Annals of Mathematics最新文献

{"title":"On Zagier-Hoffman's conjectures in positive\u0000 characteristic","authors":"Bo-Hae Im, Hojin Kim, Khac Nhuan Le, Tuan Ngo Dac, Lan Huong Pham","doi":"10.4007/annals.2021.194.1.6","DOIUrl":"https://doi.org/10.4007/annals.2021.194.1.6","url":null,"abstract":"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.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2022-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45681864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A multicenter, open-label, single-arm phase I trial of neoadjuvant nivolumab monotherapy for resectable gastric cancer.","authors":"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","doi":"10.1007/s10120-022-01286-w","DOIUrl":"10.1007/s10120-022-01286-w","url":null,"abstract":"<p><strong>Background: </strong>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.</p><p><strong>Methods: </strong>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.</p><p><strong>Results: </strong>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.</p><p><strong>Conclusions: </strong>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).</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"46 1","pages":"619-628"},"PeriodicalIF":6.0,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9013329/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90478897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prevalence of Certain Urogenital Bacterial <i>Mollicutes</i> in Patients Suffering from Infertility.","authors":"Motasem Y Al-Masri, Intesar Khaleel Ashour, Ashraf Swafta, Sami Al-Shunar","doi":"10.1155/2022/2812788","DOIUrl":"10.1155/2022/2812788","url":null,"abstract":"<p><strong>Introduction: </strong><i>Mollicutes</i> urogenital tract infections are considered a possible cause of infertility worldwide. Genital <i>Mollicutes</i> infections are difficult and impractical to diagnose by culturing or serology. <i>Mollicutes</i> included in this study were <i>Mycoplasma hominis</i>, <i>Ureaplasma urealyticum</i>, and <i>Mycoplasma genitalium</i>. This cross-sectional study aimed to determine the prevalence of <i>M. hominis</i>, <i>U. urealyticum</i>, and <i>M. genitalium</i> genital infections among infertile males and females patients.</p><p><strong>Methods: </strong>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 <i>M. hominis</i>, <i>U. urealyticum</i>, and <i>M. genitalium</i>.</p><p><strong>Results: </strong>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 <i>Mollicutes</i>, which were 16 (14.6%) <i>M. hominis</i>, 11 (10%) <i>U. urealyticum</i>, and 8 (7.3%) <i>M. genitalium</i>. Significant association were found between infections of <i>M. hominis</i> and <i>U. urealyticum</i> (<i>P</i>=0.044) and between <i>M. hominis</i> and <i>M. genitalium</i> (<i>P</i>=0.005) infections. <i>M. hominis</i> infection was found in significantly (<i>P</i>=0.048) higher percentage in males (20.6%) in comparison with females (5.7%). On the other hand, <i>M. genitalium</i> infection rate in females (8.6%) was slightly higher than males (7.4%). <i>M. hominis</i> was more prevalent in all age groups except for patient's age group 40-50 years old, where <i>M. genitalium</i> was more prevalent. <i>M. hominis</i> was also more prevalent in all occupation types and among all smokers.</p><p><strong>Conclusion: </strong>Urogenital infections caused by <i>M. hominis</i>, <i>M. genitalium</i>, and <i>U. urealyticum</i> 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.</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"12 1","pages":"2812788"},"PeriodicalIF":0.0,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8964151/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90420837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Affine Beilinson-Bernstein localization at the critical level for $mathrm{GL}_2$","authors":"David H Yang, S. Raskin","doi":"10.4007/annals.2022.195.1.4","DOIUrl":"https://doi.org/10.4007/annals.2022.195.1.4","url":null,"abstract":". 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.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46990368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Erratum: A corrected proof of the scale recurrence lemma from the paper ``Stable intersections of regular Cantor sets with large Hausdorff dimensions\"","authors":"C. Moreira, A. Zamudio","doi":"10.4007/annals.2022.195.1.6","DOIUrl":"https://doi.org/10.4007/annals.2022.195.1.6","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43384216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Erratum: Euclidean triangles have no hot spots | Annals of Mathematics","authors":"Chris Judge, Sugata Mondal","doi":"10.4007/annals.2022.195.1.5","DOIUrl":"https://doi.org/10.4007/annals.2022.195.1.5","url":null,"abstract":"<p>Original article: https://doi.org/10.4007/annals.2020.191.1.3</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"284 ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-uniqueness of Leray solutions of the forced Navier-Stokes equations","authors":"D. Albritton, Elia Bru'e, Maria Colombo","doi":"10.4007/annals.2022.196.1.3","DOIUrl":"https://doi.org/10.4007/annals.2022.196.1.3","url":null,"abstract":"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.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44333535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved bounds for the sunflower lemma | Annals of Mathematics","authors":"Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang","doi":"10.4007/annals.2021.194.3.5","DOIUrl":"https://doi.org/10.4007/annals.2021.194.3.5","url":null,"abstract":"<p> 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. </p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"589 ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"80 Years of Professor Wigner's Seminal Work \"On Unitary Representations of the Inhomogeneous Lorentz Group\"","authors":"E. Wigner","doi":"10.2307/1968551","DOIUrl":"https://doi.org/10.2307/1968551","url":null,"abstract":"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.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"40 1","pages":"149-204"},"PeriodicalIF":4.9,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2307/1968551","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43013217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rubin's conjecture on local units in the anticyclotomic tower at inert primes","authors":"Ashay A. Burungale, Shin-ichi Kobayashi, Kazuto Ota","doi":"10.4007/annals.2021.194.3.8","DOIUrl":"https://doi.org/10.4007/annals.2021.194.3.8","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44753710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}