稳定性条件

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

This method is based on the theory of stability of linear time-varying systems. It realizes the synchronization by transferring high time-varying systems into low linear constant coefficient system.

该方法基于线性时变连续系统的稳定性理论，通过把高维时变系统的稳定性判定简化为低维定常辅助方程稳定性判定，从而减弱了时变系统的稳定性条件，实现了系统的耦合同步。

By transforming the delayed neural model to the describer model and then employing the Lyapunov-Krasovskii stability theorem, linear matrix inequality LMI technique, S procedure, and some algebraic inequality method, a new sufficient condition is derived, which is determined by the coefficients of the model and includes more tuning parameters for determining the globally asymptotical stability of recurrent neural networks with time-varying delay.

首先将要研究的模型转化为描述系统模型，然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式技术、S过程和代数不等式方法，得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件，并将它应用于常时滞神经网络和时滞细胞神经网络模型，分别得到了相应的全局渐近稳定性条件。

The stability of the n director around the grooves was studied. In one-constant model for each director, the rude condition is that the elastic constant of the n director is the maximum.

研究了双轴向列相液晶在表面沟槽上锚定的稳定性问题；稳定性条件在双轴向列相单一弹性常数近似下为n指向矢的弹性常数最大。

From finite difference equation of unsteady-state heat conduction ,according to vonNeumann method about scheme stability,the explicit scheme stability condition of two dimension computational heat conduction was given.

从非稳态导热的离散方程出发，根据VonNeumann的格式稳定性判别方法，给出二维导热数值计算显式格式的稳定性条件。

Firstly,the differential equation with parameters is given,at the same time,in order to let the truncation error of differential equation reach O(Δt~2+Δx~4) as high as possible,the method of undetermined coefficent is used to appropriately select the expression of these parameters.Secondly,the stability condition of the scheme derived is given by using the Fourier method of stability analysi...

首先给出了含参变量的差分方程，并用待定系数法适当地选取了这些参数的表示式，以使差分方程的截断误差阶尽可能高地达到了O(Δt2+Δx4)；其次用稳定性分析的Fourier方法给出了所得格式的稳定性条件；然后给出了确定差分格式中参数的两种方法，得到了一个稳定性条件为r/3的分支稳定的高精度显式差分格式；最后给出了数值例子，数值结果表明了本文格式较现有同类格式的优越性和理论分析的正确性。

A variable-step modified Euler time integration method is proposed and analyzed. Four major factors that affect the efficiency of the variable-step modified Euler time integration method are discussed. These include stability and accuracy analysis for the damped fix-step modified Euler integration formula, adjustment method of the fix-step basic integration formula to accommodate step-size changes, suitable range of the step-size selection strategy based on truncation error concept and development of the step-size selection strategy based on apparent frequency concept to satisfied the specified error bound and stability condition.

提出了变步长修正Euler时间积分法，详细讨论了影响变步长修正Euler时间积分算法效率的四个主要因素，它们包括：有阻尼问题的修正Euler法的稳定性和精度分析，调整固定步长的基本积分公式使之容纳步长大小变化的研究，基于截断误差概念的步长大小选择策略适用范围的讨论，同时满足规定误差界和稳定性条件的、基于表观频率概念的步长大小选择策略的建立。

By applying game theory and contraction mapping theorem, a sufficient condition for the existence and uniqueness of Nash equilibrium in a multi-person non-cooperative game is proposed. Another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory. It can demonstrate the stability condition for supply-demand equilibrium in economic theory. So the stable supply-demand equilibrium of cobweb model in economics is in fact equivalent to the Nash equilibrium in game theory. That is a brand-new explanation for the conclusion in traditional economic theory.

应用博弈论中的有关理论与压缩映象定理寻求一类多ISP非合作对策纳什均衡存在、唯一的充分条件，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件；说明了经济学中蛛网模型的稳定供求均衡实际上就是对策理论中的纳什均衡，从而给出了传统经济理论中关于这一结论的新解释。

In this project, the stability of a class of complex dynamical system with infinite dimensions is investigated. The dynamical systems are described by the infinite differential equations with time delays. The comparison principle of the stability for the infinite dimension system is obtained.

本项目研究一类以无限个具有时间滞后的常微分方程关联而成的复杂动力系统的稳定性，建立了这类无限维系统中的比较原理，得到了无限维比较系统的稳定性条件和比较系统的集结方法，建立了无限维复杂时滞系统稳定性分析的矢量Liapunov方法。

The stability and bifurcation of a thin elastic rod under tension and twist are analyzed, and the results can be applied to determine the stability of a thin helical rod by use of the equivalent stiffness.

分析受拉扭弹性细杆的稳定性和分岔，且利用等效刚度概念将弹性杆的稳定性条件应用于对细长螺旋杆稳定性的判断。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。