特征线法

In the second chapter, the problem of the optimal inputting rate control for a class of competitive population dynamics system with age-structure is discussed. By means of characteristic line, Gronwall Lemma, Bellman Lemma, adjoint system and so on, the Lipschitz continuity properties of the system in terms of the control variable is certificated, and the necessary condition of the optimal control is obtained.

第二章讨论了一类具有年龄结构的竞争种群系统最优输入率控制问题，综合应用特征线法，Gronwall引理，Bellman引理，共轭系统等知识，证明了系统解关于控制变量的Lipschitz连续性，给出了控制为最优的必要条件。

The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland\'s variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.

用特征线法表示出偏微分方程的形式解，利用Ekeland变分原理，Gronwall引理和共轭系统证明了最优控制的存在性，并借助于法锥概念得到了最优控制的必要性条件。

Based on one-dimensional Method of Characteristics, a numerical model of pressure-wave progation if presented in this paper. A special code is programmed to analyze and calculate waterhammer resulted from rapid opening or closing of valve in the experimental sodium loop of Fast Breeder Reactor.

本文利用一维特征线法，建立了压力波传播的数学模型，并编制了专用程序，利用该程序对快堆实验钠回路中由于阀门的快速开启与关闭引起的压力波的传播进行了分析计算。

In point of the physical characters,it is better to differentiate the time derivative in the characteristic direction than intime direction.

1.4中针对流体的流动以对流为主的物理特性，采用特征线法去对时间导数项离散，使截断因子比通常的时间方向离散小得多，更好地反映了问题的物理特性。

A modified characteristic line method for numerical calculation of steady oscillating current is proposed.

本文研究了气液活塞泵的运动机理，提出了一种用于定常振荡流数值计算的"修正特征线法"。

The traffic momentum differential equation and Euler's equation for the ramp junction is founded by means of differential calculus in this paper,the traffic momentum differential coupled equation is solved by characteristic curve method,two groups of characteristic curves and corresponding related equation in high speedstates and low speedstates are presented.

采用特征线法对运动微分方程组进行分析求解，在高速低密度区和低速高密度区分别得到了两组特征线和对应的特征关系式。

The solution to the one dimensional hyperbolic runoff equations and sediment equation are obtained respectively by using the characteristics method and finite difference method.

利用水力学原理建立了坡面降雨径流和土壤侵蚀模型，分别采用特征线法和有限差分法对径流量和土壤侵蚀量进行了求解，并针对具体降雨事件进行了模拟计算，计算结果与试验小区实测值基本一致。

Solving the model by characteristic curve method, two groups of characteristic curves and corresponding related equation are gained in high speedstates and low speedstates.

5采用特征线法对模型进行分析求解，在高速低密度区和低速高密度区分别得到了两组特征线和对应的特征关系式。

Moreover, the author analyzed and researched dynamic load of the needle valve spring by adopting the method of characteristic line and proposed to design the needle valve spring using its dynamic load.

运用特征线法研究和分析针阀弹簧的动力负荷，推导出采用动载法设计针阀弹簧的方法，从而提高设计的稳健性。高压共轨喷油器精度和技术要求高，加工难度大。

This paper reviews and summarizes the progress in this field as follows: the mathematical model and the difficulty of the analytical solutions is introduced; discusses the latest progress of the numerical solutions is discussed; the finite difference method, the Godunov method, the Boltzmann method, and the KFVS method of one-dimensional dam-break problem are introduced; the TVD method, the discontinuous finite element method, the finite volume method and characteristic method of two-dimensional dam-break problem are discussed; the applicability, the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.

回顾和总结了国内外对溃坝水流演进问题的研究进展：介绍了溃坝水流的数学模型及解析解法存在的困难，进而讨论了数值解法的最新进展；论述了求解溃坝水流一维问题的有限差分法、近似黎曼解的Godunov格式法、Boltzmann法、KFVS法和二维问题的TVD格式法、间断有限元法、有限体积法、特征线法，并分析了各种方法的适用范围和优缺点，及讨论了限制函数的使用；介绍了利用自由水面追踪方法计算溃坝水流的研究进展，并根据目前存在的不足和实际工程的需要，提出了进一步研究的方向和发展趋势。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。