When we use the power function a(c + x)b and gamma density axbe-cx to fit the data by the least squares method, we have to address the question of existence. The closure of the set of each type of these functions defi...When we use the power function a(c + x)b and gamma density axbe-cx to fit the data by the least squares method, we have to address the question of existence. The closure of the set of each type of these functions defined on a finite domain is determined. We derive a way to determine the closure of a sum of nonnegative functions if the closures of the summands are available.展开更多
公共楼宇是智能电网用电环节需求响应的重要组成部分,在强不确定性环境下,为了提高公共楼宇短期负荷预测的精度,并能更好反映楼宇负荷的不确定性。提出了一种集合多维尺度分析技术(multidimensional scaling,MDS),基于Copula函数相关性...公共楼宇是智能电网用电环节需求响应的重要组成部分,在强不确定性环境下,为了提高公共楼宇短期负荷预测的精度,并能更好反映楼宇负荷的不确定性。提出了一种集合多维尺度分析技术(multidimensional scaling,MDS),基于Copula函数相关性测度、长短期记忆网络分位数回归(quantile regression long short-term memory,QRLSTM)和核密度估计(kernel density estimation,KDE)的短期公共楼宇负荷概率密度预测的方法。首先采用MDS技术对楼宇群进行初步划分,再通过基于Copula函数的相关性测度方法定量计算影响因素(外界天气、人类活动)与目标楼宇负荷的相关程度;其次,运用QRLSTM回归模型预测未来不同分位数上的负荷值。最后,通过核密度估计得到未来任意时刻预测点的概率密度函数。实验结果表明,综合考虑强相关影响因素,并结合QRLSTM回归和KDE技术,能够更好地解决短期公共楼宇负荷概率密度预测问题。展开更多
The autocorrelation function of electronic wave packet of hydrogen atom in a strong electric field below the zero-field ionization threshold is investigated in the formalism of semiclassical theory. It is found that t...The autocorrelation function of electronic wave packet of hydrogen atom in a strong electric field below the zero-field ionization threshold is investigated in the formalism of semiclassical theory. It is found that the autocorrelation depends on the applied laser pulse significantly. In the case of narrow laser pulse, the reviving peaks in the autocorrelation can be attributed to the closed orbits of electrons, which are related to the classical dynamics of the system. But this correspondence is wiped out with increasing the laser width because of the interference among the adjacent reviving peaks.展开更多
文摘When we use the power function a(c + x)b and gamma density axbe-cx to fit the data by the least squares method, we have to address the question of existence. The closure of the set of each type of these functions defined on a finite domain is determined. We derive a way to determine the closure of a sum of nonnegative functions if the closures of the summands are available.
文摘公共楼宇是智能电网用电环节需求响应的重要组成部分,在强不确定性环境下,为了提高公共楼宇短期负荷预测的精度,并能更好反映楼宇负荷的不确定性。提出了一种集合多维尺度分析技术(multidimensional scaling,MDS),基于Copula函数相关性测度、长短期记忆网络分位数回归(quantile regression long short-term memory,QRLSTM)和核密度估计(kernel density estimation,KDE)的短期公共楼宇负荷概率密度预测的方法。首先采用MDS技术对楼宇群进行初步划分,再通过基于Copula函数的相关性测度方法定量计算影响因素(外界天气、人类活动)与目标楼宇负荷的相关程度;其次,运用QRLSTM回归模型预测未来不同分位数上的负荷值。最后,通过核密度估计得到未来任意时刻预测点的概率密度函数。实验结果表明,综合考虑强相关影响因素,并结合QRLSTM回归和KDE技术,能够更好地解决短期公共楼宇负荷概率密度预测问题。
基金supported by the National"973"Program of China under Grant No.2007CB310405
文摘The autocorrelation function of electronic wave packet of hydrogen atom in a strong electric field below the zero-field ionization threshold is investigated in the formalism of semiclassical theory. It is found that the autocorrelation depends on the applied laser pulse significantly. In the case of narrow laser pulse, the reviving peaks in the autocorrelation can be attributed to the closed orbits of electrons, which are related to the classical dynamics of the system. But this correspondence is wiped out with increasing the laser width because of the interference among the adjacent reviving peaks.
