四元的

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。

Residential heating prices will be the existing building area heating 15.4 yuan per square meter adjusted to 20 yuan; government organizations and institutions, businesses, hotels, restaurants, as well as the heat-funded enterprises will be the current price per square meter construction 18.5 yuan, 21 yuan, 24 yuan for the 26 Unity adjust.

住宅供暖价格将在现有建筑面积采暖十五点四元，每平方米调整为20元；政府组织和机构，企业，宾馆，饭店，以及热资企业将是目前的价格为每平方米建筑一十八点五元， 21元，二十四元为26统一调整。

The research of matrixes is continuously an important aspect of the quaternion division algebra. The purpose of this paper is to discuss the property of skew self-conjugate matrix. The definition of skew self-conjugate matrix on real quaternion division algebra is given.

四元数体上矩阵的研究是四元数代数理论中的一个重要方面，本文研究实四元数体上斜自共轭矩阵的性质，给出实四元数体上斜自共轭矩阵的定义。

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。

Furthermore, we express a real quaternionic polynomial with four general polynomials which have real coefficients, thus build direct relation between real quaternionic polynomials and general polynomials.

新方法以四元数的复表示及其可对角化的特征结构为理论基础，将问题等价为求解2×2矩阵多项式的可对角化解；进一步将四元数多项式用四个实系数多项式表示，建立了四元数多项式与一般多项式的直接关联。

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。

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。

By using the methods of complex representation of quaternion matrices and companion vector, we study and simplify the numerical calculation methods of quaterinon matrices, and establish new aigebraic methods in quaternionic quantum mechanics.

我们通过四元数的复表示和友向量方法，研究并解决了四元数矩阵的一系列数值计算问题，给出一套四元数量子力学中的数值计算方法。

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。