利用奇点和有限集的特征，给出了首次积分存在的某些条件。

Some conditions on the existence of the first integral are given via the properties of equilibria and limit sets.

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讨论了无穷自相似函数迭代系统的分离性质，得到了一个判定函数迭代系统满足有限强开集条件的充分条件。

The separation properties of the self-similar infinite iterated function systems are disscussed, and a sufficient condition for the system satisfying the finite strong open condition is given.

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首先通过构造一个函数的有限集替代动态规划中的条件期望，其次使用蒙特卡洛模拟和最小二乘法计算第一步中的值函数。

First, in this algorithm, the condition expectation in the dynamic programming principle is replaced by projections on a finite set of functions.

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