伴随表示

We know that a Killing form is a trace form under adjoint represen-tation.

所谓killing型是指关于伴随表示的迹型。

In this paper, we develop the theory of Killing form over any finite dimensional Hopf algebras, and discuss the deep relations between the non-degeneracy of Killing form and the adjoint representations of Hopf algebras.

中文摘要：本硕士论文的主要内容是在有限维Hopf代数上建立了Killing型的一般理论，揭示了Killing型的非退化性与Hopf代数的伴随表示之间的深刻联系。

This dissertation also proposes a concept of adjunction between fuzzyconjunctions and fuzzy implications, which guarantees that fuzzy conjunctions andfuzzy implications are able to be determined uniquely each other.

我们还引入了模糊合取和蕴涵算子之间的"伴随关系"的概念，从而使得模糊合取和模糊蕴涵在"伴随关系"意义下形成一对相互之间可以唯一确定和表示的算子。

As a result, the standard union, intersection and the defined minus operation are closed under the domain of the representation.

这样， 在复形的伴随多面体表示域上，标准的集合交、并运算和定义的非流形上的标准差运算封闭。

A 2×2 matrix differential Lenard operator is extended to a 3×3 oneand the soliton hierarchy with their Lax pairs are deduced easily.

并使孤立子方程谱问题的伴随表示与Lenard算子对有机的连系在一起。

This week, with the price of oil up 25% and BA and Iberia shares down 25% and 37% respectively, the two firms said they were in talks about an all-share merger.

这周，伴随油价25%涨幅，英航和伊比利亚的股价分别下降的25%和37%。这两家公司表示他们正处于全股融合的洽谈中。

Firstly, we define the Killing form over any finite dimensional Hopf algebras using the adjoint action, then we investigate the fundamental properties of the Killing form, and obtain a decomposition of Hopf algebras under the adjoint action.

首先，利用Hopf代数的伴随作用定义了有限维Hopf代数上的Killing型，并讨论了Killing型的基本性质，得到了Hopf代数上的伴随表示分解式。

The age of a geological sample can be estimated from the ratio of radioactive to nonradioactive carbon present in the object is examined .

ED 分词用作状语时，跟-ING 分词作状语时一样，修饰主句的谓语动词，意义上相当于状语从句，表示时间，条件，原因，伴随状况等。

C,are because of the interaction between two stars that orbit each other 时说除了because 用法错误外,the prase "two stars that orbit each other" illogically suggests that there are two particular stars causing all the phenomena in question,rather than various sets of stars in various locations.

为什么这里用了that 定语从句就表示特指，而ING结构则没有该含义？——————————————that定语从句是限定性修饰，--ing是非限定性修饰。ing形式一般是表示伴随，伴随状态或者是结果，可以理解为非限制性定语从句。限制性的定语从句把原句的意思改变了。

Part II of this paper studies the structure of symmetric self-dual Lie algebras.

假设李代数g带有一个与Killing具有相同性质的型B，即具有双线性性，非退化性，对称性和不变性，由于这样的李代数g的伴随表示与它的余伴随表示等价，我们称李代数g为对称自对偶李代数，称型B为它上的一个不变数积。

He is the most remarkable man that I have ever known.

他是我知道的人中最值得注意的人。

Increased appearance of lymphocele was noticed in patients with diabetic nephropathy, congenital malformations of the urinary tract, and inflammatory diseases, including glomerulopathy and extraglomerular ones, after high-voltage radiotherapy and after removal of the renal graft.

经过高压放射疗法和切除移植肾后，在糖尿病肾病患者、泌尿系统先天性畸形患者和炎症患者身上发现淋巴囊肿有所增加，包括肾小球病和球外疾病等。