数值

Based on forecasting model, five algorithms are presented, that is, 1 algorithm for free motion of the plant when the analytical solution is available, 2 numerical differentiation algorithm, 3 improved numerical differentiation algorithm, 4 sensitivity matrix algorithm and 5 reference integral curve method.

推导了具有预测模型的算法的形成过程，指出了这种算法的物理实质，给出了基于预测模型算法的五种具体算法：1、系统自由运动有解析解时的算法；2、数值微分算法；3、改进的数值微分算法；4、灵敏度矩阵算法；5、基准积分曲线方法。

In this dissertation, based on the discussed history of numerical method of structure-born sound radiation, the boundary element integral equation is deduced, and then the numerical method of sound radiation, the theory of radiation modal and the sound radiation sensitivity analysis is discussed in details.

本文在分析了结构声辐射数值方法的历史及其现状的基础上，详细推导了结构声辐射的边界积分方程，对声辐射的数值计算方法、声辐射的模态理论以及声辐射的灵敏度分析作了深入详细的探讨。

By the theory of natural boundary reduction, the natural integral equation and the Poisson integral formula of the problem considered are obtained, and the numerical method of the natural integral equation is given.

通过自然边界归化，获得了该问题的自然积分方程和Poisson积分公式，给出了自然积分方程的数值解法，并通过数值例子以示本文方法的可行性与有效性。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

The fact that the integral variable of the inverse transform appears in the denominator of integrand reduces resolution of the numeral integral and blocks the application of them.

为此构造了一种新型的连续小波变换，不论对积分变量如何剖分，任何一种数值积分方法都具有高分辨特性，且积分变量不出现在被积函数的分母上，进而给出了相应的数值解法。

One method is the singularity transferring method for calculating integral value containing O(1/R) singularity in its integrand［1］.The other singularity is removed first and the integral contribution of this small area is proved to be zero.

另一种方法是为解决O(1/R2)高阶奇异积分的数值计算问题的，它是通过排除一包含奇点的有限小块，而这一小块区域对积分的贡献为零，从而使积分方程在整个积分域变得数值可积。

Chapter 5: Evaluate a given water-air intercooler both in academic and experimental ways so as to test the validity of the two ways.

第五章：以6BTA型水空中冷器为例，进行数值模拟评估，以验证试验平台和数值模拟评估方法的正确性。

The numerical computation results indicate that the CFD numerical simulation technology can effectively analyze the details of the flow field,helping to improve the intercooler flow path design.

数值模拟计算结果表明，CFD数值模拟技术可以有效的分析包括间冷器在内的整个流路的流场细节，改善间冷器的流路设计。

Numerical results obtained by inverse Laplace transformation were used to discuss the difference of the dynamic responses of shell under different response modes by respectively applying axial symmetry load and fluid load.

最后利用Laplace数值逆变换得到时间域中的数值结果，讨论了在球壳内作用有轴对称荷载和流体压力两种情况时不同响应模式条件下球壳动力响应。

At the same magnetic intensity, the stabilization of fluidized bed is in inverse proportion to the gas apparent velocity.

实验结果和数据也与数值模拟结果基本吻合，进一步证明了数值模拟结果的正确性。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。