Acta Mathematica Hungarica最新文献

{"title":"Set systems with k-wise (mathcal {L} )-intersections and ( mathcal {L} )-differencing Sperner families modulo prime powers","authors":"Rudy X. J. Liu","doi":"10.1007/s10474-026-01618-7","DOIUrl":"10.1007/s10474-026-01618-7","url":null,"abstract":"<div><p>   In this paper, we obtain the following improved upper bound on the size of <i>k</i>-wise <span>( mathcal {L} )</span>-intersecting families and <span>( mathcal {L} )</span>-differencing Sperner families modulo prime powers by employing linear algebra methods: </p><ol>\u0000 <li>\u0000 <span>(1)</span>\u0000 \u0000 <p>Let <span>( k ge 2 )</span> be an integer, <i>p</i> be a prime, <span>( q = p^{ alpha } )</span> be a prime power with <span>( alpha ge 1 )</span>, and let <span>( mathcal {L} subseteq {0, 1, dots , q-1} )</span> be a subset with size <span>( s &gt; 0 )</span>. Suppose that <span>( mathcal {F} )</span> is a family of subsets of [<i>n</i>] such that <span>( left| F right| notin mathcal {L} pmod {q} )</span> for each <span>( F in mathcal {F} )</span> and <span>( left| F_{i_1} cap F_{i_2} cap cdots cap F_{i_k} right| in mathcal {L} pmod {q} )</span> for every collection of <i>k</i> distinct subsets in <span>( mathcal {F} )</span>. Then </p><div><div><span>$$ left| mathcal {F} right| le left( k-1 right) left[ {{n-1} atopwithdelims (){q-1}}+ {{n-1} atopwithdelims (){q-2}}+ cdots + {{n-1} atopwithdelims (){0}} right] . $$</span></div></div><p> If in addition there exists an integer <span>( t &lt; p )</span> such that <span>( left| F right| in left{ q-t, q-t+1, dots q-1 right} pmod {q} )</span> for each <span>( F in mathcal {F} )</span>, then </p><div><div><span>$$ left| mathcal {F} right| le left( k-1 right) left[ {{n-1} atopwithdelims (){q-1}}+ {{n-1} atopwithdelims (){q-2}}+ cdots + {{n-1} atopwithdelims (){p - t -1}} right] . $$</span></div></div><p> This result not only gives an improvement to a theorem by G. Hegedüs and a theorem by Z. Xu and C. H. Yip, but also extends a theorem by L. Babai and P. Frankl.</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(2)</span>\u0000 \u0000 <p>Let <i>p</i> be a prime, <span>( q = p^{ alpha } )</span> be a prime power with <span>( alpha ge 1 )</span>, and <span>( mathcal {L} = {l_1, l_2, dots , l_s} )</span> be a subset of <span>( {1, 2, dots , q-1} )</span>. Suppose that <span>( mathcal {F} )</span> is a family of subsets of [<i>n</i>] satisfying that <span>( left| F setminus F' right| in mathcal {L} pmod {q} )</span> for all distinct pairs <span>( F, F' in mathcal {F} )</span>. Then </p><div><div><span>$$ left| mathcal {F} right| le left( {begin{array}{c}n-1 q-1end{array}}right) + left( {begin{array}{c}n-1 q-2end{array}}right) +cdots +left( {begin{array}{c}n-1 0end{array}}right) . $$</span></div></div><p> This result extends a theorem by Z. Xu and C. H. Yip to the case of general <span>( mathcal {L} )</span> with size <span>( left| mathcal {L} right| = s )</span>.</p>\u0000 \u0000 </li>\u0000 </ol></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"459 - 474"},"PeriodicalIF":0.6,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807526","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":"Finite groups with (mathcal {H}N)-subgroups","authors":"M. Ramadan","doi":"10.1007/s10474-026-01615-w","DOIUrl":"10.1007/s10474-026-01615-w","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <i>H</i> a subgroup of <i>G</i>. We say that <i>H</i> is an <span>(mathcal {H})</span>-subgroup of <i>G</i> if <span>(N_{G}(H)cap H^{g}le H)</span> for all <span>(gin G)</span>. The subgroup <i>H</i> is called an <span>(mathcal {H}N)</span>-subgroup of <i>G</i> if there exists a normal subgroup <i>T</i> with <span>((|H|,|G:HT|)=1)</span> such that <span>(N_{T}(H)cap H^{g}le H)</span> for all <span>(gin G)</span>. In this paper, some new criteria for a group <i>G</i> to be <i>p</i>-nilpotent and supersolvable are given when certain subgroups of prime power orders are <span>(mathcal {H}N)</span>-subgroups of <i>G</i>. Our results improve and generalize some recent results in the literature.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"451 - 458"},"PeriodicalIF":0.6,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807624","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":"Large orbits of Hall subgroups of solvable linear groups","authors":"Samarth Das,&nbsp;Yong Yang","doi":"10.1007/s10474-026-01608-9","DOIUrl":"10.1007/s10474-026-01608-9","url":null,"abstract":"<div><p>Suppose that <i>G</i> is a finite solvable group and let <i>H</i> be a Hall <span>(pi )</span>-subgroup, let <i>b</i>(<i>H</i>) be the largest character degree of <i>H</i>, we show that <span>(|G:O_{pi ' pi }(G)|_{pi } le b(H)^2.)