Proceedings of the American Mathematical Society最新文献

{"title":"The growth recurrence and Gelfand-Kirillov base of the ordinary cusp","authors":"Alan Dills, Florian Enescu","doi":"10.1090/proc/16913","DOIUrl":"https://doi.org/10.1090/proc/16913","url":null,"abstract":"<p>We introduce the Gelfand-Kirillov base for a numerical semigroup ring over the prime field of characteristic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is prime, and show its existence for the semigroup ring of the ordinary cusp by establishing a growth recurrence with respect to Frobenius.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"84 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945112","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}

{"title":"Yosida distance and existence of invariant manifolds in the infinite-dimensional dynamical systems","authors":"Xuan-Quang Bui, Nguyen Van Minh","doi":"10.1090/proc/16912","DOIUrl":"https://doi.org/10.1090/proc/16912","url":null,"abstract":"&lt;p&gt;We consider the existence of invariant manifolds to evolution equations &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"u prime left-parenthesis t right-parenthesis equals upper A u left-parenthesis t right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo&gt;′&lt;/mml:mo&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;u’(t)=Au(t)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A colon upper D left-parenthesis upper A right-parenthesis subset-of double-struck upper X right-arrow double-struck upper X\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mo&gt;:&lt;/mml:mo&gt; &lt;mml:mi&gt;D&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;⊂&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;X&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;→&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;X&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;A:D(A)subset mathbb {X}to mathbb {X}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; near its equilibrium &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A left-parenthesis 0 right-parenthesis equals 0\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;A(0)=0&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; under the assumption that its proto-derivative &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"partial-differential upper A left-parenthesis x right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∂&lt;/mml:mi&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;partial A(x)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; exists and is continuous in &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x element-of upper D left-parenthesis upper A right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mi&gt;D&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;xin D(A)&lt;/mml:annota","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"42 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945110","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}

{"title":"Generalized Hilbert operators arising from Hausdorff matrices","authors":"C. Bellavita, N. Chalmoukis, V. Daskalogiannis, G. Stylogiannis","doi":"10.1090/proc/16917","DOIUrl":"https://doi.org/10.1090/proc/16917","url":null,"abstract":"&lt;p&gt;For a finite, positive Borel measure &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; on &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 0 comma 1 right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;(0,1)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; we consider an infinite matrix &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma Subscript mu\"&gt; &lt;mml:semantics&gt; &lt;mml:msub&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Γ&lt;/mml:mi&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Gamma _mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, related to the classical Hausdorff matrix defined by the same measure &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, in the same algebraic way that the Hilbert matrix is related to the Cesáro matrix. When &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; is the Lebesgue measure, &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma Subscript mu\"&gt; &lt;mml:semantics&gt; &lt;mml:msub&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Γ&lt;/mml:mi&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Gamma _mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; reduces to the classical Hilbert matrix. We prove that the matrices &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma Subscript mu\"&gt; &lt;mml:semantics&gt; &lt;mml:msub&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Γ&lt;/mml:mi&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Gamma _mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; are not Hankel, unless &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mu&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; is a constant multiple of the Lebesgue measure, we give necessary and sufficien","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"80 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197099","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}

{"title":"A short note on 𝜋₁(𝐷𝑖𝑓𝑓_{∂}𝐷^{4𝑘}) for 𝑘≥3","authors":"Wei Wang","doi":"10.1090/proc/16908","DOIUrl":"https://doi.org/10.1090/proc/16908","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D i f f Subscript partial-differential Baseline left-parenthesis upper D Superscript n Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>Diff</mml:mi> <mml:mrow> <mml:mi mathvariant=\"normal\">∂</mml:mi> </mml:mrow> </mml:msub> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">operatorname {Diff}_{partial }(D^{n})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the topological group of diffeomorphisms of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D Superscript n\"> <mml:semantics> <mml:msup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">D^{n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which agree with the identity near the boundary. In this short note, we compute the fundamental group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi 1 upper D i f f Subscript partial-differential Baseline left-parenthesis upper D Superscript 4 k Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>π</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:msub> <mml:mi>Diff</mml:mi> <mml:mrow> <mml:mi mathvariant=\"normal\">∂</mml:mi> </mml:mrow> </mml:msub> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">pi _1 operatorname {Diff}_{partial }(D^{4k})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">kgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"41 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880494","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}

{"title":"A variance-sensitive Gaussian concentration inequality","authors":"Nguyen Dung","doi":"10.1090/proc/16905","DOIUrl":"https://doi.org/10.1090/proc/16905","url":null,"abstract":"<p>In this note, we obtain a Gaussian concentration inequality for a class of non-Lipschitz functions. In the one-dimensional case, our results supplement those established by Paouris and Valettas [Ann. Probab. 46 (2018), pp. 1441–1454].</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744658","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}

{"title":"Almost complex torus manifolds - a problem of Petrie type","authors":"Donghoon Jang","doi":"10.1090/proc/16768","DOIUrl":"https://doi.org/10.1090/proc/16768","url":null,"abstract":"&lt;p&gt;The Petrie conjecture asserts that if a homotopy &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C double-struck upper P Superscript n\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;C&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {CP}^n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; admits a non-trivial circle action, its Pontryagin class agrees with that of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C double-struck upper P Superscript n\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;C&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {CP}^n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Petrie proved this conjecture in the case where the manifold admits a &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Superscript n\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;T^n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-action. An almost complex torus manifold is a &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2 n\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;2n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-dimensional compact connected almost complex manifold equipped with an effective &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Superscript n\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;T^n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-action that has fixed points. For an almost complex torus manifold, there exists a graph that encodes information about the weights at the fixed points. We prove that if a &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2 n\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;2n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-dimensional almost complex torus manifold &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;M&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"121 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059893","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}

