代数等价

However, in the algebraic representation of this theory, it is difficult to understand the essence of rough set theory, and efficient algorithm of knowledge reduction has not been found.

该文首先建立了知识与信息之间的关系；然后，在此基础上给出了粗糙集理论中概念与运算的信息表示；最后，证明了知识约简在信息和代数两种不同表示下是等价的。这些结论有助于人们深刻理解粗糙集理论的本质，同时，为寻找高效的知识约简算法奠定了基础

Several elementary properties of restricted Lie color algebra are collated.

又分别讨论了φ_p-基本和φ-基本的限制李color代数，并给出了它们的几个等价条件。

In this paper,δ-continuous and almost continuous Q\-1Q\-2-mapping are introduced, and continuous,δ-continuous, almost continuous are equivalence in the semiregular de Morgan topological algebra.

Q1Q2 -映射的连续性已在 [2 ]中讨论过，在本文中引进了 Q1Q2 -映射的δ-连续性，几乎连续性，并在半正则德摩根拓扑代数中证明了三种连续性的等价

The algebraic proof of this equivalence involves the Cauchy-Binet formula and multi-Schur functions based on the complete super symmetric function.

与此等价的代数证明需要Cauchy-Binet公式和基于超完全对称函数上的multi-Schur函数两方面的知识。

Some Properties of Monad and Comonad;2. The definitions of entwining structures of monads and comonad s and entwining modules are given and the paper studied their relations with entwining structures of algebras and coalgebras in categories,then we build an adjoint functors pair between the two categories of entwining modules.

首先给出了单子和余单子的缠绕结构和缠绕模及其与代数和余代数的缠绕结构和缠绕模之间的关系，并构造了一个函子伴随对，其次定义了余单子的类群元，得出了一些相关结论，最后给出了缠绕结构之间相容的定义和等价条件。

Hence, when taking the equivalent duals of all former statements, one ends up with a number of theorems that equally apply to Boolean algebras, but where every occurrence of '' ideal '' is replaced by '' filter ''.

因此，当采用所有前者陈述的等价对偶的时候，你可能终结于同等的适用于布尔代数的定理，但是这里所有''理想''的出现都被替代为''滤子''。

The derived equivalences of extension algebras are studied in the second chapter.

第二章我们讨论扩张代数的导出等价。

Finally,through some ideas from Algebraic Geometry,we constructed strongly exceptional collections of derived sheaf categories,and solved the problem that equivalences between some posets.

最后，通过代数几何里的一些思想，我们构造了导出层范畴的强例外集合，解决了一类偏序集的等价问题。

As a consequence of an important theorem of algebraic topology, the invariants constructed by those diversity ways can be considered as identified via their unique isomorphisms. This concludes that the procedure of invariant construction gains a virtue of the model presented in this paper as being unrelated to whether there exists a symbolic represantation of images.

根据代数拓扑的重要定理，这些不同的构造方法所得的不变量在同构意义下是等价的，因此我们推论这种不变量的构造过程与图象是否有符号表示无关。

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。