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Acta Mathematica Hungarica最新文献

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On the D(1) extension of the (D(-1))-Diophantine triples induced by the (D(-1))-Diophantine pair {1,10} 关于(D(-1)) -Diophantine对诱导的(D(-1)) -Diophantine三元组的D({1)扩展1,10}
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-10-16 DOI: 10.1007/s10474-025-01561-z
Y. Briedj, S. E. Rihane
{"title":"On the D(1) extension of the (D(-1))-Diophantine triples induced by the (D(-1))-Diophantine pair {1,10}","authors":"Y. Briedj,&nbsp;S. E. Rihane","doi":"10.1007/s10474-025-01561-z","DOIUrl":"10.1007/s10474-025-01561-z","url":null,"abstract":"<div><p>Let <i>S</i> = {1, 10, <i>c</i>} be an integer set. In this paper, we show that if the product of any two elements of <i>S</i>, decreased by one, forms a perfect square, and if there exists a positive integer <i>d</i> such that <span>(d+1)</span>, <span>(10d+1)</span> and <span>(cd+1)</span> are all perfect squares, then <span>(d=d^{pm})</span> where\u0000</p><div><div><span>$$d^{pm}=19c-11pm 6sqrt{(c-1)(10c-1)}.$$</span></div></div><p>\u0000Additionally, under certain conditions, we investigate the integer points on the parametrized family of elliptic curves:\u0000</p><div><div><span>$$E: y^2 = (x+1)(10x+1)(cx+1).$$</span></div></div></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"73 - 102"},"PeriodicalIF":0.6,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754412","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 remark on the average decay of Fourier transform for regular measures 正则测度傅里叶变换的平均衰减
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-10-13 DOI: 10.1007/s10474-025-01564-w
J. Li, S. Luo, Z. Wu
{"title":"A remark on the average decay of Fourier transform for regular measures","authors":"J. Li,&nbsp;S. Luo,&nbsp;Z. Wu","doi":"10.1007/s10474-025-01564-w","DOIUrl":"10.1007/s10474-025-01564-w","url":null,"abstract":"<div><p>We obtain the estimates from below and above for the average decay of Fourier transform of <span>((alpha_1,alpha_2))</span>-Ahlfors regular measure. As an application, we obtain the upper bound of Beurling dimension of frame spectra for a class of Moran measures.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"18 - 27"},"PeriodicalIF":0.6,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754346","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 specific intersection graph of a module applying semisimple property 应用半简单属性的模块的特定相交图
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-10-13 DOI: 10.1007/s10474-025-01545-z
R. Ahmadzadeh, A. R. Moniri Hamzekolaee
{"title":"A specific intersection graph of a module applying semisimple property","authors":"R. Ahmadzadeh,&nbsp;A. R. Moniri Hamzekolaee","doi":"10.1007/s10474-025-01545-z","DOIUrl":"10.1007/s10474-025-01545-z","url":null,"abstract":"<div><p>The exploration of graphs linked to algebraic structures has emerged as a dynamic field, bridging graph theory and module theory to reveal deeper insights into module properties. In this study, we introduce and analyze the semisimple intersection graph, denoted as <span>(GSS_R(M))</span> associated with a right\u0000<span>(R )</span>-module <span>(M)</span>. The vertices of <span>(GSS_R(M))</span> are the nonzero submodules of <span>(M)</span>, with two vertices <span>(N)</span> and <span>(K)</span> connected if their intersection forms a nonzero semisimple module. We examine fundamental properties of <span>(GSS_R(M))</span> including its connectivity, diameter, and domination number, in relation to the module-theoretic characteristics of <span>(M)</span>. Additionally, the girth of <span>(GSS_R(M))</span> is determined.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"1 - 14"},"PeriodicalIF":0.6,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754345","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 note on coprime finite group action with applications 关于素数有限群作用及其应用的注解
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-10-13 DOI: 10.1007/s10474-025-01567-7
M. E. Harris
