Annals of Mathematics最新文献

英文中文

On Zagier-Hoffman's conjectures in positive characteristic 论Zagier-Hoffman的积极特征猜想

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2022-05-15 DOI: 10.4007/annals.2021.194.1.6

Bo-Hae Im, Hojin Kim, Khac Nhuan Le, Tuan Ngo Dac, Lan Huong Pham

We study Todd-Thakur's analogues of Zagier-Hoffman's conjectures in positive characteristic. These conjectures predict the dimension and an explicit basis Tw of the span of characteristic p multiple zeta values of fixed weight w which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In the present paper we first establish the algebraic part of these conjectures which states that the span of characteristic p multiple zeta values of weight w is generated by the set Tw. As a consequence, we obtain upper bounds for the dimension. This is the analogue of Brown's theorem and also those of Deligne-Goncharov and Terasoma. We then prove two results towards the transcendental part of these conjectures. First, we establish the linear independence for a large subset of Tw and yield lower bounds for the dimension. Second, for small weights we prove the linear independence for the whole set Tw and completely solve Zagier-Hoffman's conjectures in positive characteristic. Our key tool is the Anderson-Brownawell-Papanikolas criterion for linear independence in positive characteristic.

我们研究了Todd-Thakur在积极特征方面对Zagier-Hoffman猜想的类比。这些猜想预测了由Thakur作为经典欧拉多重zeta值的类似物引入的固定权重w的特征p多个zeta值的跨度的维数和显式基Tw。本文首先建立了这些猜想的代数部分，证明了权值w的特征p多个ζ值的张成空间是由集合Tw生成的。因此，我们得到了维数的上界。这是布朗定理的类似物，也是德莱尼-冈查罗夫和特拉索马的类似物。然后我们对这些猜想的超越部分证明了两个结果。首先，我们建立了Tw的一个大子集的线性无关性，并给出了维度的下界。其次，在小权重的情况下，证明了整个集合Tw的线性无关性，完全解决了正特征的Zagier-Hoffman猜想。我们的关键工具是正特征线性无关的anderson - brownwell - papanikolas准则。

引用次数: 7

A multicenter, open-label, single-arm phase I trial of neoadjuvant nivolumab monotherapy for resectable gastric cancer. 一项针对可切除胃癌的新辅助尼妥珠单抗单药治疗的多中心、开放标签、单臂 I 期试验。

IF 6 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2022-05-01 Epub Date: 2022-03-07 DOI: 10.1007/s10120-022-01286-w

Hirotaka Hasegawa, Kohei Shitara, Shuji Takiguchi, Noriaki Takiguchi, Seiji Ito, Mitsugu Kochi, Hidehito Horinouchi, Takahiro Kinoshita, Takaki Yoshikawa, Kei Muro, Hiroyoshi Nishikawa, Hideaki Suna, Yasuhiro Kodera

Background: Nivolumab monotherapy has demonstrated superior efficacy in advanced unresectable gastric cancer (GC), but its impact on resectable GC remains unknown. This phase I study aimed to evaluate safety, feasibility, and potential biomarkers of neoadjuvant nivolumab monotherapy in resectable GC.

Methods: Untreated, resectable, cT2 or more advanced gastric adenocarcinomas with clinical stage I, II, or III were treated with two doses of nivolumab before gastrectomy. Patients were excluded if their tumors may be applicable to neoadjuvant chemotherapy. The primary endpoint was the incidence of adverse event (AE) categories of special interest.

Results: All of the 31 enrolled patients completed 2 doses of nivolumab monotherapy. While 30 (97%) patients underwent surgery with curative intent, 1 patient discontinued before the planned surgical intervention because of a newly emerging liver metastasis. Seven patients (23%) had nivolumab treatment-related AEs, and one patient had a treatment-related AE of grade 3-4. The incidences of treatment-related AE categories of special interest ranged from 0 to 6%. Notable surgical complications included two cases of grade 3 anastomotic leakage and two cases of pancreatic fistula. The major pathologic response (MPR) assessed by the independent pathology review committee was achieved in five (16%) patients, of which one patient had a pathologic complete response. The MPR was mostly observed in patients with positive PD-L1 expression, high microsatellite instability, and/or high tumor mutation burden.

