不连续函数

The new threshold function overcomes the shortcomings of the hard threshold with discontinuous function and solves the problem of the permanent bias in soft threshold function,and it is more flexible than the soft threshold and hard threshold function.

新阈值函数克服了传统硬阈值函数不连续的缺点，解决了软阈值函数中存在的恒定偏差，并且具有软硬阈值函数不可比拟的灵活性。

Based on much resolutional analysis wavelet threshold de-noising method ,an improved threshold function is proposed. it overcomes the shortcomings of the hard threshold with discontinuous function ang solves the problem of the permanent bias in soft threshold function,and it is more elastic than the soft threshold and hard threshold function.

在多分辨分析小波阈值去噪的基础上，采用了一种改进的阈值函数，克服了硬阈值函数不连续的缺点，解决了软阈值函数中存在的恒定偏差，并且具有软硬阈值函数不可比拟的灵活性。

By means of the extended Dirac function, the discontinuous variation in rigidityof the rectangular plate due to the arbitrarily- disposed cylindrical voids is expressed under thecategory of a continuous function.

利用扩展的 Dirac函数，将由于空洞的存在而引起的矩形板的刚度不连续性表示成连续函数的形式，从而实现了不需修正刚度便能写出带圆柱形空洞的矩形板的运动方程。

At last the results have been applied to the tracking problem of a class of mechanical systems with discontinuous friction term. Chapter 3 mainly deals with uniformly ultimate boundedness of a class of nonautonomous systems with discontinuous right-hand sides and corresponding perturbed systems (in the sense of Filippov solutions). The definitions of globally uniformly strongly ultimate boundedness and globally uniformly weakly ultimate boundedness of discontinuous systems and the definition of globally equiuniformly strongly ultimate boundedness of corresponding perturbed systems are presented firstly.

首次给出不连续系统全局强一致最终有界、全局弱一致最终有界的定义，以及针对于扰动系统的全局强等度一致最终有界性的定义，并基于非光滑的Lyapunov函数得到了不连续系统全局一致强、弱最终有界的Lyapunov定理和扰动系统全局强等度一致最终有界性的Lyapunov定理。

Although some results on convex and concave iterative roots are known, there are no results about convexity for more general iterative equations. In this chapter, convexity of both increasing solutions and decreasing solutions is investigated by the divided difference theory and fixed point theory.

本章在连续函数构成的紧凸集上构造一个连续自映射算子，利用均差理论和不动点理论证明了线性型迭代方程的凹凸解的存在唯一性及连续依赖性。

The presence of an end-point constraint makes the value functions neither be continuously differentiable, nor be finite valued on the interior of its effective domain.

终端约束的出现使得最优控制问题的值函数不仅仅不是连续可微的，甚至是不连续的。

The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of generalized Brownian Sheet is obtained.

讨论了N指标d维广义Brownian Sheet极函数的特征，得到了满足Lipschitz条件的连续函数类与广义Brownian Sheet的极函数类之间的关系，给出了广义BrownianSheet不动点的Hausdorff维数和Kolmogorov下熵指数的一个不等式。

This threshold function has not only overcome incontinuous disadvantage of the hard threshold function, but also solved constant deviation which exists in the soft threshold function, meanwhile the new function needn't selecting parameters.

该阈值函数克服了硬阈值函数值不连续的问题和软阈值函数存在恒定偏差的问题，同时新函数不需要进行参数选择。

Digital image process technique is used in pantographic faults monitoring, and a new algorithm named window-edge tracking is proposed in this paper. Based on the binary image of edges which is detected by Canny operator, a window in proper size is set to track the discontinuous edges to estimate the position of the lost edges. With this method continuous edges will be obtained, and continuous and smooth edges will be got after least-squares curve-fitting.

中文摘要：将数字图像处理技术应用于受电弓故障监测，提出一种新型的窗口边缘跟踪算法，在采用Canny算子计算出边缘二值图的基础上，设置适当大小的窗口对初始不连续边缘进行遍历，估计断点处边缘点位置获得连续边缘，并采用最小二乘法拟和出连续平滑的曲线函数。

First, we consider nonholonomic chained systems with modeling error, in this section,based on back-stepping , using the so-called adding a integrator , state-scaling technique , we design discontinuous feedback law,such that the trival solution of the closed-loop systems global strong stable; Second,we consider high-order nonholonomic chained systems with modeling errors and external disturbances, in this section,using input/state-scaling and integrator backstepping methods , we design discontinuous feedback law and give out the switching strategy, such that the closed-loop systems global /C-exponential stable; Finally, we consider a class of more general power chained form systems with particular drift-terms, in this section , using Lyapunov method, we design time-varying feedback law , such that the closed -loop systems p—exponential stable.

第一部分考虑的模型为带有模型误差的高阶非完整链系统，我们运用加幂积分器、State-scaling技巧以及基于Back-stepping方法构造出不连续反馈律，从而使得所讨论系统的闭环系统的平凡解全局强稳定；第二部分考虑的模型为带有模型误差的不确定高阶非完整链系统，这一部分我们运用input／state scaling和integrator backstepping方法构造出不连续反馈律，并给出切换策略，使得所对应的闭环系统全局κ-指数稳定；第三部分考虑的系统是形式更为一般的且带有特殊形式漂移项的幂链系统，利用Lyapunov函数方法，设计出时变反馈律，从而使得相应的闭环系统ρ-指数稳定。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。