Acta Mathematica Hungarica最新文献_第4页

On Jensen-like form of Mikusiński's functional equation 关于Mikusiński泛函方程的类简森形式

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-07 DOI: 10.1007/s10474-025-01527-1

E. Imani, A. Najati, M. A. Tareeghee

引用次数: 0

Choquet extension of non-monotone submodular setfunctions 非单调子模集函数的Choquet扩展

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-07 DOI: 10.1007/s10474-025-01529-z

L. Lovász

引用次数: 0

Measures associated with certain ellipsephic harmonic series and the Allouche–Hu–Morin limit theorem 与某些椭圆调和级数有关的测度及Allouche-Hu-Morin极限定理

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-07 DOI: 10.1007/s10474-025-01525-3

J.-F. Burnol

引用次数: 0

Wu maps and collectively coincidence theory 吴图和集体巧合理论

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-07 DOI: 10.1007/s10474-025-01530-6

D. O’regan

引用次数: 0

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups 有限幂零群的增强幂图顶点连通性的精确枚举

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-01 DOI: 10.1007/s10474-025-01524-4

S. Bera, H. K. Dey

引用次数: 0

On several irrationality problems for Ahmes series 关于Ahmes级数的几个无理性问题

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-01 DOI: 10.1007/s10474-025-01528-0

V. Kovač, T. Tao

{"title":"On several irrationality problems for Ahmes series","authors":"V. Kovač, T. Tao","doi":"10.1007/s10474-025-01528-0","DOIUrl":"10.1007/s10474-025-01528-0","url":null,"abstract":"<div> Using basic tools of mathematical analysis and elementary probability\u0000theory we address several problems on the irrationality of series of distinct\u0000unit fractions,(sum_k 1/a_k). In particular, we study subseries of the Lambert series (sum_k 1/(t^k-1)) and two types of irrationality sequences ((a_k)) introduced by Paul\u0000Erdős and Ronald Graham. Next, we address a question of Erdős, who asked\u0000how rapidly a sequence of positive integers ((a_k)) can grow if both series (sum_k 1/a_k) and (sum_k 1/(a_k+1))have rational sums. Our construction of double exponentially\u0000growing sequences ((a_k)) with this property generalizes to any number (d) of series(sum_k 1/(a_k+j)),(j=0,1,2,ldots,d-1),and, in particular, also gives a positive answer\u0000to a question of Erdős and Ernst Straus on the interior of the set of (d)-tuples of their sums.\u0000Finally, we prove the existence of a sequence ((a_k)) such that all well-defined sums (sum_k 1/(a_k+t)),(tinmathbb{Z}), are rational numbers, giving a negative answer to a conjecture by Kenneth Stolarsky.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"572 - 608"},"PeriodicalIF":0.6,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160663","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

Maximal Tychonoff spaces and minimal paracompact (T_{2}) spaces 最大Tychonoff空间和最小仿紧(T_{2})空间

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-04-25 DOI: 10.1007/s10474-025-01516-4

S. S. Mandal

引用次数: 0

On a problem of Erdős and Graham 关于Erdős和Graham的问题

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-04-25 DOI: 10.1007/s10474-025-01515-5

