算子代数

A new algebraic system X is constructed by using the known loop algebra 1 and difference operators.

首先利用环代数1和微分算子构建一种新的代数系统X。

In this paper, a new technique (so-called large-step wavefield depth extrapolation method), that is based on the Lie algebraic integral of operator's phase to compute depth extrapolation operator efficiently, is proposed.

本文提出一种基于"算子相位"李代数积分的快速计算延拓算子的方法，称为大步长波场延拓方法。

In this paper, a new technique (socalled largestep wavefield depth extrapolation method), that is based on the Lie algebraic integral of operator's phase to compute depth extrapolation operator efficiently, is proposed.

本文提出一种基于"算子相位"李代数积分的快速计算延拓算子的方法，称为大步长波场延拓方法。

In the front of this chapter,using operator inner-outer faetorization,we reduce the estimation problem to a distance minimization between a certain operator and the nest algebra in question.

本章第一节，利用算子中的内外分解理论以及Banach空间的对偶理论，将估计问题约化为某个算子与讨论的套代数之间的一个距离问题。

How to implement FMP algorithm and FMT algorithm with Mamdani implication operator, algebra product implication operator and Zadeh implication operator are given on the basis of POFI respectively.

首先分别给出了基於POFI方法的Mamdani蕴涵算子、代数积蕴涵运算子和Zadeh蕴涵运算子的FMP算法与FMT算法中寻求推理后件的计算运算式。

Then the interpolation representations of fuzzy controllers with Mamdani implication operator, algebra product implication operator, Zadeh implication operator and implication operator are introduced separately.

然后分别获得了基於POFI方法的Mamdani蕴涵算子模糊控制器、代数积蕴涵运算子模糊控制器、Zadeh蕴涵运算子模糊控制器及加乘运算子模糊控制器的插值表示，由此发现这些模糊控制器具有函数逼近的泛性。

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。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

In this system, the lattic structure is different from Boolean algebra, the implication operator → is just the Kleene Dienes operator R KD .

研究赋值格为非线性序，其格结构不同于Boole代数，而蕴涵算子→取Kleen－Dienes算子RKD的一种新的6值逻辑系统K16的语义理论，得到若干结果

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。