具有连续变量的中立型差分方程的振动准则

研究了一类具有连续变量的中立型差分方程△τ(x(t)-px(t-τ)) q(t)mⅡi=1|x(t-σi)|αisgnx(t-σi)=0的振动性,建立了该方程振动的几个充分条件.     

具连续变量的中立型差分方程的振动性

讨论具有连续变量的中立型差分方程,建立了该方程振动的若干充分条件。     

具连续变量的阻尼中立型差分方程的振动性

针对一类具有连续变量的二阶阻尼中立型差分方程的振动性问题,利用适当的不等式、反证法和广义Riccati变换,取得了该类方程解以及有界解振动的几个充分条件.该成果在生物学、经济学、人口学、物理学以及控制论等领域有广泛的应用.     

Applying Gaussian quantum discord to quantum key distribution

In this paper, we theoretically prove that the Gaussian quantum discord state of optical field can be used to complete continuous variable （CV） quantum key distri- bution （QKD）. The calculation shows that secret key can be distilled with a Gaussian quantum discord state against entangling cloner attack. Secret key rate is increased with the increasing of quantum discord for CV QKD with the Gaussian quantum discord state. Although the calculated results point out that secret key rate using the Gaussian quantum discord state is lower than that using squeezed state and coherent state at the same energy level, we demonstrate that the Gaussian quantum discord, which only involving quantum correlation without the existence of entanglement, may provide a new resource for realizing CV QKD.     

一类三阶非线性中立型时滞差分方程的振动性

运用分析的方法研究一类具有连续变量的三阶非线性中立型时滞差分方程的振动性,给出该类方程所有有界解振动和方程振动的几个充分条件,推广并改进已有结论.