四元的

In this note, we show that for any two matrices $A$ and $B$ over a generalized quaternion algebra defined on an arbitrary field ${\bf F}$ of characteristic not equal to two, if $A$ and $B$ are similar and the main diagonal elements of $A$ and $B$ are in $\bf F$, then their traces are equal.

本文对于特征不是2的任意域${\bf F}$上定义的广义四元数代数上的两个矩阵$A$和$B$，给出如果$A$和$B$相似并且它们的主对角线上的元素在${\bf F}$中，那么它们的迹相等。

This paper firstly reviews the history of Automated Theorem Proving and Mizar,then gives a description of methods of mechanical theorem proving and verification to mathematical proposition under Mizar system.Based on that basis,the paper has done some Mizar researches on mixed operation of quaternion,differentiati- on of special composite function and the application of Rolle\'s theorem.

本文首先介绍了定理机器证明和Mizar语言系统的发展历史，其次简单描述了Mizar系统下定理机器证明和校验数学命题的方法，在此基础上对四元数的混合运算，特殊复合函数的微分以及洛尔定理的应用等方面进行了Mizar实现。

Zeros of linear polynomials with real efficients are the real solutions of the original polynomial equation.

5四元数二次方程的显式解：利用改进的新方法完全可以得到二次方程解的显式表示以及关于解的具体情况的一些充分必要条件。

The panhandling punks of yesteryear must have a bit of cash saved up, however, at a UK site called The Rally Shack the aforementioned bib slogan shirt as well as a hot pink tee adorned with a pattern of skulls and crossbones that might look more fitting donning the chest of John Lydon or Iggy Pop sells for 10.00 (about $18.00 US) and is available in 6, 18, and 24 month sizes.

该panhandling punks昔日必须有一个位元的现金储蓄起来，然而，在一个英国网站所谓的集会夏克波上述背带裤的口号，衬衫以及作为热粉红色发球装饰的格局，骷髅和交叉可能显得更加装修穿上公益金的约翰里顿或iggy流行的售价为10.00 （约$ 18.00美国），并且是可在6月， 18 ，和二四个月大小。

The ellipse curre equation of circular image is derived based on the theory of spatial analytic geometry and rotation matrix s representation with unit quaternion then a mathematical model of the distortion error is established which relates the distortion error to the foca length of the used CCD camera,the radius as well as the position and the attitude of the inspected circle directly.

研究三维视觉检测中圆的中心经针孔摄像机成像后存在畸变误差的问题，首先基于空间解析几何理论和旋转矩阵的四元数表示法推导出像平面上投影椭圆的参数方程；然后根据参数方程建立圆中心成像畸变误差的数学模型；最后对影响畸变误差的主要因素进行分析。

Per square meter price 5000-5500 yuan project are: Youth Road, Chaoyang District, located in the State of the United States and the First City, Huafang prone city, youth exchange district, located in Chaoyang Road shopping district of Huatang CASA, Huidong four subway stations on the eastern side of No. 29 Jianguo Road, West Road姚家园mouth water Gimhae嘉苑, Jiuxianqiao the ZAMA, basically can be used to buy two-bedroom 500,000 yuan.

价格为每平方米5000-5500元的项目有：青年路，朝阳区，位于该国的美国和第一城，华纺易城，青年交流区，位于朝阳路的华堂购物区小武器，四惠东地铁站东侧的建国路29号，姚家园路西口的水金海嘉苑，酒仙桥在Zama ，基本上可以用来购买两居室50万元。

In the last of this dissertation, we give necessary and sufficient conditions for the existence of and the expressions of perpositive semidefinite solutions and bipositive semidefinite solutions to some systems of quaternion matrix equations.

给出了某些四元数矩阵方程组有广亚半正定解，双半正定解的充要条件及其表达公式；研究了矩阵方程组的最小二乘解，极小范数的最小二乘解，在某些约束条件下的最小二乘解和极小范数的最小二乘解，给出了其有这些解的充要条件及其表达公式。

It includes two co-satured points, five univariant curves and four crystallization regions corresponding to NaCl,〓,〓, and 〓. It is important to investigate the phase diagrams for designing and optimizing the preparing process of the PSC adduct.

该四元体系及其三元子体系的相平衡研究，为Na〓SO〓制备〓合成工艺条件的确定和产物的分离提供了相平衡理论依据，为硫酸钠资源的综合利用提供了新的思路，具有重要的实用价值和学术意义。

As our experiments were concerned, the after growth of InGaP, GaAs was grown at a lower temperature than that for InGaP. This made the P atoms on the InGaP surface hard to desorb and greatly reduce the thickness of InGaAsP intermixing layer.

在我们的实验中，成长完磷化铟镓后，以较低的温度成长砷化镓，这将使磷化铟镓表面的磷原子较不易脱附，因此可显著的减少磷砷化铟镓四元混合层的厚度。

The orientation-singularity expression of the Stewart platform is deduced by using unit quaternion which can avoid singularity when using Euler angles to represent the orientation of rigid body, and then the algorithm of orientation-workspace of the manipulator at a certain position is proposed.

基于单位四元数描述的刚体姿态，避免了欧拉角等描述刚体姿态的奇异性问题，推导出Stewart机构处于给定位置时的姿态奇异解析表达式，并提出了该机构处于给定位置时的姿态工作空间算法，通过计算机仿真给出该机构处于一给定位置时姿态奇异轨迹和姿态工作空间的三维可视化描述。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。