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1·The uniformly valid asymptotic expansion in entire is obtained.

并得到了一致有效的渐近展开式。

2·The uniformly valid asymptotic expansion of solution for the problem is obtained.

得到了问题解的一致有效的渐近展开式。

3·The likelihood ratio criterion of sphericity test, its asymptotic expansion and limiting distribution are obtained.

论文得到了球形检验的似然比准则，它的渐近展开与极限分布。

4·Thus, the fully asymptotic expansion of the homogeneous solution within the accuracy of theory of thin shells is obtained.

这样，轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开。

5·The uniqueness of the solution is proved, and the asymptotic expansion of the solution and remainder estimation are also given.

研究了一类含有迁移项的奇摄动抛物方程的周期解问题，给出了解的存在唯一性、渐近解及其余项估计。

6·Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.

重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。

7·The existence and stability of periodic solution are studied by using the bifurcation theory, linear stability theory and the method of asymptotic expansion.

运用分歧理论、固有值的解析摄动理论和渐近展开的方法，获得了共存时间周期解的存在性和稳定性。

8·The matched-asymptotic expansion method is adopted to solve the problem of transmission and reflection of a planar soliton on a two-dimensional floating body.

本文应用渐近匹配方法探讨了孤立波遇到二维柱体时的透射与反射问题。

9·On the basis of the governing equations and the asymptotic expansion of the stress fields proposed by Gao and Hwang, a generally asymptotic analysis is performed.

基于基本方程组和高玉臣、黄克智提出的应力场的渐近展开式作了渐近分析。

10·The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.

运用分歧理论，隐函数定理，以及渐近展开的方法，获得了非平凡周期解的存在性。