导出方程

By applying the statistical theory for thermal defects of an imperfect crys-tal to polymer liquids, a simple relation between the occupied-site fraction andthe reduced temperature has been derived and the SS EOS is simplified to aso called simplified hole theory equation of state.

本工作将不完全晶体中热缺陷的统计理论用于聚合物液体中，得到被占座席分率与对比温度的一个简单关系式，导出了简化的空穴理论状态方程。

B Using the basic solutions of single inclusion and single crack, singular integral equations of plane interaction problem of line inclusion and line crack have been deduced. Numerical method is set up. Expresesions of stress intensity factor of both inclusion and crack and interface stress of the inclusion are given.

使用单夹杂和单裂纹的基本解，导出了线夹杂与线裂纹相互作用平面问题的奇异积分方程，并为其建立了数值法，给出了夹杂与裂纹端点的应力强度因子及夹杂两侧界面应力的表达式。

C Taking the short-fiber reinforced and inhomogeneity spreaded composite materials as engineering background, singular integal equations of plane problem of interaction between line inclusion and circular inclusion are deduced, and some particular cases are analysed.

以短纤维和颗粒弥散体复合材料为背景，导出了线夹杂与圆夹杂相互作用平面问题的奇异积分方程，并对一些特殊情形作了退化分析，建立了数值法，给出了圆夹杂和线夹杂两侧的界面应力及线夹杂端点的应力强度因子表达式，同时作了具体的数值计算。

When surface potential of the particles is high sinh y ≈ e y /2 in the nonlinear Poisson-Boltzmann equation.

在高电位的条件下，PB方程中的双曲正弦可以简化为指数函数，由此导出了高电位等同平板型颗粒的相互作用力与相互作用能的近似表达式。

However, the refraction of plane wave in reaction-diffusion system obeys Snell's law only for proper diffusion coefficients and system parameters.

在二维复金兹堡-朗道方程描述的反应扩散振荡系统中，就扩散对平面波折射率的影响进行了数值研究，从Snell定律出发导出了折射率的解析表达式，数值和理论结果表明：在纯扩散情况下，平面波的折射满足Snell折射定律，扩散只影响着平面波折射率的大小；在同时存在反应扩散情况下，只有在适当的扩散系数和系统参数下，平面波的折射才满足Snell折射定律。

According to Shilnikov Theorem, on the condition that satisfies the basic characteristics of heteroclinic orbit, Shilnikov inequality and the eigenvalue equation, by finding a heteroclinic orbit consist of three geometric invariant sets, namely unstable manifold, heteroclinic point, and stable manifold, a set of real parameters accordance with the condition of existing heteroclnic orbit is obtained in this chaotic system.

根据Shilnikov定理，在满足异宿轨道基本特性、Shilnikov不等式和特征方程条件下，通过寻找该系统中一条由不稳定流形、异宿点和稳定流形三个几何不变集构成的异宿轨道，在分段Sprott系统中导出了存在异宿轨道时该系统中各个参数应符合的条件，并找到了一组对应的实参数，由此证明了异宿轨道的存在性。

The balance equations as well as all boundary conditions concerned have been deduced from functional stationary value condition.

由泛函驻值条件可以导出所给问题的平衡方程及全部边界条件。

Water surface wave ; stationary wave ; rectangular water trough ; optical effect

由矩形水槽里水的表面波理论导出了驻波方程，并定量研究了标准矩形游泳池中的驻波现象，计算结果与实际现象基本符合。

The basic equations of structure are derived from Hamilton variational principle and the constitution of material utilizes the increment theory.

基于Hamilton变分原理导出圆柱壳的运动方程，本构关系采用增量理论，借助增量数值算法求解动力方程组。

The QPNS equations in entropy variables derived in the present paper have the symmetrization and satisfy the second law of thermodynamics automatically that can improve the stability of the s...

本文导出的熵变量形式QPNS方程具有对称性和自动满足热力学第二定律，这将提高解的稳定性。

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。