矢量方程

This paper, firstly, after a deep study of image mathematical models, sets up two kinds of image models namely Laplace partial differential equation model and biharmonic equation model and then obtains the eigenvectors of image by the methods of eigenfunction expansion and boundary recurrence.

本文首先较深入地研究了图象的数学描述，提出图象的Laplace偏微分方程和双调和方程两种模型，继而采用特征函数展开法和边界递推法分别求得图象的特征矢量。

Analyse the tooth geometry of Klingelnberg Cyclo-Palloid spiral bevel gear.,according to the relative position and kinematic relation of the cutter heads,virtual crown gear and the processed wheel blank,established the system of coordinates of the gear cutting, dedcuced the tooth face equation of the virtual crown gear, according to relations of the gear cutting and space theory of engagement, deduced the tooth face equation of klingelnberg Cyclo-Palloid spiral bevel gear, and drawing the three-dimensional graphs of the virutal crown gear and Klingelnberg Cyclo-Palloid spiral bevel gear according to the design and setting parameters.

根据铣齿加工中刀盘、摇台和轮坯的相对位置和相对运动关系建立了切齿啮合坐标系，由矢量的旋转推导了产形轮齿面方程；根据空间啮合原理和切齿啮合关系推导了被加工齿轮的齿面方程；由设计参数和铣齿调整参数计算得到齿面离散数据，绘制了产形轮和摆线齿锥齿轮的三维齿形。

The equilibrium equations under local coordinate are obtained through Euler angle transformation. In the modeling of warp, otter door is treated as the end node. The equilibrium equation of otter door is established through d\'Alembert\'s principle. It provides the end boundary condition of the dynamic model of warp.

通过欧拉角的转换关系获得了曳纲微元段矢量动力平衡方程在曳纲局部坐标系下的方程组形式；在建模过程中，将网板视为曳纲的尾部节点，根据达朗伯原理建立了网板的平衡方程，并将其作为曳纲模型的尾部边界条件。

Using the powerful calculation capability of MATLAB for matrix,and adopting vector ring and vector chain equation,the paper calculates and imitates the characteristic of kinematics and kinetics about equivalent force model of plane machinery.

利用MATLAB软件对矩阵强大的计算能力，采用矢量环与矢量链方程对平面机构的等效力学模型的运动学特性和动力学特性进行计算仿真，主要针对机构的速度波动特性进行了仿真和分析。

Color image sequence is presented by multivectors in geometric algebra,it is proved that if meet the constrained conditions for color optical flow analysis,a multivector instead of multichannel image processing method can be used to represent the continued distribution of images to expand the measurement range.

在几何代数域内对彩色图像序列用多重矢量表示，证明了彩色光流场分析时进行约束条件时的测量问题，通过多重矢量而非多通道的图像处理方法来表示图像连续特性，从而扩大了测量范围；然后依据物体色彩在运动过程中保持不变的原理，在几何代数域内推导了彩色图像序列的光流约束方程及其解法。

First, structure tensor is calculated to gain vector field for characterizing local structure of image. And then, total variation partial difference equation is imposed for smoothing vector field. Based on this we use line integral convolution for guide the stroke to generate virtual special effect image with fluctuant sense. Last, mergering with original real image, cylindrical panorama with virtualized relationship controlled by time can be generated, which accomplished the character of surpass the time and space in virtual reality system.

该方法通过计算结构张量获得图像曲线走向矢量场，以此刻画图像局部结构；并采用全变分偏微分方程对曲线走向矢量场自适应滤波平滑处理；在此基础上利用线积分卷积指导画笔走向模拟生成线条波动感虚化效果图像；最后结合原始真实图像和虚化效果图像，实现了一种基于时间变量的柱面场景虚化关联算法，并为虚拟现实系统超越现实时空的需要提供了一种新思路。

As a result, the mass matrix, the stiffness matrix, the damping matrix and the excitation coefficient matrices of the dynamics differential equations are random parameter matrices. According to the minimum deviation rule of the mean squares between the random parameter system and the deterministic parameter system, the random mean square deviation vector function between the two systems has been set up and the deterministic parameter system has been solved.

应用Newton-Euler矢量法对挂接车辆系统建立了质量阵、刚度阵、阻尼阵和激励系数阵皆为随机参数阵的八自由度随机参数系统动力学微分方程，并按照随机参数系统与确定性参数系统之间的均方值偏差最小的原则，建立了两系统之间的随机均方偏差矢量函数，由此解出了相应的确定性参数系统

By analyzing the technology requirement of electric actuators,RFOC（rotor field-oriented control）method was proposed. The fundamental mathematics equations of induction motor in the general synchronously rotating reference frameused for vector control were achieved by coordinate transformation.

中文摘要：分析智能型电动执行机构的技术要求，提出了转子磁场定向的空间矢量控制方案，通过坐标变换得到了适用于矢量控制的同步旋转坐标系统下的感应电机数学模型，推出了转子磁场定向方程。

This paper focuses on four important aspects as follows. The first one is the establishment of variational quations which provides the mathematics theories for the finite element method of HMT; the second one is for the study of scalar/node and vector/edge finite element method; the third one is about how to solve faster for the large-sacled matrix system of scalar/node and vector/edge finite element; and the last one is achieving the forward modeling with high precision of HMT method.

主要包括四部分：建立与高频大地电磁法边值问题相等价的变分问题，为有限元数值计算奠定数理基础；标量/矢量有限元方法的研究；加速标量/矢量有限元矩阵系统方程迭代求解技术的研究；实现高频大地电磁参数精确快速正演模拟的研究。

This theory makes direct use of the electric and magnetic field as unknowns, thus yielding uniquely defined vectors in combination with a suitable grid definition.

该理论直接以电场强度和磁感应强度为未知量，采用两套互相正交的网格，将场矢量离散为不同网格点上的一系列分量，将矢量积分方程转化为一组线性方程组。

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。