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In section 3 ,we will introduce bilinear form B on Lie colour algebra L. is called quadratic if B is color symmetric .non-degenerate and invariant .In this case ,B is called an invariant scalar product on L .

第三部分介绍了具有双线性型B的李color代数L，如果B是color对称的，非退化的和color不变的，则称是二次李color代数，B则称为不变数量积，给出了理想非退化的定义。

By using thenatural boundary element method which is set up by professor Feng Kang,the Neu-mann boundary problem of the harmonic equation on the half-upper plane is reducedto the Hadamard type singular integral equation,the integral region of which is un-bound,and then we turn it into corresponding bilinear form.

通过由冯康教授开创的自然边界元方法，将上半平面调和方程的Neumann边值问题归化为Hadamard型强奇异自然边界积分方程，并且此积分方程是无界域上的强奇异自然边界积分方程，然后将它转化为相应的变分形式。

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

The bilinear equations and bilinear B〓cklund transformation for the mKdV-SineGordon equation are obtained, and an ordinary form of B〓cklund transformation is given in passing.

仍以Toda链、Blaszak-Marciniak链和Ablowitz-Ladik链为例，但该方法也完全适用于下述更一般形式的谱问题：ψφ=λφ，ψ=〓，s 本文还对mKdV-SineGordon方程的求解进行了研究。

We also concluded the conditions to form a language monopoly and bilingualism society.

并说明了语言自然垄断地位以及双语社会形成的条件。

Lincoln's doctors told the ailing president he suffered from a cold or a "bilious fever" before one physician told him he had a mild form of smallpox.

林肯的医生曾告诉这位衰弱的总统，他得的是感冒或者肝病引起的发烧，直到一位内科医生告诉他，他有轻微的天花症状。

The return of a dishonoured Bill to the drawer or an indorser is, in point of form, deemed a sufficient notice of dishonour

这些名义上和形式上的肤浅事物都不能改变帝国实际上是希腊文化的这个事实。

The Health Committee included a form of the public option in its bill; the Finance Committee did not.

医疗卫生委员会在其议案中包含了公众意见，但财政委员会并没有。

Before permission is given to remove the goods out of customs control,the owner or agent is required to submit a Bill of Entry,Customs Declaration or Inward Permit as may be prescribed by law,in the prescribed form to enable the customs authorities to examine and appraise the goods.

在货物移出海关控制的许可证签发之前，货主或其代理必须根据法律的规定，以规定的格式递交进口报关单，海关申报单或进口许可证，以使海关当局能对货物进行检验并估价。

More padding—in the form of cash in the bank—will be necessary to secure a clean bill of health.

更多的银行存款被视为健康经营的必要保障。

In other research, chondroitin is being investigated for use in several other conditions.

在其它研究，软骨素被调查用於几个其它情况。

They would make fun of him for having to work.

他们拿他的工作来开玩笑。