查询词典 involutory algebra

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。

Quaternion is applied widely in many domains, such as algebra, geometry, physics, engineering and so on.

四元数在代数学，几何学，物理学，工程技术等方面有着广泛和重要的应用。

The concepts of MP-filters and Boolean MP-filters in NML algebras are introduced in this paper, and by using MP-filters, the structure of NML algebras are established: If F is the Boolean filters, then M/~ is the Boolean algebras, i. e. the quotient algebra of NML algebras is obtained.

讨论了NML代数的性质，并且在NML代数上引入MP-滤子与MP-理想以及布尔MP-滤子的概念，并利用布尔MP-滤子建立了NML代数的结构：若F是布尔滤子，则M/~是布尔代数，即NML代数的商代数是布尔代数。

23 Chapter 3 Number Systems and Boolean Algebra 3.1.6 Complements Today, the radix -1 complement is not used by itself; it is used as a step for finding the radix complement. The radix complement is used to represent negative numbers in modern computer systems.

如今，反码已不单独使用，而作为求补码的一个步骤使用，如今，反码已不单独使用，而作为求补码的一个步骤使用，补码是当代计算机系统表示负数的方法(反码用于早期的计算补码是当代计算机系统表示负数的方法反码用于早期的计算技术中)。

24 Chapter 3 Number Systems and Boolean Algebra 3.1.6 Complements To form the radix complement, first find the radix -1 complement, and then add a one to the result.

为得到补码，先求反码，然后将加到结果上加到结果上。为得到补码，先求反码，然后将1加到结果上。

The Method Solving ramification of algebra iterated system rapidly and exactly is suggested,which is a shortcut to chaos.

提出了快速精确计算代数迭代系统分支值的思想。这将是通向混沌的快速之路。

Based on theory of structural dynamics and differential equation, the requirement of state complete observability is infered related to vibration modes, which is more acceptable for engineering than the counterpart of modern control theory related to rank of matrix in algebra.

这一条件较之现代控制理论中以矩阵秩的形式给出的相应条件更易为工程实际所接受，对测量装置的位置设置提供了理论依据，并指出无干扰驱动项的经典的Luenberger观测器对结构控制是不适宜的。

He explained that even though algebra had been reduced to a seemingly absurd but logical set of operations, eventually some sort of meaning would be restored.

他解释即使操作是符合逻辑的，但是代数学似乎仍然会沦为荒谬，但是最终会得到某种程度的恢复。

We analyzed the main factors that influence on the quality of reconstruction image. These factors are filter function, projection data, sampling space and noise level in filter backprojection, and the choice of relaxation parameter, the fashion of data access, the choice of basis function and the estimate of optimum iterative times in algebra iterative algorithm.

详细分析了影响滤波反投影算法图像重建质量的基本因素(滤波函数的选取，投影数，抽样间距，噪音的大小)和代数重建算法图像重建质量的几个因素(松弛引子的选择，数据访问方式，基函数的选择，最优迭代次数的估计)。

For the sake of the image reconstruction efficiency we shortened the reconstruction time almost 100 times by parameter table method. In algebra iterative algorithm we found the range of relaxation parameter is very different. The range of relaxation parameter of ART was narrower than that of SIRT. Different methods of data access will influence on the quality of reconstruction image.

在代数迭代算法中，通过模拟图像的重建发现，ART算法和SIRT算法松弛因子的选择有很大的不同，SIRT的松弛因子选择范围偏小，而ART的松弛因子选择范围要宽得多；数据访问方式的不同，对重建的图像有一定的影响；提出了最优迭代次数的判据，避免了在迭代时迭代次数选取的盲目性。

However it can often be frust ating for a child when people are unable to pronounce their name.

但它往往可以令人沮丧的一个孩子当人们无法断言他们的名字。

All these compounds were obtained from this genus for the first time. Compound, 4-cumylphenol, was a new nature product.

所有化合物均为首次从本属海藻中分离得到，其中4cumylphenol为新天然产物。