{n1}-alpha_{n2}-beta_{n2}end{pmatrix} right}.$$</span></div></div><p>\u0000The associated Moran-type measure <span>(mu_{{M_n},{D_n}})</span>\u0000 is generated by the infinite convolution\u0000</p><div><div><span>$$mu_{{M_n},{D_n}}=delta_{M_{1}^{-1}D_1}astdelta_{M_{1}^{-1}M_{2}^{-1}D_2}astdelta_{M_{1}^{-1}M_{2}^{-1} M_{3}^{-1}D_3}astcdots$$</span></div></div><p>\u0000in the weak<span>(^*)</span>\u0000-topology. Our result shows that if <span>({alpha_{n1}alpha_{n2}beta_{n1}beta_{n2}}_{n=1}^{infty})</span>\u0000 is bounded, then <span>(L^{2}(mu_{{M_n},{D_n}}))</span>\u0000 admits an infinite orthogonal set of exponential functions if and only if there exists a subsequence <span>({n_{k}}_{k=1}^{infty})</span>\u0000 of <span>({n_{k}}_{k=1}^{infty})</span>\u0000 such that <span>(det(M_{n_{k}})in 2mathbb{Z})</span>\u0000.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"247 - 265"},"PeriodicalIF":0.6,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672665","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 the strong domination number of proper enhanced power graphs of finite groups 论有限群适当增强幂图的强支配数
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-14 DOI: 10.1007/s10474-024-01477-0
S. Bera
{"title":"On the strong domination number of proper enhanced power graphs of finite groups","authors":"S. Bera","doi":"10.1007/s10474-024-01477-0","DOIUrl":"10.1007/s10474-024-01477-0","url":null,"abstract":"<div><p>The enhanced power graph of a group <i>G</i> is a graph with vertex set <i>G</i>, where two distinct vertices <span>(mathbb{x})</span> and <span>(mathbb{y})</span> are adjacent if and only if there exists an element <span>(mathbb{w})</span> in <i>G</i> such that both <span>(mathbb{x})</span> and <span>(mathbb{y})</span> are powers of <span>(mathbb{w})</span>. To obtain the proper enhanced power graph, we consider the induced subgraph on the set <span>(G setminus D)</span>, where <i>D</i> represents the set of dominating vertices in the enhanced power graph. In this paper, we aim to determine the strong domination number of the proper enhanced power graphs of finite nilpotent groups.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"177 - 191"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672459","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 formation residual of factorized finite groups 因式化有限群的形成残差
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-13 DOI: 10.1007/s10474-024-01470-7
X. Li, X. Wu
{"title":"The formation residual of factorized finite groups","authors":"X. Li,&nbsp;X. Wu","doi":"10.1007/s10474-024-01470-7","DOIUrl":"10.1007/s10474-024-01470-7","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <i>G</i> be a split extension of <i>A</i> by <i>B</i>, that is, <i>G</i> is a semidirect product: <span>(G=Artimes B)</span>, where <i>A</i> and <i>B</i> are subgroups of <i>G</i>. Under the condition that <i>B</i> permutes with every maximal subgroup of Sylow subgroups of <i>A</i>, every maximal subgroup of <i>A</i> or every nontrivial normal subgroup of <i>A</i>, we prove that the supersolvable residual of <i>G</i> is the product of the supersolvable residuals of <i>A</i> and <i>B</i>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"202 - 208"},"PeriodicalIF":0.6,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672359","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 uniqueness theorem for orthonormal spline series 正交样条线序列的唯一性定理
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-13 DOI: 10.1007/s10474-024-01472-5
K. A. Keryan, A. L. Khachatryan
{"title":"A uniqueness theorem for orthonormal spline series","authors":"K. A. Keryan,&nbsp;A. L. Khachatryan","doi":"10.1007/s10474-024-01472-5","DOIUrl":"10.1007/s10474-024-01472-5","url":null,"abstract":"<div><p>We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “regular” sequence. Additionally, it is proved that the regularity of the sequence is essential.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"20 - 48"},"PeriodicalIF":0.6,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672358","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 existence of continuations for different types of metrics 不同类型度量的连续性的存在
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-10-13 DOI: 10.1007/s10474-024-01473-4
E. Petrov
{"title":"The existence of continuations for different types of metrics","authors":"E. Petrov","doi":"10.1007/s10474-024-01473-4","DOIUrl":"10.1007/s10474-024-01473-4","url":null,"abstract":"<div><p>The problems of continuation of a partially defined metric and a\u0000partially defined ultrametric were considered in [12] and [13], respectively. Using\u0000the language of graph theory we generalize the criteria of existence of continuation\u0000obtained in these papers. For these purposes we use the concept of a triangle\u0000function introduced by M. Bessenyei and Z. Páles in [6], which gives a generalization\u0000of the triangle inequality in metric spaces. The obtained result allows\u0000us to get criteria of the existence of continuation for a wide class of semimetrics\u0000including not only metrics and ultrametrics, but also multiplicative metrics and\u0000semimetrics with power triangle inequality. Moreover, the explicit formula for the\u0000maximal continuations is also obtained.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"164 - 176"},"PeriodicalIF":0.6,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672360","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 Füredi’s conjecture 关于 Füredi 的猜想
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-25 DOI: 10.1007/s10474-024-01461-8
G. Hegedüs
{"title":"On Füredi’s conjecture","authors":"G. Hegedüs","doi":"10.1007/s10474-024-01461-8","DOIUrl":"10.1007/s10474-024-01461-8","url":null,"abstract":"<div><p>We confirmed the following special case of Füredi’s conjecture:\u0000Let <span>(t)</span> be a non-negative integer. Let <span>( mathcal{ P}={(A_i,B_i)}_{1leq ileq m})</span> be a set-pair family satisfying <span>(|A_i cap B_i|leq t)</span> for <span>(1leq i leq m)</span> and <span>(|A_icap B_j|&gt;t)</span> for all <span>(1leq ineq j leq m)</span>. \u0000Define <span>(a_i:=|A_i|)</span> and <span>(b_i:=|B_i|)</span> for each <span>(i)</span>. \u0000Assume that there exists a positive integer <span>(N)</span> such that <span>(a_i+b_i=N)</span> for each <span>(i)</span>. Then \u0000</p><div><div><span>$$sum_{i=1}^m frac{1}{{a_i+b_i-2t choose a_i-t}}leq 1.$$</span></div></div></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"244 - 246"},"PeriodicalIF":0.6,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01461-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672421","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
(L_p)-Brunn–Minkowski inequality for projection bodies 投影体的布伦-闵科夫斯基不等式
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-24 DOI: 10.1007/s10474-024-01468-1
W. D. Wang
{"title":"(L_p)-Brunn–Minkowski inequality for projection bodies","authors":"W. D. Wang","doi":"10.1007/s10474-024-01468-1","DOIUrl":"10.1007/s10474-024-01468-1","url":null,"abstract":"<div><p>Lutwak established the Brunn–Minkowski inequality for projection\u0000bodies. Schuster [13] obtained the Brunn–Minkowski inequality for polar\u0000projection bodies. Associated with the <span>(L_p)</span>-Minkowski combinations of convex\u0000bodies, we extend Lutwak's result and Schuster's result to <span>(L_p)</span> forms, respectively.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"192 - 201"},"PeriodicalIF":0.6,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672563","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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