捕食者具脉冲扰动与相互干扰的阶段结构时滞捕食-食饵模型

讨论了与害虫管理相关的一类捕食者具脉冲扰动与相互干扰的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.我们的结论为现实的害虫管理提供了一定的理论依据.     

DELAY DEPENDENT ROBUST DISSIPATIVE CONTROL FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS

We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities (LMIs), then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.     

带有Neumann边界条件的$k$维Minkowski平均曲率系统解的存在性

我们运用扰动方法证明了带有Minkowski平均算子非局部Neumann系统$$\begin{aligned}\begin{cases}\Big(r^{N-1}\frac{u''}{\sqrt{1-u''^{2}}}\Big)''=r^{N-1}f(r, u),\\\ r\in(0, 1),\ \ \ u''(0)=0,\ \ \ u''(1)=\int_{0}^{1}u''(s)dg(s)\\\end{cases}\end{aligned}$$解的存在性, 其中$k, N\geq1$是整数, $f=(f_{1},f_{2},\ldots,f_{k}):[0, 1]\times\mathbb{R}^{k}\rightarrow\mathbb{R}^{k}$连续且$g:[0, 1]\rightarrow\mathbb{R}^{k}$是有界变差函数.     

Experimental studies on the multistage constant modulus array for the estimation of directions-of-arrival

The performance of the multistage Constant Modulus (CM) array, one of the most striking blind beamforming algorithms, for the source Directions-of-Arrival (DOA) estimation was analyzed via computer simulations and water tank experiments, and was compared to that of other DOA estimation algorithms including the ‘non-blind‘ and the ‘blind‘. Firstly, a nominal array model and an array model with gain and phase perturbations were established,respectively. Secondly, the multistage CM array algorithm was described and computer simulations were conducted. Simulation results showed that the multistage CM array could correctly estimate the DOA at the same time when the sources were blindly recovered, and the angle separating ability of the algorithm was beyond the Rayleigh resolution limit. By changing the variance of the array model errors, it was also verified that the multistage CM array was more robust to the errors than some other algorithms mentioned in this paper. Finally, water tank experiments and data processing results were provided. Situations with different array sizes and source angular separations were considered. It was shown that the results were in good agreement with computer simulations. Results of computer simulations and water tank experiments verified that the DOAs of the multiple independent sources could be blindly and robustly estimated with the multistage CM array.     

超Poincare不等式在Lp空间上的推广及应用

该文建立了L^p(μ )空间上的超Poincare不等式,得到了L^p(μ) 上半群的半紧性和紧性的充要条件及相应的扰动结果,同时给出超Poincare不等式成立的一个充分条件,推广了L²(μ )$上的相关结论.作为应用,文中最后讨论了黎曼流形上一类非对称扩散算子的本质谱.     

波前为运动气流的激波-激波扰动关系式

本文首先把Whitham的波前为静止均匀气体的激波-激波扰动关系推广到波前为静止非均匀气体的情况,然后在此基础上导出波前为运动气流条件下的激波-激波扰动关系的三维矢量表达式,进而给出二维和轴对称条件下的表达式.至此,加上Chester,Whitham以及作者的工作,波前为运动气流的激波动力学方程组的完整体系已基本建立.     

两种群非自治Lotka-Volterra竞争扩散系统的概周期解

本文讨论两种群概周期竞争扩散系统，利用微分不等式，证明了系统概周期解的存在、唯一性及其在壳扰动下的稳定性．     

具有未知扰动的广义系统的故障检测

研究具有未知扰动的随机广义系统的故障检测问题,在合理的条件下,利用状态变换从原系统中分离出一个与未知扰动解耦的降阶子系统,构造了该随机子系统稳定的滤波器,给出了输出偏差量的统计特性,在此基础上,实现了系统故障的检测．     

偏光棱镜调制器调制光强扰动的理论分析

以格兰-泰勒棱镜为例，根据实验现象对透射光强随旋转角扰动的原因进行了理论分析。实验中发现，透射光强曲线随着入射角的微小变化而偏离马吕斯定律，出现了周期性扰动。通过格兰-泰勒棱镜的单色偏振光束产生的干涉，再加上晶体-空气隙界面处反射比的因素，使得出射光强依赖于入射角。引入了扰动因子的概念，并系统讨论了扰动因子所造成的影响，从而得出了减小扰动的方法。理论研究结果与实验符合较好。为偏光棱镜的优化设计、生产及使用提供了理论基础。     

随机发展方程小扰动大偏差原理的统一方法

设X^ε=|X^ε(t);0≤t≤1|(ε>0)是由随机发展方程 dX^ε(t)=^ε(1/2)σ(X^ε(t))dB(t)+b(X^ε(t),ν(t))dt控制的随机过程,其中ν(t)是与Brown运动B(·)独立的随机过程。讨论了|(X^ε,ν(·));ε>0|的大偏差性质;在特殊情形下,给出了精确的速率函数,解决了Eizenberg和Freidlin所提的一个问题。此外,还得到一个一般性大偏差定理。