不连续函数

The function of the system equations is not continuous in real number set because of the existence of the "state deep trap".

系统方程的函数在实数域内不连续，存在"状态深阱"。

Not all continuous functions are differentiable.

不是所有的连续函数都是可微的。

The average state space method was employed to eliminate the discontinuous feature of the switch function, then the average state space mathematic model was obtained.

用平均状态空间法建立了整流器的平均状态空间模型，消除了开关函数的不连续特性。

Furthermore, we discussed the chaotic quasi-attractors in a simplified model and found that this chaotic set is the end-results of the image set of the discontinuous border of the system function.

另外，我们讨论了一个简化模型中的混沌类吸引子，发现这个混沌集就是映象函数不连续边界映象集的归宿。

The kernel is adding a discontinuous function for the standard approximation to account for the crack. A feasible technique is adopted for dealing with multiple cracks and intersecting cracks.

本文研究扩展有限元方法，通过改进标准有限元的单元逼近函数，使之能够表达单元内的几何不连续，从而实现切割和断裂的模拟。

In the case of time discrete model obtained by traditional scheme, for the discontinuous switch, the cost function become piecewise due to the discretized error.

在离散情况下，对不连续"开关"，离散使代价函数出现有限个间断点。

This method can overcome the defects of traditional analytical optimization methods: they are hard to suit the conditions of discontinuous objective function and disconnected constrained domain. At the same time, the quantities measured by PMU can fully give play to maximum advantage while limited PMUs are placed.

该方法克服了传统解析优化方法难以适应不连续目标函数和不连通约束域等情况的缺点，同时，在配置有限PMU的情况下使PMU量测量发挥最大效益。

To deal with this, Evolutionary Computation is introduced into the discriminative training of the models.

另外，直接基于最小分类错误的训练方法由于目标函数的不连续、不可导，也无法采用梯度方法。

2The speed of creating random series used irrational fraction arithmetic was faster than that of multiplicative congruence arithmetic. The correlative value of random series almost was zero.(3) Regarding not harm the images quality as the premise, the speed of FM screening was heightened.

主要结论：利用所建立的条件半色调函数进行图像加网，操作简单、控制精确，使发生阶调不连续处的密度差平均减少到0.01275，明显改善了调幅加网印品的质量；(2)无理数取尾法产生随机数的速度快，数列间几乎没有相关性；(3)在不损失图像质量的前提下，提高了调频加网的输出速度。

In order to solve the problem effectively, a GA-based strategy is given after the complete analysis of the features of GA, which is very efficient to solve large-scale, non-linear, uncontinuous and multiple optimums optimization problems.

论文在对GA分析的基础上，指出GA是一种通用性很强的自适应随机搜索算法，且对搜索空间要求不高，适用于全局优化，尤其在解决诸如大规模、非线性、不连续、多峰等复杂函数优化问题方面，更显示其优越性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。