We discussed the Dirichlet problem of semilinear elliptic equation (P β,ε):β 2Δu=u p +εu,u>0, in Ω;u=0, on ?Ω, where Ω?R N (N≥4) is smooth and bounded domain, ,β,ε>0. We have proved that there exist ...We discussed the Dirichlet problem of semilinear elliptic equation (P β,ε):β 2Δu=u p +εu,u>0, in Ω;u=0, on ?Ω, where Ω?R N (N≥4) is smooth and bounded domain, ,β,ε>0. We have proved that there exist positiveε 0 andε 1, such that when 0?ε?ε 0,β>√ε 1, (P β,ε) has a single-peaked solutionu β,ε; furthermore, |?u β0|2?0 in the sense of measure as ε→0 and β→0.展开更多
近年来,深度学习在许多领域取得了巨大的成功,其中,激活函数是深度学习取得巨大成功的关键因素之一。根据生物神经元特性,针对ReLU右侧响应无界问题,提出了单峰梯形线性单元(Single-Peaked Trapezoid Linear Unit,SPTLU)。SPTLU更加符...近年来,深度学习在许多领域取得了巨大的成功,其中,激活函数是深度学习取得巨大成功的关键因素之一。根据生物神经元特性,针对ReLU右侧响应无界问题,提出了单峰梯形线性单元(Single-Peaked Trapezoid Linear Unit,SPTLU)。SPTLU更加符合生物神经元特性,且取得了等同和超越ReLU的优异性能,实验表明在不同数据集上都取得了很好的效果,例如,数据集MNIST,Fashion-MNIST,SVHN,CALTECH101和CIFAR10。展开更多
Previous studies revealed the double-peak mode(DPM)in South China precipitation,corresponding to the two stages in the rainy season,i.e.the first rainy stage(FRS)and the second rainy stage(SRS).But observations in rec...Previous studies revealed the double-peak mode(DPM)in South China precipitation,corresponding to the two stages in the rainy season,i.e.the first rainy stage(FRS)and the second rainy stage(SRS).But observations in recent two decades show that the DPM has changed to a single-peak mode(SPM).Both the precipitation amount and the heavy rainfall event frequency enhanced significantly in the gap between the FRS and the SRS in 1991–2010,compared to those in 1961–1990.This change can be linked to the effects of the global warming.During the warmer period,the July sea surface temperature over the western Pacific has greater increases than that over the central and eastern Pacific,especially west of 140°E.It may generate more tropical cyclones(TCs)in the inshore areas and then more typhoon rainfall over South China.On the other hand,the increments of the air temperature over the East Asian continent are greater than those of the SST over the western Pacific under the global warming,which enlarges the land-ocean temperature/pressure contrast and leads to a trend of the earlier onset dates of the Asian summer monsoon(ASM)in recent two decades.Then,the earlier ASM will facilitate the western Pacific subtropical high(WPSH)to retreat earlier from the South China Sea and enhance the convective precipitation in South China between the FRS and the SRS.Also,due to the warmer ocean,the WPSH locates more westward in July,and more moisture will be transported to South China from the southwest side to the WPSTH.All these influences favor a remarkably increasing precipitation in the gap in the warmer period and changes the seasonal cycle from double-peak mode to single-peak mode.展开更多
基金the National Natural Science Foundation of ChinaFoundation for Fundamental Sciences of Nanchang UniversityHua-chen Found
文摘We discussed the Dirichlet problem of semilinear elliptic equation (P β,ε):β 2Δu=u p +εu,u>0, in Ω;u=0, on ?Ω, where Ω?R N (N≥4) is smooth and bounded domain, ,β,ε>0. We have proved that there exist positiveε 0 andε 1, such that when 0?ε?ε 0,β>√ε 1, (P β,ε) has a single-peaked solutionu β,ε; furthermore, |?u β0|2?0 in the sense of measure as ε→0 and β→0.
文摘近年来,深度学习在许多领域取得了巨大的成功,其中,激活函数是深度学习取得巨大成功的关键因素之一。根据生物神经元特性,针对ReLU右侧响应无界问题,提出了单峰梯形线性单元(Single-Peaked Trapezoid Linear Unit,SPTLU)。SPTLU更加符合生物神经元特性,且取得了等同和超越ReLU的优异性能,实验表明在不同数据集上都取得了很好的效果,例如,数据集MNIST,Fashion-MNIST,SVHN,CALTECH101和CIFAR10。
基金supported by the National Basic Research Program of China (2012CB417205 and 2013CB430203)the International Cooperation Program of Ministry of Science and Technology of China (2009DFA23010)+1 种基金the Special Research Fund (Meteorology) of Public Welfare Project (GYHY201306033)the National Natural Science Foundation of China (41005037)
文摘Previous studies revealed the double-peak mode(DPM)in South China precipitation,corresponding to the two stages in the rainy season,i.e.the first rainy stage(FRS)and the second rainy stage(SRS).But observations in recent two decades show that the DPM has changed to a single-peak mode(SPM).Both the precipitation amount and the heavy rainfall event frequency enhanced significantly in the gap between the FRS and the SRS in 1991–2010,compared to those in 1961–1990.This change can be linked to the effects of the global warming.During the warmer period,the July sea surface temperature over the western Pacific has greater increases than that over the central and eastern Pacific,especially west of 140°E.It may generate more tropical cyclones(TCs)in the inshore areas and then more typhoon rainfall over South China.On the other hand,the increments of the air temperature over the East Asian continent are greater than those of the SST over the western Pacific under the global warming,which enlarges the land-ocean temperature/pressure contrast and leads to a trend of the earlier onset dates of the Asian summer monsoon(ASM)in recent two decades.Then,the earlier ASM will facilitate the western Pacific subtropical high(WPSH)to retreat earlier from the South China Sea and enhance the convective precipitation in South China between the FRS and the SRS.Also,due to the warmer ocean,the WPSH locates more westward in July,and more moisture will be transported to South China from the southwest side to the WPSTH.All these influences favor a remarkably increasing precipitation in the gap in the warmer period and changes the seasonal cycle from double-peak mode to single-peak mode.
