Acta Mathematica Hungarica最新文献

{"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}

{"title":"Representation of convex geometries of convex dimension 3 by spheres","authors":"K. Adaricheva,&nbsp;A. Agarwal,&nbsp;N. Nevo","doi":"10.1007/s10474-024-01487-y","DOIUrl":"10.1007/s10474-024-01487-y","url":null,"abstract":"<div><p>A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat [1] and the Polymath REU (2020), continues to investigate representations of convex geometries with small convex dimension by convex shapes on the plane and in spaces of higher dimension. In particular, we answer in the negative the question raised by Polymath REU (2020): whether every convex geometry of convex dimension 3 is representable by circles on the plane. We show there are geometries of convex dimension 3 that cannot be represented by spheres in any <span>(mathbb{R}^k)</span>, and this connects to posets not representable by spheres from the paper of Felsner, Fishburn and Trotter [44]. On the positive side, we use the result of Kincses [55] to show that every finite poset is an ellipsoid order.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"578 - 591"},"PeriodicalIF":0.6,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01487-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994699","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":"Truncated polynomials with restricted digits","authors":"H. Liu,&nbsp;Z. Liu","doi":"10.1007/s10474-024-01490-3","DOIUrl":"10.1007/s10474-024-01490-3","url":null,"abstract":"<div><p>Many remarkable results have been obtained on important problems combining arithmetic properties of the integers and some restricted conditions of their digits in a given base. Maynard considered the number of the polynomial values with missing digits and gave an asymptotic formula. In this paper we study truncated polynomials with restricted digits by using the estimates for character sums and exponential sums modulo prime powers. In the case where the polynomials are monomial we further give exact identities.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"462 - 481"},"PeriodicalIF":0.6,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994341","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":"The solution of Drygas functional equations with additional conditions","authors":"M. Dehghanian,&nbsp;S. Izadi,&nbsp;S. Jahedi","doi":"10.1007/s10474-024-01488-x","DOIUrl":"10.1007/s10474-024-01488-x","url":null,"abstract":"<div><p>We determine the solution of the Drygas functional equation that satisfies the additional condition <span>((y^2+y)f(x)= (x^2+x)f(y))</span> on a restricted domain. Also, some other properties of Drygas functions are given as well.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"510 - 521"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994568","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":"The distribution of coefficients attached to the Dedekind zeta function over certain sparse sequences","authors":"G. D. Hua","doi":"10.1007/s10474-024-01489-w","DOIUrl":"10.1007/s10474-024-01489-w","url":null,"abstract":"<div><p>Let <span>(K_{3})</span> be a non-normal cubic extension over <span>(mathbb{Q})</span>, and let <span>(a_{K_{3}}(n))</span> be the <span>(n)</span>-th coefficient of the Dedekind zeta function <span>(zeta_{K_{3}}(s))</span>. In this paper, we investigate the asymptotic behaviour of the type\u0000</p><div><div><span>$$ notag sum_{nleq x}a_{K_{3}}^{2}(n^{ell}),$$</span></div></div><p>\u0000where <span>(ellgeq 2)</span> is any fixed integer. As an application, we also establish the asymptotic formulae of the variance of <span>(a_{K_{3}}^{2}(n^{ell}))</span>. Furthermore, we also consider the asymptotic relations for shifted convolution sums associated to <span>(a_{K_{3}}(n))</span> with classical divisor function.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"376 - 407"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994570","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 (p)-radical covers of pentavalent arc-transitive graphs","authors":"H. L. Liu,&nbsp;Y. L. Ma","doi":"10.1007/s10474-024-01491-2","DOIUrl":"10.1007/s10474-024-01491-2","url":null,"abstract":"<div><p>Let <span>(Gamma)</span> be a finite connected pentavalent graph admitting a nonabelian simple arc-transitive automorphism group <span>(T)</span> and soluble vertex stabilizers. Let <span>(p&gt;|T|_{2})</span> be an odd prime and <span>((p,|T|)=1)</span>, where <span>(|T|_{2})</span> is the largest power of 2 dividing the order <span>(|T|)</span> of <span>(|T|)</span>. Then we prove that there exists a <span>(p)</span>-radical cover <span>(widetilde{Gamma})</span> of <span>(Gamma)</span> such that the full automorphism group <span>(text{Aut}(widetilde{Gamma}))</span> of <span>(widetilde{Gamma})</span> is equal to <span>(O_{p}(text{Aut}(widetilde{Gamma})).T)</span> and the covering transformation group is <span>(O_{p}(text{Aut}(widetilde{Gamma})))</span>, where <span>(O_{p}(text{Aut}(widetilde{Gamma})))</span> is the <span>(p)</span>-radical of <span>(text{Aut}(widetilde{Gamma}))</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"539 - 544"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994567","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}