平面向量

D.Hilbert在1900年展望20世纪数学的未来时，提出的著名的23个数学问题的第16个问题，就是寻求平面向量场极限环个数的最小上界，以及这些极限环可能出现的相对位置。

Hilbert ' 16th problem is to determine the minimum upper bound for the number of limit cycles of plane vector fields , and their relative location .

高中新教材《平面向量》教学体会

Teaching Realization of Plane Vector in New Textbook in High School

平面向量场X在奇点等价于它的首次非零喷射X＿k当且仅当这奇点是X＿k的非中心孤立奇点，此外还给出了X＿k的一切拓扑结构。

A vector field X on R ￣ 2 is equivalent at a singularity to the first non-vanishing iet X_k of Xif and only if the singularity is non-central and isolated for X_k , Besides , all topological types of X_kare given .

与物理特征相关的平面向量场的拓扑简化及压缩

Physical Feature-Dependent Topological Simplification and Data Compression of Planar Vector Fields

平面向量场与曲率分析在曲面求交中的应用

Application of plane vector field and curvature analysis in surface intersection

注重加强学生学习平面向量的过程体验。

Students ' learning experience in the learning must be emphasized .

一类对称三次平面向量场的全局与局部分支

Global and Local Bifurcations in a Planar Cubic Vector Field With Symmetry

一种能有效处理平面向量场测量数据的数值技术

An Effective Numerical Technique for Processing Measured Data of Plane Vector Fields

例谈平面向量在解析几何中的应用

The Application of Plane Vector in Analytic Geometry

渗透平面向量构建知识网络

Permeating Level Vector Quantity and Structuring Knowledge Network

用拓扑结构分析法实现平面向量场可视化

Plane vector field visualization using topology analysis method

平面向量场源、汇特征检测及可视化研究

Research on Feature Detection and Visualization of Sources and Sinks in a Planar Vector Field

利用临界点聚类的平面向量场极限环的检出及可视化

A Critical Point Clustering Approach to Detection and Visualization of Limit Cycles in Planar Vector Fields

一种面向差错控制的认知观测系统模型&平面向量概念理解差错模式实证研究

A Sort of Error Cognitive Observation System Model Demonstrate Investigation of the Misunderstanding of Plane Vectors

用一种新的数值方法再现微分平面向量场离散测量数据。

A new numerical method is developed and demonstrated for representing and differentiating discretely measured vector-field data .

通过复平面向量的关系，提出了一种固体π能带的简化计算方法。

We proposed a simple method for the calculation of the solid state π band by orbital vector analysis .

向量，包括平面向量和空间向量，是高中数学新教材的主要内容之一。

Vectors , both plane and solid , are important parts in Math For Senior and key points in National Entrance Exam .

结合认知理论和系统控制理论，构造了一种面向数学概念理解差错的观测分析模型，建立了对平面向量概念体系的理解进行实证研究的观测分析流程。

According to the cognitive theory and controlling theory , the observing model had been created to encounter misunderstandings on mathematical concepts .

我们利用平面向量分析，矩阵，求导运算等工具推导出所有的结论和公式。

We apply the tools of plane vectors analysis , matrixes and derivations etc. , and obtain all the conclusions and equalities .

然后，结合向量这个特定的内容针对向量的概念教学、运算教学、平面向量基本定理教学、应用教学提出了一些建议。

And then , propositions are also made in concept teaching , operation teaching , plane surface vector theory teaching and applied teaching .

平面向量场由首次非零喷射决定奇点的充要条件

The Necessary and Sufficient Condition for the Topological Type of Singularities of Vector Fields on R ￣ 2 Determined by Their First Non-vanishing Jet

就平面向量场的分支理论而言，对于极限环分支的研究已成为人们关注的主要问题。

About bifurcation theory of plane vector fields , the study on bifurcations of the limit cycle has become an important and popular topic .

本文从平面向量的特性出发，从应用的角度初步探讨了平面向量在构建数学知识网络中的优势和重要性。

This paper , in term of characteristics and application , gives a pre-liminary discussion about its advantage and importance in structuring math knowledge network .

就平面向量场的分叉理论而言，极限环分叉的研究已成为人们关注的热点，具有极其重要的理论价值和实际应用价值。

The bifurcations of limit cycles which have important theory values and apply values are generally acknowledged as the hot areas of the research work .

平面向量是新教材新增添的一部分，是蕴含代数与几何二重性的一个概念，并且与其它章节结合紧密。

As an addition made to the new courses , plane vector is a concept combined algebra with geometry and is closely connected with other chapters .

通过对平面向量概念理解差错进行统计分析，认为数学概念学习中的理解差错，主要有两种模式：一类是概念模板差错，另一类是认知过程差错。

After clustering analysis on the misunderstanding of plane vectors , there was a common sense that the misunderstandings from the mathematical learning mainly derive from two models .

最后，笔者对平面向量与三角函数内容衔接，以及用平面向量处理几何问题做了进一步的探讨。

At last , the writer joins the contents of plain vector and trigonometric function together , and make further discussion about how to solve the geometrical problems by using plain vector .

给出了平面向量场的局部可积性条件，通过定义旋转数得到了整体可积性定理，并利用直角形闭路径给出了其证明。

In this paper , locally integrability condition of plane vector field is given at first , then the main theorem of whole integrability theorem is obtained by defining the rotation number , and is proved using the rectangular closed path .

应用平面向量场理论，讨论了系统各类平衡点的性质，指出其拓朴系统中存在三条不同的奇异线，并进一步讨论了系统参数及这些奇异线对平衡点的影响。

By employing planar vector field theory , the properties of equilibrium points have been discussed in details , and three singular lines of its topological system have been obtained . Furthermore , the influence on the equilibrium points of the parameters as well as the singular lines is investigated .

模糊超球面支持向量机（FHS-SVM）在处理一类分类问题时比超平面支持向量机泛化能力更强，特别是在雷达目标检测中得到了成功应用。

Fuzzy hypersphere support vector machine ( FHS-SVM ) has stronger generalization capability than hyperplane support vector machine in the one-class classification problem , being successful in radar target detection .