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Especially, combining with the weighted polar decomposition and simultaneous weighted polar decomposition of matrices given in this thesis, we derive two interesting characters of the new matrix partial ordering.

特别地，与本文提出的矩阵加权极分解和同时加权极分解相结合得到了两个有意义的结论。

Part 2: The quantitative analysis of Chinese urban residents size income distribution gap and pauperization together with international comparison (chapter 2, 3, 4) This part is one of the main contents: I try to apply the worldwide used methods, such as Gini Coefficient decomposition by Shorrocks and Theil Entropy Measures by Theil, to give Chinese urban residents' whole income gap, consumption gap, income resources and structure gap, regional gap, professional and ownership gap, industrial gap a detailed decomposition and analysis, as soon as to reveal the reasons which bring about the gap.

鉴于一些经济学者对我国居民收入分配差距已作了较为系统的整体分析，所以，本文选择从城镇居民收入分配的角度，以坚持和运用马克思主义的辩证唯物主义和历史唯物主义的基本分析方法为基础，批判借鉴西方新制度学派的制度分析方法，计量经济学分析方法等，对我国城镇居民规模收入分配格局的制度变迁及其特征进行较为全面的分析。

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。

Smoking cigarettes adds to the Computer Desk Computer manufacturer computer mouse Computer Computerized collar knitter machine Conduit Bodies construction board Container Bag Control Arm Cooking Thermometer general levels of air pollution as well as damaging our health.

吸烟不仅对健康有害，而且增加空气污染程度。香烟雾含有多种有害物质：不仅有致癌化学物质、有某种能阻止氧气进入血液的气体，还有引起血压增高、心速加快的被称为尼古丁的物质。

He is one of my favorite actors.

他是我最喜欢的男演员之一。