Gaussian beam is the asymptotic solution of wave equation concentred at the central ray.
高斯束是波动方程在特定射线附近的高频渐近解。
Using the perturbative method the asymptotic solution of the corresponding model is obtained.
利用摄动方法求出了相应模式的渐近解。
For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one.
使问题的维数，对各级渐近解而言，降低了一维。
The uniformly valid asymptotic solution to the original initial boundary value problems was obtained by the theory of differential inequalities.
利用微分不等式理论，得到了原初始边值问题解的一致有效的渐近解。
There has been a general method to obtain the asymptotic solution of the plane elastoplasticity problem with strain-hardening of a power series model.
具有幂级数型强化律的弹塑性平面问题已有较为一般的渐近解法。
By means of the asymptotic solution of singular perturbation problem we proved the uniform convergence of this scheme with respect to the small parameter.
我们利用问题的渐近解证明了差分格式关于小参数的一致收敛性。
In this paper, a singularly perturbed catalytic reaction problem is considered. The formal asymptotic solution is obtained and its uniform validity is proved.
本文讨论了一个奇摄动催化反应问题，得到了问题的形式渐近解，证明了它的一致有效性。
By Newton algorithm and the analysis for asymptotic solution, this paper presents a direct formula for calculating critical depths of trapezoidal open channels.
依据牛顿算法及渐近解分析，本文提出了一种梯形明渠临界流方程的直接算法。
This paper also gives the differential equation of the nonlinear vibration model, and obtains its asymptotic solution by means of singular perturbation methods.
文中给出了这一非线性振动模型的微分方程，并用奇异摄动法求得了渐近解。
Using the root of the characteristic equation, this paper studies the asymptotic solution of the characteristic equation of the open circular cylindrical thin shells.
本文利用特征方程根的性质，研究了开口圆柱薄壳精确微分方程的特征方程的渐近解。
A method is given for determining the parameters of a diffused waveguide from the observable values of mode efficient index by using the asymptotic solution equations.
给出了利用渐近解公式，由模有效折射率的测量值确定波导表面折射率和扩散深度的方法。
In this paper, a method of using initial layer correction to solve the electromechanical coupled systems is submitted, an asymptotic solution of analysis are obtained.
提出了用初始层校正法求解机电耦合系统状态方程组的方法，获得了问题的渐近解析解。
The relative permeating rate was introduced to describe the effects of the different physical processes. An asymptotic solution has been obtained by using the perturbation theory.
在模型中引入相对渗透速度来刻画药物释放过程中不同机理的影响，并用摄动方法对方程进行了求解。
Under the appropriate conditions, the asymptotic solution and its existence conditions are obtained, the results for a class of quasi-circular membrane oscillation problem is extended.
在适当的条件下，得出了这类问题的渐近解及其可解性条件，推广了一类近乎圆膜的振动问题所得的结果。
In this paper, We prove that the orthogonal condition to solve the uniform asymptotic solution of second order linear P. D. E in periodic region is the necessary and sufficient condition.
本文证明了求解周期区域上的二阶线性偏微分方程的一致有效渐近解的正交条件是充分和必要的。
Then the main parameters influencing the asymptotic solution of the transfer process are analyzed, and some new methods to improve the implicit knowledge transfer efficiency are put forward.
分析了影响组织隐性知识传播渐近解的主要参数控制，指出了一些改进隐性知识传播效率的途径。
The application of the asymptotic solution of second order linear homogeneous equation with big parameter to studying the longitudinal and twisted vibrations of tapered sticks is discussed .
讨论了含大参数的二阶线性方程的渐进解，并将其应用于楔型杆的纵振和扭振的研究。
A class of second orders homogeneous equations with varied coefficient widely applied in mechanics were studied using the amended asymptotic method, and the amended asymptotic solution was derived.
采用修正渐近法研究了在力学中应用范围比较广泛的一类具有变系数二阶线性齐次方程，并求得了其修正渐进解。
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.
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。
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。
In case the coefficients are periodic, we give some sufficient conditions for the existence and uniqueness of asymptotic periodic solution.
对于系数具有周期性时，我们给出了渐进周期解存在并且唯一的必要条件。
Asymptotic stability of the solution to a class of stochastic systems with variable delay is discussed.
讨论了一类随机可变时滞系统解的渐近稳定性。
Asymptotic stability of the solution of this system is obtained by studying spectral properties of the operator corresponding to this system.
通过研究相应算子的谱特征得到该系统解的渐近稳定性。
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。
This formulation possesses an asymptotic strong duality property and guarantees a success for identifying an optimum solution.
此公式具有渐进强对偶的特性并且可以保证找到原问题的最优解。
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。
This paper studies the asymptotic expression of solution of Cauchy's problem for a forth order equation when the limit equation has singularity.
本文研究当极限方程有奇性时四阶线性常微分方程的柯西问题解的渐近式。
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。
Finally, we discuss almost periodic phenomena, and obtain some sufficient conditions which assure the unique existence and globally asymptotic stability of almost positive periodic solution.
最后讨论了概周期解现象，得出了概周期正解的唯一存在性和全局渐进稳定性的充分条件。
Finally, we discuss almost periodic phenomena, and obtain some sufficient conditions which assure the unique existence and globally asymptotic stability of almost positive periodic solution.
最后讨论了概周期解现象，得出了概周期正解的唯一存在性和全局渐进稳定性的充分条件。
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