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Connectivity threshold for superpositions of Bernoulli random graphs. II 伯努利随机图叠加的连通性阈值。2
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-04-22 DOI: 10.1007/s10474-025-01518-2
M. Bloznelis, D. Marma, R. Vaicekauskas
{"title":"Connectivity threshold for superpositions of Bernoulli random graphs. II","authors":"M. Bloznelis,&nbsp;D. Marma,&nbsp;R. Vaicekauskas","doi":"10.1007/s10474-025-01518-2","DOIUrl":"10.1007/s10474-025-01518-2","url":null,"abstract":"<div><p>\u0000Let <span>(G_1)</span>, ..., <span>(G_m)</span> be independent\u0000Bernoulli random subgraphs of the complete graph <span>(mathcal{K}_n)</span> having\u0000random sizes <span>(X_1,dots, X_min {0,1,2,dots})</span> and edge densities <span>(Q_1)</span>, ..., <span>(Q_min [0,1])</span>. \u0000Letting <span>(n,mto+infty)</span> we establish the connectivity threshold for the union <span>( bigcup_{i=1}^mG_i)</span> defined on the vertex set of <span>(mathcal{K}_n)</span>. We show that \u0000</p><div><div><span>$$ textbf{P} bigl { bigcup_{i=1}^m G_i hbox{is connected} bigr }= e^{-e^{lambda^*_{n,m}}}+o(1) , $$</span></div></div><p>\u0000 where <span>(lambda^{*}_{n,m}= ln n - frac{1}{n} sumnolimits_{i=1}^{m} textbf{E} X_{i}(1-(1-Q_i)^{|X_i-1|}))</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"352 - 375"},"PeriodicalIF":0.6,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167909","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
Countable tightness is not discretely reflexive in (sigma)-compact spaces 可数紧性在(sigma) -紧空间中不是离散自反的
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-03-28 DOI: 10.1007/s10474-025-01521-7
I. Juhász, J. van Mill
{"title":"Countable tightness is not discretely reflexive in (sigma)-compact spaces","authors":"I. Juhász,&nbsp;J. van Mill","doi":"10.1007/s10474-025-01521-7","DOIUrl":"10.1007/s10474-025-01521-7","url":null,"abstract":"<div><p>Answering a question raised by V.V. Tkachuk in [10], \u0000we present several examples of <span>(sigma)</span>-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In fact, in some of our examples the closures of all discrete subsets are even first countable.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"543 - 549"},"PeriodicalIF":0.6,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01521-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171135","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 ( b)-concatenations of two ( k)-generalized Fibonacci numbers 关于两个( k)广义斐波那契数的( b) -连接
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-03-28 DOI: 10.1007/s10474-025-01517-3
M. Alan, A. Altassan
{"title":"On ( b)-concatenations of two ( k)-generalized Fibonacci numbers","authors":"M. Alan,&nbsp;A. Altassan","doi":"10.1007/s10474-025-01517-3","DOIUrl":"10.1007/s10474-025-01517-3","url":null,"abstract":"<div><p>Let <span>( k geq 2 )</span> be an integer. One of the generalization of the classical Fibonacci sequence is defined by the recurrence relation\u0000<span>( F_{n}^{(k)}=F_{n-1}^{(k)} + cdots + F_{n-k}^{(k)})</span> for all <span>( n geq 2)</span> with the initial values <span>( F_{i}^{(k)}=0 )</span> for <span>( i=2-k, ldots, 0 )</span> and <span>( F_{1}^{(k)}=1)</span> <span>(. F_{n}^{(k)} )</span> is an order <span>( k )</span> generalization of the Fibonacci sequence and it is called <span>( k)</span>-generalized\u0000Fibonacci sequence or shortly <span>( k)</span>-Fibonacci sequence. Banks and Luca [7], among other things, determined all Fibonacci numbers which are concatenations of two Fibonacci numbers. In this paper, we consider the analogue of this problem in more general manner by taking into account the concatenations of two terms of the same sequence in base <span>(b geq 2)</span>. First, we show that there exists only finitely many such concatenations for each <span>( k geq 2 )</span> and <span>( b geq 2 )</span>. Next, we completely determine all these concatenations for all <span>( k geq 2)</span> and <span>( 2 leq b leq 10 )</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"452 - 471"},"PeriodicalIF":0.6,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171138","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 iterates of Chatterjea contraction 查特耶收缩的迭代
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-03-28 DOI: 10.1007/s10474-025-01519-1
M. Cvetković
