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1·Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

推论1常数与无穷小的乘积是无穷小。

2·Try relaxing the value of each bounded constraint one at a time, solve the modified problem, and see what happens to the optimal value of the objective function.

一次只尝试放松每个边界约束一个单位，解决修改后的问题，看一下目标函数的优化值发生了什么变化。

3·A bounded constraint prevents the objective function from reaching a better value.

边界约束阻碍了目标函数达到更为优化的值。

4·The local robustness is described by the bounded Influence Function.

以影响函数的有界性来描述估计量的局部稳健性。

5·The cartoon component of an image is modeled by a bounded variation (BV) function; the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.

图像的卡通部分是由一个有界变差(BV)函数来刻画，相应的将BV罚项合并到变分泛函中需要解偏微分方程。

6·The paper gives the definitions of monotonic function, bounded variation function and absolute continuous function, and discusses the relationship of the three.

文章给出了单调函数、有界变差函数、绝对连续函数的定义并讨论了三者之间的关系。

7·Fan J and Gijbels I gave the asymptotic normality of local polynomial regression estimation in dependent time series, where the weighted function is bounded.

对相依时间序列数据，在一定的条件下已有人证明了局部多项式加权回归系数估计服从渐近正态分布，其中核函数是有界的。

8·This paper tries to define metric function for homeomorphic mapping, and a sufficient condition of bounded metric function is given, under which a upper bound of metric function is defined as well.

对于一个同胚映射，本文给出了度量函数的定义，并且给出了度量函数有界的一个充分条件及在此充分条件下度量函数的一个上界。

9·It is also proved as application that any bounded variation function can be seen as a differentiable function beside a set of arbitrary small measure.

作为应用，证明了任意有界变差函数都与某可微函数在除过测度任意小的集合外重合。

10·The Green's function for the Poisson equation in the domains bounded by two intersecting spheres with Dirichlet boundary conditions is presented.

给出了在狄利克雷边界条件下，由两个相交球面围成的区域中泊松方程的格林函数。