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Acta Mathematica Hungarica最新文献

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The cardinality of orthogonal exponentials for a class of self-affine measures on ( mathbb{R}^{n} ) mathbb{R}^{n} 上一类自阿芬度量的正交指数的心数
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-09 DOI: 10.1007/s10474-025-01507-5
J. L. Chen, X. Y. Yan, P. F. Zhang
{"title":"The cardinality of orthogonal exponentials for a class of self-affine measures on ( mathbb{R}^{n} )","authors":"J. L. Chen,&nbsp;X. Y. Yan,&nbsp;P. F. Zhang","doi":"10.1007/s10474-025-01507-5","DOIUrl":"10.1007/s10474-025-01507-5","url":null,"abstract":"<div><p>We study the cardinality of orthogonal exponential functions in <span>(L^{2}(mu_{{R,D}}))</span>, where <span>(mu_{{R,D}} )</span> is the self-affine measure generated by an expanding real matrix <span>( R = {rm diag}[rho_{1},rho_{2},dots,rho_{n}] )</span> and a finite digit set <span>( Dsubsetmathbb{Z}^{n} )</span>. Let <span>( m )</span> be a prime and <span>( mathcal{Z}(m_{D}) )</span> be the set of zeros of mask polynomial <span>( m_{D} )</span> of <span>( D )</span>. Suppose <span>(mathcal{Z}(m_{D}))</span> can be decomposed into the union of finite <span>(mathcal{Z} _{i}(m),)</span> where <span>(mathcal{Z} _{i}(m))</span> satisfies\u0000<span>( (mathcal{Z} _{i}(m)-mathcal{Z} _{i}(m))backslashmathbb{Z}^{n}subsetmathcal{Z} _{i}(m)subset(m^{-1}mathbb{Z}backslash mathbb{Z})^{n} )</span> and <span>( mathcal{Z} _{i}(m)nsubseteq(m_{1}^{-1}mathbb{Z}backslash mathbb{Z})^{n} )</span> for all integer <span>( m_{1}in(0,m) )</span>, then we show that <span>( L^{2}(mu_{{R,D}}))</span> admits infinite orthogonal exponential functions if and only if <span>( rho_{i}=(frac{m p_{i}}{q_{i}})^{frac{1}{r_{i}}} )</span> for some <span>( r_{i},p_{i},q_{i}inmathbb{N} )</span> with <span>( gcd(p_{i},q_{i})=1 )</span>, <span>( i=1,2,dots,n )</span>. Furthermore, if <span>( L^{2}(mu_{{R,D}}))</span> does not admit infinite orthogonal exponential functions, we estimate the number of orthogonal exponential functions in some cases.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"219 - 235"},"PeriodicalIF":0.6,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638582","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
Kepler sets of linear recurrence sequences 线性递归序列的开普勒集
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-08 DOI: 10.1007/s10474-025-01506-6
D. Berend, R. Kumar
{"title":"Kepler sets of linear recurrence sequences","authors":"D. Berend,&nbsp;R. Kumar","doi":"10.1007/s10474-025-01506-6","DOIUrl":"10.1007/s10474-025-01506-6","url":null,"abstract":"<div><p>The Kepler set of a sequence <span>((a_n)_{n=0}^infty)</span> is the closure of the set of consecutive ratios <span>({a_{n+1}/a_{n} : ngeq 0})</span>. Following several studies, dealing with Kepler sets of recurrence sequences of order 2, we study here the case of recurrences of any order.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"54 - 95"},"PeriodicalIF":0.6,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01506-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638519","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
Set systems with restricted symmetric sets of Hamming distances modulo a prime number 以素数为模的汉明距离的有限对称集的集合系统
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-08 DOI: 10.1007/s10474-025-01510-w
R. X. J. Liu
{"title":"Set systems with restricted symmetric sets of Hamming distances modulo a prime number","authors":"R. X. J. Liu","doi":"10.1007/s10474-025-01510-w","DOIUrl":"10.1007/s10474-025-01510-w","url":null,"abstract":"<div><p>Let <span>( p )</span> be a prime and let <span>( mathcal{D}={d_1, d_2, dots, d_s} )</span> be a subset of <span>( left { 1, 2, dots, p-1 right } .)</span>\u0000If <span>( mathcal{F} )</span> is a Hamming symmetric family of subsets of <span>([n])</span> such that <span>( lvert F bigtriangleup F' rvert ( bmod p ) in mathcal{D} )</span> and <span>( n- lvert F bigtriangleup F' rvert ( bmod p ) in mathcal{D} )</span> for any pair of distinct <span>( F )</span>, <span>( F' in mathcal{F} )</span>, then\u0000</p><div><div><span>$$|mathcal{F}| leq {{n-1} choose {s}}+ {{n-1} choose {s-1}}+ cdots + {{n-1} choose {0}}.$$</span></div></div><p>\u0000This result can be considered as a modular version of Hegedüs's Theorem [6] about Hamming symmetric families. We also improve the above upper bound on the size of Hamming symmetric families in the non-modular version when the size of any member of <span>( mathcal{F} )</span> is restricted. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"259 - 269"},"PeriodicalIF":0.6,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638517","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
