一般代数

To find this angle, we first work out general algebraic expression for the range.

为求这一角度，首先我们求出射程的一般代数表达式。

To find this angle, we first work out g eral algebraic expression for the range.

为求这一角度，首先我们求出射程的一般代数表达式。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

In order to investigate the existence conditions of the robust optimal state feedback of uncertain system, we have to study the problem of GARE, that is the solution existence of the following equation PA+A'P+Q-PMP=0, Q=Q', M=M' In chapter 2, using some preliminary results and properties of the Riccati differential equation, we have established the sufficient conditions for the GARE problem.

在讨论不确定性系统LQL方法的状态反馈解的存在性条件时，引出了第二章讨论一般代数Riccati方程解的存在性问题，对一般Riccati方程 PA+A'P+Q-PMP=0，Q=Q'，M=M'第二章中先列举讨论了Q、M为正、负定各种情况下的实对称解的存在条件，然后着重研究了M、Q不定的情形。

The most famous rough algebras are Rough Double Stone Algebra, Rough Nelson Algebra and Approximation Space Algebra, and their corresponding general algebra structures are regular double Stone algebra, semi-simple Nelson algebra and pre-rough algebra respectively.

其中最有影响的粗代数分别是粗双Stone代数、粗Nelson代数和近似空间代数，它们对应的一般代数结构分别是正则双Stone代数、半简单Nelson代数和预粗代数。

One is the existence problem of real symmetric solutions of the general algebraic Riccati equation , the other is the optimal output feedback problem under the LQ index.

此外，本文还涉及了两个控制理论界多年来受到广泛注意和研究的难题；其一是一般代数Riccati方程的实对称镇定解的存在性问题：其二是线性二次型指标下的直接最优输出反馈问题。

The solvable Lie algebra is corresponding to a cascade decomposition of the system and the semisimple Lie algebra is corresponding to a qasi-parallel decomposition such that the system has a parallel form of a cascade decomposition and a qasi-parallel decomposition.

任一李代数都可分解为一可解李代数与一半单李代数的半直和，可解李代数对应于系统的级联分解，半单李代数对应的是系统的准平行分解，将二者合并起来，就得到一般李群下的非线性系统的结构分解，这是一级联形式与一准平行形式的并联形式分解。

Usually the graphical or algebraic methods are used in the design of such jibs.

组合臂架的设计通常采用作图法和一般代数法。

The algebra of quaternions, the first noncommutative algebra was thus suddenly born.

它们对应的一般代数分别是正则双Stone代数、预粗代数和半简单Nelson代数。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。