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On certain classes of first Baire functionals 关于第一贝叶尔函数的某些类别
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-16 DOI: 10.1007/s10474-024-01464-5
J. Mirmina, D. Puglisi
{"title":"On certain classes of first Baire functionals","authors":"J. Mirmina, D. Puglisi","doi":"10.1007/s10474-024-01464-5","DOIUrl":"https://doi.org/10.1007/s10474-024-01464-5","url":null,"abstract":"<p>We investigate first Baire functionals on the dual ball of a separable Banach space <span>(X)</span> which are pointwise limit of a sequence of <span>(X)</span> whose closed span does not contain any copy of <span>(ell_1)</span> (or has separable dual). We propose an example of a <span>(C(K))</span> space where not all such first Baire functionals exhibit this behavior. As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity. </p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249619","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
Groups with some arithmetic conditions on real sub-class sizes 关于实子类大小的一些算术条件的群
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-16 DOI: 10.1007/s10474-024-01466-3
G. Qian, Y. Yang
{"title":"Groups with some arithmetic conditions on real sub-class sizes","authors":"G. Qian, Y. Yang","doi":"10.1007/s10474-024-01466-3","DOIUrl":"https://doi.org/10.1007/s10474-024-01466-3","url":null,"abstract":"<p>We generalize two results about conjugacy class sizes of real elements to sub-class sizes of real elements.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249620","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
Covering the permutohedron by affine hyperplanes 用仿射超平面覆盖正多面体
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-13 DOI: 10.1007/s10474-024-01462-7
G. Hegedüs, GY. Károlyi
{"title":"Covering the permutohedron by affine hyperplanes","authors":"G. Hegedüs, GY. Károlyi","doi":"10.1007/s10474-024-01462-7","DOIUrl":"https://doi.org/10.1007/s10474-024-01462-7","url":null,"abstract":"<p>An almost cover of a finite set in the affine space is a collection\u0000of hyperplanes that together cover all points of the set except one. Using the\u0000polynomial method, we determine the minimum size of an almost cover of the\u0000vertex set of the permutohedron and address a few related questions.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214273","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
Oscillation criterion for generalized Euler difference equations 广义欧拉差分方程的振荡准则
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-06 DOI: 10.1007/s10474-024-01460-9
P. Hasil, L. Linhartová, M. Veselý
{"title":"Oscillation criterion for generalized Euler difference equations","authors":"P. Hasil, L. Linhartová, M. Veselý","doi":"10.1007/s10474-024-01460-9","DOIUrl":"https://doi.org/10.1007/s10474-024-01460-9","url":null,"abstract":"<p>Using a modification of the adapted Riccati transformation, we\u0000prove an oscillation criterion for generalizations of linear and half-linear Euler difference\u0000equations. Our main result complements a large number of previously\u0000known oscillation criteria about several similar generalizations of Euler difference\u0000equations. The major part of this paper is formed by the proof of the main theorem.\u0000To illustrate the fact that the presented criterion is new even for linear\u0000equations with periodic coefficients, we finish this paper with the corresponding\u0000corollary together with concrete examples of simple equations whose oscillatory\u0000properties do not follow from previously known criteria.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214274","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 regular topology on C(X, Y) revisited 再论 C（X，Y）上的正则拓扑学
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-05 DOI: 10.1007/s10474-024-01463-6
A. Jindal
{"title":"The regular topology on C(X, Y) revisited","authors":"A. Jindal","doi":"10.1007/s10474-024-01463-6","DOIUrl":"https://doi.org/10.1007/s10474-024-01463-6","url":null,"abstract":"<p>This paper aims to study some important topological properties of the regular topology on <i>C</i>(<i>X</i>, <i>Y</i>), the set of all continuous functions from a Tychonoff space <i>X</i> to a metric space (<i>Y</i>, <i>d</i>). In particular, we study in detail the connectedness of the regular topology on <i>C</i>(<i>X</i>, <i>Y</i>). In the end, some important countability properties are studied.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214272","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 structure of the Iwasawa module for $$mathbb{Z}_{2}$$ -extensions of certain real biquadratic fields 论某些实双二次域的 $$mathbb{Z}_{2}$ 扩展的岩泽模块结构
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-05 DOI: 10.1007/s10474-024-01459-2
A. El Mahi
{"title":"On the structure of the Iwasawa module for $$mathbb{Z}_{2}$$ -extensions of certain real biquadratic fields","authors":"A. El Mahi","doi":"10.1007/s10474-024-01459-2","DOIUrl":"https://doi.org/10.1007/s10474-024-01459-2","url":null,"abstract":"<p>For an infinite family of real biquadratic fields <i>k</i> we give the structure of the Iwasawa module <span>(X=X(k_{infty}))</span> of the <span>(mathbb{Z}_{2})</span>-extension of <i>k</i>. For these fields, we obtain that <span>(lambda=mu=0 mbox{ and }nu=2)</span>. where <span>(lambda)</span>, <span>(mu)</span> and <span>(nu)</span> are the Iwasawa invariants of the cyclotomic <span>(mathbb{Z}_{2})</span>-extension of <i>k</i></p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On spaces with a $$pi$$ -base whose elements have an H-closed closure 关于元素具有 H 封闭闭合的$$/pi$$-基空间
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-08-22 DOI: 10.1007/s10474-024-01450-x
D. Giacopello