Hungarian cubes 匈牙利的多维数据集
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-08 DOI: 10.1007/s10474-025-01503-9
S. Garti
{"title":"Hungarian cubes","authors":"S. Garti","doi":"10.1007/s10474-025-01503-9","DOIUrl":"10.1007/s10474-025-01503-9","url":null,"abstract":"<div><p>We prove the consistency of the relation <span>(left(begin{matrix}nu mu lambda end{matrix}right) rightarrow left(begin{matrix} nu mu lambda end{matrix}right))</span> when <span>(lambda &lt; mu = text{cf}(mu) &lt; nu = text{cf} (nu) leq 2^{mu})</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"96 - 107"},"PeriodicalIF":0.6,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638518","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 product representations of squares 关于平方的乘积表示
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-07 DOI: 10.1007/s10474-025-01505-7
T. Tao
{"title":"On product representations of squares","authors":"T. Tao","doi":"10.1007/s10474-025-01505-7","DOIUrl":"10.1007/s10474-025-01505-7","url":null,"abstract":"<div><p>Fix <span>(k geq 2)</span>. For any <span>(N geq 1)</span>, let <span>(F_k(N))</span> denote the cardinality of the largest subset of <span>({1,dots,N})</span> that does not contain <span>(k)</span> distinct elements whose product is a square. Erdős, Sárközy, and Sós showed that <span>(F_2(N) = (frac{6}{pi^2}+o(1)) N)</span>, <span>(F_3(N) = (1-o(1))N)</span>, <span>(F_k(N) asymp N/log N)</span> for even <span>(k geq 4)</span>, and <span>(F_k(N) asymp N)</span> for odd <span>(k geq 5)</span>. Erdős then asked whether <span>(F_k(N) = (1-o(1)) N)</span> for odd <span>(k geq 5)</span>. Using a probabilistic argument, we answer this question in the negative.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"142 - 157"},"PeriodicalIF":0.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01505-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638480","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
Convergence of summability means of higher dimensional Fourier series and Lebesgue points 可和性的收敛意味着高维傅里叶级数和勒贝格点
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-07 DOI: 10.1007/s10474-025-01504-8
F. Weisz
{"title":"Convergence of summability means of higher dimensional Fourier series and Lebesgue points","authors":"F. Weisz","doi":"10.1007/s10474-025-01504-8","DOIUrl":"10.1007/s10474-025-01504-8","url":null,"abstract":"<div><p>We introduce a new concept of Lebesgue points for higher dimensional\u0000functions. Every continuity point is a Lebesgue point and almost every\u0000point is a Lebesgue point of an integrable function. Given a strictly increasing\u0000continuous function<span>(delta)</span>, we prove that the Fejér or Cesàro means<span>(sigma_n^{alpha}f)</span> of the Fourier\u0000series of a two-dimensional function <span>(fin L_1(mathbb{T}^2))</span> converge to <span>(f)</span> at each Lebesgue\u0000point as <span>(nto infty)</span> and n is in the cone around the graph of <span>(delta)</span>. We also prove this\u0000result for higher dimensional functions and for other summability means. This is\u0000a generalization of the classical one-dimensional Lebesgue’s theorem for the Fejér\u0000means.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"270 - 285"},"PeriodicalIF":0.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01504-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638478","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 diameter of finite Sidon sets 有限西顿集的直径
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-07 DOI: 10.1007/s10474-024-01499-8
D. Carter, Z. Hunter, K. O’Bryant
