查询词典 kernel of integral equation

This paper discusses the Noether theorem of complete singular integral equation which containsboth the convolution kernel and the Cauchy kernel, and comes up with the Noether theoremwhich is similar to the Fredholm integral equation, the convolution equation and the singularintegral equation.

本文讨论了既含卷积核又含Cauchy核的完全奇异积分方程的Noether定理，得到了与Fredholm积分方程、卷积型积分方程、奇异积分方程相类似的Noether定理。

It was proved that the irregularity of the kernel of integral equation could be overcome by choosing a suitable form of the normalized function.

通过寻找适当的规范化方程，来表示问题的边界，并证明积分方程核的奇异性被克服了。

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。

The methods for treating the singularities which occur in the kernel of linear integral equation and in the lift distribution functions are also discussed, with the numerical solution of the integral equation given.

本文方法可用于计算单独的和偏有部分或全翼展前后缘操纵面的机翼的升力分布，数值结果与实验数据符合得很好，与其他理论值有相同的精确度。

In Chapter Five, we compare numerical integration of the reproducing kernel with the integral equation of complexified trapezoid through a detailed solution to the initial-value problem of ordinary differential equation to exemplify that the method of interpolation spline integrating and the reproducing kernel is not only feasible in theory but also significant in pratice.

在第五章，我们通过具体的求解一个常微分方程的初值问题，把再生核方法的数值积分和复化梯形积分公式相比较，说明样条插值和再生核相结合的方法不仅是理论上可行的，而且还具有重要的实际意义。

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。

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 overcame. Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.

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；最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

Green quasifunction method is applied to Poisson's equations. Fredholm integral equations of the second kind are obtained. Irregularity of the kernel of integral equations is overcome by choosing a suitable form of the normalized boundary equation.

应用准格林函数方法，可将Poison方程化为第二类Fredholm积分方程，通过边界方程的适当选择，积分方程核的奇异性被克服了。

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。

By usingthe relation between the Bergman kernel and the Riemann mapping and Plemly for-mulae,the second boundary integral equation about the Bergman kernel is obtained,moreover,the integral kernel is a continuous,without any singularity,parametized Neu-mann kernel.We discuss the case of some symmetric property,and get correspondingresults.

主要利用Bergman核与Riemann映照之间的关系，推导出Bergman核满足带有参数化Neumann核的第二类边界积分方程，积分核是连续的没有任何奇性，并讨论了具有某种对称性质的情形。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。