查询词典 expansions

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。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。