J.-H. Fang, J.-Y. He

{"title":"On a problem of Erdős and Graham","authors":"J.-H. Fang, J.-Y. He","doi":"10.1007/s10474-025-01515-5","DOIUrl":"10.1007/s10474-025-01515-5","url":null,"abstract":"<div>For a positive real number (gamma), let (A_{gamma})\u0000be the sequence ({lfloor gammarfloor, lfloor 2gammarfloor, lfloor 2^2gammarfloor, ldots }), where (lfloor xrfloor) denotes the greatest integer not greater than (x). For positive real numbers (alpha) and (beta), write\u0000(A_{alpha,beta}=A_{alpha}cup A_{beta}). Erdős and Graham [2] posed the following problem: suppose that (alpha) and (beta) are positive real numbers with (alpha/beta) irrational. Can all sufficiently large integers be represented as the sum of distinct terms of (A_{alpha,beta})? Afterwards, Hegyvári [3] proved that, for (alphage 2) and (beta=2^nalpha) for some positive integer (n), there exist infinitely many positive integers which cannot be represented as the sum of distinct terms of (A_{alpha,beta}). Recently, Jiang and Ma [5] further consider the case (1<alpha<2). For a sequence (A) of nonnegative integers, let (P(A)) be the set of all integers which can be represented as the sum of distinct terms of (A). In this paper, for a class of positive real numbers (alpha) and (beta(=2^lalpha)), we determine all positive integers (x) \u0000such that (x+sum_{i=0}^ua_{l+i}notin P(A_{alpha,beta})) for every nonnegative integer (u). That is, (x+sum_{i=0}^ua_{l+i}notin P(A_{alpha,beta})) for every nonnegative integer (u) if and only if (1le x<a_l) and (xnotin P({a_0, ldots ,a_{l-1}})). Other related results are also obtained.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"532 - 542"},"PeriodicalIF":0.6,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168750","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

Moving recurrent problems in the nonautonomous dynamical systems corresponding to Cantor series expansions 与康托级数展开相对应的非自治动力系统中的运动递归问题

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-04-25 DOI: 10.1007/s10474-025-01514-6

Z. Shen

{"title":"Moving recurrent problems in the nonautonomous dynamical systems corresponding to Cantor series expansions","authors":"Z. Shen","doi":"10.1007/s10474-025-01514-6","DOIUrl":"10.1007/s10474-025-01514-6","url":null,"abstract":"<div>\u0000We investigate a moving recurrent problem for the nonautonomous dynamical system induced by the Cantor series expansion.\u0000To be precise, let (Q={q_{k}}_{kgeq1}) be a sequence of positive integers with (q_{k}geq2) for all (kgeq1). Put\u0000(T_{Q}^{n}(x)=q_{1}cdots q_{n}x-lfloor q_{1}cdots q_{n}xrfloor) for each (ngeq1), which gives the (Q)-Cantor series expansion.\u0000We focus on the following ({n_{k},r_{k}})-moving recurrent points proposed by Boshernitzan and Glasner:\u0000<div><div>$$inf_{kgeq1}|T^{n_{k}}_{Q}(x)-T^{n_{k}+r_{k}}_{Q}(x)|=0,$$</div></div>\u0000where ({n_{k}}_{kgeq1}) and ({r_{k}}_{kgeq1}) are two given sequences of integers. It is proved that when ({n_{k}}_{kgeq1})\u0000and ({r_{k}}_{kgeq1}) tend to infinity, the set of ({n_{k},r_{k}})-moving recurrent points is of full Lebesgue measure. In addition,\u0000we study the size of the following quantitative version of ({n_{k},r_{k}})-moving recurrent set:\u0000<div><div>$$ R({n_{k},r_{k}}):=big{xin [0,1] : |T^{n_{k}}_{Q}(x)-T^{n_{k}+r_{k}}_{Q}(x)|<varphi(k)~text{for i.m.}~kin mathbb{N}big},$$</div></div>\u0000where (varphi colon mathbb{N}rightarrowmathbb{R}^{+}) is a positive function and ``i.m.'' stands for ``infinitely many''. It is proved that when ({n_{k}}_{kgeq1}) and ({r_{k}}_{kgeq1}) tend to infinity, the\u0000Lebesgue measure and Hausdorff measure of (R({n_{k},r_{k}})) respectively fulfill a dichotomy law according to the convergence or divergence of certain series.\u0000</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"433 - 451"},"PeriodicalIF":0.6,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168751","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 order isomorphisms of norm attainment sets of continuous functions 关于连续函数范数实现集的序同构

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-04-24 DOI: 10.1007/s10474-025-01520-8

K. Igarashi, J. Nakamura, S. Roy, R. Tanaka

引用次数: 0