In this paper, we consider the semilinear equation involving the fractional Laplacian in the Euclidian space R^n：（-△）^α/2u（x） ： f（xn）u^p（x）, x ∈R^n（0.1）in the subcritical case with 1〈 p〈n＋a/n-a.Inste...In this paper, we consider the semilinear equation involving the fractional Laplacian in the Euclidian space R^n：（-△）^α/2u（x） ： f（xn）u^p（x）, x ∈R^n（0.1）in the subcritical case with 1〈 p〈n＋a/n-a.Instead of carrying out direct investigations on pseudo-differential equation （0.1）, we first seek its equivalent form in an integral equation as below：u（x）=∫R^nG∞（x, y） f（yn） u^p（y）dy,where G∞（x, y） is the Green＇s function associated with the fractional Laplacian in R^n. Employing the method of moving planes in integral forms, we are able to derive the nonexistence of positive solutions for （0.2） in the subcritical case. Thanks to the equivalence, same con- clusion is true for （0.1）.展开更多
针对连续性工业生产特点,重点关注类别不平衡造成的不合格样本召回率低问题。为了从高维数据提取有效特征,结合one class F-score和最小冗余最大相关性在特征提取方面的优势,有效降低特征维度并提取有价值特征;利用Wasserstein生成对抗...针对连续性工业生产特点,重点关注类别不平衡造成的不合格样本召回率低问题。为了从高维数据提取有效特征,结合one class F-score和最小冗余最大相关性在特征提取方面的优势,有效降低特征维度并提取有价值特征;利用Wasserstein生成对抗网络(WGAN)方法扩增不合格样本数量;通过类别权重优化Focal Loss函数以提高困难样本识别率;通过轻量级梯度提升机算法结合阈值移动策略,构建基于WGAN数据增强和难例挖掘技术的质量预测模型(WGAN_Focal Loss_LGB(TM))。将所提模型应用于开源SECOM数据集,验证了所提方法的有效性。展开更多
文摘In this paper, we consider the semilinear equation involving the fractional Laplacian in the Euclidian space R^n：（-△）^α/2u（x） ： f（xn）u^p（x）, x ∈R^n（0.1）in the subcritical case with 1〈 p〈n＋a/n-a.Instead of carrying out direct investigations on pseudo-differential equation （0.1）, we first seek its equivalent form in an integral equation as below：u（x）=∫R^nG∞（x, y） f（yn） u^p（y）dy,where G∞（x, y） is the Green＇s function associated with the fractional Laplacian in R^n. Employing the method of moving planes in integral forms, we are able to derive the nonexistence of positive solutions for （0.2） in the subcritical case. Thanks to the equivalence, same con- clusion is true for （0.1）.
文摘针对连续性工业生产特点,重点关注类别不平衡造成的不合格样本召回率低问题。为了从高维数据提取有效特征,结合one class F-score和最小冗余最大相关性在特征提取方面的优势,有效降低特征维度并提取有价值特征;利用Wasserstein生成对抗网络(WGAN)方法扩增不合格样本数量;通过类别权重优化Focal Loss函数以提高困难样本识别率;通过轻量级梯度提升机算法结合阈值移动策略,构建基于WGAN数据增强和难例挖掘技术的质量预测模型(WGAN_Focal Loss_LGB(TM))。将所提模型应用于开源SECOM数据集,验证了所提方法的有效性。
