设G为局部紧群，在一致连续函数空间U（ G）上，用两种方法证明左不变平均和拓扑左不变的等价性。
On uniformly continuous function space U(G), Equivalence of invariant mean and topological invariant mean is showed by two methods.
FD集中根据左部等价形成划分，划分的各子集根据左部的依赖关系形成一个有向图，有向图中每一个节点的FD可能是一个符合BCNF的子模式的FD，其关键字就是各子集的等价左部。
Digraph will be constructed by using the dependence of the left of subset's FD. Some nodes will help to decompose a subschema of BCNF. The key of the subschema is the left or left's equivalence.
介绍弱左正则幺半群的概念，指出在可交换半群中，完全正则、弱左(右)正则和完全幂等是等价的。
In this paper, we introduce the notion of left weakly regular semigroup and show that in a commutative semigroup, the complete regularity, regularity, left resp.
证明了对于一个环R，下列条件等价：（1）R是左凝聚的；
For a ring R, the following statements are equivalent:(1)R is left coherent;
利用四元数矩阵的加权共轭转置定义了四元数矩阵的加权左（右）序，给出了加权左（右） 序的一些等价刻画，推广了以往文献的相应结果。
The weighted right (left) star partial ordering is defined though the weighted conjugate of the matrix , some characterisation of its is obtained, the existed results are extended.
构造出了区间值三角模左连续与保任意并不等价的一个严格的反例；
A strict counter-example showing that left-continuity and union-preserving are not equivalent for interval-valued triangular norms is constructed.
构造出了区间值三角模左连续与保任意并不等价的一个严格的反例；
A strict counter-example showing that left-continuity and union-preserving are not equivalent for interval-valued triangular norms is constructed.
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