和向量

Compared with traditional methods, the method in this thesis does not need to find all the eigenvalues and eigenvectors of a system, and to do diagonalization.

与常规方法相比，本文的方法不需要求系统全部特征值和特征向量，也不需要对角化。

We then diagonalize the matrix C and obtain the eigenvalue spectrum and eigenvectors. The large eigenvalues which go beyond the upper bound of the random matrix, i.e., the Wishart matrix, reflect the local correlations between stocks. The largest eigenvalue corresponds to the market mode, and next large eigenvalues represent the interactions between stocks in a same sector.

进一步，通过对角化，我们得到矩阵C的特征值谱和特征向量，超过随机的Wishart矩阵特征值谱上边界的特征值反映了股票间的局域关联，其中最大的特征值对应于市场模式，其余的次大特征值代表了同一板块内股票间的相互作用。

As the special characteristic of nonlinearity, several notions are introduced and used in this paper, such as differential manifold, vector field, diffeomorphism, tangent space, topological equivalence. Stable manifold and unstable manifold are also introduced.

针对非线性的特殊性，本文专门介绍了非线性中几个比较特殊的概念，如微分流形、向量场、微分同胚、切空间以及等价关系等，对稳定和不稳定流形也作了介绍。

This method doesn't require differentiable function, and has the advantage of faster convergent speed, the ability of optimization within global scope and the independence between eventual optimized paramaters and initial SVM paramaters.

该方法降低了对性能函数连续且可微的要求，收敛速度快，最终优化解与支持向量机的参数初始值无关。最后，通过仿真实验表明了该方法具有更高的分类和回归准确率。

Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms.

流形上的几何学讨论的问题是微分流形，向量场和微分形式。

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier transforms and partial differential equations will also be introduced.

本课程为提供已有常微分方程式基础的同学修习，内容包括线性代数，矩阵运算，特徵值问题，向量的微分与积分，一阶线性微分方程组，傅力叶级数和正交函数，傅力叶转换，并将对椭圆，抛物线，双曲线型式的偏微分方程式作概略介绍。

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier

本课程为提供已有常微分方程式基础的同学修习、内容包括线性代数、矩阵运算、特徵值问题、向量的微分与积分、一阶线性微分方程组、傅力叶级数和正交函数、傅力叶转换、并将对椭圆、抛物线、双曲线型式的偏微分方程式作概略介绍。

Support vector machine; pattern recognition; nonlinear system modeling; the law of oil and gas distribution; curve fitting

支持向量机，模式识别，非线性系统建模，油气分布规律，试井曲线拟和

From theoretical aspect, our method can make the entropy value of sort results decrease, and the divisibility of optimal set of discriminant vectors strengthen.

理论上的分析和实验结果表明，这种方法可以使熵值减小，即分类结果的可分性增加，并且最佳鉴别向量集的分离能力得到增强，提高了分类效果。

By the analyses of different person and the same person with different expression and gesture, the number of principal component vector is determined properly under the attention to divisibility and workload.

首先对不同人以及同一个人的人脸图像进行主成分变换，然后根据得到的人脸图像类内及类间距离数值的变化结果，在充分考虑到其可分性和计算工作量的前提下，选择适当的主成分变换向量的个数并进行人脸图像的特征提取。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。