并得到了一致有效的渐近展开式。
The uniformly valid asymptotic expansion in entire is obtained.
得到了问题解的一致有效的渐近展开式。
The uniformly valid asymptotic expansion of solution for the problem is 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。
The likelihood ratio criterion of sphericity test, its asymptotic expansion and limiting distribution are obtained.
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。
Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.
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。
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.
据此利用渐近展开和分离变量相结合的方法对裂尖奇异性指数的变化进行了分析。
With the method of asymptotic and variable separation, the stress singularity near the conic-shaped crack tip at a bi-material interface is fulfilled.
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。
The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.
研究了一类ENSO摄动模型。利用摄动理论和方法，构造了相应问题的渐近展开式。
A class of ENSO perturbed model is studied. Using the perturbation theory and method, the asymptotic expansions of solution of corresponding problem are constructed.
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。
Thus, the fully asymptotic expansion of the homogeneous solution within the accuracy of theory of thin shells is obtained.
在一般的条件下，证明了解的存在性，而且得到解及其各导数的高阶一致有效渐近展开式。
Under the general conditions, we prove the existence of the solution and get the asymptotic expansions of the solution and its derivatives, which are uniformly valid for the higher orders.
然后利用摄动方法证明了这个问题解的存在唯一性，同时给出了解的渐近展开和误差估计。
The existence and uniqueness theorem of its solution is proved by the perturbation method and the estimation of error for its approximate solution is given.
从基于小参数渐近展开和摄动方法的均匀化理论出发，给出了求解细观应力的数学表达式。
A homogenization method based on the perturbation theory is presented to deduce the mathematical expression of the (micro-stress).
第五章讨论二维蜂窝结构热方程边值问题，给出了一个多尺度渐近展开式和有限元计算格式。
In Chapter 5, we study the multi-scale finite element method for the heat equation of composite materials with honeycomb structure in two dimension domain.
首先讨论了隐差分解与显差分解的关系，并利用差分解的渐近展开式构造差分校正解来提高精度。
The relation between the explicit difference solution and the implicit one is established. A correction difference solution with higher accuracy is constructed by the use 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。
The existence and stability of periodic solution are studied by using the bifurcation theory, linear stability theory and the method of asymptotic expansion.
我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。
Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.
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。
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.
当大系统的输入函数的初始参数发生偏离时，其最优简化模型的近似模型可以利用输入函数的渐近展开得到。
When parameters of the input of a large scale system deviate, its approximate reduced order model can be obtained by using the asymptotic expansion of the input function.
本文最后给出，当角频率有偏离时，其最优简化模型可以利用正弦输入函数的渐近展开式作相应的改变的结论。而且这种方法也适用于其它输入函数的参数偏离时的情形。
If a parameter in the inputs of the original large scale system deviates, the corresponding reduced order model can be changed by using the asymptotic expansion of the input functions.
为此先推导离散格林函数的权模估计和有限元解的渐近不等式展开，然后给出公式的证明。
For this, we derive the weighted estimates for discreet Green function and the asymptotic error expansion inequalities, and then the proofs of the formulas are given.
其收敛性的证明是依据其渐近扩散展开式，在边界层上得到的误差估计逼近其离散纵标方法的解。
Our proof of the convergence is based on an asymptotic diffusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete-ordinate method.
然后，运用微分不等式理论，证明了形式渐近解的一致有效性，并得出了解得任意阶的一致有效展开式。
And then, the uniform validity of solution is proved and the uniform valid asymptotic expansions of arbitrary order are obtained by using the theories of differential inequalities.
利用泰勒展开技术，给出了长波区域弯曲振动模式和伸缩振动模式的弥散曲线渐近表达式；
By means of the Taylor expansion technique, the asymptotic expressions of the dispersion curves at the long wavelength region were derived for flexural and longitudinal vibration modes.
利用泰勒展开技术，给出了长波区域弯曲振动模式和伸缩振动模式的弥散曲线渐近表达式；
By means of the Taylor expansion technique, the asymptotic expressions of the dispersion curves at the long wavelength region were derived for flexural and longitudinal vibration modes.
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