四元

According to the Vegard's law and density functional theory of quantum mechanics, the lattice match conditions of Boron-contained arsenide and antimonide quaternary materials have been deduced, the bandgap properties of such quaternary materials have been theoretically analyzed, and the bandgap bowing parameters of all ternary compounds included have been theoretically calculated.

依据维加德定理和量子力学中的密度泛函理论计算出含硼砷化合物和含硼锑化合物四元系材料与GaAs、Si晶格匹配的条件及其带隙性质，同时计算出上述四元系材料所含三元系材料的能带弯曲参数，进而推导出BInGaAs、BInAlAs、BGaAsSb和BGaPSb四元系材料的发光波长与硼元素并入比例的关系。

The research on the CCD sensor information is used to determinate the satellite attitude system without gyroscope .(1) Using quaternion and MRP as attitude representation , the attitude kinematics function are established . The satellite attitude dynamics function is established,that is disturbed by the first-order Markov force moment.(2) Using the quaternion as attitude representations, the attitude determination state estimator EKF and UKF are designed , numerical simulation is done .

基于CCD星敏感器的无陀螺测量卫星姿态确定系统的研究(1)针对地球同步轨道卫星，分别建立了以姿态四元数和修正罗德里格参数为卫星姿态描述参数的姿态运动方程；建立了卫星受一阶马尔柯夫干扰力矩时的卫星姿态动力学方程；(2)设计了采用姿态四元数为卫星姿态描述参数的EKF和UKF估计器，设计了分别以姿态四元数和修正罗德里格参数为卫星姿态描述参数的UKF估计器，并进行了数学仿真。

Rotation, store the data in the matrix as an axis/angle and do the conversions yourself or will need to convert it to a quaternion.A quaternion is composed of four components: a vector with x, y, z coordinates and a w rotation.

当用一个四元数乘以一个向量时，实际上就是让该向量围绕着这个四元数所描述的旋转轴，转动这个四元数所描述的角度而得到的向量。

The definition, operation, properties, geometric meaning of quaternion and its three expressions are discussed. It is also demonstrated how to use quaternion to transform points.

本文详细叙述了四元数的这一功能，讨论了四元数的定义、运算、性质、几何意义和它的3种表达形式，给出了使用四元数处理点的各种几何变换的一般结论。

The family of quaternions plays a role in quantum physics, geostatics, control theory and peg-top technology. It is important to know and research quaternions as the development of quaternions. Thus the real representation of quaternion matrices has been appeared.

近年来，四元数矩阵在刚体力学，量子力学，控制理论和陀螺技术中的应用日趋重要和广泛，随着上述四元数力学的不断发展，对四元数矩阵的进一步认识和研究就显得越来越重要。

Hamilton discovered the quaternion ,to the middle period of last century,the application of the quaternion and the quaternion matrix are discovered widely in geostatics,the theory of ped-top using, strap-down inertial ,naviation, enginery and organ,robot technology and artificial satellite attitude control,and so on.

R。 Hamilton发现四元数到上世纪中叶，四元数和四元数矩阵方法在刚体动力学、陀螺使用理论、捷联惯性导航、机器与机构、机器人技术、人造卫星姿态控制等领域应用非常广泛。

Rotation matrix s representation with the unit quaternion has no singular points, so the unit quaternion-based estimation method is of more practical importance, and the algorithm in this paper does not need iteration computation compared to those unit quaternion-based method proposed by Horn(1987) and Su, et al.

单位四元数表示旋转矩阵时不存在奇异点，故基于单位四元数的运动估计方法具有更大的实用价值，而本文算法无需Horn(1987)和Su等人(1989)提出的单位四元数方法的迭代运算。

In this paper,pose representation by quaternions are researched.With the basic quaternion algebra,the "quaternion based rotations combination theorem" is introduced and proved theoretically.On the basis of this theorem,a method for compute of pose nonliear state transfer function and its linearization is purposed.Then,the computing of the measurement function and the linearization is studied.With the Extended Kalman Filter,the pose is tracked and estimated.

研究用四元数表示物体的姿态，在四元数基本运算法则基础上提出并证明了"基于四元数的多个旋转运动合成规则"，然后将此规则为依据，推导出一种用来计算姿态非线性状态方程系数的方法，对非线性状态转移函数进行线性化，并且研究了测量方程函数的确定及线性化，借助扩展Kalman滤波实现了对姿态的跟踪。

In this paper, a constructive proof of singular value decomposition of quaternion matrix is given by using the complex representation and companion vector of quaternion matrix and the computational method is described.

四元数矩阵的奇异值分解是四元数矩阵理论的重要内容，奇异值分解在四元数矩阵的理论研究和数值计算中都起到非常重要的作用。

To one quaternion matrix, according to its normal form, into which a quaternion matrix is transformed after decomposed, the types of decomposition of a quaternion matrix are divided into three large classes: diagonalized decomposition, triangular decomposition and triangular-diagonalized decomposition.

对单个四元数矩阵，以分解后的四元数矩阵的标准型作为分类的标准，将四元数矩阵的分解分为三大类：对角化分解、三角化分解、三角一对角化分解。

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。