Quantum Correlations Induced by Local von Neumann Measurement

We study the total quantum correlation, semiquantum correlation and joint quantum correlation induced by local von Neumann measurement in bipartite system. We analyze the properties of these quantum correlations and obtain analytical formula for pure states. The experimental witness for these quantum correlations is further provided and the significance of these quantum correlations is discussed in the context of local distinguishability of quantum states.     

On Polynomial Representations of Lie Algebras

We study polynomial representations of finite dimensional (R or C) Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle structures.     

群胚上的Dirac结构及泊松约化

本文详细讨论了李双代数胚中的Dirac结构、群胚上的Dirac结构。利用Dirac结构的特征对的概念,给出了作用不变Dirac结构,拉回Dirac结构等概念的新的刻画。最后利用Dirac结构的有关性质,讨论了泊松齐性空间和泊松群胚作用的约化。     

On the Action of a Groupoid on a Manifold

In this paper,some properties of reduction for symplectic F-spaces are discussed.The properties of stable subgroups are discussed.We find that the symplectic action of a symplectic groupoid on a symplectic manifold can induce a symplectic map between reduced symplectic manifolds.This symplectic action can be characterized by the action of its induced symplectic groupoid on a symplectic manifold.Lastly,we shall discuss Poisson reduction and give a Poisson reduction theorem.     

基于折线采样的高分辨率成像系统设计

针对现有的提高线阵电荷耦合器件(CCD)成像系统的图像空间分辨率的方法存在的不足,提出了一种新的采样模式,并设计了一种高分辨率成像系统。该系统利用两个相同的线阵CCD相机进行特定的空间排列,即使得相机1和相机2的CCD阵列都倾斜θ来进行扫描取像,并利用图像校正和像素插值等图像重建方法,得到高分辨率的图像。实验结果表明,倾斜角取60°的情况下,相对于单个线阵相机在θ=0°的正常采样模式下得到的采样图像,图像的空间分辨率提高了1倍,且保持了成像的视野不变。本系统工程上实现简单,十分经济且便于维护,仅利用现有的成像装置即可获取更高分辨率的图像。     

On the existence of global bisections of Lie groupoids

We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of bisections through more than one prescribed point is also discussed. We give some interesting applications of these results.     

Dirac structures and poisson reductions on poisson groupoids

The notion of characteristic pairs of Dirac structures was introduced by Liu in 2000. In this paper, the invariant Dirac structures on Poisson actions and pullback Dirac structures are characterized in terms of their characteristic pairs. Poisson homogeneous spaces and Poisson reduction are discussed.     

非线性四阶周期边值问题的最优正解

该文使用锥不动点定理研究了四阶周期边值问题u⁽⁴)-m⁴u+F(t, u(τ(t)))=0, 0 < t < 2π, u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π),~ i=0,1, 2, 3, 这里 F: [0,2π ]×R⁺→R⁺ 和τ: [0, 2π]→[0, 2π] 是连续的, 0-7.     

Strong Solutions of a Class of Stochastic Differential Equations with Jumps

We study a class of stochastic integral equations with jumps under non-Lipschitz conditions. We use the method of Euler approximations to obtain the existence of the solution and give some sufficient conditions for the strong uniqueness.