{"title":"A note on coprime finite group action with applications","authors":"M. E. Harris","doi":"10.1007/s10474-025-01567-7","DOIUrl":"10.1007/s10474-025-01567-7","url":null,"abstract":"<div><p>Finite groups are pervasive in mathematics.\u0000In studies into the structure of a finite group, the action of a finite group <i>A</i> on a finite group <i>G</i> such that the orders <span>((|A|, {rm and}, |G|))</span> of <i>A</i> and <i>G</i> are coprime is a basic topic. Here we present a Theorem in this topic which extends basic results “from a single prime to a finite set of primes” and implies that for any finite group <i>G</i>, if <i>A</i> acts trivially on <span>(F^*(G))</span> (the generalized Fitting subgroup of <i>G</i>), then <i>A</i> acts trivially on <i>G</i>. Also our Theorem implies and extends a useful result of Z. Arad and G. Glauberman and implies and extends Thompson’s celebrated <span>(P times Q)</span> Lemma and an important Lemma of D. M. Goldschmidt.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"15 - 17"},"PeriodicalIF":0.6,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01567-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754343","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
Refined error estimates and Fourier techniques in the approximation of higher-order derivatives via Gegenbauer orthogonal expansions 通过Gegenbauer正交展开式在高阶导数近似中的精确误差估计和傅立叶技术
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-10-13 DOI: 10.1007/s10474-025-01560-0
F. Bouzeffour
{"title":"Refined error estimates and Fourier techniques in the approximation of higher-order derivatives via Gegenbauer orthogonal expansions","authors":"F. Bouzeffour","doi":"10.1007/s10474-025-01560-0","DOIUrl":"10.1007/s10474-025-01560-0","url":null,"abstract":"<div><p>This paper investigates the approximation of higher-order derivatives using integral operators constructed from Gegenbauer polynomials. We establish key equivalence results connecting the approximation error in the <i>L</i><sup>2</sup>-norm to the decay of high-frequency components in the Fourier domain. A notable contribution is the derivation of Titchmarsh-type theorems that relate the solid average and Lanczos operators to the smoothness of the function being approximated. Additionally, we derive conditions under which the Fourier transform of functions belongs to <span>(L^beta(mathbb{R}))</span>, depending on the smoothness of the function and the parameters of the approximation.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"28 - 40"},"PeriodicalIF":0.6,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754344","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
Generalizing a conjecture of Erdős and Graham via best Egyptian underapproximations 通过最好的埃及欠近似推广Erdős和Graham的猜想
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-10-13 DOI: 10.1007/s10474-025-01566-8
Z. Li, Q. Tang
{"title":"Generalizing a conjecture of Erdős and Graham via best Egyptian underapproximations","authors":"Z. Li,&nbsp;Q. Tang","doi":"10.1007/s10474-025-01566-8","DOIUrl":"10.1007/s10474-025-01566-8","url":null,"abstract":"<div><p>Let <span>({u_n}_{n=1}^{infty})</span> be Sylvester’s sequence (sequence A000058 in the OEIS), and let <span>(a_1 &lt; a_2 &lt; cdots)</span> be any other sequence of positive integers satisfying <span>(sum_{i=1}^infty frac{1}{a_i} = 1)</span>. Erdős and Graham conjectured that\u0000</p><div><div><span>$$ liminf_{ntoinfty} a_n^{frac{1}{2^n}} &lt; lim_{ntoinfty} u_n^{frac{1}{2^n}} = c_0 = 1.264085ldots.$$</span></div></div><p> This conjecture has recently been resolved constructively by Kamio and independently by the present authors. In this paper, we focus on a generalization of this conjecture using a non-constructive approach. Specifically, assuming the unproven claim of Erdős and Graham that every rational number admits an eventually greedy best Egyptian underapproximation, we establish a more general asymptotic inequality involving best Egyptian underapproximations.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"41 - 63"},"PeriodicalIF":0.6,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754348","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 homotopy sets of simply connected rational CW-complexes 单连通有理cw -复形的同伦集
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01554-y
M. Benkhalifa
