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New infinite families of congruences for 5-core and 7-core partitions 5 核和 7 核分区的新无限同余族
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01424-z
Z. Meng, O. X. M. Yao
{"title":"New infinite families of congruences for 5-core and 7-core partitions","authors":"Z. Meng, O. X. M. Yao","doi":"10.1007/s10474-024-01424-z","DOIUrl":"https://doi.org/10.1007/s10474-024-01424-z","url":null,"abstract":"<p>Let <span>(a_t(n))</span> denote the number of <i>t</i>-core partitions of <i>n</i>. In recent years, a number of congruences for <span>(a_t(n))</span> have been discovered for some small <i>t</i>. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for <span>(a_5(n))</span> and congruences modulo 2 for <span>(a_7(n))</span>. Motivated by their work, we prove some new infinite families of congruences modulo 3 for <span>(a_5(n))</span> and congruences modulo 2 for <span>(a_7(n))</span> by utilizing Newman's identities.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591981","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 boundary Hölder logarithmic continuity of mappings in some domains 论某些域中映射的边界荷尔德对数连续性
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01419-w
O. Dovhopiatyi, E. Sevost’yanov
{"title":"On boundary Hölder logarithmic continuity of mappings in some domains","authors":"O. Dovhopiatyi, E. Sevost’yanov","doi":"10.1007/s10474-024-01419-w","DOIUrl":"https://doi.org/10.1007/s10474-024-01419-w","url":null,"abstract":"<p>We study mappings satisfying some estimate of distortion of\u0000modulus of families of paths. Under some conditions on definition and mapped\u0000domains, we prove that these mappings are logarithmic Hölder continuous at\u0000boundary points.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592075","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
Fractal sumset properties 分形和集属性
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01421-2
D. Kong, Z. Wang
{"title":"Fractal sumset properties","authors":"D. Kong, Z. Wang","doi":"10.1007/s10474-024-01421-2","DOIUrl":"https://doi.org/10.1007/s10474-024-01421-2","url":null,"abstract":"<p>\u0000We introduce two notions of fractal sumset properties.\u0000A compact set <span>(Ksubsetmathbb{R}^d)</span> is said to have the <i>Hausdorff sumset property</i> (HSP) if for any <span>(ellinmathbb{N}_{ge 2})</span> there exist compact sets <span>(K_1,K_2)</span>,..., <span>(K_ell)</span> such that <span>(K_1+K_2+cdots+K_ellsubset K)</span> and <span>(dim_H K_i=dim_H K)</span> for all <span>(1le ile ell)</span>.\u0000Analogously, if we replace the Hausdorff dimension by the packing dimension in the definition of HSP, then the compact set <span>(Ksubsetmathbb{R}^d)</span> is said to have the <i>packing sumset property</i> (PSP).\u0000We show that the HSP fails for certain homogeneous self-similar sets satisfying the strong separation condition, while the PSP holds for all homogeneous self-similar sets in <span>(mathbb{R}^d)</span>.\u0000</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591761","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 resolvability, connectedness and pseudocompactness 关于可解析性、连通性和伪紧密性
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01423-0
A. E. Lipin
{"title":"On resolvability, connectedness and pseudocompactness","authors":"A. E. Lipin","doi":"10.1007/s10474-024-01423-0","DOIUrl":"https://doi.org/10.1007/s10474-024-01423-0","url":null,"abstract":"<p>\u0000We prove that:\u0000I. If <i>L</i> is a <span>(T_1)</span> space, <span>(|L|&gt;1)</span> and <span>(d(L) leq kappa geq omega)</span>, then\u0000there is a submaximal dense subspace <i>X</i> of <span>(L^{2^kappa})</span> such that <span>(|X|=Delta(X)=kappa)</span>. II. If <span>(mathfrak{c}leqkappa=kappa^omega&lt;lambda)</span> and <span>(2^kappa=2^lambda)</span>, then there is a Tychonoff pseudocompact globally and locally connected space <i>X</i> such that <span>(|X|=Delta(X)=lambda)</span> and <i>X</i> is not <span>(kappa^+)</span>-resolvable. III. If <span>(omega_1leqkappa&lt;lambda)</span> and <span>(2^kappa=2^lambda)</span>, then there is a regular space <i>X</i> such that <span>(|X|=Delta(X)=lambda)</span>, all continuous real-valued functions on <i>X</i> are constant (so <i>X</i> is connected) and <i>X</i> is not <span>(kappa^+)</span>-resolvable.\u0000</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592004","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
Atomic decompositions of martingale Hardy Lorentz amalgam spaces and applications 马氏哈代洛伦兹汞齐空间的原子分解及其应用
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01422-1
L. Li, Y. Wang, A. Yang
{"title":"Atomic decompositions of martingale Hardy Lorentz amalgam spaces and applications","authors":"L. Li, Y. Wang, A. Yang","doi":"10.1007/s10474-024-01422-1","DOIUrl":"https://doi.org/10.1007/s10474-024-01422-1","url":null,"abstract":"<p>We develop the martingale theory in the framework of Lorentz amalgam spaces. Atomic decompositions for the martingale Hardy Lorentz amalgam spaces are established. As applications of atomic decompositions, the dual spaces of the martingale Hardy Lorentz amalgam spaces are characterized. Furthermore, when the stochastic basis is regular, the boundedness of the fractional integrals on martingale Hardy Lorentz amalgam spaces is proved. The results obtained here generalized the corresponding known results in martingale Hardy amalgam spaces and various classical martingale Hardy spaces.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591974","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 Bounded Below, Noncontractible, Acyclic Complex Of Projective Modules 投影模块的有界、非收缩、无环复合物
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-03-13 DOI: 10.1007/s10474-024-01414-1
L. Positselski