{"title":"On the iterates of Chatterjea contraction","authors":"M. Cvetković","doi":"10.1007/s10474-025-01519-1","DOIUrl":"10.1007/s10474-025-01519-1","url":null,"abstract":"<div><p>The question of the relation between contractive conditions may\u0000be extended to the problem of their iterates. It was shown by B. Fisher that for\u0000a Banach contraction there exists an iterate that fulfills Chatterjea contractive\u0000condition, but the reverse relation holds under some restriction imposed on the\u0000metric space which assures that there exists an iterate of a Chatterjea contraction\u0000that is a Banach contraction. However, the proposed restriction holds only for the\u0000identity mapping which is not a Chatterjea contraction except for the singleton\u0000domain. We offer a possible adjustment of this approach with several examples\u0000answering some open questions on this topic.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"507 - 518"},"PeriodicalIF":0.6,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171136","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 generalized Ramanujan sum over a residually finite Dedekind domain 余数有限Dedekind区域上的广义Ramanujan和
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-03-18 DOI: 10.1007/s10474-025-01522-6
T. Qi
{"title":"A generalized Ramanujan sum over a residually finite Dedekind domain","authors":"T. Qi","doi":"10.1007/s10474-025-01522-6","DOIUrl":"10.1007/s10474-025-01522-6","url":null,"abstract":"<div><p>This paper extends the Cohen-Ramanujan sum originally defined by Cohen to arbitrary residually finite Dedekind domains. We derive further properties that can be viewed as generalizations of those provided by Zheng [16] and Zheng-Chen-Hong [27]. In particular, we illustrate that the set of the Cohen-Ramanujan sums can be used as a basis for Fourier expansions just as the classical Ramanujan sums can.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"333 - 351"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166225","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
Dimension of the Radon set 氡集的尺寸
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-24 DOI: 10.1007/s10474-024-01500-4
S. B. Choudhury, S. Deo, D. Gauld, S. Podder
{"title":"Dimension of the Radon set","authors":"S. B. Choudhury,&nbsp;S. Deo,&nbsp;D. Gauld,&nbsp;S. Podder","doi":"10.1007/s10474-024-01500-4","DOIUrl":"10.1007/s10474-024-01500-4","url":null,"abstract":"<div><p>We consider when a subset <span>(Xsubsetmathbb{R}^{d})</span> has a Radon partition <span>(X=X_{1}sqcup X_{2})</span> such that \u0000</p><div><div><span>$$dim(({rm conv} X_{1})cap({rm conv} X_{2}) )= minlbrace dim({rm conv} X_{1}), dim({rm conv} X_{2})rbrace,\u0000$$</span></div></div><p>\u0000 showing that such a partition always exists when <span>(X)</span> has at least <span>(lfloorfrac{3d}{2}rfloor+2)</span> points in general position. The latter bound is sharp.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"236 - 245"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638321","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 groups covered by relatively subnormal Černikov local systems 在相对不正常的Černikov本地系统所覆盖的组上
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-19 DOI: 10.1007/s10474-024-01486-z
E. Ingrosso, M. Trombetti
{"title":"On groups covered by relatively subnormal Černikov local systems","authors":"E. Ingrosso,&nbsp;M. Trombetti","doi":"10.1007/s10474-024-01486-z","DOIUrl":"10.1007/s10474-024-01486-z","url":null,"abstract":"<div><p>Let <span>(mathcal L_{mathfrak F})</span> be the class of groups having a local system <span>({X_i : iin I})</span> of finite subgroups such that <span>(X_i)</span> is subnormal in <span>(X_j)</span> whenever <span>(X_ileq X_j)</span>. It has been shown by Rae in \u0000[19] that the class of soluble <span>(mathcal L_{mathfrak F})</span>-groups is closer to the class of soluble periodic <i>FC</i>-groups than might be expected. The aim of this paper is to prove that, under some additional finite-rank assumptions, one can extend Rae's results to local systems of Černikov subgroups, showing for example that the locally nilpotent residual is always covered by normal Černikov subgroups of the group, and that the factor group by the Hirsch–Plotkin radical has Černikov conjugacy classes of elements (see Theorem 5.9).</p><p>In [2], Reinhold Baer introduced a characteristic subgroup of a group which coincides with the hypercentre in the finite case (we call this subgroup the <i>Baer centre</i> of the group); actually, as shown in [4], this subgroup coincides with the hypercentre even in periodic <i>FC</i>-groups. Extending these results, we prove that this equivalence holds in many relevant universes of locally finite groups (see Theorem 6.2) and in particular in certain classes of locally finite groups having local systems of the above-mentioned type (see Theorem 6.9).</p><p>Finally, in order to better understand the behaviour of the Baer centre in our context, we introduce and study a new class of groups that is strictly contained between the classes of periodic <i>FC</i>-groups and periodic <i>BFC</i>-groups, and that could be very useful from a computational point of view (see Section 7).\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"185 - 218"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638457","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 affine subspace concentration inequality for centered convex bodies 中心凸体的仿射子空间集中不等式
