代数

It is a natural generalization of the notion of implicative ideals in BCK algebras.

证明了BCI代数的一个非空子集是BCI关联理想当且仅当它既是BCI交换理想又是BCI正定关联理想，从而揭示了这三类理想之间的内在联系，并将BCK代数中知名论断：BCK代数的一个非空子集是关联理想当且仅当它既是交换理想又是正定关联理想，推广到BCI代数上去。

In chapter 2, we consider the isomorphisms of integral table algebras. For integral table algebras with integral table basis B we can consider integral R-algebra RB over a subring R of 〓, the ring of the algebraic integers.

第二章 我们考虑了有理整表代数间的同构问题：对任意整表基为B的整表代数，我们研究了代数整数环〓的一个子环R上的整R-代数RB。

For integral table algebras with integral table basis B we can consider integral R-algebra RB over a subring R of 〓, the ring of the algebraic integers.

第二章 我们考虑了有理整表代数间的同构问题：对任意整表基为B的整表代数，我们研究了代数整数环〓的一个子环R上的整R-代数RB。

Uncertain temporal relations can be represented and reasoned by IA. IA has strong expressive ability in tense, and it can represent all natural temporal relations. At the same time, temporal relation represented by IA is highly visual and comprehensive. In additional, IA has been extended from one-dimension temporal area to two-dimension spatial area, that is to say, interval algebra can be developed to rectangle algebra for two-dimension reasoning.

用区间代数能表示不确定的时态关系，可以很方便地用于时态推理，表达能力强；时态关系的区间表示比较直观，可理解性强；同时区间代数可以进一步扩展到二维空间领域，即将区间代数拓展为矩阵代数，实现二维空间推理。

In reference [15], Muhly discribe the isometric algebral isomorphism and isometric reflixive algebra isomorphism on some triangle subalgebra og Nenclear algebra with diagonent. The first problem of this chapter is analyzing furtherlythe concrete form of the isometry on TUHF algebra.

Muhly等在文献[15]中讨论了带有对角的Nuclear C~*-代数中的某些三角子代数上的等距代数同构和等距反代数问题，本章讨论的第一各方面就是借助于Muhly的结论进一步分析TUHF代数上等距的具体表达形式。

And using thinking of evolvable hardware design,it had realized a novel way in simplifying the given logic function,which was different from conventional method,such as algebra way and Karnaugh map way.Experiments showed that evolvable hardware method could solve simplification of large scale logic function.

作者在对演化硬件设计理论的学习研究中，尝试了用遗传算法在可编程逻辑器件上应用来实现对某一给定的逻辑函数进行化简。2代数法和卡诺图法介绍[1]先给定一个逻辑函数F，并对其进行化简：F=A+ABC+AC+CD(1)2.1代数法化简代数法化简就是运用代数的公理、定理和规则对逻辑函数进行化简。

In Reference [3], Cao and Tan described the automorphisms of Lie algebra of the strictly upper triangular matrices over R which is a maximal nilpotent subalgebra of the A_n type classical simple Lie algebra.

在参考文献[3]中，曹和谭把由所有严格上三角矩阵所构成的李代数的自同构问题已经完整的解决了，而这样的李代数恰好就是A_n型李代数的一个极大幂零子代数。

Some properties, such as primeness, semiprimeness and nondegeneracy are introduced. The primeness and semiprimeness are lifted from a Lie color algebra to its algebras of quotients.

在此基础上，本文提出了Lie color代数的商代数和弱商代数的概念，定义了Lie color代数的一些性质如素性、半素性和非退化性等，并将素性和半素性推广到Lie color代数的商代数中。

The questions covering pre-algebra and elementary algebra make up the Pre-Algebra/Elementary Algebra Sub score. The questions covering intermediate algebra and coordinate geometry make up the Intermediate Algebra/Coordinate Geometry sub score. The questions covering plane geometry and trigonometry make up the Plane Geometry/Trigonometry sub score.

包含有基础初等代数和初等代数的考题构成了基础初等代数/初等代数的技能分数，涉及到中等代数和坐标几何的考题构成了中等代数/坐标几何的技能分数，而涵盖平面几何和三角函数的考题则构成了平面几何/三角函数的技能分数。

By utilizing the concepts and methods developed in Algebra Topology,Algebra Geometry and Algebra Representations,we first depicted the concepts and results of Incidence Algebra which reflects the linear structure of underlying posets and Sheaf theory which reflects the topological structure of underlying poset in the framework of Category Theory.

本文综合运用了代数拓扑、代数几何及代数表示论里发展起来的概念与方法，首先在范畴的框架下，对和偏序集的线性结构密切相关的Incidence代数，及与偏序集的拓扑结构紧密联系的层，进行了刻画。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。