查询词典 quaternion

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

In this paper, we describe the history of Mizar system and the method to use theMizar system. Then we give the definition of quaternion numbers, module, algebrastructre etc, and then we prove its properties.

本文首先介绍了Miza(来源：ABC论文61网www.abclunwen.com)r系统的计算机操作原理和使用方法，给出了在Mizar语言系统下四元数、四元数的运算、共轭、内积、模等代数结构理论的证明，所做结论都通过了Mizar系统的验证，发表在波兰的《Formalized Mathematics》杂志上，并被收录到MML数据库中。

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 existence and forms of the generalized righteigenvalues of real nonsingular quaternion matrix were put forward.

给出了实四元数矩阵正则对的广义右特征值的存在性和表达形式。

In this paper, based on the concept of normal quaternion, a new algorithm for the initial alignment of the integrated system is studied; the alignment algorithm is processed only on the basis of the position and velocity data of GPS.

基于规范化四元数的概念，研究了一种仅利用GPS的位置和速度数据对组合系统进行初始对准的新算法，克服了传统滤波方法进行初始对准存在的诸多局限性。

We also give out Schur decomposition for normal quaternion matrix.

对四元数正规矩阵，给出了其Schur分解，使得对某些四元数矩阵的计算得到了进一步的简化。

The earth is modeled as an oblate and rotating spheroid, and higher order terms in the multiple expansion of gravitational fields are considered. To avoid singularities in computations, the quaternion representation of the spacecraft attitude is used in the angular kinetic model equations.

其中地球被描述为绕短轴自转的椭球体，重力场梯度由四阶Jeffery常数描述，航天飞机的姿态运动用四元素法描述，以避免模型方程中的数值奇异点。

The former is an iterative method, and quaternion was utilized to simplify the matrix orthogonalization procedure.

改进的单点估计算法是一种迭代算法，它计算简单，收敛速度快，同时由于采用四元数表示姿态矩阵，简化了矩阵的正交化过程。

The computational flow of light propagation and the key techniques of visualization are presented. An optical system was employed to verify the correctness and feasibility of quaternion method in the calculation of beam propagation, and the pincushion distortion caused by the optical system was successfully simulated.

通过对某光学系统的仿真分析，成功仿真出图像经过光学系统产生的枕形畸变，证明四元数方法在光线传输运算中的正确性与可行性，为复杂光学系统的空间光线传输计算提供了另一种方法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。