{"title":"On the diameter of finite Sidon sets","authors":"D. Carter,&nbsp;Z. Hunter,&nbsp;K. O’Bryant","doi":"10.1007/s10474-024-01499-8","DOIUrl":"10.1007/s10474-024-01499-8","url":null,"abstract":"<div><p>We prove that the diameter of a Sidon set (also known as a Babcock sequence, Golomb ruler, or <span>(B_2)</span> set) with <span>(k)</span> elements is at least <span>(k^2-b k^{3/2}-O(k))</span> where <span>(ble 1.96365)</span>, a comparatively large improvement on past results. Equivalently, a Sidon set with diameter <span>(n)</span> has at most <span>(n^{1/2}+0.98183n^{1/4}+O(1))</span> elements. The proof is conceptually simple but very computationally intensive, and the proof uses substantial computer assistance. We also provide a proof of <span>(ble 1.99058)</span> that can be verified by hand, which still improves on past results. Finally, we prove that <span>(g)</span>-thin Sidon sets (aka <span>(g)</span>-Golomb rulers) with <span>(k)</span> elements have diameter at least <span>(g^{-1} k^2 - (2-varepsilon)g^{-1}k^{3/2} - O(k))</span>, with <span>(varepsilonge 0.0062g^{-4})</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"108 - 126"},"PeriodicalIF":0.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01499-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638479","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
Haagerup property of semigroup crossed products by left Ore semigroups 左半群间半群交叉积的haagup性质
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-07 DOI: 10.1007/s10474-025-01511-9
Q. Meng
{"title":"Haagerup property of semigroup crossed products by left Ore semigroups","authors":"Q. Meng","doi":"10.1007/s10474-025-01511-9","DOIUrl":"10.1007/s10474-025-01511-9","url":null,"abstract":"<div><p> We study the Haagerup property of certain semigroup crossed products. Let \u0000<i>P</i> be a left Ore semigroup. Then <i>P</i> generates a group <i>G</i>. We assume that there is an action <span>(alpha)</span> of <i>G</i> on a unital <span>({rm C}^*)</span>-algebra <i>A</i>. If <i>A</i> has an <span>(alpha)</span>-invariant state <span>(tau)</span> and <span>(D^G_P)</span> has a <i>GP</i>-invariant state, then <span>(tau)</span> induces a state <span>(tau')</span> on the reduced semigroup crossed product <span>(Artimes_{alpha,r} P)</span>. If <span>((Artimes_{alpha,r} P,tau'))</span> has the Haagerup property, then both <span>((A,tau))</span> and <i>G</i> have the Haagerup property. Conversely, the Haagerup property of <span>((A,tau))</span> implies that of <span>((Artimes_{alpha,r} P,tau'))</span>, when <i>G</i> is amenable.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"246 - 258"},"PeriodicalIF":0.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638477","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 minimal Kurepa line 最小库雷柏线
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-06 DOI: 10.1007/s10474-025-01509-3
H. Lamei Ramandi
{"title":"A minimal Kurepa line","authors":"H. Lamei Ramandi","doi":"10.1007/s10474-025-01509-3","DOIUrl":"10.1007/s10474-025-01509-3","url":null,"abstract":"<div><p>We show it is consistent with <span>(ZFC)</span> \u0000that there is an everywhere Kurepa line which is order \u0000isomorphic to all of its dense <span>(aleph_2)</span>-dense suborders.\u0000Moreover, this Kurepa line does not contain any Aronszajn suborder.\u0000We also show it is consistent with <span>(ZFC)</span> that there is a minimal Kurepa line which does not contain any Aronszajn suborder.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"37 - 53"},"PeriodicalIF":0.6,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638344","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 cup-length of the oriented Grassmann manifolds (widetilde G_{n,4}) 关于定向格拉斯曼流形的杯长 (widetilde G_{n,4})
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-01-25 DOI: 10.1007/s10474-024-01502-2
T. Rusin
{"title":"On the cup-length of the oriented Grassmann manifolds (widetilde G_{n,4})","authors":"T. Rusin","doi":"10.1007/s10474-024-01502-2","DOIUrl":"10.1007/s10474-024-01502-2","url":null,"abstract":"<div><p>For the Grassmann manifold <span>(widetilde G_{n,4})</span> of oriented 4-planes in <span>(mathbb{R}^{n})</span> no\u0000full description of its cohomology ring with coefficients in the two element field <span>(mathbb {Z}_{2})</span>\u0000is available. It is known however that it contains a subring that can be identified\u0000with a quotient of a polynomial ring by a certain ideal. Examining this quotient\u0000ring by means of Gröbner bases we are able to determine the <span>(mathbb {Z}_{2})</span>-cup-length \u0000of <span>(widetilde G_{n,4})</span> for \u0000<span>(n=2^t,2^t-1,2^t-2)</span>for all \u0000<span>(t geq 4)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"127 - 141"},"PeriodicalIF":0.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01502-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638398","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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