Relativistic Exponential Gravitation and Exponential Potential of Electric Charge

We present theories of gravitation and electric potentials with exponential dependence on the reciprocal distance. In the context of this kind of electric potential we investigate the dynamics of a relativistic electron interacting with a proton.     

变反射率镜非稳腔的研究进展

回顾了变反射率镜非稳腔的研究历史,总结了实现变反射率的方法,分析了它们的优缺点,最后列表总结了典型使用VRM作为非稳腔输出耦合器的实验参数和结果.为大能量固体激光器的设计提供了理论和实验参考.     

变栅距光栅实现啁啾脉冲光谱整形

为了充分利用放大介质的增益带宽,获得脉宽更短,功率更高的输出脉冲,需要将输入到主放大链的种子脉冲进行光谱整形来补偿放大过程中的增益窄化效应。提出了利用变栅距反射光栅实现中心波长1053nm,谱宽6nm啁啾脉冲的光谱整形。运用严格的光栅衍射耦合波理论分析光栅的衍射特性,发现该方案不会引入相位畸变。分别计算和分析了刻槽深度、入射角大小、光栅周期以及入射光波长的变化对衍射效率的影响,通过选取适当的光栅参量可获得0.5%~84%的光谱调制深度。     

高能物理中的Bell不等式

评述了在高能物理中检验量子力学的完备性, 特别是检验Bell不等式的研究工作进展情况, 简略地介绍了Einstain, Podolsky和Rosen (EPR)佯谬及其相应的光子实验得到的结果. 概括地阐述了在高能物理中早期利用粒子衰变中的自旋关联以及后来用中性介子的混合形成的准自旋纠缠态检验Bell不等式的各种尝试, 给出了K⁰和B⁰系统的相关实验结果. 介绍了一种可在φ工厂中实施实验检验的, 基于非最大纠缠态的新的方案. 最后还讨论了把这一实验方案推广到τ-粲工厂的可能性.     

Generation of GHZ-like and cluster-like quadripartite entangled states for continuous variable using a set of quadrature squeezed states

We designed the experimental generation system of the optical GHZ-like and cluster-like quadripartite entangled states for continuous variables. We theoretically demonstrated that the two different types of quadripartite entangled states can be obtained by the linearly optical transformation of four amplitude-quadrature and phase-quadrature squeezed states produced from a pair of nondegenerate optical parametric amplifiers under appropriate phase relations. The criteria for full inseparability of quadripartite cluster-like state were deduced, and the dependency of the quadripartite entanglement on the initial squeezing degree, the transmission efficiencies of the system and the detection efficiency of homodyne detection were numerically calculated. Supported by the National Natural Science Foundation of China (Grant Nos. 10674088 and 60608012) and Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0516)     

A Three Dimensional Chemostat with Quadratic Yields

A three dimensional chemostat with two microorganisms which are both with quadratic yields is studied. The stability of the equlibrium points, the existence of limit cycles, the Hopf bifurcation, and the positive invariant set for the system are discussed. We also prove the conditions that guarantee two limit cycles in the model.     

变系数(2+1)维Broer-Kaup方程的新精确解P

通过一个简单的变换,变系数(2+1)维Broer-Kaup方程被简化为人们熟知的变系数Burgers方程.利用近年来广泛使用的齐次平衡法和tanh-函数法,获得了变系数(2+1)维Broer-Kaup方程的一些新的精确解.     

A new instrumental variable estimation for diffusion processes

We consider the problem of parametric inference from continuous sample paths of the diffusion processes {x(t)} generated by the system of possibly nonstationary and/or nonlinear Ito stochastic differential equations. We propose a new instrumental variable estimator of the parameter whose pivotal statistic has a Gaussian distribution for all possible values of parameter. The new estimator enables us to construct exact level-α confidence intervals and tests for the parameter in the possibly non-stationary and/or nonlinear diffusion processes. Applications to several non-stationary and/or nonlinear diffusion processes are considered as examples. This work was supported by Korea Research Foundation Grant (KRF-2001-015-DP0057).     

Some applications of free Fisher information on frame theory

We introduce the notion of operator-valued free Fisher information with respect to a positive map of a random variable in an operator-valued noncommutative probability space and point out its close relations to the modular frames arising from conditional expectations. Then we can apply this notion on the study of frame theory, especially on the disjointness problem of modular frames arising from conditional expectations.     

Hardy type estimates for commutators of singular integrals

In this paper we study the Hardy type estimates for commutators Tb of standard Calderon-Zygmund singular integral operators T with a Lipschitz function b. The corresponding results are also obtained on the commutators Sb generated by b with singular integral operators S with variable kernels.