Transactions of the American Mathematical Society最新文献_第3页

Equivariant 3-manifolds with positive scalar curvature 具有正标量曲率的等变 3-漫游

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-04-03 DOI: 10.1090/tran/9181

Tsz-Kiu Aaron Chow, Yangyang Li

{"title":"Equivariant 3-manifolds with positive scalar curvature","authors":"Tsz-Kiu Aaron Chow, Yangyang Li","doi":"10.1090/tran/9181","DOIUrl":"https://doi.org/10.1090/tran/9181","url":null,"abstract":"In this paper, for any compact Lie group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we show that the space of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-equivariant Riemannian metrics with positive scalar curvature (PSC) on any closed three-manifold is either empty or contractible. In particular, we prove the generalized Smale conjecture for spherical three-orbifolds. Moreover, for connected <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we make a classification of all PSC <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-equivariant three-manifolds.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"20 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

𝐾𝐾-duality for self-similar groupoid actions on graphs 图上自相似群元作用的 "徘徊 "对偶性

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-04-03 DOI: 10.1090/tran/9183

Nathan Brownlowe, Alcides Buss, Daniel Gonçalves, Jeremy Hume, Aidan Sims, Michael Whittaker

{"title":"𝐾𝐾-duality for self-similar groupoid actions on graphs","authors":"Nathan Brownlowe, Alcides Buss, Daniel Gonçalves, Jeremy Hume, Aidan Sims, Michael Whittaker","doi":"10.1090/tran/9183","DOIUrl":"https://doi.org/10.1090/tran/9183","url":null,"abstract":"We extend Nekrashevych’s <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K upper K\"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">KK</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-duality for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a graph, removing the recurrence condition entirely and generalising from a finite alphabet to a finite graph. More precisely, given a regular and contracting self-similar groupoid <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper G comma upper E right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(G,E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acting faithfully on a finite directed graph <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=\"application/x-tex\">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we associate two <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebras, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper O left-parenthesis upper G comma upper E right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"script\">O</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {O}(G,E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"ModifyingAbove script upper O With caret left-parenthesis upper G comma upper E right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi mathvariant=\"script\">O</mml:mi> </mml:mrow> <mml:m","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"17 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Identification of Genetic Variants in Exon 4 of TP53 in Lung Carcinoma and in Silico Prediction of Their Significance. 肺癌 TP53 第 4 外显子基因变异的鉴定及其重要性的硅预测

IF 2.1 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-04-01 Epub Date: 2022-12-08 DOI: 10.1007/s12291-022-01099-9

Rajendra Prasad, Kirti Sharma, Karanpreet Bhutani, Suvarna Prasad, Sunita Manhas, Jai Kishan

{"title":"Identification of Genetic Variants in Exon 4 of TP53 in Lung Carcinoma and in Silico Prediction of Their Significance.","authors":"Rajendra Prasad, Kirti Sharma, Karanpreet Bhutani, Suvarna Prasad, Sunita Manhas, Jai Kishan","doi":"10.1007/s12291-022-01099-9","DOIUrl":"10.1007/s12291-022-01099-9","url":null,"abstract":"Lung cancer is a severe and the leading cause of cancer related deaths in men and women all over the world. Tumor suppressor protein (TP53) encoded by the TP53 gene which plays a pivotal role in various cellular tumor suppression processes viz cell cycle arrest and apoptosis. Henceforth, the present study was aimed to TP53 exon4 variants from lung carcinoma. Histopathologic and clinically proven 20 patients of lung cancer were enrolled in this study the average age of patients was 45 ± 8 years which categorized as early onset of lung cancer. Genomic DNA was isolated from the blood specimen of patients. Extracted DNA was subjected to PCR amplification for exon 4 of TP53 using appropriate primers and subsequently amplified products were applied to nucleotide alterations via using the DNA sanger sequencing. The genetic analysis documented five variants in exon4 of TP53 which include viz. 4 substitutions [c.215 > C at codon 72, C. 358-359AA > GG at codon 120] were highly prevalent, occurring in 63% and 25% frequency in patients. Other two variants viz. C. 358 A > C at codon 120, C. 365T > G at codon 122 were present at frequency of 15% whilst one deletion variant [152 del C] was found with 5% frequency. Furthermore, alterations on codon 72, 120,122 and 51 were characterized as possibly damaging by Poly Phen-2 and decreased stability using stability bioinformatic tool. Taken together all these findings infer that TP53 gene involved in modulation and susceptibility to lung cancer.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"91 1","pages":"276-282"},"PeriodicalIF":2.1,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10987423/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82685530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Sharp weighted log-Sobolev inequalities: Characterization of equality cases and applications 尖锐加权对数-索博列夫不等式：平等情况的特征及应用

