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The paper has used concise methods of logical analysis and reasoning to describe the relation between the first-order quasilinear partial differential equation and its system of characteristic equation.

对一阶拟线性偏微分方程与其特征方程组的关系,文中给出了简洁的逻辑分析和推导方法。

Using tools from dynamical system theory, such as phase space diagrams, Frequency analysis, Poincare sections and the calculation of statistical quantity of chaos: the correlation dimension, Reni entropy, Laypunov exponent and so on, the different solutions to the Navier-Stokes equations at different values of the Reynolds number have been identified and characterized through reconstructing the phase space of velocity time series by means of time delay and dimension embeding.

通过时间延迟和维数的嵌入对速度时间序列重构相空间,利用非线性动力系统理论方法诸如相空间分析,频谱分析,Poincare映射,以及通过对混沌统计量:关联维数,Reni熵,Laypunov指数等计算,对不同雷诺数N-S方程解的特征作了分辨。

Here we take the characteristic functions of Laplace operator as coordinate functions, then a standard Galerkin method naturally leads to a semidiscrete scheme with structure preserving property for the continuous system.

这样的离散化模型含有原连续模型的几何与物理特征,用它能够更好的模拟发展型微分方程的长时间的和全局的动力行为。

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As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸,那乌黑、忧郁的眼睛,她便会相信,他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失

But because of its youthful corporate culture—most people are hustled out of the door in their mid-40s—it had no one to send.

但是因为该公司年轻的企业文化——大多数员工在40来岁的时候都被请出公司——一时间没有好的人选。