发布求助
文献互助 智能选刊 最新文献

Archiv der Mathematik最新文献

筛选
英文 中文
Lie product type formulas for the logarithm 对数的Lie积型公式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-27 DOI: 10.1007/s00013-025-02201-2
Dumitru Popa
{"title":"Lie product type formulas for the logarithm","authors":"Dumitru Popa","doi":"10.1007/s00013-025-02201-2","DOIUrl":"10.1007/s00013-025-02201-2","url":null,"abstract":"<div><p>In this paper, we prove various Lie product type formulas for the logarithm. A sample result: Let <span>(kge 2)</span> be a natural number, <span>(X_{1})</span>,..., <span>(X_{k})</span>, <i>Y</i> Banach algebras with unit and <span>(T:X_{1}times cdot cdot cdot times X_{k}rightarrow Y)</span> a continuous <i>k</i>-linear operator such that <span>(Tleft( textbf{1},...,textbf{1}right) =textbf{1})</span>. Let <span>(left( a_{n}right) _{nin mathbb {N}})</span> be a sequence of natural numbers with <span>( lim _{nrightarrow infty }a_{n}=infty )</span>. Then for all <span>(left( x_{1},...,x_{k}right) in X_{1}times cdot cdot cdot times X_{k})</span> we have </p><div><div><span>$$begin{aligned} &amp; lim limits _{nrightarrow infty }left[ Tleft( textbf{1}+ln left( textbf{1}+frac{x_{1}}{a_{n}}right) ,...,textbf{1}+ln left( textbf{1}+ frac{x_{k}}{a_{n}}right) right) right] ^{a_{n}} &amp; quad =e^{Tleft( x_{1},textbf{1},...,textbf{1}right) +Tleft( textbf{1},x_{2},textbf{1},...,textbf{1}right) +cdot cdot cdot +Tleft( textbf{1},...,textbf{1},x_{k}right) }. end{aligned}$$</span></div></div></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"177 - 186"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342383","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
Stability estimate for an inverse potential problem in time-fractional diffusion problem 时间分数扩散问题中逆势问题的稳定性估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-26 DOI: 10.1007/s00013-025-02185-z
Hamza Kahlaoui
{"title":"Stability estimate for an inverse potential problem in time-fractional diffusion problem","authors":"Hamza Kahlaoui","doi":"10.1007/s00013-025-02185-z","DOIUrl":"10.1007/s00013-025-02185-z","url":null,"abstract":"<div><p>We investigate the inverse problem of identifying a space-depen- dent potential in a Caputo time-fractional diffusion equation from boundary observations. Our analysis establishes a maximum principle for subdiffusion equations with non-homogeneous Neumann boundary conditions, demonstrating the positivity of solutions under specific assumptions on the boundary data. Building upon this result, we leverage the Gâteaux differentiability of the forward map and the non-vanishing property of its derivative to derive a local Lipschitz stability estimate for the inverse potential problem. This provides a rigorous foundation for the stable reconstruction of the potential, highlighting the interplay between fractional dynamics and stability in inverse problems.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"87 - 105"},"PeriodicalIF":0.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969474","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
The median trick does not help for fully nested scrambling 中值技巧对完全嵌套的置乱没有帮助
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-26 DOI: 10.1007/s00013-025-02205-y
Takashi Goda, Kosuke Suzuki
{"title":"The median trick does not help for fully nested scrambling","authors":"Takashi Goda,&nbsp;Kosuke Suzuki","doi":"10.1007/s00013-025-02205-y","DOIUrl":"10.1007/s00013-025-02205-y","url":null,"abstract":"<div><p>In randomized quasi-Monte Carlo methods for numerical integration, average estimators based on digital nets with fully nested and linear scramblings, respectively, are known to exhibit the same variance. In this note, we show that this equivalence does not extend to the median estimators. Specifically, while the median estimator with linear scrambling can achieve faster convergence for smooth integrands, the median estimator with fully nested scrambling does not exhibit this advantage.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"221 - 230"},"PeriodicalIF":0.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342315","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
Maximal minors of 1-generic matrices have rational singularities 1-泛矩阵的极大子阵具有有理奇异性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-26 DOI: 10.1007/s00013-025-02202-1
Trung Chau, Manoj Kummini
{"title":"Maximal minors of 1-generic matrices have rational singularities","authors":"Trung Chau,&nbsp;Manoj Kummini","doi":"10.1007/s00013-025-02202-1","DOIUrl":"10.1007/s00013-025-02202-1","url":null,"abstract":"<div><p>We show that the quotient ring by the ideal of maximal minors of a 1-generic matrix has rational singularities. This answers a conjecture of Eisenbud (Amer J Math 110(3):541–575, 1988) that such rings are normal, and generalizes a result of Conca et al. (Adv Math 335:111–129, 2018) that generic Hankel determinantal rings have rational singularities in characteristic zero.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"267 - 274"},"PeriodicalIF":0.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341910","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
Integrability of Kepler billiards at zero-energy 零能量下开普勒台球的可积性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-25 DOI: 10.1007/s00013-025-02204-z
Lei Zhao
