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The stable wave-field propagators of one-way wave equation for Born and Rytov approximations are derived by using the local Born and local Rytov approximation methods in the scatter theory of wave-field propagation, and their application effects in prestack depth migration imaging of wave equation are compared theor...

利用波场传播散射理论中的局部Born近似和局部Rytov近似，分别导出了单程波方程的稳定的Born近似波场传播算子和稳定的Rytov近似波场传播算子，然后从理论和实践上比较了它们在地震数据波动方程叠前深度偏移成像中的应用效果。

First, the linear combinations of basic set of solutions to Laplace equation under polar coordinate system are chosen as the approximations for the solution of temperature fields,boundary residual collocation method are applied to calculate the distribution of the temperature fields for single-particle model.

本论文主要完成了两方面的工作，一方面是采用加权残值法和边界元法对不同复合材料模型的2D稳态热传导的温度场进行了求解分析。

During the process of numerical approximations, the difference formula of time transient terms, and the central/upwind difference expressions for acquiring boundary value are chosen.

在方程离散过程中，给出了时间瞬态项的差分格式以及求解边值的中心和上风差分格式。

These approximations differ from the chapeau rule in that they relax, respectively, the reference to the like product, the reference to the exporter concerned, or both references, spelled out in that rule ...

在这个规则中阐明：这个近似规则与起首规则不同，起首规则涉及同类产品，近似规则则涉及出口商，或者还同时涉及同类产品

The Computer-aided method also exploits the characteristic of linear differential equation with two additional approximations.

计算机辅助法也充分利用了线性微分方程的特点及另外两个合理的近似条件。

Let Un the Chebyshev polynomials of the second kind and the associated functions In this paper we discuss the approximations of the partial sums for the biorthogonal series based on and the corresponding conjugate series.

记Un是第二类Chebyshev多项式，伴随函数，这里讨论基于的双正交级数和其共轭级数的部分和逼近问题。

The major subjects in the approximation of operators are to study the convergent property of a sequence of linear operators, the quantization of its convergence rate and the saturation results in the theory of approximations.

算子逼近论主要是研究线性算子列的收敛性质，收敛速度的量化以及逼近论中的饱和现象。

We have also shown that our general formula for thepion decay constant 〓 reduces to the well-known Pagels-Stokar formula undercertain approximations.

同时，我们证明了，在一定近似下，可以从我们对π介子衰变常数〓的一般定义推出著名的Pagels-Stokar公式。

In order to avoid the Maratos effect, the merit functions used are approximations to Fletchers differentiable exact penalty function. Global convergence is proved on some conditions, and some numerical results are given .

为避免Maratos效应，此方法采用Fletcher的光滑精确罚函数的逼近形式作为价值函数，在一定条件下证明了算法的全局收敛性并且给出数值结果。

However, to establish global convergence for these latter methods, one must enforce either sufficient decrease conditions (the Armijo-Goldstein-Wolfe conditions)or a fraction of Cauchy decrease condition - all of which rely on explicit numerical function values, as well as explicit approximations to the directional derivative at the current iterate.

但是，为了保证后面方法的全局收敛，必须有足够的减少条件（Armijo-Goldstein-Wolfe条件）或者部分柯西减少条件——它们全都依赖于外在的数值函数值，就和在当前迭代逼近方向导数一样。

Who? I never heard of him, Paul said, before asking teammate James Posey if he had heard of him.

赛后，科比说，他一直都是一名非常出色的射手，今天他打得很棒。

When I joined the company, I rotated around the different sections.

我加入这个公司时，轮换过几个不同的部门。