Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T _c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T _c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T _c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.      

Maximally Clustered Elements and Schubert Varieties

We introduce and study a class of “maximally clustered” elements for simply laced Coxeter groups. Such elements include as a special case the freely braided elements of Green and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. We show that any reduced expression for a maximally clustered element is short-braid equivalent to a “contracted” expression, which can be characterized in terms of certain subwords called “braid clusters”. We establish some properties of contracted reduced expressions and apply these to the study of Schubert varieties in the simply laced setting. Specifically, we give a smoothness criterion for Schubert varieties indexed by maximally clustered elements. Received December 30, 2005     

UPML formulation for truncating conductive media in curvilinear coordinates

This work presents a formulation based on UPML for truncating conductive media by using a local and non-orthogonal coordinate system to solve Maxwell’s equations by the FDTD method. The detailed procedure for obtaining the UPML equations for this case is shown and the complete equation set is provided.     

逐步增加的Ⅱ型截尾下系统可靠性的Bayes分析及寿命预测

在逐步增加的型截尾模型下,研究部件寿命服从双参数指数分布的冷贮备串联系统可靠性指标的Bayes估计及单样本场合未来观测值的预测问题.在两个参数均未知的情形下,分别在平方损失(SE)、LINEX损失和熵(General Entropy,GE)损失函数下给出两个参数及可靠性指标的Bayes估计,对于超参数的确定,给出一种新的方法;并讨论了单样本场合未来观测值的预测问题,给出预测分布及预测区间;最后利用随机模拟方法进行比较,并对结果进行了讨论.     

Complex projections of completely positive quaternionic maps

We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007.     

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将理想全二维磁流体(MHD)稳定性数值代码GATO成功移植到HL-2A高性能计算系统,并用其模拟研究了HL-2A装置一次典型弹丸注入实验的等离子体的理想MHD稳定性。利用HL-2A装置第4050次放电的实验数据,应用EFIT代码重建了几个时间片的平衡位形,然后应用GATO代码对每个平衡位形的MHD稳定性进行了计算。通过对结果进行分析比较得出初步结论,由于弹丸注入而造成的反剪切位形的致稳作用,可以提高等离子体的约束性能。     

一类具有脉冲效应的食饵依赖捕食系统分析

基于害虫防治,该文提出了一类具有脉冲效应的食饵依赖捕食系统并进行了分析,根据Floquet乘子理论,我们获得了害虫根除周期解全局渐近稳定与系统持续生存条件.     

一类哈密顿系统的Abel积分之比单调性的判据

研究了一类哈密顿系统的两个Abel积分比值的单调性的条件,指出这个单调性条件可由文中给出的两个判定函数直接确定.     

脉冲时滞抛物型偏微分方程组解的振动性

研究一类脉冲时滞抛物型偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在两类不同边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

Email: valery{at}techunix.technion.ac.il Received on January 31, 2006; Accepted on October 5, 2006 An infinite horizon linear-quadratic optimal control problemfor a singularly perturbed system with multiple point-wise anddistributed small delays in the state variable is considered.The set of Riccati-type equations, associated with this problemby the control optimality conditions, is studied. Since thesystem in the control problem is singularly perturbed, the equationsof this set are also perturbed by a small parameter of the singularperturbations. The zero-order asymptotic solution to this setof equations is constructed and justified. Based on this asymptoticsolution, parameter-free sufficient conditions for the existenceand uniqueness of solution to the original optimal control problemare established.