一道电动力学题的多种解法

:对一道电动力学题用五种不同的方法作出解答

二维空间带正则位势项的Landis猜想的证明

本文在V_(W^(1,∞)(R^2)≤1的条件下,证明了定量版的二维Landis猜想.与已有的结果不同,不需要位势函数非负的要求,但需要其导数在全空间有界以及H-?+V是正算子的条件.当V是一个实函数,满足V_(W^(1,∞)(R^2))≤1且H≥0,u是偏微分方程Hu-?u+Vu=0在二维空间的实解,假定u(0)=1和|u(z)|exp(C_0|z|),则u满足inf|z_0|=R_(|z-z_0|)sup<1^(|u(z)|)≥exp(-CR log R).本文也得到了一些更一般的结果.

Infinite Clusters in Locally Dependent Percolation on Z^d

Techniques of Burton-Keane,developed earlier for independent percolation on Zd,are adapted to the setting of locally dependent percolation on Zd for d 2.The main result of this paper is a uniqueness theorem,that there exists almost surely a unique infinite out-cluster in locally dependent percolation on Zd,under the finite energy condition.