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Local gradient estimates for a type of fully nonlinear equations 一类全非线性方程的局部梯度估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-17 DOI: 10.1007/s00013-024-01992-0
Wei Wei
{"title":"Local gradient estimates for a type of fully nonlinear equations","authors":"Wei Wei","doi":"10.1007/s00013-024-01992-0","DOIUrl":"10.1007/s00013-024-01992-0","url":null,"abstract":"<div><p>Assuming that the solution is bounded from one-side, by Bernstein-type arguments, on <span>((M^{2},g),)</span> we prove the local gradient estimates for a type of fully nonlinear equation from conformal geometry.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140615148","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
Vanishing of Ext modules over algebras 代数上 Ext 模块的消失
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-13 DOI: 10.1007/s00013-024-01981-3
Ali Mahin Fallah
{"title":"Vanishing of Ext modules over algebras","authors":"Ali Mahin Fallah","doi":"10.1007/s00013-024-01981-3","DOIUrl":"10.1007/s00013-024-01981-3","url":null,"abstract":"<div><p>Recently, Kimura, Otake, and Takahashi proved a theorem about the vanishing of Ext of finitely generated modules over Cohen–Macaulay rings. The aim of this paper is to obtain extensions of their result over algebras.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561304","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
Operator mean inequalities and Kwong functions 算子均值不等式和邝函数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-12 DOI: 10.1007/s00013-024-01980-4
Nahid Gharakhanlu, Mohammad Sal Moslehian, Hamed Najafi
{"title":"Operator mean inequalities and Kwong functions","authors":"Nahid Gharakhanlu,&nbsp;Mohammad Sal Moslehian,&nbsp;Hamed Najafi","doi":"10.1007/s00013-024-01980-4","DOIUrl":"10.1007/s00013-024-01980-4","url":null,"abstract":"<div><p>In this paper, we study operator mean inequalities for the weighted arithmetic, geometric, and harmonic means. We give a slight modification of Audenaert’s result to show the relation between Kwong functions and operator monotone functions. Operator mean inequalities provide some analogs of the geometric concavity property for Kwong functions, operator convex, and operator monotone functions. Moreover, we give our points across by way of some examples which show the usage of our main results.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561177","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 real analytic functions on closed subanalytic domains 关于闭合子解析域上的实解析函数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-12 DOI: 10.1007/s00013-024-01983-1
Armin Rainer
{"title":"On real analytic functions on closed subanalytic domains","authors":"Armin Rainer","doi":"10.1007/s00013-024-01983-1","DOIUrl":"10.1007/s00013-024-01983-1","url":null,"abstract":"<div><p>We show that a function <span>(f: X rightarrow {mathbb {R}})</span> defined on a closed uniformly polynomially cuspidal set <i>X</i> in <span>({mathbb {R}}^n)</span> is real analytic if and only if <i>f</i> is smooth and all its composites with germs of polynomial curves in <i>X</i> are real analytic. The degree of the polynomial curves needed for this is effectively related to the regularity of the boundary of <i>X</i>. For instance, if the boundary of <i>X</i> is locally Lipschitz, then polynomial curves of degree 2 suffice. In this Lipschitz case, we also prove that a function <span>(f: X rightarrow {mathbb {R}})</span> is real analytic if and only if all its composites with germs of quadratic polynomial maps in two variables with images in <i>X</i> are real analytic; here it is not necessary to assume that <i>f</i> is smooth.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01983-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561303","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
Minimal periods for semilinear parabolic equations 半线性抛物方程的最小周期
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-12 DOI: 10.1007/s00013-024-01970-6
Gerd Herzog, Peer Christian Kunstmann
{"title":"Minimal periods for semilinear parabolic equations","authors":"Gerd Herzog,&nbsp;Peer Christian Kunstmann","doi":"10.1007/s00013-024-01970-6","DOIUrl":"10.1007/s00013-024-01970-6","url":null,"abstract":"<div><p>We show that, if <span>(-A)</span> generates a bounded holomorphic semigroup in a Banach space <i>X</i>, <span>(alpha in [0,1))</span>, and <span>(f:D(A)rightarrow X)</span> satisfies <span>(Vert f(x)-f(y)Vert le LVert A^alpha (x-y)Vert )</span>, then a non-constant <i>T</i>-periodic solution of the equation <span>({dot{u}}+Au=f(u))</span> satisfies <span>(LT^{1-alpha }ge K_alpha )</span> where <span>(K_alpha &gt;0)</span> is a constant depending on <span>(alpha )</span> and the semigroup. This extends results by Robinson and Vidal-Lopez, which have been shown for self-adjoint operators <span>(Age 0)</span> in a Hilbert space. For the latter case, we obtain - with a conceptually new proof - the optimal constant <span>(K_alpha )</span>, which only depends on <span>(alpha )</span>, and we also include the case <span>(alpha =1)</span>. In Hilbert spaces <i>H</i> and for <span>(alpha =0)</span>, we present a similar result with optimal constant where <i>Au</i> in the equation is replaced by a possibly unbounded gradient term <span>(nabla _H{mathscr {E}}(u))</span>. This is inspired by applications with bounded gradient terms in a paper by Mawhin and Walter.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01970-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561398","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
