代数等价

Arad and Blau proved that an abelian table algebra can be viewed as a group algebra of some abelian group G. Chapter 3 of this paper gives the structural theorem of abelian table algebras by defining a group structure in table basis. Furthermore, the structure of elementary abelian table algebras is discussed using the number of composition series of table algebras.

Arad和Blau证明了abel表代数等价于某个有限生成abel群G的群代数，受此启发本文第3节通过定义表基的一个群结构给出了abel表代数的结构定理，并从合成列数目的角度对初等abel表代数进行了细致刻画。

Consider the identification of a continuous linear system The identification of its algebraic equivalent system or transfer function can be obtained.

在一般情况下，对于连续线性系统可以获得其代数等价系统或传递函数的辨识。

For the sake of getting more economic or effective controllers, a mapping law is proposed that the sub-systems in a space are mapped algebraic equally into another space to reduce differences by optimal theory. No any restrictions are added to the controlled systems, and without need to solve coupled Lyapunove or Riccati equalities.

2考虑了各子系统之间的层次差异，提出了变换规则，通过代数等价变换将各子系统映射到另一空间，借助优化理论，消除各子系统之间的差异，从而获得更经济、更有效的控制器。

In interior-point methods, different trajectories to the optimal set are formed from different algebraically equivalent paths.

在内点法中，采用不同的代数等价路径形成了通向最优解的不同轨迹。

The first is based on the algebraically equivalent transformation to the standard centering equation xs=μe.

首先通过对中心化方程xs=μe实施代数等价变换，得到了新的不同的摄动方程组。

Further some equivalent conditions for a trivial algebra are given, and that the mapping which maps the subset of the universal to the maximal congruence that saturates the subset being a -homomorphism, being order preserving, being constant mapping, the algebra being trivial are equivalent is proved.

最后利用该同余给出了关于平凡代数的几个等价条件，证明了泛代数的子集到渗透该集的最大同余的映射为保序映射、该映射为-同态、该泛代数平凡等是等价的。

Adopting generalized Jordan block and algebra equivalence transform method, all of the transfer functions at different load points can be transformed to state-space description with time variable. The steady robustness of three different mode of control systems were researched by mathematic analysis. It shows that: for the high order inertia controlled object with the characteristic of nonlinear and time-variable that described by the set of transfer functions, the Luenberger function observer established according to its any algebra equivalence state-space description, if some conditions can be met, there would be a matrix of T with n′n satisfied the Sylvester matrix equation TA- FT=GC.

采用广义约当块及代数等价变换方法，可将分段的传递函数描述转换为变参数的状态空间描述，对3种典型控制系统的稳定鲁棒性所进行的理论研究表明，对同一组传递函数描述的具有非线性和时变特性的高阶惯性受控对象，依据其任一代数等价的状态空间描述所构建的Luenberger函数观测器，在满足一定的条件时，存在n′n解阵T满足Sylvester矩阵方程TA- FT=GC。

In Chapter 3,we classify a binary-coded individual space equivalently withthe help of the ideals of Boolean algebra and analyze the search capabilitiesof a new kind of algebraic crossover operator in these equivalence classes,thenprovide the algebraic representation of a type of genetic algorithms by usingthe permutation group,therefore we can derive a lot of new forms of geneticalgorithms.

第三章运用Boole代数的理想将二进制编码的个体空间进行等价分类，分析了一类代数杂交算子在这些等价类上的搜索能力；然后利用置换群给出一类遗传算法的代数表示，由此导出多种新形式的遗传算法，并给出其中两类算法形式的收敛性结果。

Afterward Waldhausen ([7]) showed that this topological hypothesis was true. Besides, Stallings ([11]) gave another conjecture that was equivalent to Poincare"s Conjecture. Thus we know both conjectures made respec- tively by Traub and Stallings are equivalent to Poincare"s Conjecture.

另外Stallings([11])又提出了另一个代数的猜想并同时证明也证明了这个猜想与庞加莱猜想是等价的，由此可知Traub所给的猜想与Stallings的猜想都与庞加莱猜想是等价的，从而这两个代数的猜想也是等价的。

In this paper, we discuss effect algebra and related topics. The main results are the following:1. Effect algebra is a commutative algebraic structure. To get a non-commutative algebraic structure.we introduced the concepts of left difference and right difference, and we also introduced the concept of the Bi-difference sets, the concept of pseudo-difference poset, and proved that pseudo-difference poset is equivalent to pseudo-effect algebra.

效应代数描述的是具有交换性的量子系统，我们借助于差运算的思想研究了不可交换的量子逻辑结构，建立了左差、右差、伪差偏序集、双差集等概念，证明了伪差偏序集与伪效应代数等价，并得到了双差集的幺半群表示定理。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