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Morevoer, on basis of the weighted polar decomposition, the simultaneous weighted polar decomposition of matrices is also defined and studied.

在对加权极分解研究的基础上，我们定义并讨论了矩阵的同时加权极分解。

Polar decomposition and generalized polar decomposition of matrices are always the main research subjects of matrix theory. In the present thesis, we generalize them horizontally.

此外，我们还研究并给出了关于加权广义逆的Lavoie不等式，2×2分块矩阵的加权Moore-Penrose逆的显式表达式等。

By using the polar decomposition, spectral decomposition, the spectral theory of operators, the intersection of the spectra of operator completions are obtained.

5深刻研究缺项算子矩阵Mx存在逆补的一般性条件，并获得了补矩阵Mx的所有预解集交集的特性。

The software has the following features:(1) it includes large deformation theory based on S-R decomposition theorem first time as well as one based on polar decomposition theorem for comparison the latter is included by most commercial finite element software;(2) three design methods for nonlinear mechanical problem i.e.

采用飞箭软件公司的有限元程序自动生成系统作为软件开发平台，进行"深部软岩工程大变形力学分析设计系统"的合作开发工作。

Meanwhile, we also provide methods for computing the weighted polar decomposition, and study error bounds for the approximate generalized positive semidefinite polar factor and perturbation bounds for weighted polar decomposition in various norms.

针对这个新的矩阵分解，我们证明了其唯一性定理，给出了其唯一性条件，讨论了其极因子的最佳逼近性质；同时，我们还探讨了矩阵加权极分解的计算问题，研究了由迭代算法引起的极因子的误差界，极因子在各种范数下的各种形式的扰动界等。

Primary thermal decomposition temperatures of AP decrease 33.7, 40, 50.8 ℃ respectively, and thermal decomposition peak temperatures decrease 14.7, 22.9, 26.4 ℃ respectively when addition amounts of CNTs/Fe2O3 are up to 1%, 3% and 5%.

添加了1%、3%和5%CNTs/Fe2O3纳米粒子的AF的初始分解温度分别降低了33.7，40，50.8 ℃，热分解峰温分别降低了147，229，26.4 ℃。

Primary thermal decomposition temperatures of ADN and AN decrease 12.1, 3.6 ℃ respectively, thermal decomposition peak temperatures decrease 18.6, 6.6 ℃ respectively when addition amountof CNTs/Fe2O3 is up to 1%.

添加1% CNTs/Fe2O3纳米粒子的ADN和AN的初始分解温度分别降低了12.1，3.6 ℃，热分解峰温分别降低了18.6，6.6 ℃。

SVD is the general method for linear decomposition of a matrix into independent principal components, and is a form of Eigenvalue-Eigenvector analysis or principal components decomposition and, in a more general sense, of multi-dimensional scaling.

SVD分解根据矩阵的运算计算出矩阵的奇异值，然后根据奇异值计算出矩阵的两个奇异矩阵，将矩阵分解为三个矩阵的乘积形式。

In 1987, the well-know mathematician Yousef Alavi and other famous mathematicians defined a new decomposition of graph-Ascending Subgraph Decomposition which is on the condition of proper subgraph isomorphic, and in the same paper they proposed the following ASD conjecture: every graph of positive size has an ASD.

升分解(ascending subgraph decomposition，简记为ASD)是1987年闻名世界的数学家Alavi与其他几位著名数学家给出的一种在真子图同构意义下的图的新分解，并且在同一论文中他们还提出了一个升分解猜想：任意有正数条边的图都可升分解。

The environmental factors such as air temperature and humidity also affect the putrefaction and decomposition of plant litter, and the rise in air temperature and the increase in humidity will enhance the decomposition of plant litter by microbes.

环境因素对藨草残体的腐烂分解有着十分重要的影响，温度升高、湿度增大，则加速微生物对植物碎屑的分解。

If you were not , and OS X just booted normally, have no fear.

如果你没有，和OS X刚刚启动通常，没有恐惧。

I only want to preserve our all .

我只想保存好我们的一切