Conclusions: Neoadjuvant nivolumab monotherapy is feasible with an acceptable safety profile and induces a MPR in certain patients with resectable GC. (Registration: clinicaltrials.jp, JapicCTI-183895).

背景：尼妥珠单抗单药已在晚期不可切除胃癌（GC）中显示出卓越疗效，但其对可切除胃癌的影响仍然未知。这项 I 期研究旨在评估新辅助 nivolumab 单药治疗可切除 GC 的安全性、可行性和潜在生物标志物：临床分期为I、II或III期的未治疗、可切除、cT2或更晚期胃腺癌患者在胃切除术前接受两种剂量的nivolumab治疗。如果患者的肿瘤可能适用于新辅助化疗，则排除在外。主要终点是特别关注的不良事件（AE）发生率：所有31名入组患者均完成了2次nivolumab单药治疗。30名患者（97%）接受了治愈性手术，但有1名患者因新出现肝转移灶而在计划的手术干预前中止了治疗。7名患者（23%）出现了与nivolumab治疗相关的AE，1名患者出现了3-4级治疗相关AE。特别关注的治疗相关AE类别的发生率从0%到6%不等。值得注意的手术并发症包括两例3级吻合口漏和两例胰瘘。5例（16%）患者获得了独立病理审查委员会评估的主要病理反应（MPR），其中1例患者获得了病理完全反应。主要病理反应主要出现在PD-L1表达阳性、微卫星不稳定性高和/或肿瘤突变负荷高的患者中：结论：新辅助nivolumab单药治疗是可行的，安全性可接受，并能诱导某些可切除GC患者出现MPR。(注册：clinicaltrials.jp，JapicCTI-183895）。

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引用次数: 0

Prevalence of Certain Urogenital Bacterial Mollicutes in Patients Suffering from Infertility. 不孕症患者中某些泌尿生殖道细菌的流行率。

1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2022-03-22 eCollection Date: 2022-01-01 DOI: 10.1155/2022/2812788

Motasem Y Al-Masri, Intesar Khaleel Ashour, Ashraf Swafta, Sami Al-Shunar

Introduction: Mollicutes urogenital tract infections are considered a possible cause of infertility worldwide. Genital Mollicutes infections are difficult and impractical to diagnose by culturing or serology. Mollicutes included in this study were Mycoplasma hominis, Ureaplasma urealyticum, and Mycoplasma genitalium. This cross-sectional study aimed to determine the prevalence of M. hominis, U. urealyticum, and M. genitalium genital infections among infertile males and females patients.

Methods: This study included 103 patients who visited Al-Shunar Clinic in Nablus city in Palestine and diagnosed with infertility during January 2018 to October 2018. The semen, urine, and/or vaginal swab specimens collected from patients were examined by PCR for detection of M. hominis, U. urealyticum, and M. genitalium.

Results: A total of 57 semen, 37 urine, and 16 vaginal swab specimens were collected. Out of the 110 examined specimens, 35 (31.8%) were PCR positive for at least one Mollicutes, which were 16 (14.6%) M. hominis, 11 (10%) U. urealyticum, and 8 (7.3%) M. genitalium. Significant association were found between infections of M. hominis and U. urealyticum (P=0.044) and between M. hominis and M. genitalium (P=0.005) infections. M. hominis infection was found in significantly (P=0.048) higher percentage in males (20.6%) in comparison with females (5.7%). On the other hand, M. genitalium infection rate in females (8.6%) was slightly higher than males (7.4%). M. hominis was more prevalent in all age groups except for patient's age group 40-50 years old, where M. genitalium was more prevalent. M. hominis was also more prevalent in all occupation types and among all smokers.

