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Thus using the perturbation method the asymptotic expansions of solution for the original problem are obtained.

于是利用摄动方法得到了原问题解的渐近展开式。

Finally, using the theory of differential inequality, the uniformly valid asymptotic expansions of solution for the original problem are obtained.

最后，利用微分不等式理论，得到了原问题解的一致有效的渐近展开式。

Using the fixed point principle and the theory of differential inequality, we prove the existence of the solution and an uniformly valid asymptotic expansions of the solution is given as well.

利用不动点原理及微分不等式理论，我们证明了边值问题解的存在性，并给出了解的一致有效渐近展开式。

Dramatic expansions of primary school completion can only be accomplished with a comparable expansion in the number of teachers.

只有教师的数量跟上教育扩张的步伐，才能完成对初等教育的急剧扩张。

If the power series ∑anxn an ∑anxn and ∑bnxn satisfy the condition r =∑bn xn, we obtain the twin combinatorial identity theorem between the sequences {an} and bn}.We also obtain some specific twin combinatorial identities by using the expansion on the binomial expression formula, including two expansions of combinatorial number(rsn and ...

如果幂级数∑anxn与∑bnxn满足条件r＝∑bnxn 时，获得数列｛an｝与｛bn｝之间孪生组合恒等式的定理，应用在二项式定理等展开式上得出具体的多组孪生组合恒等式，其中包含组合数的两种展开法，Bernoulli数直接表达式的新证等结果。

Expansions in orthogonal functions is used to solve the Orr-Sommerfeld equation in studies of the linear stability of parallel flow. For the plane Poiseuille flow the critical Reynold number is given accurately. Furthermore, the Blasius flow which is considered locally parallel has been studied, and the neutral stability curves, which are very important for the stability study, are given.

对于平行流的托尔明—施里希廷(Tollmien-Schlichting，T-S)波的线性稳定性，采用谱方法求解平面Poiseuille流的Orr-Sommerfeld方程，得到了精确的临界雷诺数；并研究了局部平行假设下的Blasius边界层流动，分别给出对稳定性研究至关重要的中性稳定性曲线。

The nonlinear stability of three-dimensional disturbances for the Blasius boundary layers is studied. We adopted here the high accuracy method of using the expansions in orthogonal functions along the normal direction and the effective algebraic mapping to deal with the problem in the infinite region. The initial solutions of two-dimensional harmonic waves are given by Landau expansion, and the mean-flow-distortion is calculated by the approximation equation.

运用Landau展开给出了二维谐波的初始解、通过求解线性PSE而得到TS波和C型亚谐扰动的初始站值、以及近似地模拟初始站的均流变形值，以此为初始条件，并结合迭代-预估校正方法来实现非线性PSE的求解和推进，详细地研究了非平行边界层三维扰动C型失稳过程。

In this paper, using the concept of the contact angle and considering the capillarity action, the method of small-time expansions is developed to solve accurately nonlinear wave due to the horizental of the plate towards the fluild with an acceleration.

采用对时间t作幂级数展开的方法，利用接触角的概念，并考虑了表面张力的作用，对垂直平板在静止的液体中突然起动所产生的非线性波进行了求解，得到了速度势函数、压强及自由面形状的解析表达式，并对一种特例计算了作用在平板上的动水压强。

Boundary conditions on the surface of an airfoil are implemented by using their first-order expansions on the mean chord line.

提出了一种应用近似边界条件在固定的笛卡尔网格上求解非定常欧拉方程来解决气动弹性的方法。

The lauan wood is used as a template to prepare Al/C and Al/ composites. Porous carbon is first pyrolyzed from the wood template. The final composites having wood structure are obtained by injecting aluminum alloy and silicone resin into the porous carbon. The microstructures, thermal expansions, and thermal conductivity of these products are analyzed by the scanning microscope, dilatometer, and conductometer. The model of thermal conduction is established.

该文以柳桉木材为模板，先将其转变为多孔碳，再通过铝合金和硅树脂的浸渍，制备了具有木材结构的Al/C、Al/两种铝基复合材料，并通过扫扫电镜、热膨胀仪和导热仅对复合材料的微观结构、热膨胀性能及导热性能进行了研究，建立了导热模型。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。