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V-system is a complete orthogonal system on L_2[0,1], which was constructed in 2005 by the author of this paper. V-system of degree k is composed of piecewise k-order polynomials, has multiresolution property, and is a generalization of Harr wavelet.

V系统是作者2005年构造的一类L_2[0，1]空间上的正交完备函数系。k次V系统由k次分片多项式组成，具有多分辨特性，是Haar小波函数的推广。

The V-system is a new class of complete orthogonal functions system in L2[0,1], which is composed of piecewise kth-order polynomials. There are continuous functions as well as discontinuous functions in V-system.

V-系统是一类由分片多项式构成的正交函数系，函数系中既有连续函数又有间断函数。

In the studies of EEG forward problems, primarily the EEG computation models are established, the analysis solution for concentric circle models and the boundary element method for piecewise humongous models are developed. These provide the basis for EEG inverse problems.

在EEG正问题的研究中，首先建立EEG计算模型，研究了针对同心球模型的解析解法和针对任意分层均匀介质的边界元法，为EEG逆问题研究奠定了基础。

In this paper we investigate the dynamical properties of continuous mapson a class of hereditarily decomposable chainable continua and the structure ofthe inverse limit space using a piecewise monotone continuous map with zerotopological entropy on a finite graph as a single bonding map.

本文研究了一类遗传可分可链连续统上连续自映射的动力性质并且对有限图上逐段单调且具有零拓扑熵的连续自映射的逆极限空间的拓扑结构进行了较为细致的刻画。

Conley index; prime isolated invariant set; bifurcation point; discontinuity dynamical systems; finite piecewise continuous map; coding; rigorous computer assisted proof; chaos; Ikeda map

基础科学，数学，动力系统理论Conley指标；素孤立不变集；分支点；间断动力系统；有限分片连续映射；编码；计算机严格辅助证明；混沌； Ikeda映射

Under the assumptionthat the covariant derivative of the sections satisfies the Lipschitz condition with L-averagealong the piecewise geodesic, a unified convergence criterion for Newton\'s method and theradii of the uniqueness balls of singular points around the initial points of sections are es-tablished.

本章的主要内容包括以下两个方面：当截面的协变导数满足沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出了关于截面的Newton法收敛的统一判据，同时给出了在初始点附近的关于截面的奇异点的唯一性球的半径的估计。

However, the smoothness and convergence of these methods are not satisfactory. Because cubic spline function can be a piecewise, and its second order derivative is continuous, it is smooth and convergent.

但以上算法的光滑性和收敛性不好，而三次样条函数具有连续的二阶导数，且可采用分段函数的形式，具有很好的光滑性和收敛性。

The technique of parameters normalization based on piecewise estimating the cumulative distribution function is performed in this paper. In this way the non-Gaussianity in the means of the cumulative distribution of Mel-cepstral parameters is decreased. Thus GMMs with fewer mixtures could model them precisely.

本文提出了一种基于分段估计概率分布函数的规整方法，在概率分布的意义上降低特征参数偏离高斯分布的程度，从而可以用较低混合度的高斯混合模型对其建模。

One of them is piecewise continuous argument delay differential equation, simply called EPCA.

其中第一类为分段连续的时滞微分方程，简称为EPCA。

In this scheme, the unitary evolution is followed by a measurement and vise versa. The whole process is in fact a piecewise deterministic process which is famous in open system theory.

该算法实际上可以看作确定性幺正演化和测量导致的随机塌缩交替进行的过程，类似于开放系统的分段确定性过程。

In this paper, the requirement analysis, design and implementation of the system are introduced in detail.

此论文详细介绍了系统的需求分析，系统设计和具体实现。

In the context of economic globalization is increasingly deepening, China's economy can not be spared.

在经济全球化日益加深的背景下，中国经济不可能做到独善其身。