On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sh...On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.展开更多
We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much ...We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.展开更多
高压开关柜是电力系统中的关键设备之一,其内部电气元件分布繁多、排列紧密、绝缘裕度很小,易出现局部放电现象。为此以准确定位局部放电的位置为目的,提出了基于梯度收缩法的超声波定位算法,具体介绍该方法的基本原理、检测方法和判断...高压开关柜是电力系统中的关键设备之一,其内部电气元件分布繁多、排列紧密、绝缘裕度很小,易出现局部放电现象。为此以准确定位局部放电的位置为目的,提出了基于梯度收缩法的超声波定位算法,具体介绍该方法的基本原理、检测方法和判断结果。将此算法用于某企业的35 k V真空开关柜局部放电检测中,检测结果表明,该方法对高频干扰下的局部放电现象的检测更为精确有效,也为高压开关柜的故障检测以及安全运行提供了技术依据。展开更多
基金partially supported by the National Natural Science Foundation of China(11671141)the Natural Science Foundation of Shanghai(17ZR1412800)。
文摘On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.
基金supported by National Natural Science Foundation of China(11301191)supported by MOST(MOST107-2115-M-110-007-MY2)
文摘We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.
文摘高压开关柜是电力系统中的关键设备之一,其内部电气元件分布繁多、排列紧密、绝缘裕度很小,易出现局部放电现象。为此以准确定位局部放电的位置为目的,提出了基于梯度收缩法的超声波定位算法,具体介绍该方法的基本原理、检测方法和判断结果。将此算法用于某企业的35 k V真空开关柜局部放电检测中,检测结果表明,该方法对高频干扰下的局部放电现象的检测更为精确有效,也为高压开关柜的故障检测以及安全运行提供了技术依据。
基金Supported by National Natural Science Foundation of China(50802064,51072137,and 11074189)New Century Excellent Talents in University of China(NCET-08-0405)National Science and Technology Support Program(2009BAC62B02)
