A Receiver Operating Characteristic(ROC)analysis of a power is important and useful in clinical trials.A Classical Conditional Power(CCP)is a probability of a classical rejection region given values of true treatment ...A Receiver Operating Characteristic(ROC)analysis of a power is important and useful in clinical trials.A Classical Conditional Power(CCP)is a probability of a classical rejection region given values of true treatment effect and interim result.For hypotheses and reversed hypotheses under normal models,we obtain analytical expressions of the ROC curves of the CCP,find optimal ROC curves of the CCP,investigate the superiority of the ROC curves of the CCP,calculate critical values of the False Positive Rate(FPR),True Positive Rate(TPR),and cutoff of the optimal CCP,and give go/no go decisions at the interim of the optimal CCP.In addition,extensive numerical experiments are carried out to exemplify our theoretical results.Finally,a real data example is performed to illustrate the go/no go decisions of the optimal CCP.展开更多
Radio frequency capacitively coupled plasmas(RF CCPs)operated in Ar/O_(2)gas mixtures which are widely adopted in microelectronics,display,and photovoltaic industry,are investigated based on an equivalent circuit mode...Radio frequency capacitively coupled plasmas(RF CCPs)operated in Ar/O_(2)gas mixtures which are widely adopted in microelectronics,display,and photovoltaic industry,are investigated based on an equivalent circuit model coupled with a global model.This study focuses on the effects of singlet metastable molecule O_(2)(b^(1)∑_(8)^(+)),highly excited Herzberg states O_(2)(A^(3)∑_(u)^(+),A^(3)△_(u),c^(1)∑_(u)^(-)),and the negative ion O_(2)^(-),which are usually neglected in simulation studies.Specifically,their impact on particle densities,electronegativity,electron temperature,voltage drop across the sheath,and absorbed power in the discharge is analyzed.The results indicate that O_(2)(b^(1)∑_(8)^(+))and O_(2)^(-)exhibit relatively high densities in argon-oxygen discharges.While O_(2)(A^(3)∑_(u)^(+),A^(3)△_(u),c^(1)∑_(u)^(-))play a critical role in O_(2)b1S+g production,especially at higher pressure.The inclusion of these particles reduces the electronegativity,electron temperature,and key species densities,especially the O^(-)and O^(*)densities.Moreover,the sheath voltage drop,as well as the inductance and resistance of the plasma bulk are enhanced,while the sheath dissipation power and total absorbed power decrease slightly.With the increasing pressure,the influence of these particles on the discharge properties becomes more significant.The study also explores the generation and loss of main neutral species and charged particles within the pressure range of 20 mTorr-100 mTorr(1 Torr=1.33322×10^(2)Pa),offering insights into essential and non-essential reactions for future low-pressure O_(2)and Ar/O_(2)CCP discharge modeling.展开更多
基金supported by the National Social Science Fund of China(Grand No.21XTJ001).
文摘A Receiver Operating Characteristic(ROC)analysis of a power is important and useful in clinical trials.A Classical Conditional Power(CCP)is a probability of a classical rejection region given values of true treatment effect and interim result.For hypotheses and reversed hypotheses under normal models,we obtain analytical expressions of the ROC curves of the CCP,find optimal ROC curves of the CCP,investigate the superiority of the ROC curves of the CCP,calculate critical values of the False Positive Rate(FPR),True Positive Rate(TPR),and cutoff of the optimal CCP,and give go/no go decisions at the interim of the optimal CCP.In addition,extensive numerical experiments are carried out to exemplify our theoretical results.Finally,a real data example is performed to illustrate the go/no go decisions of the optimal CCP.
基金supported by the National Natural Science Foundation of China(Grant Nos.12020101005,12475202,12347131,and 12405289).
文摘Radio frequency capacitively coupled plasmas(RF CCPs)operated in Ar/O_(2)gas mixtures which are widely adopted in microelectronics,display,and photovoltaic industry,are investigated based on an equivalent circuit model coupled with a global model.This study focuses on the effects of singlet metastable molecule O_(2)(b^(1)∑_(8)^(+)),highly excited Herzberg states O_(2)(A^(3)∑_(u)^(+),A^(3)△_(u),c^(1)∑_(u)^(-)),and the negative ion O_(2)^(-),which are usually neglected in simulation studies.Specifically,their impact on particle densities,electronegativity,electron temperature,voltage drop across the sheath,and absorbed power in the discharge is analyzed.The results indicate that O_(2)(b^(1)∑_(8)^(+))and O_(2)^(-)exhibit relatively high densities in argon-oxygen discharges.While O_(2)(A^(3)∑_(u)^(+),A^(3)△_(u),c^(1)∑_(u)^(-))play a critical role in O_(2)b1S+g production,especially at higher pressure.The inclusion of these particles reduces the electronegativity,electron temperature,and key species densities,especially the O^(-)and O^(*)densities.Moreover,the sheath voltage drop,as well as the inductance and resistance of the plasma bulk are enhanced,while the sheath dissipation power and total absorbed power decrease slightly.With the increasing pressure,the influence of these particles on the discharge properties becomes more significant.The study also explores the generation and loss of main neutral species and charged particles within the pressure range of 20 mTorr-100 mTorr(1 Torr=1.33322×10^(2)Pa),offering insights into essential and non-essential reactions for future low-pressure O_(2)and Ar/O_(2)CCP discharge modeling.