Conclusion: Urogenital infections caused by M. hominis, M. genitalium, and U. urealyticum could be a possible cause of infertility among patients with different age groups, genders, and occupations. Thus, more attention by infertility centers and physicians is required in adopting molecular methods for diagnosis of infections by these microorganisms.

导言：泌尿生殖道毛霉菌感染被认为是全球不孕不育的可能原因之一。通过培养或血清学诊断生殖器莫来菌感染既困难又不切实际。本研究中的支原体包括人型支原体、尿解支原体和生殖器支原体。这项横断面研究旨在确定不育男性和女性患者中人型支原体、解脲支原体和生殖器支原体生殖器感染的发病率：本研究纳入了 2018 年 1 月至 2018 年 10 月期间在巴勒斯坦纳布卢斯市 Al-Shunar 诊所就诊并被诊断为不孕症的 103 名患者。采集患者的精液、尿液和/或阴道拭子标本，通过 PCR 检测人乳酵母菌、尿酵母菌和生殖器酵母菌：结果：共采集了 57 份精液标本、37 份尿液标本和 16 份阴道拭子标本。在 110 份受检标本中，35 份（31.8%）标本中至少有一种毛霉菌的 PCR 呈阳性，其中 16 份（14.6%）为人乳头状瘤菌，11 份（10%）为尿道脲原体，8 份（7.3%）为生殖器畸形芽孢杆菌。在人疟原虫和尿毒症脲原体感染（P=0.044）以及人疟原虫和生殖器疟原虫感染（P=0.005）之间发现了显著的关联。与女性（5.7%）相比，男性（20.6%）感染人疟原虫的比例明显更高（P=0.048）。另一方面，女性的生殖器疟原虫感染率（8.6%）略高于男性（7.4%）。除 40-50 岁年龄组的患者生殖器疟原虫感染率较高外，其他年龄组的人疟原虫感染率均较高。人疟原虫在所有职业类型和所有吸烟者中的发病率也较高：结论：在不同年龄段、性别和职业的患者中，由人乳头瘤病毒、生殖器畸形病毒和尿道畸形病毒引起的泌尿生殖系统感染可能是导致不孕不育的原因之一。因此，不孕不育中心和医生需要更加重视采用分子方法来诊断这些微生物的感染。

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引用次数: 0

Affine Beilinson-Bernstein localization at the critical level for $mathrm{GL}_2$ $mathrm临界水平上的Affine-Beilinson-Bernstein局部化{GL}_2$

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2022-01-01 DOI: 10.4007/annals.2022.195.1.4

David H Yang, S. Raskin

. We prove the Frenkel-Gaitsgory localization conjecture describing regular Kac-Moody representations at critical level via eigensheaves on the aﬃne Grassmannian using categorical Moy-Prasad theory. This extends previous work of the authors.

．我们利用范畴Moy-Prasad理论证明了在仿射Grassmannian上通过特征轴在临界水平上描述正则Kac-Moody表示的Frenkel-Gaitsgory局部化猜想。这扩展了作者以前的工作。

引用次数: 2

Erratum: A corrected proof of the scale recurrence lemma from the paper ``Stable intersections of regular Cantor sets with large Hausdorff dimensions" 对“具有大Hausdorff维数的正则Cantor集的稳定交”一文中尺度递归引理的更正证明

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2022-01-01 DOI: 10.4007/annals.2022.195.1.6

C. Moreira, A. Zamudio

引用次数: 0

Erratum: Euclidean triangles have no hot spots | Annals of Mathematics 校误:欧几里得三角形没有热点|数学年鉴

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2022-01-01 DOI: 10.4007/annals.2022.195.1.5

Chris Judge, Sugata Mondal

Original article: https://doi.org/10.4007/annals.2020.191.1.3

原创文章:https://doi.org/10.4007/annals.2020.191.1.3

引用次数: 0

Non-uniqueness of Leray solutions of the forced Navier-Stokes equations 强迫Navier-Stokes方程Leray解的非唯一性

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2021-12-06 DOI: 10.4007/annals.2022.196.1.3

D. Albritton, Elia Bru'e, Maria Colombo

In the seminal work [39], Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. We exhibit two distinct Leray solutions with zero initial velocity and identical body force. Our approach is to construct a `background' solution which is unstable for the Navier-Stokes dynamics in similarity variables; its similarity profile is a smooth, compactly supported vortex ring whose cross-section is a modification of the unstable two-dimensional vortex constructed by Vishik in [43,44]. The second solution is a trajectory on the unstable manifold associated to the background solution, in accordance with the predictions of Jia and v{S}ver'ak in [32,33]. Our solutions live precisely on the borderline of the known well-posedness theory.

