在前人工作的基础上,利用门限极值的广义Pareto分布理论和超出阈值峰(Peak Over Threshold,POT)方法,提出了一种确定湖泊参照状态浓度的新方法.该方法不仅能够给出更为精确的置信区间,而且克服了广义极值分布理论取用数据浪费等缺陷....在前人工作的基础上,利用门限极值的广义Pareto分布理论和超出阈值峰(Peak Over Threshold,POT)方法,提出了一种确定湖泊参照状态浓度的新方法.该方法不仅能够给出更为精确的置信区间,而且克服了广义极值分布理论取用数据浪费等缺陷.将该方法应用到太湖的水质基准参照状态中,通过POT方法对太湖8个站点1995~2006年总氮(TN),总磷(TP)和叶绿素a(Chl-a)的数据进行预处理,分别以-1.0mg/L,-0.05mg/L与-4μg/L作为它们观测值相反数的门限值,结果表明观测值的相反数符合广义Pareto分布,验证了方法的可行性.推荐采用25%分位点的值作为太湖总氮,总磷和叶绿素a的参照状态,即太湖的参照状态是:总氮0.66mg/L;总磷0.023mg/L;叶绿素a为1.27μg/L.最后分别得出了它们各自的95%置信区间,而且其精度明显高于广义极值分布理论结果.展开更多
For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut + Au + (|x|^-γ * |u|2)u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground st...For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut + Au + (|x|^-γ * |u|2)u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ + Q = (|x|^-γ * |Q|^2)Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0,1) if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^(sc= r-2/2). In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation (0.1).展开更多
文摘在前人工作的基础上,利用门限极值的广义Pareto分布理论和超出阈值峰(Peak Over Threshold,POT)方法,提出了一种确定湖泊参照状态浓度的新方法.该方法不仅能够给出更为精确的置信区间,而且克服了广义极值分布理论取用数据浪费等缺陷.将该方法应用到太湖的水质基准参照状态中,通过POT方法对太湖8个站点1995~2006年总氮(TN),总磷(TP)和叶绿素a(Chl-a)的数据进行预处理,分别以-1.0mg/L,-0.05mg/L与-4μg/L作为它们观测值相反数的门限值,结果表明观测值的相反数符合广义Pareto分布,验证了方法的可行性.推荐采用25%分位点的值作为太湖总氮,总磷和叶绿素a的参照状态,即太湖的参照状态是:总氮0.66mg/L;总磷0.023mg/L;叶绿素a为1.27μg/L.最后分别得出了它们各自的95%置信区间,而且其精度明显高于广义极值分布理论结果.
基金supported by the National Natural Science Foundation of China(11371267)Sichuan Province Science Foundation for Youths(2012JQ0011)
文摘For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut + Au + (|x|^-γ * |u|2)u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ + Q = (|x|^-γ * |Q|^2)Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0,1) if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^(sc= r-2/2). In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation (0.1).