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The orthogonality principle for Osserman manifolds 奥瑟曼流形的正交原理
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-05 DOI: 10.1007/s10474-024-01434-x
V. Andrejić, K. Lukić
{"title":"The orthogonality principle for Osserman manifolds","authors":"V. Andrejić,&nbsp;K. Lukić","doi":"10.1007/s10474-024-01434-x","DOIUrl":"10.1007/s10474-024-01434-x","url":null,"abstract":"<div><p>We introduce a new potential characterization of Osserman algebraic curvature tensors. \u0000An algebraic curvature tensor is Jacobi-orthogonal if <span>(mathcal{J}_XYperpmathcal{J}_YX)</span> holds for all <span>(Xperp Y)</span>,\u0000where <span>(mathcal{J})</span> denotes the Jacobi operator.\u0000We prove that any Jacobi-orthogonal tensor is Osserman, while all known Osserman tensors are Jacobi-orthogonal.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"246 - 252"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141385938","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 prime-counting Copeland–Erdős constant 素数哥白兰-厄尔多常数
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-05 DOI: 10.1007/s10474-024-01437-8
J. M. Campbell
{"title":"The prime-counting Copeland–Erdős constant","authors":"J. M. Campbell","doi":"10.1007/s10474-024-01437-8","DOIUrl":"10.1007/s10474-024-01437-8","url":null,"abstract":"<div><p>Let <span>((a(n) : n in mathbb{N}))</span> denote a sequence of nonnegative integers. Let <span>(0.a(1)a(2) ldots )</span> denote the real number obtained by concatenating the digit expansions, in a fixed base, of consecutive entries of <span>((a(n) : n in mathbb{N}))</span>. Research on digit expansions of this form has mainly to do with the normality of <span>(0.a(1)a(2) ldots )</span> for a given base. Famously, the Copeland-Erdős constant <span>(0.2357111317 ldots {})</span>, for the case whereby <span>(a(n))</span> equals the <span>(n^{text{th}})</span> prime number <span>(p_{n})</span>, is normal in base 10. However, it seems that the “inverse” construction given by concatenating the decimal digits of <span>((pi(n) : n in mathbb{N}))</span>, where <span>(pi)</span> denotes the prime-counting function, has not previously been considered. Exploring the distribution of sequences of digits in this new constant <span>(0.0122 ldots 9101011 ldots )</span> would be comparatively difficult, since the number of times a fixed <span>(m in mathbb{N} )</span> appears in <span>((pi(n) : n in mathbb{N}))</span> is equal to the prime gap <span>(g_{m} = p_{m+1} - p_{m})</span>, with the behaviour of prime gaps notoriously elusive. Using a combinatorial method due to Szüsz and Volkmann, we prove that Cramér’s conjecture on prime gaps implies the normality of <span>(0.a(1)a(2) ldots )</span> in a given base <span>(g geq 2)</span>, for <span>(a(n) = pi(n))</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"101 - 111"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500537","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
No selection lemma for empty triangles 没有空三角形的选择 Lemma
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-23 DOI: 10.1007/s10474-024-01431-0
R. Fabila-Monroy, C. Hidalgo-Toscano, D. Perz, B. Vogtenhuber
{"title":"No selection lemma for empty triangles","authors":"R. Fabila-Monroy,&nbsp;C. Hidalgo-Toscano,&nbsp;D. Perz,&nbsp;B. Vogtenhuber","doi":"10.1007/s10474-024-01431-0","DOIUrl":"10.1007/s10474-024-01431-0","url":null,"abstract":"<div><p>\u0000Let <i>P</i> be a set of <i>n</i> points in general position in the plane. \u0000The Second Selection Lemma states that for any family of <span>(Theta(n^3))</span> triangles spanned by <i>P</i>, there exists a point of the plane that lies in a constant fraction of them.\u0000For families of <span>(Theta(n^{3-alpha}))</span> triangles, with <span>(0le alpha le 1)</span>, there might not be a point in more than <span>(Theta(n^{3-2alpha}))</span> of those triangles.\u0000An empty triangle of <i>P</i> is a triangle spanned by <i>P</i>\u0000not containing any point of <i>P</i> in its interior. Bárány conjectured that there exists an edge\u0000spanned by <i>P</i> that is incident to a super-constant number of empty triangles of <i>P</i>. The number of empty triangles\u0000of <i>P</i> might be as low as <span>(Theta(n^2))</span>; in such a case, on average, every edge spanned by <i>P</i> is incident to a constant number\u0000of empty triangles. The conjecture of Bárány suggests that for the class of empty triangles the above upper bound\u0000might not hold. In this paper we show that, somewhat surprisingly,\u0000the above upper bound does in fact hold for empty triangles. \u0000Specifically, we show that for any integer <i>n</i> and real number <span>(0leq alpha leq 1)</span> there exists a point set of size <i>n</i> with <span>(Theta(n^{3-alpha}))</span> empty triangles such that any point of the plane is only in <span>(O(n^{3-2alpha}))</span> empty triangles.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"52 - 73"},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01431-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141103518","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
