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In this paper the defect of the traditionary boundary layer methods (including the method of matched asymptotic expansions and the method of Visik-Lyusternik) is noted, from those methods we cannot construct the asymptotic expansion of boundary layer term really.

本文指出传统的边界层方法包括匹配法和Vi(？ik—Lyusternik方法的不足：不能作出边界层项的渐近展开式。提出多重尺度构造边界层项的方法，得到符合实情的结果。

The finite element method was combined with homogenization theory based on asymptotic expansion for predicting effective properties of crystal polymer nanocomposites, double nanoscopic level homogenizations and one microscopic homogenization were used.

利用数学上的渐近均匀化理论，结合有限元方法，经二次纳观层次的均匀化和一次细观层次的均匀化，预测了聚合物基纳米复合材料的有效性能。

At present no mathematical tables could be utilized and no detail characteristics could be known. This paper makes use synthetically of Taylor series expansion and asymptotic expansion of complex argument Fresnel integral and argument transition function and the connections of the two expansions are analysized and found.

本章综合运用了小宗量级数展开和大宗量渐近展开，并且找到了小宗量和大宗量的衔接部，圆满地解决了复宗量菲涅耳积分和复宗量过度函数在整个复平面上的计算机计算问题。

Different from the scattering theory used in the derivation of conventional generalized screen propagator, in this paper, a high order formula of generalized screen propagator for oneway wave equation is proposed by using the asymptotic expansion of singlesquareroot operator.

不同于常规广义屏传播算子的推导中使用散射理论，本文利用单平方根算子的渐近展开，推导出了单程波方程广义屏传播算子的高阶表达式。

The uniformly valid asymptotic expansion of the solution to a class of time delay differential equations with damping term and general forcing term was obtained and a simple analytic approximate expression for the resonance solution was given.

对于一类带阻尼和一般力的时滞微分方程问题求得一致有效渐近展开式，给出了共振解筒洁的近似解析表达公式。

These include an asymptotic formula in a neighborhood of the origin,a result which as far as we are aware has not yet been obtained previously.

其中有一个在原点的领域附近的渐近公式。据我们所知，这个结果之前还没有被得到过。

Some accurate asymptotic formula for it was proven.

获得了关于这个数论函数的一些较精确的渐近公式。

We shall derive an explicit asymptotic formula for the tail probability of Z.

在ι和t固定的条件下，我们得到了L_ι和E_ι的尾概率准确的渐近估计。

Studying the mean value of two Smarandache LCM Functions by using elementary and analytic method,and giving their asymptotic formula.

利用初等方法研究了两个包含Smarandache LCM函数的均值性质，并给出其渐近公式。

In this paper,we use elementary and analytic methods to study some problems on some special sequences and functions,and give their mean values,concisely counting formula and asymptotic formulae.

基于对上面所述问题的兴趣，本篇硕士论文利用初等及解析的方法研究了Smarandache教授提出的一些数论中的特殊序列及函数的性质，并且推广相关函数的结果，给出它们的均值计算公式和渐近公式。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。