向量分解

On the basis of the conclusion above, the nonlinear weak controllable vectors can be obtained, which compose the second class of weak controllable matrix, by means of matrix transfermations of the first class of weak controllable matrix. Furthmore the second criterion of weak controllability, accessibility and strong accessibility, which is more standard, more succinct and more practical, is obtained. On the basis of the first criterion and the second criterion, several important problems about nonlinear controllability are discussed, which include 1 local controllability; 2 three classes of local controllable decomposition, separately by means of local coordinate changes in the neighborhood of a nonsingular point, a point on a singular surface or a designated point x〓 with a designated input u〓; 3 the character of controllability of the ith state variable x〓 in different controllable areas and their boundaries.

在第一判别定理和第二判别定理的基础上，我们分析了非线性系统受控性质中的几个重要问题，所得到的结论包括i得到了非线性系统在可平衡点附近的能控性判别定理；ii分别给出了非线性系统在非奇异点、s阶奇面以及在状态空间内给定的一点x〓和输入u〓上的三种状态分解形式以及相应的求解方法；利用系统的Ⅰ型弱能控矩阵与Ⅱ型弱能控矩阵秩相等的条件，得到了只用系统的前n个弱能控向量来判断系统的弱能控性的判别定理；iii通过引入系统状态分量的三类受控区域边界的定义及相应的求解方法，初步探讨了非线性系统各个状态分量在不同的受控区域及其边界上的受控性质。

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

The third key technique is discrete vector field decomposition.

第三项关键技术是离散向量场的分解。

Vector field decomposition is proposed in data visualization area recently.

向量场分解是数据可视化领域近几年刚提出的研究课题。

EOF, EOF procedures, principal component analysis procedure, suitable for vector field orthogonal decomposition.

经验正交函数，EOF程序，主成分分析程序，适合做向量场的正交分解。

The optimal set of discriminant vectors can be acquired througn singular value decomposition theorem.

利用奇异值分解定理，将求取鉴别矢量转化为对矩阵求奇异向量。

The method first analyses the wave decompound traffic data, sets up support vector machine model separately on basic signals and disturbing signals of different resolving rate, then compounds several forecasting results, finally the traffic forecasting result is obtained. With examples, the result shows that the model has relatively lower error rate and quite reliable.

首先对交通量数据进行小波分解，然后分别对基本信号和不同分辨率的干扰信号建立支持向量机模型，最后对多个预测结果进行合成，从而得到交通量的预测结果，并利用实例计算显示模型具有较低的误差，证明了该方法具有很好的可靠性。

By the EEOF analysis of subsurface ocean temperature anomaly in the equatorial Pacific Ocean, It is founded that, the first eigenvector is the mode about El Nino and it reflects the entire generation, persistence and diminishment process of El Nino phenomenon, there is good contemporary correlation between the corresponding time coefficient and the Nino3 index.

本文通过对赤道太平洋次表层海温距平场的EEOF分解，发现第一特征向量是关于El Nino的模态，它反映了El Nino的发生持续消亡的整个过程，对应的时间系数与Nino3指数有很好的同时相关。

As a foundation, the definition of elementary integral transformation and the method to factorize an integral matrix with elementary integral transformation is proposed firstly. After that, the problem how to find identification vectors in Modular-S-invariants is solved.

文中首先给出初等整数变换的概念，之后借助初等整数变换对整数矩阵进行分解，并在此基础上给出从加模S-不变量中求取不可达见证向量的方法。

Boley and Golub used Gauss quadrature formula to solve the inverse problem, but I used other different methods and thoughts. I obtained a new decomposition form of orthogonal matrix consisted by the unit eigenvectors of Jacobi matrix and found the direct relations between the first row and the orther rows of this orthogonal matrix.

Boley和Golub的算法是用高斯求积公式，而本人另辟蹊径，推出了关于Jacobi矩阵单位特征向量组成的正交阵的一种分解形式，并找到此正交阵第一行和其它行的直接联系，由此避免了通过求特征多项式计算尾主子阵的特征值，得到了新的稳定解法。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。