四元

Is rising in the Quaternion Bridge Lido shopping district, was among the first foreigners to gather.

正在崛起中的四元桥丽都商圈，是第一批外国人来收集。

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

本文对于特征不是2的任意域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F中，那么它们的迹相等。

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。

It helps to research the solution of the situation and stability of the real quaternion matrix equation.

由此有助于研究实四元数矩阵方程的解的情况和解的稳定性。

Use four yuan Group to achieve rotation matrix with six cameras peacekeeping function.

使用四元组实现矩阵旋转功能，具有6维功能的摄像机。

Vibration frequency modes of quasi-one-dimensional SiO2 clusters with one chain, two chain, three- and four- membered ring structures were calculated according to the density-functional theory.

运用密度泛函理论，计算了4～24个单元的准一维单链、双链、三元环、四元环管状构型SiO2团簇的振动频率。

Bernstein type theorem; Quaternion Euclidean space; minimal Lagrangian graphs; Twisted special Lagrangian submanifold; twisted normal bundle; Austere submanifolds; Real space form; Complex space form; Hamiltonian minimal submanifold; A Lagrangian submanifold with conformal Maslov form

基础科学，数学，几何、拓扑伯恩斯坦型定理；四元数欧氏空间；极小拉格朗日图；扭曲特殊拉格朗日子流形；扭曲法丛； Austere子流形；实空间形式；复空间形式；哈密尔顿极小子流形；具有共形Maslov形式的拉格朗日子流形

Computer; mathematical problems; Mizar project; quaternion numbers; algebra structure

计算机；数学问题； Mizar系统；四元数；代数结构

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。

The results showed that the technology of higher Mooney rubber polymerized by the catalyst system was feasible.

结果表明，四元催化体系合成高门尼粘度橡胶并经充油生产BR9073在技术上是可行的。

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。