在开创性的工作[39]中，Leray证明了三维Navier-Stokes方程的全局弱解的存在性。我们展示了两个不同的Leray解，初始速度为零，物体力相同。我们的方法是构造一个“背景”解，该解对于相似变量中的Navier-Stokes动力学是不稳定的；它的相似轮廓是一个光滑、紧支撑的涡环，其横截面是Vishik在[43，44]中构建的不稳定二维涡的修改。根据Jia和v的预测，第二个解是与背景解相关的不稳定流形上的轨迹{S}ver'ak在[32，33]中。我们的解决方案正是在已知的适定性理论的边界上。

引用次数: 58

Improved bounds for the sunflower lemma | Annals of Mathematics 向日葵引理的改进界|数学年鉴

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2021-11-02 DOI: 10.4007/annals.2021.194.3.5

Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang

A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all of them. Erdős and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower with $r$ petals. The famous sunflower conjecture states that the bound on the number of sets can be improved to $c^w$ for some constant $c$. In this paper, we improve the bound to about $(log, w)^w$. In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is sharp up to lower order terms.

一朵有$r$花瓣的向日葵是$r$组花瓣的集合，因此每一对花瓣的交点等于所有花瓣的交点。Erdős和Rado证明了向日葵引理:对于任何固定的$r$，任何大小为$w$的集合族，至少有$w^w$的集合，必须包含有$r$花瓣的向日葵。著名的向日葵猜想指出，对于某个常数c，集合数的界可以改进为c^w。在本文中，我们改进了这个界约$(log， w)^w$。事实上，我们证明了一个鲁棒的向日葵概念的结果，对于这个概念，我们得到的界在低阶项上是尖锐的。

引用次数: 0

80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group" 维格纳教授80年的开创性著作《论非齐次洛伦兹群的酉表示》

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2021-11-01 DOI: 10.2307/1968551

E. Wigner

It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ,Φ) of two normalized wave functions ψ and Φ is called the transition probability from the state ψ into Φ, or conversely. This is supposed to give the probability that an experiment performed on a system in the state Φ, to see whether or not the state is ψ, gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.

这可能是量子力学最基本的原理，状态系统形成一个线性流形，其中定义了一个酉标量积这些状态通常用波函数表示，即φ和φ的常数倍表示相同的物理状态。因此，将波函数归一化是可能的，也就是说，将它乘以一个常数因子，使它与自身的标量积变为1。然后，波函数中只有一个常数系数1，即所谓的相位，是不确定的。波函数的线性特性称为叠加原理。两个归一化波函数ψ和Φ的幺正标量积(ψ，Φ)的模的平方称为从态ψ到Φ的跃迁概率，或者反过来说。这个假设给出了在状态Φ的系统上进行的实验的概率，看看状态是否为ψ，得到的结果是ψ。如果有两个或更多不同的实验来决定这一点(例如，本质上相同的实验，在不同的时间进行)，它们都应该给出相同的结果，即，转移概率具有不变的物理意义。

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引用次数: 1895

Rubin's conjecture on local units in the anticyclotomic tower at inert primes 鲁宾关于惰性质数下抗细胞分裂塔局部单元的猜想

IF 4.9 1区数学 Q1 MATHEMATICS

Annals of Mathematics

Pub Date : 2021-11-01 DOI: 10.4007/annals.2021.194.3.8

Ashay A. Burungale, Shin-ichi Kobayashi, Kazuto Ota

引用次数: 11

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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Annals of Mathematics

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