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Connected sums of Brieskorn contact 5-spheres Brieskorn接触5球的连通和
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-16 DOI: 10.1007/s00013-025-02167-1
Florian Buck, Kai Zehmisch
{"title":"Connected sums of Brieskorn contact 5-spheres","authors":"Florian Buck,&nbsp;Kai Zehmisch","doi":"10.1007/s00013-025-02167-1","DOIUrl":"10.1007/s00013-025-02167-1","url":null,"abstract":"<div><p>In dimension 5, the contact connected sum of Brieskorn contact spheres is, in general, not a Brieskorn contact sphere.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"521 - 531"},"PeriodicalIF":0.5,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02167-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On integral consecutive arithmetic means of the first Fibonacci numbers 第一斐波那契数的整数连续算术平均数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-15 DOI: 10.1007/s00013-025-02166-2
Florian Luca, Diego Marques
{"title":"On integral consecutive arithmetic means of the first Fibonacci numbers","authors":"Florian Luca,&nbsp;Diego Marques","doi":"10.1007/s00013-025-02166-2","DOIUrl":"10.1007/s00013-025-02166-2","url":null,"abstract":"<div><p>In this note, we prove a conjecture of Fatehizadeh and Yaqubi regarding the arithmetic mean of the first <i>n</i> Fibonacci numbers. More precisely, we show that there are infinitely many positive integers <i>n</i> such that <span>(n mid sum _{i=1}^{n} F_i)</span> and <span>(n+1 mid sum _{i=1}^{n+1} F_i)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"505 - 511"},"PeriodicalIF":0.5,"publicationDate":"2025-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Existence and asymptotic behavior of normalized solutions to fractional Schrödinger equations with combined nonlinearities 组合非线性分数阶Schrödinger方程归一化解的存在性及渐近性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-13 DOI: 10.1007/s00013-025-02159-1
Sijian Cheng, Wenting Zhao, Xianjiu Huang
{"title":"Existence and asymptotic behavior of normalized solutions to fractional Schrödinger equations with combined nonlinearities","authors":"Sijian Cheng,&nbsp;Wenting Zhao,&nbsp;Xianjiu Huang","doi":"10.1007/s00013-025-02159-1","DOIUrl":"10.1007/s00013-025-02159-1","url":null,"abstract":"<div><p>In the present paper, we consider the following fractional Schrödinger equations with combined nonlinearities </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} (-Delta )^su+lambda u=|u|^{q-2}u+|u|^{p-2}u textrm{in} {mathbb {R}}^N, int _{{mathbb {R}}^N}u^2textrm{d} x=a^2, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(Nge 2)</span>, <span>(sin (0,1))</span>, <span>(a&gt;0)</span>, <span>(2&lt;q&lt;p&lt;2^{*}_{s}=frac{2N}{N-2s})</span>, and <span>((-Delta )^s)</span> is the fractional Laplace operator. Under various conditions on <span>(q&lt;p)</span>, <span>(a&gt;0)</span>, we investigate the existence of ground state normalized solutions by applying variational methods. Moreover, the asymptotic behavior of mountain pass type normalized solutions is also considered. We generalize the corresponding results in Qi and Zou (J Differ Equ 375:172–205, 2023), which concerns nonlinear Schrödinger equations with combined nonlinearities, to fractional nonlinear Schrödinger equations with combined nonlinearities.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"545 - 560"},"PeriodicalIF":0.5,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 pre-compactness criterion of subsets in subspaces spanned by compactly supported smooth functions 紧支持光滑函数张成的子空间中子集的预紧性准则
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-12 DOI: 10.1007/s00013-025-02152-8
Denny Ivanal Hakim, Yoshihiro Sawano
{"title":"A pre-compactness criterion of subsets in subspaces spanned by compactly supported smooth functions","authors":"Denny Ivanal Hakim,&nbsp;Yoshihiro Sawano","doi":"10.1007/s00013-025-02152-8","DOIUrl":"10.1007/s00013-025-02152-8","url":null,"abstract":"<div><p>Fréchet and Kolmogorov characterized pre-compact sets in Lebesgue spaces. Since then, many characterizations of various function spaces have been developed. Although Morrey spaces are extensions of Lebesgue spaces, characterizing pre-compact sets within Morrey spaces remains open. This paper suggests that certain closed subspaces of Morrey spaces are more manageable compared to the Morrey spaces themselves. It provides a characterization of pre-compactness for subsets in the closure of compactly supported smooth functions in Banach lattices. This finding refines and broadens the characterization of pre-compact subsets in Morrey spaces.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"303 - 310"},"PeriodicalIF":0.5,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundary layer profiles of positive solutions for logistic equations with sublinear nonlinearity on the boundary 边界上具有次线性非线性的logistic方程正解的边界层轮廓
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-08 DOI: 10.1007/s00013-025-02161-7
Kenichiro Umezu
