向量的

From Poisson matrix, we can observe volume-preserving vector fields. By using Geiges-Gonzalo's existence of contact circle Theorem [3] , we show the existence of volume-preserving circle on3-manifolds which says that every3-manifold admits two linear independent vector fields preserving a same volume form.

通过Poisson矩阵可以观察出保积向量场，再利用Geiges-Gonzalo的接触圆存在性定理[3]，我们证明了保积圆的存在性：每个闭的3-流形上都存在两个处处线性无关的保积向量场并且它们的常系数线性组合仍是保积向量场。

The accurate solution of linear equations could be expressed linearly by the conjugate vector base, and the iterative strategy was used to construct the conjugate vector base groups and the corresponding coefficient. The constructed conjugate vector base groups were proved to be conjugated.

线性方程组的精确解能够由共轭向量基线性表示，利用迭代的方式给出了构造共轭向量基以及对应系数的方法，证明了算法所构造的向量基的共轭性。

The article by several opposite examples illustrated the former method of finding vector group's maximum linearly independent vector group is imperfect, sometimes even lead to wrong results. The method is that make use of row vector as matrix and then change matrix by performing elementary row operation.

本文通过几个反例说明了在求向量组的极大无关组时，以往普遍使用的以向量为行向量作矩阵，再对矩阵作初等行变换的方法是不完善的，甚至会导致错误的结果。

Constructed by standard binary classes support vector machine, present multiclass SVMs are usually very slow to be trained. When a large number of categories of data are to be classified, the training work could be very difficult. By extending the hypersphere one-class SVM to a hypersphere multiclass SVM, we build a fast training classifier HSOC-SVM. Its training speed is higher than that of the present multiclass classifiers, because each category data trains only one HSOC-SVM.

目前的多类分类器大多是经二分类器组合而成的，存在训练速度较慢的问题，在分类类别多的时候，会遇到很大困难，超球体多类支持向量机将超球体单类支持向量机扩展到多类问题，由于每类样本只参与一个超球体支持向量机的训练，因此，这是一种直接多类分类器，训练效率明显提高。

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

While matching, only the principal component directions corresponding to the rows of the same serial numbers in searching area are needed to be extracted for the computation of projection value so as to form the vectors of projection values. The distances between MM-vectors and the vectors formed by projection values are computed, and whether the two kinds of vectors are matchable should be in accordance to those distances.

在匹配时，只需抽取搜索区域中相同序号的列向相应的主元方向作投影运算，从而构成投影值向量，进而计算该向量与预处理中所得的最大最小值构成向量间的距离，从而根据距离的大小判断是否匹配。

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

The generalized reliability of single failure mode component and unit structure under different kinds of uncertainty factors is treated perspicuously and classified. Combined with the three class fortify standard of aseismic design code,the conception of reliability vector of structures and systems with intermediate state before failure is put forward, and the calculation model of reliability vector with three stage working modes of "safety-intermediate-failure" and the operation rules of reliability vector of the simple aseismic engineering systems composed by structures are established.

针对各种不确定性因素下的单失效模式构件和单体结构，进行了广义可靠性的明晰化分类处理，结合抗震设计规范的三级设防标准，提出了具有中介状态结构与系统可靠性向量概念，建立了具有"安全-中介-失效"三级工作模式的可靠性向量计算模型，及其由结构组成的简单抗震工程系统的可靠性向量运算规则。

The update model of the probability vector in compact GA is characterized by random walk, based on which the components update of the probability vector in the CGA with binary code is studied. A novel algorithm is proposed consequently. By using this algorithm, the fitness difference of the two competitors is increased. This can guarantee the probability vector updates availably.

紧致遗传算法中概率向量进化的模型是随机游动模型，据此研究了二进制编码中向量分量的进化特性，提出了分级竞争紧致遗传算法（grading competition compact genetic algorithm，GCCGA），加大参与竞争的两个个体的适应度的差距，使概率向量有效进化。

Then for an artificial given solenoidal vector field, the problem how to construct another solenoidal vector field to make its curl equal with the given field was discussed.

作为它的逆问题，对于任意给定的一个标量场和一个无散向量场，求解另一个向量场，使该向量场的散度和旋度分别等于两个给定场的问题，只有在适定的边界条件下才能得到确定的解。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。