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9163

Zoltán Balogh, Sebastiano Don, Alexandru Kristály

{"title":"Sharp weighted log-Sobolev inequalities: Characterization of equality cases and applications","authors":"Zoltán Balogh, Sebastiano Don, Alexandru Kristály","doi":"10.1090/tran/9163","DOIUrl":"https://doi.org/10.1090/tran/9163","url":null,"abstract":"By using optimal mass transport theory, we provide a direct proof to the sharp <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-log-Sobolev inequality <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis p greater-than-or-equal-to 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(pgeq 1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> involving a log-concave homogeneous weight on an open convex cone <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E subset-of-or-equal-to double-struck upper R Superscript n\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>⊆</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Esubseteq mathbb R^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The perk of this proof is that it allows to characterize the extremal functions realizing the equality cases in the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-log-Sobolev inequality. The characterization of the equality cases is new for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than-or-equal-to n\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≥</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">pgeq n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> even in the unweighted setting and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E equals double-struck upper R Superscript n\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">E=mathbb R^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. As an application, we provide a sharp weighted hypercontractivity estimate for the Hopf-Lax semigroup related to the Hamilton-Jacobi equation, characterizing also t","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Symmetric function generalizations of the 𝑞-Baker–Forrester ex-conjecture and Selberg-type integrals △-贝克-福雷斯特前猜想的对称函数广义和塞尔伯格型积分

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9142

Guoce Xin, Yue Zhou

{"title":"Symmetric function generalizations of the 𝑞-Baker–Forrester ex-conjecture and Selberg-type integrals","authors":"Guoce Xin, Yue Zhou","doi":"10.1090/tran/9142","DOIUrl":"https://doi.org/10.1090/tran/9142","url":null,"abstract":"It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Morris constant term identity[J. Combin. Theory Ser. A 81 (1998), pp. 69–87]. This conjecture was proved and extended by Károlyi, Nagy, Petrov, and Volkov (KNPV) in 2015 [Adv. Math. 277 (2015), pp. 252–282]. In this paper, we obtain two symmetric function generalizations of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Baker–Forrester ex-conjecture. These include: (i) a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Baker–Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV’s result.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"43 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces 度量空间中梯度流和近点序列全局收敛的局部条件

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9156

Lorenzo Dello Schiavo, Jan Maas, Francesco Pedrotti

{"title":"Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces","authors":"Lorenzo Dello Schiavo, Jan Maas, Francesco Pedrotti","doi":"10.1090/tran/9156","DOIUrl":"https://doi.org/10.1090/tran/9156","url":null,"abstract":"This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript n\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {R}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript n\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {R}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"23 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Dichotomy results for eventually always hitting time statistics and almost sure growth of extremes 最终总是命中时间统计和几乎肯定的极端增长的二分法结果

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9102

Mark Holland, Maxim Kirsebom, Philipp Kunde, Tomas Persson

{"title":"Dichotomy results for eventually always hitting time statistics and almost sure growth of extremes","authors":"Mark Holland, Maxim Kirsebom, Philipp Kunde, Tomas Persson","doi":"10.1090/tran/9102","DOIUrl":"https://doi.org/10.1090/tran/9102","url":null,"abstract":"Suppose <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis f comma script upper X comma mu right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">X</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(f,mathcal {X},mu )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a measure preserving dynamical system and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi colon script upper X right-arrow double-struck upper R\"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>:</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">X</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">→</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">phi colon mathcal {X}to mathbb {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a measurable function. Consider the maximum process <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M Subscript n Baseline colon-equal max left-brace right-brace comma comma upper X 1 comma ellipsis comma Xn\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>≔</mml:mo> <mml:mo movablelimits=\"true\" form=\"prefix\">max</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">M_n≔max {X_1,ldots ,X_n}</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=\"upper X Subscript i Baseline equals phi ring f Superscript i minus 1\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>∘</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">X_i=phi circ f^{i-1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a time series of observations on the system. Suppose that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis u Subscript n Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\"","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 complex case of Vojta’s general abc conjecture and cases of Campana’s orbifold conjecture 沃伊塔一般abc猜想的复杂情况和坎帕纳球面猜想的情况

