正如每个整数都可用一些质数的积表示，任一对象的对称都可由所谓简单群的基本构件集合构造出来。
Much as every integer can be broken down into a product of prime Numbers, the symmetries of any object can be constructed from a collection of basic building blocks known as simple groups.
它是纯对称的积；因此，它是完全可交换的。
It is the purely symmetric product; therefore, it is completely commutative.
在域上，开解正交变换表成对称之积，因子个数的多少，是用变换的剩余数来标定的。
On the field, the number of factors in solving the symmetrical product is calibrated by the remainders of the transformation.
第四纪最大沉降中心、湖积台地及第四纪褶皱分布呈对角对称。
The distribution of the most-subsided areas, lacustrine terrace and Quanternary fold is characterised by the diagonal symmetry.
引入了卡氏和张量混合积空间上的对称化算子和相应的分块矩阵上的混合矩阵函数，给出了关于它们的若干关系式。
Symmetrizing operators on mixed cartesian and tensor product spaces and corresponding mixed matrix functions on partitioned matrices are introduced. Some relation formulae on them are given.
本文利用对称复制及平移复制概念，研究了沃尔什函数的构成，并以矩阵的克罗内克积的形式给出了递推关系。
Making use of the concept of symmetry copy and shift copy, the construction of Walsh functions is studied. Recursive relations are given in the form of Kroneker product of matrix.
定积分的计算是高等数学的重要内容之一，但在积分计算时可以结合积分区域的对称性和被积函数的奇偶性来简化计算。
Optimal calculation of definite integral can be obtained by combination of the odevity of function and the symmetry of integral domain.
通过研究双对称代数的对偶结构，主要讨论双对称余代数的张量积及双对称代数和双对称余代数之间的对偶关系。
The tensor products of double-symmetric coalgebras and the dual relationships between double-symmetric algebras and double-symmetric coalgebras are discussed.
我们发现对轴对称扰动稳定的吸积流外激波对非轴对称扰动却是不稳定的。
We find that the outer shock solution, which was previously found to be stable with respect to axisymmetric perturbations, is, however, generally unstable to non-axisymmetric ones.
摘要本文利用次线性项在零点附近的凹性和可积性，用移动平面法给出了一类次线性椭圆方程正解的对称性。
With the concavity and integrability of sublinear terms near zero, the symmetry results for a class of sublinear elliptic equations are given by making use of the moving-plane method.
此前对微分算子的积算子自伴的研究主要集中于由同一个对称微分算式生成的两个或多个微分算子积的自伴问题上，取得了一些成果。
In this paper, we get the self-adjointness of the product operators generated by different two differential expressions by operator theory and matrix calculation.
第一章：引言和预备知识部分，主要是关于微分算子的积算子自伴的研究情况和对称微分算子的一些基本知识。
Chapter one is divided into two parts: in the first part, we give the simple summarize of adjointness of differential operator product;
第一章：引言和预备知识部分，主要是关于微分算子的积算子自伴的研究情况和对称微分算子的一些基本知识。
Chapter one is divided into two parts: in the first part, we give the simple summarize of adjointness of differential operator product;
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