在量子光学、凝聚态物理、原子分子物理中存在许多典型的具有三生成元李代数结构的量子系统或模型。
There exist a number of typical systems and models which possess the three generator Lie algebraic structure in quantum optics, atomic and molecular physics and condensed matter physics.
八元数实在是个古怪的东西，它们是仅有的可能做除法的四种数制中之一，因此容许运行满量程的代数运算。
They are one of only four number systems in which division is possible, and so allow the full range of algebraic operations to be performed.
元微分算子代数的导子李代数结构。
Lie algebras of derivations of n-differential operator algebra.
流代数的基本概念是各种“流”算子的矩阵元在物理实验中是可以测量的。
The essential idea of current algebra is that matrix elements of various "current" operators are measurable in physical experiments.
代数的比重则会增加，考生要在线性方程、不等式、二元方程等方面做好准备。
Algebra is stepping up: Prepare for linear equations and inequalities, and systems of equations in two variables.
对于非线性问题，采用二元代数插值参数标定方法，并就提高测量改进方法进行了探讨。
For non-linear reason, the method of parameter demarcating by dualistic algebraic interpolation was used in data processing.
在一元泛代数上引入了双同余关系，从而使双同态映射与双同构映射得到了沟通。
In this paper we have given the concept of double-congruence, by which the concepts of double-homomorphism and double-isomorphism in a unary algebra are linked together.
八元数实在是个古怪的东西，它们是仅有的可能做除法的四种数制中之一，因此容许运行满量程的代数运算。
Octonions are indeed odd creatures. They are one of only four number systems in which division is possible, and so allow the full range of algebraic operations to be performed.
本文用生成元和定义关系的方法，对每个可解可补李代数给出一个定义矩阵。
A defining matrix is given for the solvable and complemental Lie algebras with a generator relation method.
基于旋转群代数，以航天器姿态控制研究为背景，提出了四元数的核心矩阵的概念。
A concept of kernel matrix of quaternion is proposed, which is based on rotation group algebra and with spacecraft attitude control as its background.
基于代数特征值逆问题理论，提出了一种利用静力试验数据修正有限元模型方法。
Based on the theory of inverse algebraic eigenvalue problem, a method for correction finite element model by using test data is presented in this paper.
本文主要对求解二维弹性力学问题高次有限元方程的代数多重网格(amg)方法进行了讨论与探讨。
In this paper, we discussed to Algebraic Multigrid (AMG) method for higher-order finite element equations in two dimensional linear elasticity.
本文建立了八元向量代数，它既是一种方阵代数，又作为一个更加完备的运算系统而包含了复数、矢量和四元数。
The eight-vecter algebra is found in the paper, as a kind of square matrix algebra and as more complete operation system containing the complex number vecter algebra and quaternion numbers.
将代数学中的幂零元概念作适当的解析学上的推广，可以绘出一个很满意回答。
A very satisfactory answer can be given in terms of the appropriate analytic generalization of the algebraic concept of nilpotence.
在有单位元的交换环上，可应用生成元和定义关系的方法给出仿型李代数的定义。
On commutative ring with the identity, the definition of affine Lie algebras was given by applying the means of generator and defining relation.
使关系元组在由外存至主机的流动过程中就并行完成筛选、投影关系代数的一元运算。
When relational tuples are flowing from mass storage to host via this filter, the unary operations of relational algebra for them such as projection and selection are completed parallelly.
数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。
Numerical experiments show our AMG method is robust and efficient for solving the quadratic Lagrangian finite element system.
给出了布尔群代数半群中的幂等元、极大子群和正则元的结构以及幂等元和正则元的个数。
The structure of the idempotent elements, regular elements and maximal subgroups and the number of the idempotent elements and regular elements in Boolean group algebra are given.
证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
利用一个特殊非协调矩形元导出了一个新的使用节点少而代数精度高的非常规数值积分公式。
In this paper, a new unconventional numerical quadrature with fewer node values is established based on a special nonconforming rectangular finite element.
“四元术”是中国古代数学最杰出的成就之一。
"Siyuanshu" was one of the most distinguished achievements in the ancient mathematics in China.
认为中国古代数学家求解这类问题的基本思想方法是设法减少题目中未知元的个数，使不定解的问题转化为确定解的问题。
It points out that the main idea of ancient Chinese mathematicians for calculating such problems was to change an indeterminate problem into a determinate one.
本文引进并研究了三元代数的相对乘子代数，建立了一个同构定理。
This paper given the definition of the relative double multiplier on a ternary algebra, and study the isomorphic problem of the relative multiplier algebra.
八元数是一种不结合代数，关于它的结合运算性质知之甚少。
Octonion algebra is a non_associative algebra, and only a few associative calculating properties are known.
这是一个递归构造的方法，利用该方法，对任意的奇数，都可以构造相同变元数量的代数免疫最优布尔函数。
It's a recursive construction. Given any odd number, we can construct Boolean function with optimum algebraic immunity in the same number of variables.
本文将应用广义限制李代数的概念来研究具有三角分解李代数的积分元和中心扩张的关系。
In this paper, we apply the concept of the generalized restricted Lie algebra to study the relation of the integral and central extensions of a Lie algebra with a triangular decomposition.
但由于边界元法得到的求解代数方程组的系数矩阵是满阵，对其解题规模有很大的制约作用。
But the scale of the problem that can be solved by BEM is greatly limited, because the matrix of the system equations generated by BEM is fully populated and unsymmetrical.
应用三元数运算，推导得到了一般三次代数方程的求根公式，结果证明与卡尔丹公式是一致的。
Applying the operation on three ary number, we got the formula that was applied to seeking the roots of normally cubic equation, and proved that the result is consistent with Cardans formula.
对气液两相非定常一元流动方程组导出了两套代数显式解析解。
Two sets of algebraically explicit analytical solution are derived for the partial differential equation set describing the one dimensional unsteady gas-liquid two phase flow.
利用这一结果，给出了两个广义四元数代数同构的一个充分必要条件。
Wehave determind completely these representations. Using this result, we gave a necessary and sufficient condition about the problem of the isomorphism of two generalized quaternion algebras.
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