Transmission characteristics of photonic crystal fiber gas cell used in frequency stabilized laser

We measure the transmission characteristics of hollow-core photonic crystal fiber （HC-PCF） gas cells with ferrule- and fusion-spliced configurations, and near- and far-field images of the HC-PCF are observed. Results show that the center of mass （COM） of the far-field image varies with the laser frequency and temperature, and the moving COM relates to the oscillatory transmission. Using a model of the spatial interference, we first demonstrate that mainly the modes with asymmetric phase distributions affect the COM position. The frequency stabilization performances of the lasers are compared. The fusion-spliced gas cell shows better performance than the ferrule-spliced one.     

切换奇异系统的有限时间稳定

本文研究了一类连续切换奇异系统的有限时间稳定和状态反馈控制问题.首先,讨论了连续切换奇异系统解的存在条件,然后给出连续切换奇异系统有限时间稳定和有限时间有界的概念;其次,利用模型依赖平均驻留时间方法和Lyapunov函数方法,分别给出切换奇异系统是正则、脉冲自由且有限时间稳定和有限时间有界的充分条件,并设计状态反馈控制器,使得闭环系统有限时间稳定和有限时间有界且具有H∞性能指标γ;最后通过数值算例验证了本文方法的有效性.     

循环频移方法中射频信号的相位偏移对多载波稳定性及平坦度的影响(英文)

为了得到高性能的多载波光源,研究了射频信号中不同相位差对光多载波的影响.通过理论分析可得,随着相位差从90°降至0°,光多载波性能会逐渐变差,但是相位差偏与90°相差不大时,性能不会下降太多.实验中通过移相器改变相位差,使相位差为90°,45°,0°,得到循环前IQ调制器的输出光谱,并对比循环后光多载波性能.实验结果显示,相位差为90°时,循环前IQ调制器输出为较好的单边带光谱,循环后输出50条平坦稳定光多载波;相位差为45°时,光多载波质量变差;相位差为0°时,得不到光多载波.因此,射频信号相位差为90°时,光多载波的性能最佳,随着相位差变小,性能下降,但是相位差为45°时,产生的光多载波仍可应用于光通信.     

基于成像分辨率的光电成像系统抖动要求

针对图像抖动导致光电成像系统的成像分辨率降低的问题,提出了一种基于成像分辨率的光电成像系统抖动要求分析方法.根据抖动频率将抖动分为高频抖动与低频抖动,高频抖动按高斯、正弦、线性等三种抖动分布考虑,低频抖动按线性抖动分布考虑,给出了各抖动分布对应的调制传递函数模型,进而建立了含抖动全系统调制传递函数模型.基于成像分辨率要求与调制传递函数模型,给出了抖动要求定量分析方法,并给出了相应分析流程与算法.根据流程,结合特定系统参量,进行了仿真分析,结果表明:在一定成像分辨率条件下,低频视轴抖动可允许值最大,其次为高频线性抖动可允许值,最后为高频正弦与高斯抖动可允许值.     

Stable weakly shadowable volume-preserving systems are volume-hyperbolic

We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.     

Stability vs. optimality in selfish ring routing

We study asymmetric atomic selfish routing in ring networks, which has diverse practical applications in network design and analysis. We are concerned with minimizing the maximum latency of source-destination node-pairs over links with linear latencies. We show that there exists an optimal solution that is a 9-approximate Nash equilibrium, significantly improving the existing upper bound of 54 on the instability factor. We present fast implementation of the best response dynamics for computing a Nash equilibrium. Furthermore, we perform empirical study on the price of stability, narrowing the gap between the lower and upper bounds to 0.7436.     

非线性时变系统的Aeyels-Peuteman类型的Matrosov定理

主要讨论非线性时变系统的一致渐近稳定性,给出Aeyels-Peuteman类型的Matrosov定理定理.与一般的关于一致渐近稳定性的Matrosov定理不同,对Lyapunov函数的要求是不必可微的,并且Lyapunov函数的导数不必严格小于等于零.     

一类三种群捕食者-食饵模型中交错扩散导致的Turing不稳定

本文研究一类具有种内竞争的三种群捕食者-食饵模型的强耦合交错扩散系统,发现当捕食者对食饵的捕获水平高于食饵的种内竞争水平时,捕食者的大的交错扩散系数能够导致Turing不稳定.     

UNSTABLE SOLUTIONS TO A CLASS OF VECTOR DIFFERENTIAL EQUATIONS OF SIXTH ORDER

In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provide an example to show the feasibility of our results. Our results extend and improve two related results in the previous literature from scalar cases to vectorial cases.     

一类广义变分不等式问题的神经网络模型

基于解的充分必要条件,提出一类广义变分不等式问题的神经网络模型.通过构造Lyapunov函数,在适当的条件下证明了新模型是Lyapunov稳定的,并且全局收敛和指数收敛于原问题的解.数值试验表明,该神经网络模型是有效的和可行的.