查询词典 conditional equation

The mild-slope equation with current effects is reformulated to an inhomogeneous Helmholtz equation. Applying the conventional boundary element method to this inhomogeneous equation, the inhomogeneous part will result in a domain integral which makes the computation complicated and messy. To improve this drawback, the DRBEM is adopted to transform the domain integral to boundary integral.

首先将含水流效应之缓坡方程式重新整理为非齐次之Helmholtz方程式，再利用Green公式改写为积分方程式，但利用一般传统边界元素法解析时，将存在一领域积分项，使得边界元素法显得繁杂且不完美，为改善此一缺陷，本文乃应用双互换边界元素法之技巧，以节省大量之数值计算时间。

This article is based on the material balance equation and the no fixed water inroad equation,educe the equation of the no water recovery and the water coming time.

以物质平衡方式和不定态水侵公式等油藏工程理论为基础，得出无水期采收率和油藏见水时间的计算公式。

There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性。

Next, the boundary value problem is changed into an integral equation by applying a Green function. Then, by establishing a normalized boundary equation, the irregularity of the kernel of integral equation is overcome.

弹性扭转问题可看成是Poisson方程的边值问题，R 函数理论保证了对于任何复杂的区域，总可以找到一个规范化方程，从而可以将弹性扭转问题化为一个无奇异性的第二类Fredholm积分方程。

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。

In the computation of aerodynamic forces, the present work is based on the work of Morino et al., but the following aspects are improved:(1) In computing the steady transonic aerodynamic load, the steady transonic nonlinear integral equation is solved by relaxation-iteration method in this thesis, instead of solving the time dependent transonic nonlinear integral equation, so that the computing time is saved greatly;(2) The influence coeifficients represented by volume integral are transformed to surface integral by using the Gaussian Theorem, so the analytical form of these coeifficients can be obtained and this leads to be more convenient to analyse and compile computer program;(3) The shock capturing method is used in every time step in present work, no shock moving term is added in the integral equation, so that it is more convenient and simpler to treat.

在气动力计算方面，本文基于Morino等人的工作，作了如下几方面的改进：（1）在计算定常跨音速流场（作为非定常绕流计算的初场）时，本文采用松驰迭代法直接求解跨音速定常非线性积分方程，而不是采用时间相关法求解非定常非线性积分方程，这样大大节省了计算机时；（2）将以体积分形式出现的影响系数化为面积分，并获得解析公式，这样便于分析和编写程序；（3）对运动的激波，本文通过在每一个时间步长上采用激波捕捉法而得到，而不是在积分方程中附加激波运动项，因而处理起来简单方便得多。

In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro -differential equation. The equation is further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam.

对于两端简支的情形，采用Galerkin方法简化为常微分－积分方程；然后通过引进附加变量的方法进一步简化为常微分方程；最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。

From K-G Equation and Dirac equation,using 2-D invariant line element, the radius equation and event horizon formula of particles are obtained.A simpler method to the research of quantum effect of the scalar and vector particles in black hole with spherical symmetry is singgested.

分别从K-G方程和Dirac方程入手，利用简化后的二维不变线元，直接给出了粒子的径向方程和视界面方程公式，为研究球对称黑洞中标量粒子和矢量粒子的量子效应提供了一个更简单的方法。

Based on the transformation between position space and spinor space in geometric algebra system,the perturbing Kepler equation was transformed to a linear and regular form(also called Kustaanheimo-Stiefel equation or KS equation).

利用几何代数体系中的位置空间与旋量空间之间的转换关系，将摄动Kep ler方程转化为线性、正则的旋量方程，并给出Kep ler旋量方程的解。

Wave equation, heat conduction equation and Laplace's equation are the second-order linear equations.

波动方程、热传导方程和拉普拉斯方程都是二阶线性方程。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。