查询词典 simple algebra

However, despite such categorical pronouncements as "…the above shows that the ring is not the fundamental system for associative algebra of double composition "found in [Vandiver,1939], semirings never became popular and the interest in them among algebraists gradually petered out, although it never died completely.

这些年来，半环被各类研究者所探究或者是在他们的本身及尝试从半群理论和环论中拓展研究方法，或者联系于各种应用。然而，尽管这种范畴的看法"…上面表明环不是最基本的系统对于双复合结合代数"（这句话出自[Vandiver ，1939]）。半环没有受到他们的欢迎和引起他们的兴趣进而逐渐淡化，尽管没有彻底的消亡。

The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.

这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。

In chapter two, firstly I discuss the linear problem of local automorphism on AF C* algebra.

在证明过程中充分利用了代数的特殊结构—矩阵单位系这个工具。

Based on the new theories developed in biology,the basic theoreticalproblems of the genetic algorithm,which are the representation scheme,co-nvergence and convergence rates of the genetic algorithms,etc.,are discussedwith Boolean algebra,group theory,martingale theory and axiomatic method inthe framework of the Markov chain.

本文以生物学发展的新理论为背景，在遗传算法的Markov链框架下运用Boole代数、群、鞅及公理化方法研究遗传算法的表示、收敛性与收敛速度等基本理论问题。

In the ordinary axiomatization of probability theory by means of measure theory , the problem is to construct a sigma-algebra of measurable subsets of the space of all functions, and then put a finite measure on it.

在普通公理化的概率论的方式衡量理论，问题是要建设一个六西格玛代数的可衡量的亚空间的所有功能，然后把有限的程度上它。用于这一目的的一个传统使用的方法称为柯尔莫哥洛夫延长。

Early in the 1950s, in algebraic topology, the concept of graded Hopf algebras was derived from an axiomatization of the works of H. Hopf relating to topological properties of Lie groups. Hence the name,'Hopf algebra'.

50年代初，H.Hopf在研究李群的拓扑性质这一代数拓扑领域的理论工作中引入了分次Hopf代数的概念，"Hopf代数"由此而得名。

In chapter 5,we introduce the De Morgan algebra of metric and investigate the pseudo-metric Uniformity and the pseudo-metric topology and the separation axioms in De Morganalgebra of metric.We establish the Baire category theorem and the Banach contraction theo-rem,the Edelstein contraction theorem and other fixed quasi-atom theorems in De Morganalgebra of metric.In final,we give a sufficient condition for the metrization of a De Morganalgebra of topology.

在第五章里，我们地德摩根代数中引进了伪度量，探讨了伪度量一致和伪度量拓扑以及德摩根度量代数的分离公理，得到了Baire范畴定理、Banach收缩定理、Edelstein收缩定理以及其它不动拟原子定理，最后给出一个德摩根拓扑代数可度量化的充分条件。

In chapter 2, the realization and decoupling of linear systems over a commutative Banach algebra have been studied.

第二章，研究了交换Banach代数上线性系统的实现与解耦控制。

The paper addresses the existence problem of generalized inverses for elements of a Banach algebra under perturbations and derives a sufficient and necessary condition for the existence of generalized inverse.

文中讨论了Banach代数元扰动后广义逆的存在性问题。用线性算子广义逆的稳定性问题的方法，得到Banach代数元扰动后广义逆存在的充分必要条件以及稳定的一个充分条件

In chapter 1, the relations between spectrum displacement problem and controllability, observabiity for linear systems over a commutative Banach algebra have been discussed, the open problem about spectrum displacement posed by Kaashoek have been solved, and the if and only if conditions for stability, stabiizabit~ detectability have been obtained.

第一章，讨论了交换Banach代数上线性系统的谱配置问题与可控性、可观性的关系，解决了Kaashoek等提出的关于谱配置的公开问题，给出并证明了判定其稳定性、可稳定性、可检测性的充要条件。

Cable dampener cannot be rolled up but must be hung over the cable.

缆帆不能被卷起，必须保证处于展开状态

"This skylark is a present from my master," he says.

"这只云雀是我主人献上的礼物。"他说。