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On combinatorial properties of Gruenberg–Kegel graphs of finite groups 论有限群的格伦伯格-凯格尔图的组合特性
Monatshefte für Mathematik Pub Date : 2024-08-20 DOI: 10.1007/s00605-024-02005-6
Mingzhu Chen, Ilya Gorshkov, Natalia V. Maslova, Nanying Yang
{"title":"On combinatorial properties of Gruenberg–Kegel graphs of finite groups","authors":"Mingzhu Chen, Ilya Gorshkov, Natalia V. Maslova, Nanying Yang","doi":"10.1007/s00605-024-02005-6","DOIUrl":"https://doi.org/10.1007/s00605-024-02005-6","url":null,"abstract":"<p>If <i>G</i> is a finite group, then the spectrum <span>(omega (G))</span> is the set of all element orders of <i>G</i>. The prime spectrum <span>(pi (G))</span> is the set of all primes belonging to <span>(omega (G))</span>. A simple graph <span>(Gamma (G))</span> whose vertex set is <span>(pi (G))</span> and in which two distinct vertices <i>r</i> and <i>s</i> are adjacent if and only if <span>(rs in omega (G))</span> is called the Gruenberg–Kegel graph or the prime graph of <i>G</i>. In this paper, we prove that if <i>G</i> is a group of even order, then the set of vertices which are non-adjacent to 2 in <span>(Gamma (G))</span> forms a union of cliques. Moreover, we decide when a strongly regular graph is isomorphic to the Gruenberg–Kegel graph of a finite group.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sparse bounds for oscillating multipliers on stratified groups 分层群振荡乘数的稀疏边界
Monatshefte für Mathematik Pub Date : 2024-08-16 DOI: 10.1007/s00605-024-02000-x
Abhishek Ghosh, Michael Ruzhansky
{"title":"Sparse bounds for oscillating multipliers on stratified groups","authors":"Abhishek Ghosh, Michael Ruzhansky","doi":"10.1007/s00605-024-02000-x","DOIUrl":"https://doi.org/10.1007/s00605-024-02000-x","url":null,"abstract":"<p>In this article, we address sparse bounds for a class of spectral multipliers that include oscillating multipliers on stratified Lie groups. Our results can be applied to obtain weighted bounds for general Riesz means and for solutions of dispersive equations.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some sharp inequalities for norms in $$mathbb {R}^n$$ and $$mathbb {C}^n$$ $$mathbb {R}^n$$ 和 $$mathbb {C}^n$$ 中规范的一些尖锐不等式
Monatshefte für Mathematik Pub Date : 2024-08-14 DOI: 10.1007/s00605-024-02004-7
Stefan Gerdjikov, Nikolai Nikolov
{"title":"Some sharp inequalities for norms in $$mathbb {R}^n$$ and $$mathbb {C}^n$$","authors":"Stefan Gerdjikov, Nikolai Nikolov","doi":"10.1007/s00605-024-02004-7","DOIUrl":"https://doi.org/10.1007/s00605-024-02004-7","url":null,"abstract":"<p>The main result of this paper is that for any norm on a complex or real <i>n</i>-dimensional linear space, every extremal basis satisfies inverted triangle inequality with scaling factor <span>(2^n-1)</span>. Furthermore, the constant <span>(2^n-1)</span> is tight. We also prove that the norms of any two extremal bases are comparable with a factor of <span>(2^n-1)</span>, which, intuitively, means that any two extremal bases are quantitatively equivalent with the stated tolerance.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ill-posedness for the gCH-mCH equation in Besov spaces 贝索夫空间中 gCH-mCH 方程的非问题性
Monatshefte für Mathematik Pub Date : 2024-08-13 DOI: 10.1007/s00605-024-02002-9
Yanghai Yu, Hui Wang
{"title":"Ill-posedness for the gCH-mCH equation in Besov spaces","authors":"Yanghai Yu, Hui Wang","doi":"10.1007/s00605-024-02002-9","DOIUrl":"https://doi.org/10.1007/s00605-024-02002-9","url":null,"abstract":"<p>In this paper, we consider the Cauchy problem to the generalized Fokas–Qiao–Xia–Li/generalized Camassa–Holm-modified Camassa–Holm (gFQXL/gCH-mCH) equation, which includes the Camassa–Holm equation, the generalized Camassa–Holm equation, the Novikov equation, the Fokas–Olver–Rosenau–Qiao/Modified Camassa–Holm equation and the Fokas–Qiao–Xia–Li/Camassa–Holm-modified Camassa–Holm equation. We prove the ill-posedness for the Cauchy problem of the gFQXL/gCH-mCH equation in <span>(B^s_{p,infty })</span> with <span>(s&gt;max {2+1/p, 5/2})</span> and <span>(1le ple infty )</span> in the sense that the solution map to this equation starting from <span>(u_0)</span> is discontinuous at <span>(t = 0)</span> in the metric of <span>(B^s_{p,infty })</span>.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of pseudo peakons for a new fifth order CH type equation with cubic nonlinearities 具有立方非线性的新五阶 CH 型方程的伪峰值子稳定性
