自对偶的

We prove that any irreduciblesymmetric self-dual Lie algebra 〓 whose Cartan subalgebra consists of semi-simpleelements is in one of the following classes:(1)〓 is simple;(2)〓 is 1-dimensional;(3)〓is solvable.

第五节讨论Cartan子代数由半单元构成的对称自对偶李代数的结构，证明了不可约对称自对偶李代数g如果它的Cartan子代数由半单元构成，那么它只能是下列情形之一：（1）g为单李代数；（2）g是1维的；（3）g是可解的。

At length 50, we got 3 inequivalent extremal self-dual [50,25,10] codes.

将这个性质用在寻找长度为66的自对偶码，我们得到至少五十个对应於w2互不等价的极端自对偶[66，33，12]码与一个对应於w1，β=32的极端自对偶[66，33，12]码；用在寻找长度为50的自对偶码上，我们得到三个互不等价的极端自对偶[50，25，10]码。

Because Conference matrices and Hadamard matrices are related to Paley matrices,in this paper we define the normalized Conference matrices and generalized normalized Hadamard matrices,and we show some special properties of them. Also we constructed a doubly even self-orthogonal code from normalized Conference matrix and a doubly even self-dual code from generalized normalized Hadamard matrix.

由于Conference矩阵，Hadamard矩阵与Paley矩阵紧密相联，本文定义了正规Confersnce矩阵和正规Hadamard矩阵，讨论了他们的一些特性，并且利用正规Conference矩阵构造了一个自正交的双偶码刷用正规Hadamard矩阵构造了一种自对偶的双偶码。

Recently, many coding experts have studied much of the Z_4-cyclic code(which is not necessarily linear) and its Gray map, and obtained a set of equivalent conditions in which a family of cyclic codes are linear, and the condition that this family codes are self-dual cyclic, and in this condition Nechaev-Gray image of the cyclic codes are self-dual cyclic.

近年来，已有编码学家对Z 4-循环码和Z 4上的映射作了深入研究，得到一类循环码是线性码的一系列等价条件，以及这类线性码是自对偶线性循环码的条件，在此条件下它的Nechaev-Gray像也是自对偶线性循环码。

On the basis of a unified definition of the dual operation and theself dual operation, the connection s of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity.

利用内外指标的对偶运算及自对偶运算的统一定义，将su(2 ，2 |1)主丛联络作为基本场变量来构建自对偶的共形超引力拉氏函数。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

By using the gauge potential decomposition, we have discussed the self-dual equation and its solution in Jackiw-Pi model. We obtained a new concrete self-dual equation and find relationship between Chern-Simons vortex solution and topological number which is determined by Hopf indices and Brouwer degrees of φ-mapping.

运用规范势分解理论研究了Jackiw-Pi模型中的自对偶方程，得到一个新的自对偶方程，发现了Chern-Simons多涡旋解与拓扑荷之间的联系。

The peculiarity of self-dual code makes the research on self-dual code having academic value, and it also can be wildly applied in practice.

自对偶码的特殊性使得研究自对偶码有丰富的学术价值并且被广泛的应用于实践当中。

Using the concept of regular elements,we obtain some results on the classificationof dipolarizations in general symmetric self-dual Lie algebras.

在第六节中，我们把半单李代数的特征元的概念推广到任意带有双极化的对称自对偶李代数上〓用正则元的概念，得到了一般对称自对偶李代数上双极化的一些分类结果。

On the other hand,withthe development of the Ashtekar gravitational theory,much attention has re-cently been paid to the Euclidean self-dual theory with Euclidean spacetimesignature.

另一方面，随着阿西特卡自对偶引力理论的发展，具有欧几里德时空号差的欧几里德自对偶引力理论的研究近年来也引起极大关注。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。