Specific properties of Lipschitz class functions Lipschitz 类函数的具体性质
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-10 DOI: 10.1007/s10474-024-01432-z
A. Kashibadze, V. Tsagareishvili
{"title":"Specific properties of Lipschitz class functions","authors":"A. Kashibadze,&nbsp;V. Tsagareishvili","doi":"10.1007/s10474-024-01432-z","DOIUrl":"10.1007/s10474-024-01432-z","url":null,"abstract":"<div><p>We consider the Lipschitz class functions on [0, 1]\u0000and special series of their Fourier coefficients with respect to general\u0000orthonormal systems (ONS).\u0000The convergence of classical Fourier series (trigonometric, Haar, Walsh systems) of Lip 1 class functions is a trivial problem and is well known. But general Fourier series, as it is known, even for the function <i>f </i>(<i>x</i>) = 1 does not converge.\u0000On the other hand, we show that such series do not converge with respect to general ONSs. In the paper we find the special conditions on the functions <span>(varphi_{n})</span> of the system <span>((varphi_{n}))</span> such that the above-mentioned series are convergent for any Lipschitz class function. The obtained result is the best possible.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"154 - 168"},"PeriodicalIF":0.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925785","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
Zero free region for spectral averages of Hecke–Maass L-functions Hecke-Maass L 函数谱平均的无零区
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-09 DOI: 10.1007/s10474-024-01430-1
E. M. Sandeep
{"title":"Zero free region for spectral averages of Hecke–Maass L-functions","authors":"E. M. Sandeep","doi":"10.1007/s10474-024-01430-1","DOIUrl":"10.1007/s10474-024-01430-1","url":null,"abstract":"<div><p>We provide a non-vanishing region for an infinite sum of weight zero Hecke–Maass <i>L</i>-functions for the full modular group inside the critical strip. For given positive parameters <i>T</i> and <span>(1 leq M ll frac{T}{log T})</span>, <i>T</i> large, we also count the number of Hecke–Maass cusp forms whose <i>L</i>-values are non-zero at any point <i>s</i> in this region and whose spectral parameters <span>(t_j)</span> lie in short intervals.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"253 - 285"},"PeriodicalIF":0.6,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925784","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 G-Drazin partial order in rings 论环中的 G-Drazin 偏序
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-08 DOI: 10.1007/s10474-024-01429-8
G. Dolinar, B. Kuzma, J. Marovt, D. Mosić
{"title":"On G-Drazin partial order in rings","authors":"G. Dolinar,&nbsp;B. Kuzma,&nbsp;J. Marovt,&nbsp;D. Mosić","doi":"10.1007/s10474-024-01429-8","DOIUrl":"10.1007/s10474-024-01429-8","url":null,"abstract":"<div><p>We extend the concept of a G-Drazin inverse from the set <span>(M_n)</span> of all <span>(ntimes n)</span> complex matrices to the set <span>(mathcal{R}^{D})</span> of all Drazin invertible elements in a ring <span>(mathcal{R})</span> with identity. We also generalize a partial order induced by G-Drazin inverses from <span>(M_n)</span> to the set of all regular elements in <span>(mathcal{R}^{D})</span>, study its properties, compare it to known partial orders, and generalize some known results.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"176 - 192"},"PeriodicalIF":0.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01429-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925922","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
Products of unipotent matrices of index 2 over division rings 除法环上指数为 2 的单能矩阵的乘积
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-06 DOI: 10.1007/s10474-024-01427-w
M. H. Bien, T. N. Son, P. T. T. Thuy, L. Q. Truong
{"title":"Products of unipotent matrices of index 2 over division rings","authors":"M. H. Bien,&nbsp;T. N. Son,&nbsp;P. T. T. Thuy,&nbsp;L. Q. Truong","doi":"10.1007/s10474-024-01427-w","DOIUrl":"10.1007/s10474-024-01427-w","url":null,"abstract":"<div><p>Let <i>D</i> be a division ring. The first aim of this paper is to describe all unipotent matrices of index 2 in the general linear group <span>(mathrm {GL}_n(D))</span> of degree <i>n</i> and in the Vershik–Kerov group <span>(mathrm{GL} _{rm VK}(D))</span>. As a corollary, the subgroups generated by such matrices are investigated. The next aim is to seek a positive integer <i>d</i> such that every matrix in these groups is a product of at most <i>d</i> unipotent matrices of index 2. For example, we show that if every element in the derived subgroup <span>(D')</span> of <span>(D^*=Dbackslash {0})</span> is a product of at most <i>c</i> commutators in <span>(D^*)</span>, then every matrix in <span>(mathrm{GL}_n(D))</span> (resp., <span>(mathrm{GL} _{rm VK}(D))</span>, which is a product of some unipotent matrices of index 2, can be written as a product of at most 4+3<i>c</i> (resp.,5 + 3<i>c</i>) of unipotent matrices of index 2 in <span>(mathrm{GL}_n(D))</span> (resp., <span>(mathrm{GL}_{rm VK}(D)))</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"74 - 100"},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882635","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 first Banach problem concerning condensations of absolute (kappa)-Borel sets onto compacta 关于绝对 $$kappa$ -Borel 集在紧凑集上的凝聚的第一个巴拿赫问题
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-06 DOI: 10.1007/s10474-024-01428-9
A. V. Osipov
{"title":"On the first Banach problem concerning condensations of absolute (kappa)-Borel sets onto compacta","authors":"A. V. Osipov","doi":"10.1007/s10474-024-01428-9","DOIUrl":"10.1007/s10474-024-01428-9","url":null,"abstract":"<div><p>It is consistent that the continuum be arbitrary large and no absolute <span>(kappa)</span>-Borel set X of density <span>(kappa)</span>, <span>(aleph_1&lt;kappa&lt;mathfrak{c})</span>,condenses onto a compactum.</p><p>It is consistent that the continuum be arbitrary large and any absolute <span>(kappa)</span>-Borel set X of density <span>(kappa)</span>, <span>(kappaleqmathfrak{c})</span>, containing a closed subspace of the Baire space of weight <span>(kappa)</span>, condenses onto a compactum.</p><p>In particular, applying Brian's results in model theory, we get the following unexpected result. Given any <span>(Asubseteq mathbb{N})</span> with <span>(1in A)</span>, there is a forcing extension in which every absolute <span>(aleph_n)</span>-Borel set, containing a closed subspace of the Baire space of weight <span>(aleph_n)</span>, condenses onto a compactum if and only if <span>(nin A)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"169 - 175"},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882736","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
Kannappan–Wilson and Van Vleck–Wilson functional equations on semigroups 半群上的 Kannappan-Wilson 和 Van Vleck-Wilson 函数方程
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-06 DOI: 10.1007/s10474-024-01433-y
Y. Aserrar, E. Elqorachi
{"title":"Kannappan–Wilson and Van Vleck–Wilson functional equations on semigroups","authors":"Y. Aserrar,&nbsp;E. Elqorachi","doi":"10.1007/s10474-024-01433-y","DOIUrl":"10.1007/s10474-024-01433-y","url":null,"abstract":"<div><p>Let <span>(S)</span> be a semigroup, <span>(Z(S))</span> the center of <span>(S)</span> and <span>(sigma colon S rightarrow S)</span> is an\u0000involutive automorphism. Our main results is that we describe the solutions of\u0000the Kannappan-Wilson functional equation</p><p><span>(int_{S} f(xyt), dmu(t) + int_{S} f(sigma(y)xt), dmu(t)= 2f(x)g(y), x,yin S,)</span></p><p>and the Van Vleck-Wilson functional equation</p><p><span>(int_{S} f(xyt), dmu(t) - int_{S} f(sigma(y)xt), dmu(t)= 2f(x)g(y), x,yin S,)</span></p><p>where <span>(mu)</span> is a measure that is a linear combination of Dirac measures <span>((delta_{z_i})_{iin I})</span>,\u0000such that <span>(z_iin Z(S))</span> for all <span>(iin I)</span>. Interesting consequences of these results are\u0000presented.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"193 - 213"},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882822","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 Hardy–Littlewood maximal operator on discrete weighted Morrey spaces 离散加权莫雷空间上的哈代-利特尔伍德最大算子
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-22 DOI: 10.1007/s10474-024-01420-3
X. B. Hao, B. D. Li, S. Yang
{"title":"The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces","authors":"X. B. Hao,&nbsp;B. D. Li,&nbsp;S. Yang","doi":"10.1007/s10474-024-01420-3","DOIUrl":"10.1007/s10474-024-01420-3","url":null,"abstract":"<div><p>We introduce a discrete version of weighted Morrey spaces,\u0000and discuss the inclusion relations of these spaces. In addition, we obtain the\u0000boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete\u0000weighted Lebesgue spaces by establishing a discrete Calderón-Zygmund decomposition\u0000for weighted <span>(l^1)</span>-sequences. Furthermore, the necessary and sufficient\u0000conditions for the boundedness of the discrete Hardy-Littlewood maximal operators\u0000on discrete weighted Morrey spaces are discussed. Particularly, the necessary\u0000and sufficient conditions are also discussed for the discrete power weights.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"172 2","pages":"445 - 469"},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800972","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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