{"title":"A Bounded Below, Noncontractible, Acyclic Complex Of Projective Modules","authors":"L. Positselski","doi":"10.1007/s10474-024-01414-1","DOIUrl":"https://doi.org/10.1007/s10474-024-01414-1","url":null,"abstract":"<p>We construct examples of bounded below, noncontractible, acyclic\u0000complexes of finitely generated projective modules over some rings <i>S</i>,\u0000as well as bounded above, noncontractible, acyclic complexes of\u0000injective modules. The rings <i>S</i> are certain rings of infinite matrices with entries in\u0000the rings of commutative polynomials or formal power series in\u0000infinitely many variables. In the world of comodules or contramodules over coalgebras over\u0000fields, similar examples exist over the cocommutative symmetric\u0000coalgebra of an infinite-dimensional vector space. A simpler, universal example of a bounded below, noncontractible,\u0000acyclic complex of free modules with one generator, communicated to\u0000the author by Canonaco, is included at the end of the paper.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126371","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
Visibility Properties Of Lattice Points In Multiple Random Walks 多重随机行走中网格点的可见性
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-03-13 DOI: 10.1007/s10474-024-01412-3
M. Lu
{"title":"Visibility Properties Of Lattice Points In Multiple Random Walks","authors":"M. Lu","doi":"10.1007/s10474-024-01412-3","DOIUrl":"https://doi.org/10.1007/s10474-024-01412-3","url":null,"abstract":"<p>This paper concerns the visibility properties of lattice points\u0000in multiple random walks on <span>(mathbb{N}^k)</span>, where <span>(kgeq 2)</span> is an integer. We study two aspects\u0000of the visibility: simultaneous visibility in multiple random walkers; and\u0000that only some of these walkers are visible. Combining tools from number theory\u0000and probability theory, we prove the corresponding densities of the above two\u0000parts.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126376","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
Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups 具有半面体 Sylow 2 子群的有限群的 Coleman 自形变
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-03-13 DOI: 10.1007/s10474-024-01408-z
R. Aragona
{"title":"Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups","authors":"R. Aragona","doi":"10.1007/s10474-024-01408-z","DOIUrl":"https://doi.org/10.1007/s10474-024-01408-z","url":null,"abstract":"<p>We study some families of finite groups having inner class-preserving\u0000automorphisms. In particular, let <i>G</i> be a finite group and <i>S</i> be a\u0000semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not\u0000a homomorphic image of <i>G</i> and <span>(Z(S) &lt; Z(G))</span> or <i>G</i> is nilpotent-by-nilpotent, we\u0000have that all the Coleman automorphisms of <i>G</i> are inner. As a consequence, these\u0000groups satisfy the <i>normalizer problem</i>.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126458","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
Central limit theorem for the average closure coefficient 平均闭合系数的中心极限定理
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-03-13 DOI: 10.1007/s10474-024-01416-z
{"title":"Central limit theorem for the average closure coefficient","authors":"","doi":"10.1007/s10474-024-01416-z","DOIUrl":"https://doi.org/10.1007/s10474-024-01416-z","url":null,"abstract":"<h3>Abstract</h3> <p>Many real-world networks exhibit the phenomenon of edge clustering,which is typically measured by the average clustering coefficient. Recently,an alternative measure, the average closure coefficient, is proposed to quantify local clustering. It is shown that the average closure coefficient possesses a number of useful properties and can capture complementary information missed by the classical average clustering coefficient. In this paper, we study the asymptotic distribution of the average closure coefficient of a heterogeneous Erdős–Rényi random graph. We prove that the standardized average closure coefficient converges in distribution to the standard normal distribution. In the Erdős–Rényi random graph,the variance of the average closure coefficient exhibits the same phase transition phenomenon as the average clustering coefficient.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126374","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
Numbers expressible as a difference of two Pisot numbers 可表示为两个皮索特数之差的数
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-03-04 DOI: 10.1007/s10474-024-01410-5
A. Dubickas
{"title":"Numbers expressible as a difference of two Pisot numbers","authors":"A. Dubickas","doi":"10.1007/s10474-024-01410-5","DOIUrl":"https://doi.org/10.1007/s10474-024-01410-5","url":null,"abstract":"<p>We characterize algebraic integers which are differences of two\u0000Pisot numbers. Each such number <span>(alpha)</span> must be real and its conjugates over <span>(mathbb{Q})</span> must\u0000all lie in the union of the disc <span>(|z|&lt;2)</span> and the strip <span>(|Im(z)|&lt;1)</span>. In particular, we\u0000prove that every real algebraic integer <span>(alpha)</span> whose conjugates over <span>(mathbb{Q})</span>, except possibly\u0000for <span>(alpha)</span> itself, all lie in the disc <span>(|z|&lt;2)</span> can always be written as a difference of\u0000two Pisot numbers. We also show that a real quadratic algebraic integer <span>(alpha)</span> with\u0000conjugate <span>(alpha')</span> over <span>(mathbb{Q})</span> is always expressible as a difference of two Pisot numbers except\u0000for the cases <span>(alpha&lt;alpha'&lt;-2)</span> or <span>(2&lt;alpha'&lt;alpha)</span> when <span>(alpha)</span> cannot be expressed in that\u0000form. A similar complete characterization of all algebraic integers <span>(alpha)</span> expressible\u0000as a difference of two Pisot numbers in terms of the location of their conjugates\u0000is given in the case when the degree <span>(d)</span> of <span>(alpha)</span> is a prime number.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036942","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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