{"title":"On the homotopy sets of simply connected rational CW-complexes","authors":"M. Benkhalifa","doi":"10.1007/s10474-025-01554-y","DOIUrl":"10.1007/s10474-025-01554-y","url":null,"abstract":"<div><p>Let <i>X</i> and <i>Y</i> be two simply connected rational CW-complexes, and <span>(n in mathbb{N})</span>. We study the homotopy set <span>([P^nX, P^nY])</span>, where <i>P</i><sup><i>n</i></sup><i>X</i> and <i>P</i><sup><i>n</i></sup><i>Y</i> are the <span>(n)</span>-th Postnikov sections of <i>X</i> and <i>Y</i>, respectively. An equivalence relation is defined on this set, revealing connections with the cohomology groups. This approach uses rational homotopy theory to uncover new structural insights.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"522 - 531"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01554-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230450","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
Clustering in typical unit-distance avoiding sets 典型单位距离回避集的聚类
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01556-w
A. Cohen, N. Mani
{"title":"Clustering in typical unit-distance avoiding sets","authors":"A. Cohen,&nbsp;N. Mani","doi":"10.1007/s10474-025-01556-w","DOIUrl":"10.1007/s10474-025-01556-w","url":null,"abstract":"<div><p>In the 1960s Moser asked how dense a subset of <span>(mathbb{R}^d)</span> can be if no pairs of points in the subset are exactly distance 1 apart.\u0000There has been a long line of work showing upper bounds on this density. One curious feature of dense unit distance avoiding sets is that they appear to be ''clumpy,'' i.e. forbidding unit distances comes hand in hand with having more than the expected number distance <span>(approx 2)</span> pairs. </p><p>In this work we rigorously establish this phenomenon in <span>(mathbb{R}^2)</span>. We show that dense unit distance avoiding sets have over-represented distance <span>(approx 2)</span> pairs, and that this clustering extends to typical unit distance avoiding sets. To do so, we build off of the linear programming approach used previously to prove upper bounds on the density of unit distance avoiding sets.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"473 - 497"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230448","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
Measure theoretic equicontinuity and sensitivity via Furstenberg family 通过Furstenberg族测量理论的等连续性和灵敏度
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01558-8
H. Ju, Y. Ju, J. Kim
{"title":"Measure theoretic equicontinuity and sensitivity via Furstenberg family","authors":"H. Ju,&nbsp;Y. Ju,&nbsp;J. Kim","doi":"10.1007/s10474-025-01558-8","DOIUrl":"10.1007/s10474-025-01558-8","url":null,"abstract":"<div><p>We consider measure theoretic equicontinuity and sensitivity via Furstenberg family. We introduce the notion of <span>(mathcal {F})</span>-<span>(mu)</span>-equicontinuity which is the refined version of <span>(mu )</span>-equicontinuity using Furstenberg family <span>(mathcal {F})</span> and prove that when <span>(mathcal {F})</span> is a filter, a given dynamical system <span>((X,T))</span> is <span>(mathcal {F})</span>-<span>(mu)</span>-equicontinuous if and only if it is <span>(mathcal {F})</span>-<span>(mu)</span>-<span>(f)</span>-equicontinuous with respect to every continuous function <span>(f colon {X to mathbb {C}} )</span>. In addition, under certain conditinos, we prove that an ergodic measure theoretic dynamical system is either <span>(kmathcal {F})</span>-<span>(mu )</span>-sensitive or <span>(mathcal {F})</span>-<span>(mu)</span>-equicontinuous.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"291 - 312"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230395","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
Problems in additive number theory. VI: Sizes of sumsets of finite sets 加性数论中的若干问题。有限集合的集合的大小
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01559-7
M. B. Nathanson
{"title":"Problems in additive number theory. VI: Sizes of sumsets of finite sets","authors":"M. B. Nathanson","doi":"10.1007/s10474-025-01559-7","DOIUrl":"10.1007/s10474-025-01559-7","url":null,"abstract":"<div><p>In the study of sums of finite sets of integers, most attention has been paid to sets with small sumsets (Freiman's theorem and related work) and to sets with large sumsets (Sidon sets and <span>(B_h)</span>-sets). This paper focuses on the full range of sizes of <span>(h)</span>-fold sums of a set of <span>(k)</span> integers. Many new results and open problems are presented.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"498 - 521"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230393","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
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