无穷远点处与Schr?dinger算子相关的极细集

本文首先得到了一些新的关于锥中无穷远点处与Schr?dinger算子相关极细集的判定准则,其证明是基于对带有修改测度的Green-Sch位势在无穷远点处渐近行为的估计.接着,刻画了这类极细集的几何性质.最后,通过一个反例来说明,所得几何性质的逆命题并不成立.

无穷远点处与Schrdinger算子相关极细集性质的应用

设u是定义在锥中的超函数.作为无穷远点处与Schrdinger算子相关的极细集判定准则和几何性质的应用,本文证明锥中的例外集{P=(r,Θ)∈C_n(?);u(P)>V(r)φ(Θ)}和{P=(r,Θ)∈C_n(?);u(P)>V(r)}分别是锥中无穷远点处与Schrdinger算子相关的极细集和稀薄集当且仅当与u相关的测度满足特定的积分条件.

Dolomite apatite separation by amphoteric collector in presence of bacteria

Bioflotation represents one of the growing trends to enhance the selectivity of conventional flotation processes. It utilizes the micro-organisms to replace or to interact with the chemical reagents to increase the gap between surface properties of similar minerals and to enhance the separation selectivity. In this work, dolomite-phosphate separation was investigated using amphoteric collector （dodecyl-N-carboxyethyl-N-hyroxyethyl-imidazoline） in presence of bacteria. Two types of bacteria, Corynebacterium- diphtheriae-intermedius （CDI）, and Pseudomonas aeruginosa （PA）, were used. The collector-bacteria interaction was characterized by Fourier transform infra-red （FTIR）, frothing height and Zeta potential. The results show that the collector-bacteria interaction improves the flotation selectivity. Although, the PA positively affects the separation results, the CDI cannot lower the MgO to less than 1%. A phosphate content of 0.7% MgO and 31.77% P205 with a recovery of 68% at pH 11, 3.0 kg/t amphoteric collector, 4× 10^7 cells of PA is obtained.

修正Green-Sch能量的构造及应用

本文通过构造锥中修正的Green-Sch能量,不仅证明了锥中稳态Schrdinger方程弱解在无穷远点处除去一个例外集后的渐近行为,而且得到了锥中无穷远点处与Schrdinger算子相关的极细集和稀薄集新的性质.

锥中与稳态的薛定谔算子相关的容度与广义Green能量（英文）

本文首先引入了与稳态的薛定谔算子相关的广义容度和Green能量,然后得到它们和概率测度间的相互关系.进而,利用容度工具刻画了锥中与稳态的薛定谔算子相关的极细集和稀疏集.