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Using this method,we discussed for generalized Burger equation with variable coefficients and linear danping,obtained its symmetry group,simliar reduced equations,infinitesimal generator and Lie algebras;In chapter 6,using the Exp-function method,the generalized solutions of combined KdV-mKdV equation with variable coefficients are discussed.

首先介绍了Lie群分析法的基本思想，其次用Lie群分析法得到了带线性阻尼项的变系数广义Burgers方程的无穷小变换、无穷小算子的李代数结构，并具体求出了带线性阻尼项的变系数广义Burger方程的群不变解和约化方程。

In chapter 2, we consider the isomorphisms of integral table algebras.

本文由四章内容组成

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。

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

We give the description of meet irreducible ideals in terms of matrix units in the limit of a direct sum of nest algebras.For each MI-chain ,the ideal I associated with it is meet irreducible.Conversely,every proper meet irreducible ideal is induced by some MI-chain,but there is not a 1-1 correspondence between MI-chain and meet irreducible ideals.

接下来我们用MI-链刻画了套代数直和的极限即NSAF代数的交不可约理想，与MI-链相对应的理想就是交不可约的，任给一个交不可约理想能找到一个MI-链与之对应，但它们不是一一应。

In the final section, we give the form of surjective isometric Jordan isomorphisms on triangular Banach algebras, and prove that such isomorphisms .

第四节给出了三角Banach代数上满等距Jordan同构的一般形式，并证明了一些特殊的三角Banach代数上满等距Jordan同构的酉空间实现性。

As well as we introduce some property of Killing form. Finally, we use Killing form to decide if YD-Lie algebras are semisimple.

则称为L的Killing型，以及给出了Killing型的性质，最后用Killing型去判断半单点YD-李代数。

Then a special subclass of the Hopf*-algebras related to a Latin square is given.

作为应用，给出了和拉丁方有着紧密联系的一类R-矩阵和Hopf*-代数。

We found , however, that the concept of hyper-operator itself is very important for quantum physics , group representation and Lie algebras.

本文内容的具体安排如下：第一章介绍了线性空间，赋范线性空间，Banach 空间，内积空间和Hilbert 空间的概念。

In this thesis, we mainly discuss the linear preserver problems on operator algebras.

本文主要讨论算子代数上有关线性保持的一些问题，全文共分四章。

I think people in this lifetime in a rebirth.

我觉得人在这一生里其实也在轮回。

He had to tie her hands together.

他不得不把她的双手绑在一起。