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-12 DOI: 10.1007/s10474-025-01508-4
K. Eller, A. Freyer
{"title":"The affine subspace concentration inequality for centered convex bodies","authors":"K. Eller,&nbsp;A. Freyer","doi":"10.1007/s10474-025-01508-4","DOIUrl":"10.1007/s10474-025-01508-4","url":null,"abstract":"<div><p>An affine version of the linear subspace concentration inequality as proposed by Wu in [11] is established for centered convex bodies. This generalizes results from [11] and [8] on polytopes to convex bodies.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"26 - 36"},"PeriodicalIF":0.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01508-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638134","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
A characterization result for compactness of semicommutators of Toeplitz operators Toeplitz算子半变子紧致性的一个表征结果
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-11 DOI: 10.1007/s10474-025-01513-7
R. Rajan
{"title":"A characterization result for compactness of semicommutators of Toeplitz operators","authors":"R. Rajan","doi":"10.1007/s10474-025-01513-7","DOIUrl":"10.1007/s10474-025-01513-7","url":null,"abstract":"<div><p>In this paper, we investigate the compactness of semicommutators of Toeplitz operators on Hardy spaces and Bergman spaces, focusing on the operators of the form <span>(T^{H}_{|f|^{2}}-T^{H}_{f}T^{H}_{overline{f}})</span> and <span>(T^{H}_{|tilde{f}|^{2}}-T^{H}_{tilde{f}}T^{H}_{overline{tilde{f}}} )</span>, where <span>(tilde{f}(z)=f(z^{-1}))</span>. We establish that the compactness of these operators can be characterized through the convergence of the sequence <span>({T^{H}_{n}(|f|^{2})-T^{H}_{n}(f)T^{H}_{n}(overline{f})})</span> in the sense of singular value clustering. This provides a method for determining the compactness of semicommutators by examining the corresponding Toeplitz matrices derived from the Fourier coefficients of the symbol functions.\u0000Furthermore, we identify the function space <span>(VMO cap L^{infty}(mathbb{T}))</span> as the largest <span>(C^{*})</span>-subalgebra of <span>(L^{infty}(mathbb{T}))</span> such that, for any <span>(f, g in VMO cap L^{infty}(mathbb{T}) )</span>, sequence <span>({T^{H}_{n}(fg)-T^{H}_{n}(f)T^{H}_{n}(g)})</span> converges in terms of singular value clustering. It is already known that <span>( VMO cap L^{infty}(mathbb{T}))</span> is the largest <span>(C^{*})</span>-subalgebra of <span>(L^{infty}(mathbb{T}))</span> such that, for any <span>(f, g in VMO cap L^{infty}(mathbb{T}) )</span>, the operator <span>(T^{H}_{fg}-T^{H}_{f}T^{H}_{g})</span> is compact. Similar considerations are made for Bergman spaces <span>(A^{2}(mathbb{D}))</span>, where we obtain partial results. This work links operator theory, numerical linear algebra, and function spaces, providing new insights into the compactness properties of Toeplitz operators and their semicommutators.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"286 - 304"},"PeriodicalIF":0.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638130","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
Estimates for approximately Jensen convex functions 近似Jensen凸函数的估计
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-02-11 DOI: 10.1007/s10474-025-01512-8
G. M. Molnár, Zs. Páles
{"title":"Estimates for approximately Jensen convex functions","authors":"G. M. Molnár,&nbsp;Zs. Páles","doi":"10.1007/s10474-025-01512-8","DOIUrl":"10.1007/s10474-025-01512-8","url":null,"abstract":"<p>In this paper functions <span>(f colon D tomathbb{R})</span> satisfying the inequality\u0000</p><p>\u0000are studied, where <span>(D)</span> is a nonempty convex subset of a real linear space <span>(X)</span> and <span>(varphi colon {frac12(x-y) : x,y in D}tomathbb{R})</span> is a so-called error function. In this situation <span>(f)</span> is said to be <span>(varphi)</span>-Jensen convex. The main results show that for all <span>(varphi)</span>-Jensen convex function <span>(f colon D tomathbb{R})</span>, for all rational <span>(lambdain[0,1])</span>and <span>(x,yin D)</span>, the following inequality holds</p><p>\u0000The infinite series on the right hand side is always convergent, moreover, for all rational <span>(lambdain[0,1])</span>, it can be evaluated as a finite sum.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"305 - 331"},"PeriodicalIF":0.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01512-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638597","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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