激光与DNA作用系统的随机共振研究

建立了激光与ＤＮＡ分子系统相互作用的Ｆｏｋｋｅｒ－Ｐｌａｎｃｋ方程，通过对该方程的数值研究，发现在绝热近似下，系统发生随机共振，噪声强度，激光振幅和频率协同作用共同制约着生物系统的演化过程，噪声强度在生物系统遗传变异过程中可能起重要作用。     

生产函数的优化回归方法

本文讨沦了生产函数的理论定 义及常用方法，并提出了生产函数的一种优化技术．利用数据包络分析方法确定生产前沿面，求样本点在该边界面上的投影，然后对投影点进行统计回归即获得随机前沿生产函数．     

三维随机Ising模型的亚稳态性(Ⅱ)

讨论三维格点环面上随机Ising模型当温度趋向零时的亚稳态性,确定从自旋全为-1的组态到自旋全为+1的组态的最大似然路径和临界组态,并计算出从自旋全为-1的组态出发首次到达自旋全为+1的组态的首达时间的渐近对数估计。证明利用一族带指数扰动的Markov链的大偏差估计。     

Energy-Momentum Pseudo-Tensor of Relic Gravitational Wave of Both the Polarized States

Unlike usual celestial gravitational waves, the relic gravitational waves （RGWs） form random signals in curved spacetime background. We calculate the energy-momentum pseudo-tensor of a certain component of the RGWs propagating along arbitrary directions in Cartesian coordinates. It is found that the energy density of RGWs is positive definitely, and the momentum density components have reasonable behaviour. Such results may provide a theoretical basis for the detection of RGWs.     

损伤断裂图型演化的统计描述

本文采用动力学演化与随机跃迁并存的模型,研究损伤断裂图型的演化规律。根据演化的终态,损伤演化可分为整体稳定(GS)和演化引起剧变(EIC)两种模式,后者联系于断裂现象。本文引入统计描述,并指出,即使微损伤的连接规律是确定性的,无序介质中断裂的出现亦应以概率分布函数描写。     

SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS

The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs.     

线性复值随机跳跃——扩散方程隐Miltein格式的渐近稳定性

给出了线性复值随机跳跃－扩散方程隐Ｍｉｌｔｅｉｎ格式的渐近均方的必要条件，并揭示了离散步长的稳定区域与格式隐性之间的关系。     

A Simple Calculation Approach for the Second－Harmonic Sound Beam Generated by an Arbitrary Distribution Source

We present a simple calculation approach for the fundamental and second-harmonic sound beams with an arbitrary distribution source in the quasilinear approximation. The analysis is based on the assumption that the source function with an arbitrary geometry and distribution is expanded into the sum of a set of two-dimensional Gaussian functions. The two- and five-dimensional integral solutions for the fundamental and second-harmonic fields are, respectively, reduced in terms of Gaussian functions and simple one-dimensional integrals. The numerical evaluation of field distributions is then greatly simplified.