On Tanaka formulae for (α,d,β)-superprocesses

In this paper,Tanaka formulae for (α,d,β)-superprocesses in the dimensions where the local time exists are established under the optimal initial condition.     

Evolution of Weighted Networks by Duplication-Divergence Mechanism

The duplication and divergence process is ubiquitous in nature and man-made networks. Motivated by the duplication-divergence mechanism which depicts the growth of protein networks, we propose a weighted network model in which topological evolution is coupled with weight dynamics. Large scale numerical results indicate that our model can naturally generate networks with power-law-like distributions of degree, strength and weight. The degree-strength correlation is illustrated as well. These properties are in agreement well with empirical data observed in real-world systems. Furthermore, by altering the retention probability δ, weighted, structured exponential networks are realized.     

Teleportation for an Ionic Entangled Internal State by Entanglement Swapping

We present an effective scheme to teleport an unknown ionic entangled internal state via trapped ions without joint Bell-state measurement. In the constructed quantum channel process, we adopt entanglement swapping to avoid decrease of entanglement during the distribution of particles. Thus our scheme provides new prospects for quantum teleportation over longer distance. The distinct advantages of our scheme are that our scheme is insensitive to heating of vibrational mode and can be generalized to teleport an N-ion electronic entangled GHZ class state. Furthermore, in our scheme the success probability can reach 1.     

Vacuum Fluctuations and Motion of a Charged Test Particle in a Cylindrical Spacetime

The effects of quantum electromagnetic fluctuations upon the motion of a test charged particle are examined in a cylindrical spacetime in which one spatial is compactified. The mean squared fluctuations in the velocity and position of the test particle are calculated. It is found that the random motion of the test particle will be anisotropic. The possible consequences for theories with extra compactified spatial dimensions are discussed.     

THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE SOLVABILITY OF A CLASS OF THE MATRIX INVERSE PROBLEM

Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. The best approximate solution by the above solution set is given. Thus the open problem in [1] is solved.     

置换环上的稳定矩阵

本文证明了置换环上的正则稳定矩阵是幂等矩阵和可逆矩阵的积,进一步证明了置换环上的正则稳定矩阵可以对角化。     

尾年金分布的存在性和结构

本文主要是在年金分布的基础上, 推广、定义并研究了一类$r$尾年金分布的存在性和结构, 给出了这类分布的存在性条件, 证明了在一定条件下, $r$尾年金分布是年金分布与某一特殊$r$尾年金分布的混合.     

Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES

This article will combine the finite element method, the interpolated coefftcient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.     

Epidemic Dynamics with Feedback Mechanism in Exponential Networks

We introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals, Furthermore, it does not change the epidemic threshold （critical point） λc. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections.