HEAT KERNEL ON RICCI SHRINKERS(II)

This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.

R^(n+1) 上self-shrinkers的谱特征

本文研究了self-shrinkers谱与几何的关系.利用渐进展开式系数相等的方法,获得了如下结果:设M是R^(n+1)上的n(n≥2)维闭self-shrinkers,且M和s^n(2n^(1/2))有相同的平均曲率,如果spec^p(M)=spec^p(s^n(2n^(1/2)),则M是s^n(2n^(1/2),并推广了R^(n+1)上self-shrinkers的特征.

Some Results on Space-Like Self-Shrinkers

We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps.

Gradient Estimates and Harnack Inequalities for Positive Solutions of ■ on Self-shrinkers

In this paper, we investigate the positive solutions of ■u =■υ/■t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.

Lorentz空间R_1^(n+1)中类空λ-超曲面的刚性定理（英文）

本文研究了Lorentz空间R_1^(n+1)中完备的类空λ-超曲面的刚性问题.利用推广了的L-算子的性质和一些积分不等式,最终得到了关于这类超曲面的若干刚性定理,其中包括R_1^(n+1)中加权的完备类空自收缩子的刚性,推广了此前欧氏空间完备λ-超曲面的相关结果.

C^(3)中曲面Kahler角的刚性定理（英文）

浸入到近复Hermit流形的曲面的Khler角是一个重要的不变量,可以用于刻画曲面偏离拟全纯曲线的程度.近年来,具有常Khler角的曲面仍是很有意义的研究对象.对于3维复欧氏空间C^3中具有常Khler角的曲面收缩子,本文证明了两个刚性定理.这些定理是有关C^3中曲面自收缩子的相应定理的直接拓展.

基于Apriori和GPS识别甘肃省2021-2022年疫苗安全信号

目的在电子医疗记录数据中识别与疫苗相关的不良事件信号。方法对2020—2022年甘肃省的电子医疗记录和疫苗接种数据进行数据清洗,使用先验(Apriori)算法和伽马泊松收缩估计法(Empirical Bayes Gamma-Possion Shrinker,GPS)算法进行信号识别,并按性别和年龄组进行分层分析。结果共确定33个统计信号,Apriori方法识别出7个信号,GPS方法识别出26个信号,在两种方法、两种信号阈值下未发现有重合的信号。结论在电子医疗记录中应用GPS和Apriori识别的疫苗安全信号可靠和准确,但需要进一步研究以确定GPS算法识别的疫苗安全信号之间的相关性。