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9175

Ji Guo, Julie Wang

{"title":"A complex case of Vojta’s general abc conjecture and cases of Campana’s orbifold conjecture","authors":"Ji Guo, Julie Wang","doi":"10.1090/tran/9175","DOIUrl":"https://doi.org/10.1090/tran/9175","url":null,"abstract":"We show a truncated second main theorem of level one with explicit exceptional sets for analytic maps into <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb P^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> intersecting the coordinate lines with sufficiently high multiplicities. The proof is based on a greatest common divisor theorem for an analytic map <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon double-struck upper C right-arrow from bar double-struck upper P Superscript n\"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">C</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">↦</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">f:mathbb Cmapsto mathbb P^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and two homogeneous polynomials in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n plus 1\"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">n+1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> variables with coefficients which are meromorphic functions of the same growth as the analytic map <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. As applications, we study some cases of Campana’s orbifold conjecture for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb P^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and finite ramified covers of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb P^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with three components admitting sufficiently large multiplicities. In addition, we explicitly determine the exc","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"156 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Lie groups with all left-invariant semi-Riemannian metrics complete 具有所有左不变半黎曼度量的完整李群

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9160

Ahmed Elshafei, Ana Cristina Ferreira, Miguel Sánchez, Abdelghani Zeghib

{"title":"Lie groups with all left-invariant semi-Riemannian metrics complete","authors":"Ahmed Elshafei, Ana Cristina Ferreira, Miguel Sánchez, Abdelghani Zeghib","doi":"10.1090/tran/9160","DOIUrl":"https://doi.org/10.1090/tran/9160","url":null,"abstract":"For each left-invariant semi-Riemannian metric <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a Lie group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we introduce the class of bi-Lipschitz Riemannian <italic>Clairaut</italic> metrics, whose completeness implies the completeness of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. When the adjoint representation of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfies an at most linear growth bound, then all the Clairaut metrics are complete for any <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We prove that this bound is satisfied by compact and 2-step nilpotent groups, as well as by semidirect products <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K left-normal-factor-semidirect-product Subscript rho Baseline double-struck upper R Superscript n\"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:msub> <mml:mo>⋉</mml:mo> <mml:mi>ρ</mml:mi> </mml:msub> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">K ltimes _rho mathbb {R}^n</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=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the direct product of a compact and an abelian Lie group and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho left-parenthesis upper K right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation en","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Global dynamics above the ground state energy for the energy-critical Klein-Gordon equation 能量临界克莱因-戈登方程基态能量以上的全局动力学

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI: 10.1090/tran/9158

Tristan Roy

{"title":"Global dynamics above the ground state energy for the energy-critical Klein-Gordon equation","authors":"Tristan Roy","doi":"10.1090/tran/9158","DOIUrl":"https://doi.org/10.1090/tran/9158","url":null,"abstract":"Consider the focusing energy-critical Klein-Gordon equation in dimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d element-of StartSet 3 comma 4 comma 5 EndSet\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>∈</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d in { 3,4,5 }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartLayout Enlarged left-brace 1st Row 1st Column partial-differential Subscript t t Baseline u minus normal upper Delta u plus u 2nd Column a m p semicolon equals StartAbsoluteValue u EndAbsoluteValue Superscript StartFraction 4 Over d minus 2 EndFraction Baseline u comma 2nd Row 1st Column u left-parenthesis 0 comma x right-parenthesis 2nd Column a m p semicolon colon-equal f 0 left-parenthesis x right-parenthesis comma 3rd Row 1st Column partial-differential Subscript t Baseline u left-parenthesis 0 comma x right-parenthesis 2nd Column a m p semicolon colon-equal f 1 left-parenthesis x right-parenthesis EndLayout\"> <mml:semantics> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtable columnalign=\"left left\" rowspacing=\".2em\" columnspacing=\"1em\" displaystyle=\"false\"> <mml:mtr> <mml:mtd> <mml:msub> <mml:mi mathvariant=\"normal\">∂</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> <mml:mi>u</mml:mi> <mml:mo>−</mml:mo> <mml:mi mathvariant=\"normal\">Δ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>u</mml:mi> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mfrac> <mml:mn>4</mml:mn> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mo>≔</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:msub> <mml:mi mathvariant=\"normal\">∂</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>x</m","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"296 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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