</span></p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"446 - 450"},"PeriodicalIF":0.6,"publicationDate":"2026-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01608-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807382","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":"Axisymmetric solutions of the (lambda )-singular minimal surface equation","authors":"Seher Kaya,&nbsp;Rafael López","doi":"10.1007/s10474-026-01613-y","DOIUrl":"10.1007/s10474-026-01613-y","url":null,"abstract":"<div><p>Given a unit vector <span>(vec {v}in mathbb {R}^3)</span> and <span>(lambda ,alpha in mathbb {R})</span>, a surface <span>(Sigma subset mathbb {R}^3)</span> is called <span>(lambda )</span>-singular minimal surface if its mean curvature <i>H</i> satisfies <span>(H(p)=alpha frac{langle N(p),vec {v}rangle }{langle p,vec {v}rangle }+lambda )</span> for all <span>(pin Sigma )</span>, where <i>N</i> is the unit normal to <span>(Sigma )</span>. In this paper, we study the axisymmetric solutions of this equation, identifying two types of surfaces depending on whether the rotation axis is parallel or orthogonal to <span>(vec {v})</span>. For the first type, we prove the existence of surfaces that orthogonally intersect the rotation axis. For the second type, we provide a complete geometric description.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"425 - 445"},"PeriodicalIF":0.6,"publicationDate":"2026-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01613-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807336","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":"Averages of Gauss map iterations in arithmetic progressions","authors":"Mumtaz Hussain,&nbsp;Bixuan Li,&nbsp;Nikita Shulga","doi":"10.1007/s10474-026-01611-0","DOIUrl":"10.1007/s10474-026-01611-0","url":null,"abstract":"<div><p>The theory of uniform Diophantine approximation concerns the study of Dirichlet improvable (or non-improvable) numbers. The metrical aspect of this theory leads to the study of the products of partial quotients in continued fractions. It is known that the dimension of the set of Dirichlet non-improvable numbers depends upon the number of partial quotients in the product string. However, the Hausdorff dimension is the same when partial quotients in the product are separated with a gap of fixed length. In this paper, we provide a detailed Hausdorff dimension analysis of the set of real numbers with a large product of partial quotients with indices in arithmetic progressions. This poses significant challenges as opposed to the considerations of consecutive partial quotients. As an application of our general theorem, in particular, we obtain the Hausdorff dimension of the set </p><div><div><span>$$begin{aligned} E(psi ):=left{ xin [0, 1): root n of {a_{n}(x)a_{2n}(x)cdots a_{n^2}(x)}ge psi (n) mathrm{for infinitely many} nin mathbb {N}right} . end{aligned}$$</span></div></div></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"392 - 424"},"PeriodicalIF":0.6,"publicationDate":"2026-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01611-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807328","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":"The logarithmic Sobolev capacity in the Heisenberg group","authors":"Yingjie Luo,&nbsp;Mingwei Shi,&nbsp;Nan Zhao,&nbsp;Yu Liu","doi":"10.1007/s10474-026-01616-9","DOIUrl":"10.1007/s10474-026-01616-9","url":null,"abstract":"<div><p>In this paper, we consider the logarithmic Sobolev capacity <span>(text {Cap}^{mathbb {H}^n}_{ log ,gamma ,p})</span> in the Heisenberg group <span>(mathbb {H}^n)</span>, a capacity generated by the logarithmic Sobolev space <span>(W^{ log ,gamma }_{p}(mathbb {H}^n))</span>, where <span>((gamma , p)in (0,infty )times [1,infty ))</span>. In particular, we investigate several properties of the space <span>(W^{ log ,gamma }_{p}(mathbb {H}^n))</span>, including completeness, min-max estimation and density. In addition, we investigate the properties of the logarithmic Sobolev capacity and the logarithmic perimeter in the Heisenberg group. Furthermore, we deal with the relationship between <span>(text {Cap}^{mathbb {H}^{n}}_{ log ,gamma ,p})</span> and the Hausdorff capacity in the Heisenberg group. As an application, we prove the corresponding capacity estimate and the tracing principle.