{"title":"Boundary layer profiles of positive solutions for logistic equations with sublinear nonlinearity on the boundary","authors":"Kenichiro Umezu","doi":"10.1007/s00013-025-02161-7","DOIUrl":"10.1007/s00013-025-02161-7","url":null,"abstract":"<div><p>In this paper, we consider the logistic elliptic equation <span>(-Delta u = u- u^{p})</span> in a smooth bounded domain <span>(Omega subset {mathbb {R}}^{N},)</span> <span>(Nge 2,)</span> equipped with the sublinear Neumann boundary condition <span>(frac{partial u}{partial nu } = mu u^{q})</span> on <span>(partial Omega ,)</span> where <span>(0&lt;q&lt;1&lt;p,)</span> and <span>(mu ge 0)</span> is a parameter. With sub- and supersolutions and a comparison principle for the equation, we analyze the asymptotic profile of the unique positive solution for the equation as <span>(mu rightarrow infty .)</span></p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"433 - 443"},"PeriodicalIF":0.5,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
(L^2)-boundedness for 1-D wave equations with time variable coefficients (L^2)时变系数一维波动方程的-有界性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-08 DOI: 10.1007/s00013-025-02162-6
Ryo Ikehata
{"title":"(L^2)-boundedness for 1-D wave equations with time variable coefficients","authors":"Ryo Ikehata","doi":"10.1007/s00013-025-02162-6","DOIUrl":"10.1007/s00013-025-02162-6","url":null,"abstract":"<div><p>We consider the <span>(L^{2})</span>-boundedness of the solution of the Cauchy problem for a wave equation with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space <span>(textbf{R})</span>. We adopt a simple multiplier method by using a special property of the one dimensional space.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"445 - 453"},"PeriodicalIF":0.5,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02162-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundary estimates of solutions of sum Hessian equations in half spaces 半空间和Hessian方程解的边界估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-08 DOI: 10.1007/s00013-025-02164-4
Xiaobiao Jia, Wenfeng Yang
{"title":"Boundary estimates of solutions of sum Hessian equations in half spaces","authors":"Xiaobiao Jia,&nbsp;Wenfeng Yang","doi":"10.1007/s00013-025-02164-4","DOIUrl":"10.1007/s00013-025-02164-4","url":null,"abstract":"<div><p>In this paper, we consider Pogorelov type estimates up to the flat boundary for <i>k</i>-convex solutions of sum Hessian equations with right hand term <i>f</i>(<i>x</i>, <i>u</i>).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"533 - 543"},"PeriodicalIF":0.5,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Finite soluble groups that act with fixity 2 or 3 固定度为2或3的有限可溶基团
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-08 DOI: 10.1007/s00013-025-02156-4
Paula Hähndel, Christoph Möller, Rebecca Waldecker
{"title":"Finite soluble groups that act with fixity 2 or 3","authors":"Paula Hähndel,&nbsp;Christoph Möller,&nbsp;Rebecca Waldecker","doi":"10.1007/s00013-025-02156-4","DOIUrl":"10.1007/s00013-025-02156-4","url":null,"abstract":"<div><p>In this article, we prove results about finite soluble groups that act with fixity 2 or 3.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"339 - 352"},"PeriodicalIF":0.5,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02156-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The affine group of a local field is Hermitian 局域场的仿射群是厄米的
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-06 DOI: 10.1007/s00013-025-02158-2
Max Carter
{"title":"The affine group of a local field is Hermitian","authors":"Max Carter","doi":"10.1007/s00013-025-02158-2","DOIUrl":"10.1007/s00013-025-02158-2","url":null,"abstract":"<div><p>The question of whether the group <span>({mathbb {Q}}_p rtimes {mathbb {Q}}_p^*)</span> is Hermitian has been stated as an open question in multiple sources in the literature, even as recently as a paper by R. Palma published in 2015. In this note, we confirm that this group is Hermitian by proving the following more general theorem: given any local field <span>({mathbb {K}})</span>, the affine group <span>({mathbb {K}} rtimes {mathbb {K}}^*)</span> is a Hermitian group. The proof is a consequence of results about Hermitian Banach <span>(*)</span>-algebras from the 1970s. In the case that <span>({mathbb {K}})</span> is a non-archimedean local field, this result produces examples of totally disconnected locally compact Hermitian groups with exponential growth, and these are the first examples of groups satisfying these properties. This answers a second question of Palma about the existence of such groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"361 - 367"},"PeriodicalIF":0.5,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Criteria for nilpotency of higher commutator subgroups 高换子子群幂零的判据
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-05 DOI: 10.1007/s00013-025-02157-3
Raimundo Bastos, William Cocke, Carmine Monetta
{"title":"Criteria for nilpotency of higher commutator subgroups","authors":"Raimundo Bastos,&nbsp;William Cocke,&nbsp;Carmine Monetta","doi":"10.1007/s00013-025-02157-3","DOIUrl":"10.1007/s00013-025-02157-3","url":null,"abstract":"<div><p>In this note, we provide some nilpotency criteria for the terms of the lower central series of a finite group involving the order of their standard generators. Moreover, when the finite group is solvable, we provide a characterization for the nilpotency of the terms of the derived series of the group.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"353 - 360"},"PeriodicalIF":0.5,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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