本文首先归纳总结了凸函数的几个不同的定义，并说明其等价性。
In the first part of this paper, we gave several different definition of convex functions and equivalent proposition.
现代科学证明过去与来来不是等价的，混沌理论说明了非线性系统长期行为的难预测性。
It is proved by modern science that the past cannot be equivalent to the future. The chaos theory has revealed the difficulty to foresee the long - term behavior of nonlinear system.
为了消除噪声的影响，在进行计算时，选择某些集团重心位置作为迭代过程中的等价强反射层位置。在人工合成数据上的实验结果说明了方法的有效性。
To eliminate the influence of noise, the positions of centroids of clusters computed from the synthetic reflection coefficients can be selected as the new positions in the iterative processes.
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