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The Chebyshev polynomial approximation is used to investigate the stochastic bifurcation of van der Pol system with two-sided barriers.

利用随机光滑动力系统的Chebyshev正交多项式逼近方法，研究了双边约束条件下随机van der Pol系统的分岔现象。

The random system is reduced to its equivalent deterministic one by Chebyshev polynomial approximation, and the response of the stochastic system can be obtained by the deterministic methods.

首先用Chebyshev多项式逼近法将随机系统化成与其等价的确定性系统，然后通过等价确定性系统来探索随机Duffing-Van der pol系统的对称破裂分岔现象。

Numerical simulations show that similar to their counterpart in deterministic nonlinear system some symmetry-breaking bifurcation may occur in the stochastic Duffing-Van der pol system, and Chebyshev polynomial approximation is an effective approach in solving dynamical problems of nonlinear system with random parameter.

数值模拟显示随机Duffing-Van der pol系统与确定性均值参数系统有着类似的对称破裂分岔行为，文中的主要数值结果表明Chebyshev多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法。

Numerical results for the original stochastic Duffing-van der Pol system obtained separately by the Mento-Carlo method and the Chebyshev polynomial approximation are compared to show the effectiveness and efficiency of the latter method in solving the nonlinear dynamical problems of system with bounded random parameters.

数值模拟结果显示，Chebyshev正交多项式逼近法是研究含有界随机参数的耦合非线性动力学系统的一种有效方法。

By this means,the problem of deciding whether an n×n doubly stochastic circulant matrix A of order 3 is a prime is complet...

应用此原理，本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题，并给出了n阶双随机循环矩阵中一类具有位数4的素元。

By this means, the problem of deciding whether an n x n doubly stochastic circulant matrix A of order 3 is a prime is completely solved.

应用此原理，本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题，并给出了n阶双随机循环矩阵中一类具有位数4的素元。

Doubly stochastic circulant matrix ; shift ; prime matrix

双随机循环矩阵；移位；素元

The classification of primes in the doubly stochastic circulant matrices is now explored.

本文研究了双随机循环矩阵中素元的分类问题。

In Chapter 2,we deal with the robust stability and stabilization problems for a class of stochastic time-delay interval uncertain systems with nonlinear dis-turbances by developing delay-dependent analysis techniques,where the It?

第二章通过发展一个时滞依赖分析技巧，讨论了一类带有非线性干扰和区间不确定参数的随机时滞系统的鲁棒镇定问题。

In the fifth and the sixth chapter, a class of interval BAM neural networks withmixed delays under uncertainty and a class of stochastic interval BAM neural networkswith mixed delays are introduced and studied, which include many well-known neuralnetworks as special cases.

第五章和第六章分别介绍了一类具有不确定性的带混合时滞的区间BAM神经网络和一类带混合时滞的区间随机BAM神经网络，这里混合时滞意味着同时出现离散和分布时滞。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。