分段线性函数

Based on general orthogonal polynomials and general hybrid orthogonal functions, a new linear, continuous and bounded operator has been proposed in the dissertation. The definitions and properties of PGOPO are given, a various operational rules of the operator have been set up in a systematic way, the convergence of approximate solutions has been discussed. After introducing PGOPO and discussing its main properties and operational rules, a systematic methodology for solving various control problems via PGOPO has been developed.

本文在广义正交多项式及广义混合正交函数的基础上，提出了一种新的线性、连续、有界算子—分段广义正交多项式算子，探讨了这种算子的基本性质，并系统地建立了与该算子有关的各种运算规则及收敛性结论，给出了它在控制理论中的各种应用。

We firstly look back thebirth of SD method,and then present the SD scheme presented by Johnson et.al.forlinear problem to explain the basic idea and implementation:At step 1,we change the testfunctionwhere(1,β)t is the streamline or character direction decidedby hyperbolic operator of the continuous problem,therefore the SD method belongs tothe Petrov-Galerkin method;At step 2,we adopt time-space finite element space,whoseelement is only continuous in space variables x but discontinuous in time variable t.

首先回顾了SD方法的产生过程，然后以线性问题为模型，描述了SD方法的基本思想和具体实现：第一步，将标准有限元方法的检验函数ν改成其中(1，β)t是连续问题的双曲算子部分所确定的流线方向。换言之，SD方法是一种Peterov-Galerkin有限元方法；第二步，采用时空有限元空间，其元素关于空间变量x是连续的，但关于时间变量t仅分段连续。

Test and simulation shows that the method can eliminate the unsmooth shortcoming caused by subsection low order interpolation with its inherent feature, and can meet the vision effect in inner capacity reconstruction. Further more the volume measurement error are reduced after interpolated by cubic spline without increasing any calculation, and the measurement relative error could reach 2‰ required by the system.

实验和仿真结果证明：该方法能够克服直接累加和传统的分段低次线性插值方法由于函数本身的特性，在各次间歇测量点处产生的衔接不光滑性，满足了变径内腔内表面容积重建中的视觉需求；同时在不增加计算量的前提下使得插值后容积的测量精度得到了提高，且满足2‰测量误差的要求。

Since the objective function of the model is nonlinear, the gradient of which is piecewise constant, the normal nonlinear programming algorithm can not be used.

该模型是非线性的且目标函数的梯度是分段常数，不能采用常规的非线性规划算法进行求解。

In this paper, a new kind of transfer function of the neuron is defined as a piece-wise linear N-shaped function, which is a novelty that allows control of the collective chaotic neurons.

本文然后从一被广泛采用的混沌节点函数模型出发，抽取其优良的混沌特性，摒弃应用中的缺陷，构造了一线性分段的一波三折函数。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新