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Based on pedagogical experience, a scheme of diagrammatic representation of fundamental dependent equations relating thermodynamic functions is suggested.

通过多年教学实践，归纳出热力学函数间基本关系式的图示法。

This was demonstrated by a simulation with spatial dependent rate equations and experiment results of a plano-concave Nd:YVO4 laser.

我们利用一个纵向相关的速率方程式来描述与研究这个在平凹共振腔掺钕钒酸钇雷射的实验。

Based on the conventional SIMPLE algorithm, a set of new dependent variables of momentum equations is introduced to extend the application of the pressure correction method for compressibe viscous flows and to accelerate the convergence.

在传统SIMPLE算法的基础上，本文提出了一种新的动量方程流场控制变量的选取方法，进而使本文所提出的压力修正法更适用于可压粘性流动的数值求解，同时也加快了收敛速度。

Thus, the coefficients of governing equations are pressure dependent and consequently the analysis of transients in the two-component flows is more complex and difficult than in single-component flows.

而且，控制方程的系数是与压力相关的，因此在含有两种物质瞬变流动分析比单相流动更为复杂和困难。

Many natural phenomena and physical laws can be described by time dependent nonlinear differential equations, such as heat conduction equation, sound wave and elastic wave equation, reaction diffusion and convection diffusion equation, fluid and aerodynamics equations, etc.

大多数的自然现象与物理规律都可归结为与时间相关的非线性偏微分方程，诸如热传导方程、声波与弹性波方程、反应扩散与对流扩散方程、流体与气体力学方程组等发展方程。

And then the influence of two of the damage models, the Kachanov and the gradient dependent constitutive equations, on the well posed properties of the fundamental equations in continuum damage mechanics is studied according to th.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即 Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

The Galerkin's method was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary differential equations with time dependent coefficients,which can be solved with numerical methods.

对于电梯工业来说，目前世界上绝大部分电梯仍然是依靠钢丝绳提升的曳引式电梯。

The phase separation kinetics of liquid crystalline polymer/flexible polymer blend was studied with the coupled time dependent Ginzberg Landau equations for compositional order parameter and orientational order parameter S ij , which were numerically solved by means of the cell dynamical system in two dimensions .

利用元胞动力学方法在二维情况下对浓度、取向序参量的含时Ginzberg Landau方程进行数值求解，研究了液晶聚合物/柔性链聚合物共混体系的相分离动力学，考察了浓度、取向有序过程的耦合对相分离形态的影响。结果表明，此耦合作用对相分离的时间进程以及相分离图样的空间排布都有影响。

By using the theory of linear evolution systems and Sadovskii's fixed point theorem, chapter3 deals with the existence of mid-solutions,strong solutions for the Cauchy problems of neutralabstract functional differential equations dependent on time with unbounded delay, here theright function in the equations satisfies the Caratheodory conditions.

第三章利用线性发展系统理论和Sadovskii不动点定理研究了具有无穷时滞中立型时变泛函微分方程Cauchy问题mild-解、强解的存在性。其中方程的右端函数满足Caratheodory条件。

The governing equations of laminate-faced sandwich cylindrical shallow shells based on the first-order shear theory with large deflection are high-order partial differential equations. Four dependent functions are involved.

大挠度剪切理论下复合材料夹层圆柱扁壳的稳定性控制方程是一组非线性高阶常系数偏微分方程，其中包含四个独立的函数，它们分别为横向挠度w、参考曲面的法线转角Φx、Φy和应力函数F。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。