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1·The operator norm of T is the essential supremum of h.

“ T ”的操作规范是“ h ”的本质上确界。

2·The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement.

实数集的上确界公理用到了实数集的子集，这是一种二阶逻辑的陈述。

3·Third, the convergence and supremum of the algorithm were proved, and the asymptotic time complexity was analyzed;

并分析了该算法的收敛性及渐进时间复杂度；

4·Furthermore, we give the supremum-minimum distance of 36 kinds of structure and comparing their mean pick-the -winners by computer experiments.

我们还计算出36种结构的极大最小距离，并通过计算机验证比较了它们的平均冒尖性。

5·At last we obtain the supremum estimation of the finite time ruin probability and the infinite time ruin probability in the third new risk model.

对第三类风险模型进行研究，得到了有限时间破产概率和终极时间破产概率的上界估计。

6·According to the definite condition, the paper USES the theorem of supremum and infimum to study characteristic of mapping function and get its important law of the mapping.

运用上确界与下确界存在定理，在一定条件下，研究了连续函数的映射特点，得到一个连续函数所独有的映射规律。

7·The infimum and supremum of operators, and generalized inverse of operators are heated topics in operator theory and also have important value in both theory and application.

算子的确界性质和广义逆是近年来算子理论中比较活跃的一些研究课题，在算子理论的研究中有着重要的理论价值和应用价值。