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"365 - 391"},"PeriodicalIF":0.6,"publicationDate":"2026-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807327","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":"Schmidt’s game on parameter space and ((alpha ,beta ))-transformation with nondense orbits","authors":"Hui Hu,&nbsp;Zhihui Li,&nbsp;Yueli Yu","doi":"10.1007/s10474-026-01587-x","DOIUrl":"10.1007/s10474-026-01587-x","url":null,"abstract":"<div><p>For any <span>(x,yin [0,1])</span> and <span>(alpha in [0,1))</span>, we consider the set <span>(E_{alpha }(x,y))</span> of <span>(beta &gt;1)</span> such that the orbits of <i>x</i> under <span>(T_{alpha ,beta })</span> are bounded away from <i>y</i>, i.e., </p><div><div><span>$$begin{aligned} E_{alpha }(x,y)={beta&gt;1: inf limits _{ige 1}|T_{alpha ,beta }^i(x)-y|&gt;0}, end{aligned}$$</span></div></div><p>where <span>(T_{alpha ,beta })</span> is the <span>((alpha ,beta ))</span>-transformation defined by <span>(T_{alpha ,beta }(x)=beta x+alpha (textrm{mod } 1))</span>. We prove that <span>(E_{alpha }(x,y))</span> is always 1/2-winning in the sense of Schmidt’s game if <span>((x,y)ne (0,alpha ))</span>, which extends the result of Langeveld and Samuel [14] to the parameter space and improves upon some known results about <span>(E_{alpha }(x,y))</span>. As an application, a question mentioned in [20] on the Hausdorff dimension of the set of <span>(beta )</span> for which <span>(T_{alpha ,beta })</span> has the specification property for a given <span>(alpha )</span> is solved.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"343 - 364"},"PeriodicalIF":0.6,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807566","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 remark on three consecutive powerful numbers","authors":"Tran Duc Son","doi":"10.1007/s10474-026-01607-w","DOIUrl":"10.1007/s10474-026-01607-w","url":null,"abstract":"<div><p>In this note, we prove that there do not exist three consecutive powerful numbers, one of which is of the form <span>(x^{n}pm 1)</span> and whose <i>cubic square-free part</i> (i.e., the unique square-free integer <i>b</i> such that the number can be written as <span>(a^{2}b^{3})</span>) is either 1 or the product of distinct primes.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"339 - 342"},"PeriodicalIF":0.6,"publicationDate":"2026-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807386","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":"Existence of a Sidon set for the distinct distance constant","authors":"Robin Riblet,&nbsp;Titien Schehr","doi":"10.1007/s10474-026-01604-z","DOIUrl":"10.1007/s10474-026-01604-z","url":null,"abstract":"<div><p>We highlight a certain compactness of Sidon sets and <span>(B_2[g])</span>-sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose reciprocal sum is equal to the distinct distance constant. We also improve the best known bounds for this constant.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"323 - 338"},"PeriodicalIF":0.6,"publicationDate":"2026-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01604-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807653","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":"Spectrality of a class of Moran measures with product-form digit sets","authors":"Kailing Lai","doi":"10.1007/s10474-026-01605-y","DOIUrl":"10.1007/s10474-026-01605-y","url":null,"abstract":"<div><p>In this paper, we investigate the spectrality of a class of Moran measures <span>(mu _{{R_{n}},{B_{n}}})</span> generated by a sequence of integers <span>({R_{n}}_{n=1}^{infty })</span> and a sequence of product-form digit sets <span>({B_{n}}_{n=1}^{infty })</span>, where <span>(R_{n}=N^{q_{n}})</span>, <span>(B_{n}={0,1,ldots ,N-1}oplus N^{p_{n}}{0,1,ldots ,N-1})</span> with <span>(Nge 2)</span> and <span>(q_{n},~p_{n})</span> are positive integers for <span>(nge 1)</span>. We give some sufficient conditions for <span>(mu _{{R_{n}},{B_{n}}})</span> to be a spectral measure, i.e., there exists a countable set <span>(Lambda )</span> such that <span>({e^{2pi ilambda cdot x}:lambda in Lambda })</span> is an orthonormal basis in <span>(L^2(mu _{{R_{n}},{B_{n}}}))</span>. Our results partially extend the work of Liu et al. [19], where <span>(p_n=p)</span> and <span>(q_n=q)</span> for all <span>(nge 1)</span>. Furthermore, we show that our results can be extended to higher-dimensional settings.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"305 - 322"},"PeriodicalIF":0.6,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807490","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}