几何向量

There is extensive application, especially two-dimensional、three-dimensional vector quantity in a lot of fields of modern mathematics in the vector quantity, they have a form of expression of the array, there are ocular geometry meanings, so can become the effective tool which study the geometry problem of middle school.

向量在近代数学的很多领域中都有广泛的应用，特别是二维、三维的向量，它们既有数组的表现形式，又有直观的几何意义，因此能成为研究中学几何问题的有效工具。

You need to know what the cross product is and what it means geometrically (a vector perpendicular to the vectors with a length equal to the sine of the angle between them).

你需要知道向量积是什么，以及它的几何意义(一个和两个向量都垂直的向量，长度等于原来两向量的长度乘以两向量的夹角的正弦)。

Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not.

几何向量引入了更为先进的方法，它不仅汇集了许多传统的治疗无所适从，而且还导致进入载体的实际用途，一般直接通过仔细分离曲线的拓扑关系是从那些没有不变的坐标。

The vector has the rich actual background and the widespread application function, it has the algebra and the geometry dual statuses, causes the algebra geometrization, the geometry algebra, has communicated the algebra, the geometry and the trigonometric function, has the good analysis method and the complete structure.

向量具有丰富的实际背景和广泛的应用功能，它具有代数和几何双重身份，使代数几何化、几何代数化，沟通了代数、几何与三角函数，具有良好的分析方法和完整的结构。

It defines the vector norms as satisfaction function to revise the weighting factors of metrics given by analytic hierarchy process. Meanwhile, the scheme exploits vector geometrical relationships in Hilbert sub-space basing on revised weights to measure similarities between vectors of network ability and user target.

该算法定义Hilbert空间中的向量范数表征满意函数，以修正由层次分析法给出的各指标权重因子；并利用基于修正权重因子的Hilbert子空间中向量间的几何关系，衡量网络参考向量与用户目标向量间的相似性，选择与用户需求最匹配的网络。

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。

During the course of the well-known "new mathematics" campaign, the status of Euclidean geometry was completely overthrown in I960" s. After deeply thought of "new mathematics", the standpoint that geometry curriculum should reflect the content and method of modern geometry and be in touch with the student" s real life was agreed on. Other countries have tried some significant attempts. We can find from some geometry textbooks that the methods of transform and vector have appeared as a normal part. Simultaneous, not only the new developments of geometry such as Topology have been referred , but also the connection between geometry and practice has been strengthened.In China, geometry curriculum is also in the during of innovation.

而学校几何课程在二千年的时间里一直没有多大的变化，直到二十世纪初"克莱因—培利运动"的第一次冲击，到60年代"新数学"运动的全盘改革，以及之后的深入反思，中学几何课程要反映现代几何学的内容和方法以及紧密联系于实践的观点已经受到普遍的重视，国外的几何课程已经在这方面做了不少有意义的尝试，从国外的一些几何教材中可以发现：变换、向量等工具已经作为正式的内容进入几何教学，拓扑学等几何的新发展也开始在教材中有所体现；几何课程与实践之间的联系更是在很大程度上得以加强。

If the pertubation factors in judgments are stochastic,it was proved in this paper that the matrix of GMJ will converge in probability at a consistent positive reciprocal matrix whose vector of priorities is just the geometric mean of the vectors of p...

如果判断矩阵的干扰因子是随机的，文章证明了几何平均综合矩阵将依概率收敛于一个一致性的正互反矩阵，其排序向量刚好是各判断矩阵的几何平均综合排序向量。无疑这对于在群组决策时几何平均综合判断矩阵法的使用是重要的。

The multi-dimensional signals measured by sensors with a machine working under normal condition or fault condition, can be used to build Q statistic and T^2 statistic respectively to detect the state of the machine. Meanwhile, the feature vector is constructed by the Q value and the T^2 value, the geometrical distance between the normal feature vector and the feature vector H when the machine goes wrong is used to realize the fault location. The results show that the method is feasible.

利用多个传感器测量的异步电机多维信号参量，构建电机在正常工作和发生故障时的Q统计和T^2统计，以实现电机的状态检测；利用Q统计和T^2统计值构建电机的状态特征向量，通过比较度量当前电机的特征向量与电机发生故障时的特征向量H的几何距离来实现电机故障的定位与分离实验证明，该方法可以有效地实现故障的诊断与分离。

The number of support, vectors is decreased by 28%. Then, the structure of the Riemannian geometry is introduced in the input space, and using the Riemannian geometric modifies the kernel function of the classifier and gets less improved support vectors at the second training.

在第一次训练后产生的支持向量的基础上，将黎曼几何结构引入到输入空间，利用黎曼几何结构将分类器中的核函数进行修改，在第二次训练中再次减少了支持向量数目。

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。