{"title":"Elliptic equations with matrix weights and measurable nonlinearities on nonsmooth domains","authors":"Sun-Sig Byun, Yumi Cho, Ho-Sik Lee","doi":"10.1090/proc/16770","DOIUrl":"https://doi.org/10.1090/proc/16770","url":null,"abstract":"<p>We study general elliptic equations with singular/degenerate matrix weights and measurable nonlinearities on nonsmooth bounded domains to obtain a global Calderón-Zygmund type estimate under possibly minimal assumptions that the logarithm of the matrix weight has a small bounded mean oscillation (BMO) norm, the nonlinearity is allowed to be merely measurable in one variable but has a small BMO norm in the other variables and that the boundary of the domain is sufficiently flat in Reifenberg sense.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"23 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151832","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}

{"title":"On invariant generating sets for the cycle space","authors":"Ádám Timár","doi":"10.1090/proc/16910","DOIUrl":"https://doi.org/10.1090/proc/16910","url":null,"abstract":"<p>Consider a unimodular random graph, or just a finitely generated Cayley graph. When does its cycle space have an invariant random generating set of cycles such that every edge is contained in finitely many of the cycles? Generating the free Loop <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">O(1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> model as a factor of iid is closely connected to having such a generating set for FK-Ising cluster. We show that geodesic cycles do not always form such a generating set, by showing for a parameter regime of the FK-Ising model on the lamplighter group the origin is contained in infinitely many geodesic cycles. This answers a question by Angel, Ray and Spinka. Then we take a look at how the property of having an invariant locally finite generating set for the cycle space is preserved by Bernoulli percolation, and apply it to the problem of factor of iid presentations of the free Loop <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">O(1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> model.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"79 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197103","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}

{"title":"Nonradial solutions of a Neumann Hénon equation on a ball","authors":"Craig Cowan","doi":"10.1090/proc/16897","DOIUrl":"https://doi.org/10.1090/proc/16897","url":null,"abstract":"&lt;p&gt;In this work we examine the existence of positive classical solutions of &lt;disp-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartLayout Enlarged left-brace 1st Row 1st Column minus normal upper Delta u plus u equals StartAbsoluteValue x EndAbsoluteValue Superscript alpha Baseline u Superscript p minus 1 Baseline 2nd Column a m p semicolon in upper B 1 comma 2nd Row 1st Column u greater-than 0 2nd Column a m p semicolon in upper B 1 comma 3rd Row 1st Column partial-differential Subscript nu Baseline u equals 0 2nd Column a m p semicolon on partial-differential upper B 1 comma EndLayout\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;{&lt;/mml:mo&gt; &lt;mml:mtable columnalign=\"left left\" rowspacing=\".2em\" columnspacing=\"1em\" displaystyle=\"false\"&gt; &lt;mml:mtr&gt; &lt;mml:mtd&gt; &lt;mml:mo&gt;−&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Δ&lt;/mml:mi&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo&gt;+&lt;/mml:mo&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;α&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;−&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;/mml:mtd&gt; &lt;mml:mtd&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mi&gt;m&lt;/mml:mi&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:mtext&gt; in &lt;/mml:mtext&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;B&lt;/mml:mi&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;/mml:mtd&gt; &lt;/mml:mtr&gt; &lt;mml:mtr&gt; &lt;mml:mtd&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mtd&gt; &lt;mml:mtd&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mi&gt;m&lt;/mml:mi&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:mtext&gt; in &lt;/mml:mtext&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;B&lt;/mml:mi&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;/mml:mtd&gt; &lt;/mml:mtr&gt; &lt;mml:mtr&gt; &lt;mml:mtd&gt; &lt;mml:msub&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∂&lt;/mml:mi&gt; &lt;mml:mi&gt;ν&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mtd&gt; &lt;mml:mtd&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mi&gt;m&lt;/mml:mi&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:mtext&gt; on &lt;/mml:mtext&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∂&lt;/mml:mi&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;B&lt;/mml:mi&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;/mml:mtd&gt; &lt;/mml:mtr&gt; &lt;/mml:mtable&gt; &lt;mml:mo fence=\"true\" stretchy=\"true\" symmetric=\"true\"/&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;begin{equation*} begin {cases} -Delta u +u = |x|^alpha u^{p-1} &amp; text { in } B_1, u&gt;0 &amp; text { in } B_1, partial _nu u= 0 &amp; text { on } partial B_1, end{cases} end{equation*}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/disp-formula&gt; where &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 1\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;p&gt;1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xm","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"363 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872176","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}

{"title":"Improved regularity for a Hessian-dependent functional","authors":"Vincenzo Bianca, Edgard Pimentel, José Urbano","doi":"10.1090/proc/16894","DOIUrl":"https://doi.org/10.1090/proc/16894","url":null,"abstract":"<p>We prove that minimizers of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript d\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^{d}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-norm of the Hessian in the unit ball of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript d\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {R}^d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are locally of class <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript 1 comma alpha\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{1,alpha }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Hölder regularity theory available for elliptic equations in double-divergence form.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945111","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}