向量方程

Some nonexistence results for p-degenerate sub-elliptic first order evolution inequalities associated with the generalized Baouendi-Grushin vector fields are given. The method is an improvement of the admissible function method in Euclidean space. The proof hardly depends on the properties of the generalized Baouendi-Grushin vector fields.

通过改进欧氏的容许函数法，应用广义Baouendi-Grushin向量场的一些性质，选取特殊的容许函数，利用Hlder不等式和Young不等式，证明了由广义Baouendi-Grushin向量场构成的p-退化次椭圆一阶发展不等方程，在适当条件下非平凡弱解的不存在性。

The bifurcation theory of the plane polynomial vector fields is one important research domain of the theory of ordinary differential equation.

平面多项式向量场的分岔理论是常微分方程定性理论的重要研究领域之一，主要研究依赖于参数的向量场的全局轨线拓扑结构随参数变化的规律。

In the paper, we use the same idea to solve the variational equation,which equivalent to the Fredholm integral equation of the first kind with constraint.

这个积分方程的解只能确定到相差一个与边界的法向量成比例的向量，且在边界上的积分必须为零。

Then with the use of general inverse and matrix projection theorem,a new parameter with good identification effect is deduced,which is called projection modulus of residual vector ,and with which the damaged element is easily identi.

为了找到一个对小损伤较敏感的参数，在结构自由振动微分方程基础上，结合损伤结构的测试数据(用有限元模型的计算结果来模拟)，得到残余向量，利用广义逆和矩阵投影定理，导出了一个具有很好识别效果的参数：残余向量投影范数。

"Transform",The Laplace transform can be used to solve the state equations for the state and output vectors.

"，"拉普拉氏转换可以用来解状态方程的状态向量和输出向量。

Then the connection of left and right eigenvector and state matrix is deduced by using left and right eigenvector of free vibration differential equation in linear damped discrete system.

首先介绍了复模态理论，然后利用线性阻尼离散系统的自由振动微分方程的左右特征向量，推导出状态矩阵与振动系统的左右特征向量之间的关系。

Provide an opportunity for them to appreciate the application of direction of a line and the normal of a plane.

使学生体会直线方向向量，平面法向量的作用，加深对直线或平面方程中点坐标的理解。

This paper has obtained following three results about the new scheme:(1) The hardness of recovering the private key from the public key is based on the hardness of the shortest vector problems of several lattices;(2) The hardness of forging a signature is equivalent to the hardness of the closest vector problem of some lattice;(3) Each signature will leak information on the private key,but the final shape of the unlimited leakage is just a group of complicated non-linear equations.

文中给出新方案的3个结果：(1)由公钥恢复出私钥的困难性基于若干格上的最小向量问题；(2)由公钥伪造签名的困难性等价于某个格上的最近向量问题；(3)每个签名值仍然会泄露私钥的一些信息，但无限制泄露的最终形式只是关于私钥的一组复杂的非线性方程。

As it can be expressed easily by argument equations, we use the conicoid as the criteria of points" classification. Based on the point"s normal and the adjacent field, corresponding to the conicoid equation such as plane, ball and cylinder, we search the points that fit the equation along the adjacent field. Using this method, we realized the automatic classification of unorganized points.The experiments using the algoritlim and criteria approved from this thesis are also carried out.

本文采用了可以比较方便地用参数方程表示的二次曲面作为数据点的分类标准，根据点的法向量以及其邻域结点的各种属性，对应于平面、球面、柱面等二次曲面，依据曲面方程的特点，从起始点开始沿邻域深度优先递归寻找符合方程的数据点，实现了散乱数据点的自动分类。

Prediction approach of potentiality for environmental factors pH,temperature and dissolution oxygen on yeast fermentation was proponed,Based on constructing the membership functions of environmental factors on fermentation process,the fuzzy relation equation model was formed from fuzzy evaluation vector,membership grade matrix and factor weight vector.

提出一种预测环境因子pH、温度和溶氧对酵母发酵影响潜力的方法。在构造环境因子对发酵过程评价的隶属函数的基础上，建立由模糊评价向量、隶属度矩阵和因子权重向量构成的模糊关系方程模型。

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。