Monatshefte für Mathematik Pub Date : 2024-08-10 DOI: 10.1007/s00605-024-02001-w
Zhigang Li
{"title":"Stability of pseudo peakons for a new fifth order CH type equation with cubic nonlinearities","authors":"Zhigang Li","doi":"10.1007/s00605-024-02001-w","DOIUrl":"https://doi.org/10.1007/s00605-024-02001-w","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141919682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of pseudo peakons for a new fifth order CH type equation with cubic nonlinearities 具有立方非线性的新五阶 CH 型方程的伪峰值子稳定性
Monatshefte für Mathematik Pub Date : 2024-08-10 DOI: 10.1007/s00605-024-02001-w
Zhigang Li
{"title":"Stability of pseudo peakons for a new fifth order CH type equation with cubic nonlinearities","authors":"Zhigang Li","doi":"10.1007/s00605-024-02001-w","DOIUrl":"https://doi.org/10.1007/s00605-024-02001-w","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141920165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The difference of weighted composition operators on Fock spaces Fock 空间上的加权合成算子之差
Monatshefte für Mathematik Pub Date : 2024-08-10 DOI: 10.1007/s00605-024-02003-8
Zicong Yang
{"title":"The difference of weighted composition operators on Fock spaces","authors":"Zicong Yang","doi":"10.1007/s00605-024-02003-8","DOIUrl":"https://doi.org/10.1007/s00605-024-02003-8","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141920285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weyl multipliers for $$(L^p, L^q)$$ (L^p，L^q)$$的韦尔乘数
Monatshefte für Mathematik Pub Date : 2024-07-16 DOI: 10.1007/s00605-024-01997-5
Arup Kumar Maity, P. Ratnakumar
{"title":"Weyl multipliers for $$(L^p, L^q)$$","authors":"Arup Kumar Maity, P. Ratnakumar","doi":"10.1007/s00605-024-01997-5","DOIUrl":"https://doi.org/10.1007/s00605-024-01997-5","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141642079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some results on conjugacy class sizes of primary elements of a finite group 关于有限群主元共轭类大小的一些结果
Monatshefte für Mathematik Pub Date : 2024-07-10 DOI: 10.1007/s00605-024-01999-3
Yongcai Ren
{"title":"Some results on conjugacy class sizes of primary elements of a finite group","authors":"Yongcai Ren","doi":"10.1007/s00605-024-01999-3","DOIUrl":"https://doi.org/10.1007/s00605-024-01999-3","url":null,"abstract":"<p>We establish results on the conjugacy class sizes of elements of of prime-power order in a finite group. On the way, we improve results by a number of authors.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 solutions to the weighted biharmonic equation in the unit disk 关于单位盘中加权双谐方程的解
Monatshefte für Mathematik Pub Date : 2024-07-08 DOI: 10.1007/s00605-024-01998-4
Peijin Li, Yaxiang Li, Saminathan Ponnusamy
{"title":"On the solutions to the weighted biharmonic equation in the unit disk","authors":"Peijin Li, Yaxiang Li, Saminathan Ponnusamy","doi":"10.1007/s00605-024-01998-4","DOIUrl":"https://doi.org/10.1007/s00605-024-01998-4","url":null,"abstract":"<p>In this paper, we investigate the solutions of the weighted biharmonic differential equation <span>(Delta big ((1-|z|^2)^{-1}Delta big ) Phi =0)</span> in the unit disk <span>(|z|&lt;1)</span>, where <span>(Delta =4frac{partial ^2}{partial zpartial overline{z}})</span> denotes the Laplacian. The primary aim of the paper is to establish counterparts of several important results in the classical geometric function theory for this class of mappings. The main results include Schwarz type lemma and Landau type theorem. A continuous increasing function <span>(omega :, [0, infty )rightarrow [0, infty ))</span> with <span>(omega (0)=0)</span> and <span>(omega (t)/t)</span> is non-increasing for <span>(t&gt;0)</span> is called a <i>fast majorant</i> if for some <span>(delta _0&gt;0)</span> and <span>(0&lt;delta &lt;delta _0)</span>, the inequality </p><span>$$begin{aligned} int ^{delta }_{0}frac{omega (t)}{t}dtle Comega (delta ), end{aligned}$$</span><p>holds for some positive constant <i>C</i>. Then we obtain <span>(omega )</span>-Lipschitz continuity for the solutions to the weighted biharmonic equation, when <span>(omega )</span> is a fast majorant.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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