Acta Mathematica Hungarica最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"title":"Vector-type precise large deviations for a nonstandard multidimensional risk model with some arbitrary dependence structures","authors":"B. Geng,&nbsp;S. Wang,&nbsp;W. Zhu","doi":"10.1007/s10474-024-01501-3","DOIUrl":"10.1007/s10474-024-01501-3","url":null,"abstract":"<div><p>Consider a nonstandard multidimensional risk model in which\u0000the claim sizes from all lines of businesses, sharing a common claim-arrival renewal\u0000process, constitute a sequence of independent and identically distributed\u0000nonnegative random vectors, the common inter-arrival times are assumed to be\u0000arbitrarily dependent and the dependence between claim size vectors and their\u0000waiting times are also allowed to be arbitrary. Moreover, the claim sizes from\u0000different lines of businesses are supposed to be extended negatively dependent.\u0000Under some mild conditions, this paper achieves some vector-type precise large\u0000deviation formulae for aggregate claims of such multidimensional risk model in the\u0000presence of dominatedly-varying claim sizes. The obtained results extend some\u0000existing ones in the literature.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"158 - 173"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638564","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}

{"title":"An upper bound for the minimum modulus in a covering system with squarefree moduli","authors":"M. Cummings,&nbsp;M. Filaseta,&nbsp;O. Trifonov","doi":"10.1007/s10474-024-01496-x","DOIUrl":"10.1007/s10474-024-01496-x","url":null,"abstract":"<div><p>Based on work of P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba [5], we show that if a covering system has distinct\u0000squarefree moduli, then the minimum modulus is at most 118. We also show\u0000that in general the <span>(k)</span>-th smallest modulus in a covering system with distinct moduli (provided it is required for the covering) is bounded by an absolute constant.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"1 - 25"},"PeriodicalIF":0.6,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638300","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}

{"title":"On the convergence of random walks in one-dimensional space","authors":"T.-B.-B Duong,&nbsp;H. -C Lam","doi":"10.1007/s10474-024-01497-w","DOIUrl":"10.1007/s10474-024-01497-w","url":null,"abstract":"<div><p>The study aims to investigate the weak convergence of nearest\u0000neighbor random walks in one-dimensional space, with the assumption that the\u0000transition probabilities tend towards a constant within the range <span>([ 0, 1/2 ])</span>. The\u0000paper will demonstrate limit theorems based on the bias or balance of the random\u0000walk, utilizing the method of moments.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"174 - 184"},"PeriodicalIF":0.6,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638299","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}

{"title":"On a finite group with OS-propermutable Sylow subgroup","authors":"E. Zubei","doi":"10.1007/s10474-024-01495-y","DOIUrl":"10.1007/s10474-024-01495-y","url":null,"abstract":"<div><p>A Schmidt group is a non-nilpotent group whose every proper subgroup is nilpotent. A subgroup <i>A</i> of a group <i>G</i> is called <i>OS-propermutable</i>in <i>G</i> if there is a subgroup <i>B</i> such that <span>(G = NG(A)B)</span>, where <i>AB</i> is a subgroup of <i>G</i> and <i>A</i> permutes with all Schmidt subgroups of <i>B</i>. We proved <span>(p)</span>-solubility of a group in which a Sylow <span>(p)</span>-subgroup is <i>OS</i>-propermutable, where <span>(pgeq 7)</span> 7. For <span>(p &lt; 7)</span> all non-Abelian composition factors of such group are listed.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"570 - 577"},"PeriodicalIF":0.6,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994405","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}

{"title":"Ellis' theorem, minimal left ideals, and minimal/maximal idempotents without (mathsf{AC})","authors":"E. Tachtsis","doi":"10.1007/s10474-024-01494-z","DOIUrl":"10.1007/s10474-024-01494-z","url":null,"abstract":"<div><p>In [18], we showed that the Boolean prime ideal theorem (<span>(mathsf{BPI})</span>) suffices to prove the celebrated theorem of R. Ellis, which states: ``Every compact Hausdorff right topological semigroup has an idempotent element''. However, the natural and intriguing question of the status of the reverse implication remained open until now. We resolve this open problem in the setting of <span>(mathsf{ZFA})</span> (Zermelo–Fraenkel set theory with atoms), namely we establish that Ellis' theorem does not imply <span>(mathsf{BPI})</span> in <span>(mathsf{ZFA})</span>, and thus is strictly weaker than <span>(mathsf{BPI})</span> in <span>(mathsf{ZFA})</span>. From the above paper, we also answer two more open questions and strengthen some theorems.</p><p>Typical results are:</p><p>1. Ellis' theorem is true in the Basic Fraenkel Model, and thus Ellis' theorem does not imply <span>(mathsf{BPI})</span> in <span>(mathsf{ZFA})</span>.</p><p>2. In <span>(mathsf{ZF})</span> (Zermelo–Fraenkel set theory without the Axiom of Choice (<span>(mathsf{AC})</span>)), if <span>(S)</span> is a compact Hausdorff right topological semigroup with <span>(S)</span> well orderable, then every left ideal of <span>(S)</span> contains a minimal left ideal and a minimal idempotent element. In addition, every such semigroup <span>(S)</span> has a maximal idempotent element.</p><p>3. In <span>(mathsf{ZF})</span>, if <span>(S)</span> is a compact Hausdorff right topological abelian semigroup, then every left ideal of <span>(S)</span> contains a minimal left ideal.</p><p>4. In <span>(mathsf{ZF})</span>, <span>(mathsf{BPI})</span> implies ``Every compact Hausdorff right topological abelian semigroup <span>(S)</span> has a minimal idempotent element''.</p><p>5. In <span>(mathsf{ZFA})</span>, the Axiom of Multiple Choice (<span>(mathsf{MC})</span>) implies ``Every compact Hausdorff right topological abelian semigroup <span>(S)</span> has a minimal idempotent element''.</p><p>6. In <span>(mathsf{ZFA})</span>, <span>(mathsf{MC})</span> implies ``Every compact Hausdorff right topological semigroup <span>(S)</span> with <span>(S)</span> linearly orderable, has a minimal idempotent element''.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"545 - 569"},"PeriodicalIF":0.6,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994448","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}