{"title":"Integrability of Kepler billiards at zero-energy","authors":"Lei Zhao","doi":"10.1007/s00013-025-02204-z","DOIUrl":"10.1007/s00013-025-02204-z","url":null,"abstract":"<div><p>We consider a Kepler billiard with zero-energy in the plane defined inside a smooth closed connected simple curve which intersects all focused parabola at at most two points. We show that if it has an invariant curve consisting of 2-periodic orbits and there exists a <span>(C^{1})</span>-first integral with non-vanishing gradient in the region between the invariant curve and the boundary curve, then the system is defined actually inside an ellipse with the Kepler center occupying one of the foci. This statement is obtained as a simple “translation” of the theorem of Bialy–Mironov [3] with Levi–Civita transformation.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"329 - 333"},"PeriodicalIF":0.5,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341681","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 matrix differential Harnack estimate for a class of hypoelliptic evolution equations 一类次椭圆演化方程的矩阵微分哈纳克估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-20 DOI: 10.1007/s00013-025-02197-9
Bin Qian, Beibei Zhang
{"title":"A matrix differential Harnack estimate for a class of hypoelliptic evolution equations","authors":"Bin Qian,&nbsp;Beibei Zhang","doi":"10.1007/s00013-025-02197-9","DOIUrl":"10.1007/s00013-025-02197-9","url":null,"abstract":"<div><p>In this paper, we derive a matrix differential Harnack estimate for a class of hypoelliptic evolution equations satisfying the Hörmander condition, which solves the second conjecture in the paper by Huang (Potent Anal 41(3):771–782, 2014).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"199 - 207"},"PeriodicalIF":0.5,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340886","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
Decompositions of Scherk-type zero mean curvature surfaces scherk型零平均曲率曲面的分解
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-14 DOI: 10.1007/s00013-025-02196-w
Subham Paul, Priyank Vasu, Siddharth Panigrahi, Rahul Kumar Singh
{"title":"Decompositions of Scherk-type zero mean curvature surfaces","authors":"Subham Paul,&nbsp;Priyank Vasu,&nbsp;Siddharth Panigrahi,&nbsp;Rahul Kumar Singh","doi":"10.1007/s00013-025-02196-w","DOIUrl":"10.1007/s00013-025-02196-w","url":null,"abstract":"<div><p>In this paper, by using a special Euler–Ramanujan identity and the idea of Wick rotation, we show that a one-parameter family of solutions to the zero mean curvature equation in the Lorentz–Minkowski 3-space <span>(mathbb {E}_1^3)</span>, namely Scherk-type zero mean curvature surfaces, can be expressed as an infinite superposition of dilated helicoids. Further, we also obtain different finite decompositions for these surfaces. We end this paper with an application of these decompositions to formulate maximal codimension 2 surfaces into finite and infinite “sums” of weakly untrapped and <span>(*)</span>-surfaces in the Lorentz–Minkowski 4-space.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"107 - 120"},"PeriodicalIF":0.5,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969464","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
Gradient estimates for a class of p-Laplacian equations 一类p-拉普拉斯方程的梯度估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-14 DOI: 10.1007/s00013-025-02192-0
Guangyue Huang, Jingxu Liu, Zhen Wang
{"title":"Gradient estimates for a class of p-Laplacian equations","authors":"Guangyue Huang,&nbsp;Jingxu Liu,&nbsp;Zhen Wang","doi":"10.1007/s00013-025-02192-0","DOIUrl":"10.1007/s00013-025-02192-0","url":null,"abstract":"<div><p>By virtue of the Nash–Moser iteration, we obtain a local gradient estimate of positive weak solutions to the weighted <i>p</i>-Laplacian equation </p><div><div><span>$$begin{aligned} Delta _{p,f}u+a(x)uln u=0 end{aligned}$$</span></div></div><p>defined on a complete smooth metric measure space under the condition that the <i>m</i>-Bakry–Émery Ricci curvature has a lower bound, where <span>(p&gt;2)</span> and the function <span>(a(x)le 0.)</span> As applications, Liouville-type theorems for positive solutions to the above equation are achieved.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"71 - 85"},"PeriodicalIF":0.5,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969478","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
On simplicial complexes with maximal total bigraded Betti number 具有最大总梯度Betti数的简单复形
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-12 DOI: 10.1007/s00013-025-02195-x
Pimeng Dai, Li Yu
{"title":"On simplicial complexes with maximal total bigraded Betti number","authors":"Pimeng Dai,&nbsp;Li Yu","doi":"10.1007/s00013-025-02195-x","DOIUrl":"10.1007/s00013-025-02195-x","url":null,"abstract":"<div><p>We determine which simplicial complexes with a given number of vertices have the maximum sum of bigraded Betti numbers.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"41 - 51"},"PeriodicalIF":0.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969476","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 generating set for the Johnson kernel 约翰逊核的一个发电集
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-11 DOI: 10.1007/s00013-025-02190-2
Marco Boggi
{"title":"A generating set for the Johnson kernel","authors":"Marco Boggi","doi":"10.1007/s00013-025-02190-2","DOIUrl":"10.1007/s00013-025-02190-2","url":null,"abstract":"<div><p>For a connected orientable hyperbolic surface <i>S</i> without boundary and of finite topological type, the Johnson kernel <span>(mathcal {K}(S))</span> is the subgroup of the mapping class group of <i>S</i> generated by Dehn twists about separating simple closed curves on <i>S</i>. We prove that <span>(mathcal {K}(S))</span> is generated by the Dehn twists about separating simple closed curves on <i>S</i> bounding either: a closed subsurface of genus 1 or 2; a closed subsurface of genus 1 minus one point; a closed disc minus two points.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"13 - 20"},"PeriodicalIF":0.5,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969475","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书