{"title":"On spaces with a $$pi$$ -base whose elements have an H-closed closure","authors":"D. Giacopello","doi":"10.1007/s10474-024-01450-x","DOIUrl":"https://doi.org/10.1007/s10474-024-01450-x","url":null,"abstract":"<p>We deal with the class of Hausdorff spaces having a <span>(pi)</span>-base whose elements have an H-closed closure. Carlson proved that <span>(|X|leq 2^{wL(X)psi_c(X)t(X)})</span> for every quasiregular space <span>(X)</span> with a <span>(pi)</span>-base whose elements have an H-closed closure. We provide an example of a space <span>(X)</span> having a <span>(pi)</span>-base whose elements have an H-closed closure which is not quasiregular (neither Urysohn) such that <span>(|X|&gt; 2^{wL(X)chi(X)})</span> (then <span>(|X|&gt; 2^{wL(X)psi_c(X)t(X)})</span>). Always in the class of spaces with a <span>(pi)</span>-base whose elements have an H-closed closure, we establish the bound <span>(|X|leq2^{wL(X)k(X)})</span> for Urysohn spaces and we give an example of an Urysohn space <span>(Z)</span> such that <span>(k(Z)&lt;chi(Z))</span>. Lastly, we present some equivalent conditions to the Martin's Axiom involving spaces with a <span>(pi)</span>-base whose elements have an H-closed closure and, additionally, we prove that if a quasiregular space has a <span>(pi)</span>-base whose elements have an H-closed closure then such a space is Baire.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214275","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 algebraic conditions for the non-vanishing of linear forms in Jacobi theta-constants 关于雅可比θ常数中线性形式不消失的代数条件
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-08-16 DOI: 10.1007/s10474-024-01449-4
C. Elsner, V. Kumar
{"title":"On algebraic conditions for the non-vanishing of linear forms in Jacobi theta-constants","authors":"C. Elsner, V. Kumar","doi":"10.1007/s10474-024-01449-4","DOIUrl":"https://doi.org/10.1007/s10474-024-01449-4","url":null,"abstract":"<p>Elsner, Luca and Tachiya proved in [4] that the values of the Jacobi-theta constants <span>(theta_3(mtau))</span> and <span>(theta_3(ntau))</span> are algebraically independent over <span>(mathbb{Q})</span> for distinct integers <span>(m)</span>, <span>(n)</span> under some conditions on <span>(tau)</span>. On the other hand, in [3] Elsner and Tachiya also proved that three values <span>(theta_3(mtau),theta_3(ntau))</span> and <span>(theta_3(ell tau))</span> are algebraically dependent over <span>(mathbb{Q})</span>. In this article we prove the non-vanishing of linear forms in <span>(theta_3(mtau))</span>, <span>(theta_3(ntau))</span> and <span>(theta_3(ell tau))</span> under various conditions on <span>(m)</span>, <span>(n)</span>, <span>(ell)</span>, and <span>(tau)</span>. Among other things we prove that for odd and distinct positive integers <span>(m,n&gt;3)</span> the three numbers <span>(theta_3(tau))</span>, <span>(theta_3(mtau))</span> and <span>(theta_3(n tau))</span> are linearly independent over <span>(overline{mathbb{Q}})</span> when <span>(tau)</span> is an algebraic number of some degree greater or equal to 3. In some sense this fills the gap between the above-mentioned former results on theta constants. A theorem on the linear independence over <span>(mathbb{C(tau)})</span> of the functions <span>(theta_3(a_1 tau), dots, theta_3(a_m tau))</span>for distinct positive rational numbers <span>(a_{1}, {dots}, a_{m})</span> is also established.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214276","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
Parallel packing squares into a rhombus 将正方形平行打包成菱形
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-08-16 DOI: 10.1007/s10474-024-01446-7
M. Liu, Z. Su
{"title":"Parallel packing squares into a rhombus","authors":"M. Liu, Z. Su","doi":"10.1007/s10474-024-01446-7","DOIUrl":"https://doi.org/10.1007/s10474-024-01446-7","url":null,"abstract":"<p> Suppose that <span>(R_{alpha})</span> is a rhombus with side length <span>(1)</span> and with acute angle <span>(alpha)</span>. Let <span>({S_{n}})</span> be any collection of squares. In this note a tight upper bound of the sum of the areas of squares from <span>({S_{n}})</span> that can be parallel packed into <span>(R_{alpha})</span> is given.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214277","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
Element orders in extraspecial groups 特异群中的元素顺序
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-08-12 DOI: 10.1007/s10474-024-01454-7
M.-S Lazorec
{"title":"Element orders in extraspecial groups","authors":"M.-S Lazorec","doi":"10.1007/s10474-024-01454-7","DOIUrl":"https://doi.org/10.1007/s10474-024-01454-7","url":null,"abstract":"<p>By using the structure and some properties of extraspecial and generalized/almost extraspecial <span>(p)</span>-groups, we explicitly determine the number of elements of specific orders in such groups. As a consequence, one may find the number of cyclic subgroups of any (generalized/almost) extraspecial group. For a finite group <span>(G)</span>, the ratio of the number of cyclic subgroups to the number of subgroups is called the cyclicity degree of <span>(G)</span> and is denoted by cdeg <span>((G))</span>. We show that the set containing the cyclicity degrees of all finite groups is dense in <span>([0, 1])</span>. This is equivalent to giving an affirmative answer to the following question posed by Tóth and Tărnăuceanu: “For every <span>(ain [0, 1])</span>, does there exist a sequence <span>((G_n)_{ngeq 1})</span> of finite groups such that <span>( lim_{ntoinfty} text{cdeg} (G_n)=a)</span>?”. We show that such sequences are formed of finite direct products of extraspecial groups of a specific type. </p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941490","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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