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Algebraic curve is commonly used in CAGD. Traditional curve interpolation is in various forms of spline fuction. Although better result can be obtained by spline curve, the former two of elliptic, hyperbolic and parabolic shapes can not be represented by spline curve. An exploring research in this aspect is made in this thesis.

代数曲线是CAGD中经常用到的曲线，以往的曲线插值基本上是采用样条函数的形式，采用这种形式虽然能够获得很好的效果，但样条函数所能表达的形状都是抛物线型，对椭圆型与双曲线型曲线的表示是无能为力的。

In this paper,the B-spline curve is supposed as boundary curves,when they are in two paralled plane and two arbitrary plane,the condition about the control vertex of characteristic polygon when the ruled surface is developable are gained,solved the designing problem of degree and degree B-spline curve .Throughing (2,3) degree and (2,2) degree B-spline ,we haveproved the validity and utility of this method.

本文用两条B样条曲线作边界曲线，当它们位于两平行平面上和两任意平面上时，研究得到了由它们形成的直纹面为可展面时它们的特征多边形顶点满足的条件，解决了(n，n+1)次和次可展B样条曲面的设计问题，然后以(2，3)次和(2，2)次B样条曲面为构造实例，证明了该算法的正确性和实用性。

Lastly,we present an algorithm to isolate real roots of a univariate spline, i.e., computing asequence of disjoint intervals such that each of them contains exactly one real root of agiven spline function, which is primarily based on the use of Descartes\' rule of signs withits B-spline coefficients and de Casteljau algorithm of B?

最后，基于B-样条系数的Descartes符号准则和Bézier曲线的de Casteljau算法，我们给出了一元样条实根分离算法，也就是计算出一列不相交区间，使得每个区间恰好只包含此样条函数的一个实根。

Lastly,we present an algorithm to isolate real roots of a univariate spline, i.e., computing asequence of disjoint intervals such that each of them contains exactly one real root of agiven spline function, which is primarily based on the use of Descartes rule of signs withits B-spline coefficients and de Casteljau algorithm of Bzier curve.

最后，基于B-样条系数的Descartes符号准则和Bézier曲线的de Casteljau算法，我们给出了一元样条实根分离算法，也就是计算出一列不相交区间，使得每个区间恰好只包含此样条函数的一个实根。

Bring forward a kind of learning algorithm fitting on the base of spline function, because the spline function has good flexibility and quadratic smoothing property, the search problem of network weight functions training can be converted into the resoluting extreme value problem of the plurality function through using spline function to represent network input and link weight functions, thus the PNN can be trained with the help of the existing neural network learning algorithms;④build a kind of learning algorithm base on the alternate of Walsh function, the complexity of network computing can be decreased through using the complete orthogonality of Walsh function corollary.

应用结果表明该算法收敛速度快，稳定性好；③提出了一种基于样条函数拟和的学习算法，由于样条函数具有很好的柔韧性和二次光滑性，将网络输入函数和连接权函数用样条函数的形式表示，可把网络权函数训练的函数寻优问题转换为多元函数求极值的问题，从而可借助于现有的神经网络学习算法训练过程神经元网络；④建立了一种基于Walsh函数变换的学习算法，利用Walsh函数系的完备正交性，可大大降低网络计算的复杂度。

Then, have stressed kinds of technology cubic Hermite function and cubic spline function, step by step, expand dual-cubic Hermite and dual-cubic spline function to progressively, sum up in the point that trinary cubic Hermite and trinary cublic spline finally.

讨论时重点突出了三次埃尔米特函数和三次样条函数，表达方式由浅入深，逐步扩展到双三次埃尔米特函数和双三次样条函数，最后归结到三三次埃尔米特函数和三三次样条函数。

The LMD algorithm uses extrema to define the local mean and envelope, then to smooth the mean and envelope. To decrease errors in the smoothing process by using moving averaging, a new local mean and envelope definition method (the spline-based LMD) is proposed. The upper envelope and the lower envelope are obtained by connecting the local maxima and the local minima using a cubic spline line. The local mean is defined as a mean of the upper envelope and the lower envelope. A nonlinear simulation signal and a practical vibration signal are decomposed by the LMD and the spline-based LMD.

LMD算法用极值点来定义局部均值函数和局域包络函数，然后用滑动平均来平滑均值和包络函数，针对用滑动平均平滑均值和包络函数误差较大的缺点，提出了采用三次样条对上、下极值点分别插值求得上下包络线，然后由上下包络线的平均获得局部平均函数，由上下包络线相减的绝对值获得局部包络的方法。

By a more precise estimation of maximum value of a B-spline basis function and utilizing of the local support property of B-spline basis function, the control points of a set of compatible B-spline curves are reduced, which makes the skinning algorithm more effective.

对B样条基函数的最大值进行了更为精确的估计，并且充分利用B样条基函数的局部支撑性，尽可能多地删除相容性处理后B样条曲线的控制点，使得蒙皮算法更加有效。

As to nonparametric and semiparametric regression models, the most widely used regression methods include: local smoothness, including Nadaraya-Watson kernel estimate, Gasser-Muller estimate, local polynomial method; spline method(such as smoothing spline, spline penalies and so on); other is orthogonal series estimates, such as Fourier series and so on.

本文主要介绍Nadaraya-Watson核估计方法对非参数模型估计的思路和估计方法，变系数模型中函数系数的局部多项式估计，包括估计思路，估计计算。

As to nonparametric and semiparametric regression models, the most widely used regression methods include, spline method(such as smoothing spline, penalized spline and so on); local smoothness, such as Nadaraya-Watson kernel estimate, Gasser-Muller estimate, local polynomial method; the third is orthogonal series, including Fourier series and so on.

所以三次光滑样条应用比较广泛。本文应用三次光滑样条方法来估计单指标部分线性模型中单指标参数和变系数部分线性模型中的函数系数。

This immediately brings us to the next part of this article: creating an output "replace function".

下面进入文章的第二部分：建立一个"缓存处理函数"。

He was elected as an International Ornithological Committee member in 2002 during the 24th IOC held in Beijing.

现为中国鸟类学会理事和WPA 专家组成员。2002年被推选为国际鸟类委员会委员。