查询词典 general algebra

Firstly, this paper definited pseudometric d for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions.

首先，对已知集X的子集的σ-代数A的n-折积A^n，定义了伪度量d，给出了相应的特征函数〈h，Is〉；其次，通过特征函数给出了集函数在S 可微的定义及集函数在S 关于第i个变量Si的偏导数定义；给出了多目标规划问题的弱有效解概念及的最优性必要条件；最后，分别在目标函数和约束函数的3种较弱凸性条件下，研究n-集函数多目标规划问题的对偶问题，获得了3个弱对偶结果和强对偶结果。

As human epistemology is concerned, there are at least five kinds of natural basic means for human to know about the universe: sensibility (time-space, algebra, geometry and all sensory abilities of human), intellectuality, aesthetic appreciation and aesthetic purposiveness and supreme rationality, which constitute the connection between subject and object. People use these basic ways to recognize themselves and all things in the universe.

关于人类认识论：人类认识宇宙的先天基本方式至少有五种，感性（时空、代数、几何及人类所有的感官能力）、知性、审美、审目的和最高理性等，它们构成了主体与客体之间的联系，人类用这些基本方式来认识自身及宇宙万事万物。

Though vector algebra, the theory of Pythagorean Theorem in Three-dimensional Euclidean Space was generalized with n-dimensional Eudidean space.

以向量代数为工具，将三维欧氏空间上的勾股定理在n维欧氏空间上进行了推广，得到了广义勾股定理。

Simple and quadratic equation and some skills of operation in Algebra may come from Babylon.

《代数学》中所讨论的一次和二次方程以及某些运算技巧可能源于巴比伦。

Everything in algebra was boring extrapolation after that, including the quadratic equation, which I have never used in my life.

以后代数中的种种推论都很枯燥，包括二次方程式，我这辈子从未用过它。

The branch of algebra that deals with quadratic equation.

二次方程式论处理二次方程式的代数分支。

In this paper,order structure of quasi left alternating BCI algebra is discussed,the Hasse graph is given,and the operating law is clearly described.

讨论了拟左交错BCI－代数的序结构，给出了其哈斯图，揭示了图中元素间的运算关系。

This paper adopts new algebra structure of quaternion matrix,to study how to apply a variety of iterative algorithm to quaternion linear systems.

本文通过引入四元数矩阵的新代数结构表示运算，研究如何将多种迭代算法应用于四元数线性系统上。

Because of Its wide-ranging connection with many applied science, such as the quantum physics, geostatic, the figure and pattern recognition and the space telemetry and so forth, the research in quaternion algebra is valuabe.

四元数在众多的应用问题中存在广泛的联系，如四元数在量子力学，刚体力学方面的应用，在计算机图形图像处理和识别方面的应用，在空间定位方面的应用等。

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。

Researches reveal that students who suffer from corporal punishment tend to resort to violence in their future life.

研究表明遭受过肉体惩罚的孩子倾向于在他们今后的人生中使用暴力。

Total sugar of sarcocarp and chlorophyll of pericarp increased firstly, and then decreased afterward along with altitude; Titratable acidity, ascorbicacid and anthocyanin of pericarp were increased along with altitude; The content of protein increased firstly and decreased afterward along with altitude; Carotenoid of pericarp were decreased along with altitude.

果肉总糖和果皮叶绿素含量随海拔高度升高先升高后降低；可滴定酸、维生素C和果皮花青苷含量均随海拔升高而升高；蛋白质在1720m处最大，1420m处最小；果皮类胡萝卜素随海拔升高而降低。