Numerical study of threshold gain behavior for a THz random laser in a two-dimensional active disordered medium with a three-level atomic system

By numerically solving Maxwell’s equations and rate equations in a two-dimensional (2D) active random media made of ruby grains with a three-level atomic system, the threshold gain behavior for a THz random laser is investigated. The spectral intensity variation with the pumping rate is calculated for both the transverse magnetic (TM) field and the transverse electric (TE) field. The computed results show that THz random lasing could occur in a 2D disordered medium for both the TM and TE cases. Further analysis reveals that the THz lasing threshold for TM fields is lower than that for TE fields.     

RESEARCH NOTES On the support of super-Brownian motion with super-Brownian immigration

The support properties of the super Brownian motion with random immigration Xρ1 are considered,where the immigration rate is governed by the trajectory of another super-Brownian motion ρ. When both the initial state Xρo of the process and the immigration rate process ρo are of finite measure and with compact supports, the probability of the support of the process Xρi dominated by a ball is given by the solutions of a singular elliptic boundary value problem.     

随机Taylor级数的增长级

讨论了复平面上的随机Ｔａｙｌｏｒ级数ｆｗ（ｚ）的增长级，证明了ｆｗ（ｚ）沿任一射线的增长级几乎必然（ａ．ｓ．）为ρ。     

模糊随机微分方程

讨论了模糊随机微分方程解的存在唯一性,并给出一阶线性模糊随机微分方程解的表达式.     

伯努利集上的两个组合结论的推广

得到了伯努利集在n个字母情况下的两个组合性质,从而推广了Aldo de Luca相应的研究结果,同时给出了n=3时的两个推论.     

连续时间随机多址系统性能分析

采用平均周期分析方法对时间连续型随机多址系统进行了分析，得到了系统的报文分组发送成功的平均长度公式、报文分组发生碰撞的平均长度公式和空闲时间的平均长度公式，给出了系统的吞吐量、碰撞率和空闲率．最后，还给出了系统的计算机模拟实验结果．     

独立B值随机元序列的Wittmann型极限定理

给出在没有附加 Ｓｎ／ａｎ Ｐ ０ 等概率条件下， 独立 Ｂ 值随机元序列的 Ｗ ｉｔｔｍ ａｎｎ 型极限定理的一般形式     

自校正控制器加权网络选取的限制条件

从理论上分析了采用自校正控制器设计系统时，目标函数加权网络的选取对系统稳态偏差的影响，给出了使系统无稳态偏差对加权网络选取的限制条件。     

关于随机环境中下临界分枝过程灭绝时均值的界

在经典分枝过程的基础上研究了随机环境中的分枝过程,运用泰勒定理、中值定理得出了随机环境中下临界分枝过程的灭绝时均值的界,对分枝过程的发展有重要作用.并且在二项分布繁衍概率母函数的两状态独立同分布随机环境情况下,对灭绝时均值的界的确定给出了一个算例.     

Value distribution of a random analytic Dirichlet series of order zero

The value distribution of a kind of random analytic Drichlet series with order zero is studied.