奇异变换

While calculating tensor Green's functions, the algorithm of secondary division is adopted to solve the singular problem. The Gaussian quadrature and continued fraction is adopted to calculate the integral with Bessel function. This method not only can ensure the right calculation of tensor Green's functions but also can get high precision.

求取张量格林函数积分时，采用二次剖分算法解决计算中奇异值问题，对于含有贝塞尔函数的积分项，利用结合连分式展开的高斯求积代替常规的快速汉克尔变换方法，确保了张量格林函数的正确计算并提高了计算精度。

Furthermore, it can be changed into singular integral equations with Cauchy kernel by introducing Sherman transformation. Then , the numerical example of the elastic welding problem with symmetric cracks is given, and the stress intensity factors can be obtained.

通过应用平面弹性复变方法，把满足已知边界条件的弹性平衡问题转化为解析函数的边值问题，再通过引入Sherman变换，把边值问题化为Cauchy核的奇异积分方程组。

In this paper, taking the downward continuation of potential field as an inverse problem of upward continuation, we obtain a convolution type linear integral equation for downward continuation. Making use of the orthogonal symmetry characteristic of Fourier transform matrix, and combining the principles of singular value decomposition of matrix and generalized inverse, we proposed a stable generalized inverse method for downward continuation of potential field, called wavenumber domain generalized inverse algorithm, which doesn't need the computation for inverse matrix. It resolves the instability of potential field downward continuation of large depth.

本文通过把位场向下延拓视为向上延拓的反问题，得到向下延拓的褶积型线性积分方程，再利用Fourier变换矩阵的正交对称特性，并结合矩阵的奇异值分解和广义逆原理，提出了一种稳定的不需要进行求逆运算的位场向下延拓广义逆方法——波数域广义逆算法，解决了位场大深度向下延拓的不稳定性问题。

The wavelet analytic method can find out global and local singularity and singular points of function by local maximum of wavelet transform of Lagrangian function which is made up of two constraint functions without regard for contents of optimization and constraint situation.

不管优化内容及约束情况如何，由对约束函数两两构成的拉格朗日函数的小波变换求局部极大值，将奇异点求解出来。本文对n维空间的小波变换寻优方法给予了理论上的研究与证明，并给出了具体的求解方法。

The results indicate that the improved grey target could meet the invariance of effect samples after nonsingular linear transformation caused by clout distance; the weighted Mahalanobis distance is just the weighted Euclidean distance when there is no correlation among observed indexes, which avoids correlation of decision indexes, influences of different dimension and differences of importance on effect of decisions, and the incompatibility of grey target transformation.

结果表明，改进后的灰靶满足：靶心距对效果样本作非奇异线性变换的不变性；当观测指标间不存在相关性时，加权马氏距离就是加权欧氏距离。避免了决策指标间的相关性、不同量纲和重要性差异对决策效果的影响以及灰靶变换的不相容问题。

A dynamic model was developed with kinematic differential equation derived for a dual-disc over-hung rotor system with rub-impact fault. The stability of the system and stability regions were studied by setting up nonsingular linear transform matrix and by use of Jacobi matrix in combination with the theory of Routh Hurwitz. Then, the effects on the stability regions of the system were discussed with relevant parameters.

建立了悬臂双盘碰摩转子系统的动力学模型和运动微分方程，通过创建该系统的非奇异线性变换矩阵并利用变换矩阵的Jacobi矩阵结合Routh Hurwitz理论，研究了悬臂双盘碰摩转子系统的稳定性和稳定区域，并进行了相应的参数讨论。

On this problem mentioned above, a new target feature extracting method is presented. It is a matrix describing method based on scale transformation.

为解决这一技术难题，提出了基于尺度奇异值变换的红外图像目标特征提取方法，该方法是一种基于尺度变换的矩阵表示方法。

The implement algorithm of adaptive fuzzy image enhancement is proposed in ridgelet transform domain.

提出了基于脊小波变换域的模糊自适应图像增强算法，利用脊小波变换在表示图像线性奇异边缘时具有独特的优越性，达到突出边缘和抑制噪声的目的。

Based on the phase-space generating functional for a system with a singular higher-order Lagrangian,the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived.

基于高阶微商奇异拉氏量系统的相空间生成泛函，导出了定域和非定域变换下的量子正则Noether恒等式；对高阶微商规范不变系统，导出了位形空间中定域和非定域变换下的量子Noether恒等式。

A new method of automatic segmentation is developed based on the extreme point properties of wavelet transform. The method consists of two main steps: 1. Using the multi-resolution properties of wavelet transform, we can get the information of shape variation with space coordination.

该方法包括两个主要步骤，一是利用小波变换的多分辨率特性得到测井曲线的形态特性随空间坐标的变化信息；二是利用小波变换过零点的特征在不同尺度上的反映，提取不同尺度下的奇异点作为分层的待参考点，结合实际情况最终确定分层点。

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。