Cohen-Macaulay weighted oriented chordal and simplicial graphs 科恩-麦考莱加权定向弦图和单纯图
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-10 DOI: 10.1007/s00013-024-01990-2
Kamalesh Saha
{"title":"Cohen-Macaulay weighted oriented chordal and simplicial graphs","authors":"Kamalesh Saha","doi":"10.1007/s00013-024-01990-2","DOIUrl":"10.1007/s00013-024-01990-2","url":null,"abstract":"<div><p>Herzog, Hibi, and Zheng classified the Cohen-Macaulay edge ideals of chordal graphs. In this paper, we classify Cohen-Macaulay edge ideals of (vertex) weighted oriented chordal and simplicial graphs, a more general class of monomial ideals. In particular, we show that the Cohen-Macaulay property of these ideals is equivalent to the unmixed one and hence, independent of the underlying field.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561176","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
Full k-simplicity of Steinberg algebras over Clifford semifields with application to Leavitt path algebras 克利福德半场上的斯坦伯格代数的全 k-简约性及其在 Leavitt 路径代数中的应用
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-09 DOI: 10.1007/s00013-024-01975-1
Promit Mukherjee, Sujit Kumar Sardar
{"title":"Full k-simplicity of Steinberg algebras over Clifford semifields with application to Leavitt path algebras","authors":"Promit Mukherjee,&nbsp;Sujit Kumar Sardar","doi":"10.1007/s00013-024-01975-1","DOIUrl":"10.1007/s00013-024-01975-1","url":null,"abstract":"<div><p>As a continuation of the study of the Steinberg algebra of a Hausdorff ample groupoid <span>({mathcal {G}})</span> over commutative semirings by Nam et al. (J. Pure Appl. Algebra 225, 2021), we consider here the Steinberg algebra <span>(A_S({mathcal {G}}))</span> with coefficients in a Clifford semifield <i>S</i>. We obtain a complete characterization of the full <i>k</i>-ideal simplicity of <span>(A_S({mathcal {G}}))</span>. Using this result for the Steinberg algebra <span>(A_S({mathcal {G}}_Gamma ))</span> of the graph groupoid <span>({mathcal {G}}_Gamma )</span>, where <span>(Gamma )</span> is a row-finite digraph and <i>S</i> is a Clifford semifield, we characterize the full <i>k</i>-simplicity of the Leavitt path algebra <span>(L_S(Gamma ))</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561087","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
Fubini’s theorem for Daniell integrals 达尼尔积分的富比尼定理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-09 DOI: 10.1007/s00013-024-01988-w
Götz Kersting, Gerhard Rompf
{"title":"Fubini’s theorem for Daniell integrals","authors":"Götz Kersting,&nbsp;Gerhard Rompf","doi":"10.1007/s00013-024-01988-w","DOIUrl":"10.1007/s00013-024-01988-w","url":null,"abstract":"<div><p>We show that in the theory of Daniell integration iterated integrals may always be formed, and the order of integration may always be interchanged. By this means, we discuss product integrals and show that the related Fubini theorem holds in full generality. The results build on a density theorem on Riesz tensor products due to Fremlin, and on the Fubini–Stone theorem.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01988-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561088","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 field of moduli of sets of points in (mathbb {P}^{2}) $$mathbb {P}^{2}$ 中点集合的模域
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-09 DOI: 10.1007/s00013-024-01984-0
Giulio Bresciani
{"title":"The field of moduli of sets of points in (mathbb {P}^{2})","authors":"Giulio Bresciani","doi":"10.1007/s00013-024-01984-0","DOIUrl":"10.1007/s00013-024-01984-0","url":null,"abstract":"<div><p>For every <span>(nge 6)</span>, we give an example of a finite subset of <span>(mathbb {P}^{2})</span> of degree <i>n</i> which does not descend to any Brauer–Severi surface over the field of moduli. Conversely, for every <span>(nle 5)</span>, we prove that a finite subset of degree <i>n</i> always descends to a 0-cycle on <span>(mathbb {P}^{2})</span> over the field of moduli.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01984-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561171","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
A remark on toric foliations 关于环状叶子的评论
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-04-09 DOI: 10.1007/s00013-024-01991-1
Osamu Fujino, Hiroshi Sato
{"title":"A remark on toric foliations","authors":"Osamu Fujino,&nbsp;Hiroshi Sato","doi":"10.1007/s00013-024-01991-1","DOIUrl":"10.1007/s00013-024-01991-1","url":null,"abstract":"<div><p>If a toric foliation on a projective <span>({mathbb {Q}})</span>-factorial toric variety has an extremal ray whose length is longer than the rank of the foliation, then the associated extremal contraction is a projective space bundle and the foliation is the relative tangent sheaf of the extremal contraction.\u0000</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561307","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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