Acta Mathematica Hungarica最新文献_第4页

Closed embeddings of spaces and groups into pseudocompact (k_mathbb {R})-groups 将空间和群闭合嵌入到伪紧(k_mathbb {R}) -群中

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-13 DOI: 10.1007/s10474-026-01602-1

Saak Gabriyelyan, Jan van Mill, Evgenii Reznichenko

{"title":"Closed embeddings of spaces and groups into pseudocompact (k_mathbb {R})-groups","authors":"Saak Gabriyelyan, Jan van Mill, Evgenii Reznichenko","doi":"10.1007/s10474-026-01602-1","DOIUrl":"10.1007/s10474-026-01602-1","url":null,"abstract":"<div>A well-known theorem of Noble states that each Tychonoff space X is homeomorphic to a closed subspace of a pseudocompact (k_mathbb {R})-space. We strengthen this result by showing that any Tychonoff space X is homeomorphic to a closed subspace of an abelian pseudocompact (k_mathbb {R})-group G such that (w(G)le aleph _1cdot w(X)), and if, in addition, X is a precompact group, then X is topologically isomorphic to a closed subgroup of G. It is constructed the first examples of pseudocompact groups (G_1) and (G_2) (in fact, they are even countably compact and of weight (aleph _2)) such that (G_1) is Ascoli but not a (k_mathbb {R})-space, and (G_2) is a (k_mathbb {R})-space but not a k-space. Under (mathrm {MA+lnot CH}), we show that any pseudocompact group of weight (aleph _1) is Ascoli. These results are proved using topological properties of pseudocompact spaces X of weight (aleph _1) and of (Sigma )-products in products of compact spaces. Being motivated by these results and the countably compact part of Noble’s theorem, it is shown by a well-known technique that each countably compact infinite group has a separable countably compact subgroup of cardinality continuum.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"261 - 278"},"PeriodicalIF":0.6,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01602-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285382","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

For any space X, either (C_p(X)) or (C_pC_p(X)) is (psi )-separable 对于任意空间X， (C_p(X))或(C_pC_p(X))都是(psi ) -可分离的

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-13 DOI: 10.1007/s10474-026-01603-0

J. A. Aguilar-Velázquez, V. V. Tkachuk

引用次数: 0

Explicit lower bounds for opaque sets of unit square and unit disc 单位正方形和单位圆盘的不透明集合的显式下界

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-13 DOI: 10.1007/s10474-026-01606-x

Markus Kiderlen, Florian Pausinger

引用次数: 0

Classification of orbit spaces of free (mathbb {S}^3)- actions on the product of three spheres 自由轨道空间的分类(mathbb {S}^3) -对三球积的作用

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-11 DOI: 10.1007/s10474-026-01601-2

Dimpi, Jitendra Kumar Maitra

引用次数: 0

Addendum to “Entropy on quasi-uniform spaces” [Acta Math. Hungar., 171 (2023), 241-266] “准均匀空间上的熵”[数学学报]。Hungar。， 171 (2023), 241-266]

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-09 DOI: 10.1007/s10474-026-01597-9

Paulus Haihambo, O. Olela Otafudu

引用次数: 0

Uncertainty principle, annihilating pairs and Fourier restriction 不确定原理，湮灭对和傅立叶限制

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-08 DOI: 10.1007/s10474-026-01589-9

A. Iosevich, P. Jaming, A. Mayeli

{"title":"Uncertainty principle, annihilating pairs and Fourier restriction","authors":"A. Iosevich, P. Jaming, A. Mayeli","doi":"10.1007/s10474-026-01589-9","DOIUrl":"10.1007/s10474-026-01589-9","url":null,"abstract":"<div>Let (G) be a locally compact Abelian group, and let (widehat{G}) denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any (S subset G) and (Sigma subset widehat{G}), there exists a constant (C(S, Sigma )) such that for any (f in L^2(G)), the following inequality holds: <div><div>$$ Vert fVert _{L^2(G)} le C(S, Sigma ) bigl ( Vert fVert _{L^2(G setminus S)} + Vert widehat{f}Vert _{L^2(widehat{G} setminus Sigma )} bigr ), $$</div></div>where (widehat{f}) denotes the Fourier transform of (f). This variant of the uncertainty principle is particularly useful in applications such as signal processing and control theory. The purpose of this paper is to show that such estimates can be strengthened when (S) or (Sigma ) satisfies a restriction theorem and to provide an estimate for the constant (C(S, Sigma )). This result serves as a quantitative counterpart to a recent finding by the first and last author [24]. In the setting of finite groups, the results also extend those of Matolcsi–Szűcs and Donoho–Stark.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"220 - 238"},"PeriodicalIF":0.6,"publicationDate":"2026-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285390","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

Legendrian non-simple Whitehead doubles of the trefoil 传说中的非简单白头双三叶草

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-06 DOI: 10.1007/s10474-026-01600-3

Saliha Kivanç

引用次数: 0

Explicit discriminant and integral basis of ({{textbf{Q}}}(root p^2 of {a})) 的显式判别和积分基础 ({{textbf{Q}}}(root p^2 of {a}))

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-04 DOI: 10.1007/s10474-026-01598-8

Anuj Jakhar

{"title":"Explicit discriminant and integral basis of ({{textbf{Q}}}(root p^2 of {a}))","authors":"Anuj Jakhar","doi":"10.1007/s10474-026-01598-8","DOIUrl":"10.1007/s10474-026-01598-8","url":null,"abstract":"<div>Let (K = {{textbf{Q}}}(theta )) be an algebraic number field, where (theta ) is a root of the irreducible polynomial (x^n - a in {{textbf{Q}}}[x]) of degree n, and let ({textbf {Z}}_K) denote the ring of integers of K. In general, for arbitrary integers n and a, the explicit computation of the discriminant and an integral basis of K remains unresolved, except in special cases such as (n = 4), 8, 9, a prime p, or a product pq of distinct primes p and q. Most existing results assume either that a is square-free or that (gcd (a, n) = 1). In this article, we address the case (n = p^2) for an odd prime p, without imposing any condition on a. Using the theory of Newton polygons of first and second order, we determine the exact power of each prime q dividing the index ([{textbf {Z}}_K : {textbf {Z}}[theta ]]). This allows us to construct explicitly a q-integral basis of K for each prime q, which in turn yields a complete integral basis of K. Several illustrative examples are provided. As an application, we show that if a is square-free and satisfies (a^{p-1} not equiv 1 pmod {p^2}), then K admits a power basis; that is, ({textbf {Z}}_K = {textbf {Z}}[theta ]).</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"169 - 192"},"PeriodicalIF":0.6,"publicationDate":"2026-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285380","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 shortest distance between orbits of two different dynamical systems 两个不同动力系统轨道之间的最短距离

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-05-04 DOI: 10.1007/s10474-026-01596-w

Saisai Shi, Jia Liu, Yuan Zhang

引用次数: 0

Higher order Wiener–Wintner systems: examples and applications 高阶维纳-温特纳系统：例子和应用

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2026-04-30 DOI: 10.1007/s10474-026-01595-x

Idris Assani, Jacob Folks, Ryo Moore

引用次数: 0