Statistically periodic processes and toeplitz(α by β) matrices

If each element in a Toeplitz matrix is replaced by an by matrix and the original constraints preserved, the result is a doubly infinite matrix with periodic structure called a toeplitz_{( by)} matrix. Such matrices are a basic tool for describing, generating, estimating, filtering, synchronizing, and analyzing information-theoretic functions for statistically periodic processes.     

一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型的Hopf分岔与周期解问题

研究了一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型. 给出了产生Hopf分岔的临界时滞条件, 利用Mawhin重合度理论,探讨了该模型的周期解问题. 关键词： 时滞 厄尔尼诺-南方涛动模型 Hopf分岔 周期解     

高功率光纤中传输光模式与其波长相关性研究

针对高功率光纤激光模式诊断和光谱诊断的需求,研究了光纤中传输模式的波长相关性,数值计算了光纤中各个模式的模场分布随波长的变化曲线及相应的光束质量,采用双傅里叶变换F~2法实际测量了光纤模式成分与波长的关系曲线.结果表明,光纤中各个模式的模场分布随波长变化,波长越长,模场面积越大;模式的光束质量随波长变化不大,但在截止频率附近明显变差;光纤中各个模式的功率占比与波长有关.     

复杂网络中考虑不完全免疫的病毒传播研究

复杂网络中不完全免疫包括免疫失败和免疫失效两种情况,本文研究两者同时存在对网络病毒传播行为的影响,基于平均场理论,提出一种新的传播模型.理论分析表明,免疫失败和免疫失效同时存在显著降低了网络的传播临界值,增强了病毒的感染程度.根据传播临界值与免疫节点密度、免疫成功率以及免疫失效率之间的关系,给出有效控制网络病毒传播的策略.通过数值仿真进行验证。     

Multivariate stochastic delay differential equations and CAR representations of CARMA processes

In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a CAR($\infty$) representation. Furthermore, we show how the CAR($\infty$) representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.     

Unbound States in an Almost Infinite Deep Potential

The behavior of a quantum particle in an almost infinite deep potential is investigated. By means of analytical and numerical methods, it is demonstrated that even if the potential is infinitely deep, the particle's eigenstate can still be unbound, which contradicts the previous belief that an infinite deep potential can only sustain bound states. These findings shed new light on the eigenstate problem of quantum mechanics.     

A note on the existence of stochastic integro‐differential equations with memory

In this study, we investigate the existence of mild solutions for a class of impulsive neutral stochastic integro‐differential equations with infinite delays, using the Krasnoselskii–Schaefer type fixed point theorem combined with theories of resolvent operators. As an application, an example is provided to illustrate the obtained result. Copyright © 2014 John Wiley & Sons, Ltd.