查询词典 singular boundary

Using the method of blow up lower and upper solutions, the existence and boundary behavior of positive boundary blow up solutions for some elliptic systems of competitive type with singular weight functions are obtained, here the singular weight functions are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts.

利用爆破上、下解方法，本文建立了带奇异权函数的竞争型椭圆方程组正的边界爆破解的存在性和边界行为，这里奇异权函数可以在边界的某一部分有界，而在其他的部分趋于无穷或者震荡。

By means of analyzing the noise error, it is proposed to use an algorithm of singular value decomposition total least squares to conduct the interharmonics estimation, namely taking the noise interference at both sides of the matrix equation into account simultaneously and solving the minimum norm problem by least square method under such condition. In the proposed algorithm by means of singular value decomposition of a new augmented matrix and by use of a simple and practical method to determine the number of principal singular value related to signal to noise ratio, the storage calculation of right singular matrix is performed, thus a more accurate frequency estimation of interharmonics can be obtained.

通过分析噪声误差，提出采用奇异值总体最小二乘(singular value decomposition total least squares，SVDTLS)算法进行间谐波频率估计，即同时考虑矩阵方程两边的噪声干扰，采用SVDTLS算法求解该情况下的最小范数解，通过对增广矩阵进行奇异值分解(singular value decomposition，SVD)，采用简单实用的与信噪比相关的主奇异值个数确定方法对分解的右奇异矩阵进行存储计算，得到了较精确的间谐波频率估计结果。

The problem of a curved rigid line or crack crossing the interface of the circular inclusion are studied by the principal part analysis method of Cauchy type integral equation. The singular stress index at the intersection and the singular stress at the angular regions near the intersection are obtained. The singular stress coefficients of rigid line at intersection and the stress intensity factors of crack at intersection are defined by using the singular stress.

利用Cauchy型奇异积分方程的主部分析方法对曲线型刚性线和曲线裂纹和圆夹杂界面的相交问题进行了研究，得出刚性线以及裂纹和界面交点处的奇性应力指数以及交点处角形域内的奇性应力，并利用奇性应力分别定义了刚性线在交点处的应力奇异因子和裂纹在交点处的应力强度因子。

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

If singular value curve is convex in the coordinates 'k' of maximum peak of curvature spectrum, then the number of effective singular values is k; if singular value curve is concave in the coordinates 'k', then the number of effective singular values is k-1, and this rule is tested by the signal processing examples.

如果奇异值曲线在曲率谱最大峰值的位置坐标k处是凸出的，则有效奇异值的个数为k；如果奇异值曲线在k处是凹进的，则有效奇异值的个数为k-1，通过信号处理实例证实了这种结论。

Based on this result,the intrinsic reasons that singular value vector-based recognition methods have the low recognition accauracy are follows: singular value vectors of arbitrary two face images have not the equivalent basis space in general;there is no one-to-one correspondence between singular value vector and face image;singular value vectors are not separated.

进一步研究发现，导致基于奇异值向量人脸识别算法识别率低的根本原因是：不同人脸图像对应的奇异值向量所在的基空间不一致、奇异值向量与人脸图像之间并不存在一一对应关系、奇异值向量具有不可分割性。

Seeing image as a matrix, the method applied singular value decomposition on image matrix to decompose image information to a series of sub-spaces correspond to singular value and singular value vector, and then by reconstruction of image matrix using effective singular value to remove noising.

从矩阵的角度出发，通过对图像矩阵进行奇异值分解，将包含图像信息的矩阵分解到一系列奇异值和奇异值矢量对应的子空间中，然后通过有效奇异值重构图像矩阵达到去噪目的。

The singular values of the project can be used as the character vector. The singular values of the scaling invariant can be obtained by the statistical characteristics of Radon transform. Since the singular values of the matrix are uncorrelated with the position of the column or the row of the matrix. In this way, the character vector of singular values with shift, scaling and rotational invariant is arrived at by this algorithm.

针对各颜色分量，利用Radon变换的奇异值的统计特性提取了具有尺度不变性的奇异值，由于矩阵的奇异值分解具有旋转不变性，因此该奇异值为平移、尺度和旋转不变的特征向量。

By the analysis for the characteristic of singular value of ideal signal and noise, it's pointed out that there is a big turning point in the singular value curve of ideal signal, but not in the one of noise, so the concept of curvature spectrum of singular value is proposed, which can effectively describe the turning point state of singular values of noisy signal.

分析了在Hankel矩阵方式下理想信号和噪声的奇异值特点，指出理想信号的奇异值曲线存在一个很大的转折点，而噪声的奇异值曲线则很平坦。

In this paper we suggesst a finite element method for singular two point boundary value problems with singular solution by introducing singular basis with local support.

采用具有小支集的奇异基函数的有限元方法求解奇异两点边值问题的奇异解。

Warden: That's a beautiful dog, but don't bring her again.

那是条漂亮的狗，但是不要再把她带来了。

You get up in the morning – no hangover!

你第二天早上起来的时候—不会宿醉！