逼近的

In this dissertation, the best simultaneous approximation with weight to infinite sequence from simultaneous-suns in complex normed linear space is considered, and in the case when the weight satisfies a certain condition, the characterizations of approximation from a simultaneous-sun and uniqueness of approximation from a RS-set are obtained; moreover, in the case when the weight is free, the characterizations of approximation to a totally bounded sequence from a convex set are established.

本文在复赋范空间中研究了同时太阳集对无限序列的加权同时逼近问题，在权满足一定条件时，通过把所研究问题转化为连续向量值函数空间中相应集对一个上半连续函数的最佳逼近问题，得到了逼近的特征和RS集逼近的唯一性定理，有例表明它们是已有结果的本质推广；在权不受限制时，得到了凸集对全有界序列逼近的特征。

The author investigates simultaneous approximation by Gama operators and the rate of pointwise convergence by new Gamma type operators.

本论文讨论了Gamma算子的同时逼近，Gamma算子线性组合同时逼近的等价定理以及新的Gamma型算子的逼近速度。

The close relationship between the Hybrid polynomial approximation and the classical Hermite polynomial approximation to rational curves and surfaces are studied, Hermite approximation is in fact a special case of Hybrid approximation. The sufficient and necessary condition for the convergence of Hybrid approximation to rational Bézier surface is deduced and proved.

围绕着有理曲线曲面的Hybrid逼近，作者研究了有理曲线曲面的Hybrid多项式逼近与传统的Hermite多项式逼近之间的密切关系，并指出Hermite逼近事实上是Hybrid逼近的一种特例，此后演绎并证明了有理Bézier曲面的Hybrid多项式逼近收敛的充分必要条件。

In this paper,a rational approximation method of the norm of parametric speed is given,which is more effective than the polynomial approximation.

文章根据等距曲线逼近的关键在于对其参数速度模的逼近，提出了对参数速度模有理逼近的2种形式，在此基础上给出了平面Bézier曲线等距曲线的逼近函数和误差估计函数，并导出了保持法矢平移方向的代数方式的等距有理逼近算法。

The problem of parametric speed approximation of a curve is raised in this paper.

该文提出了曲线的参数速度逼近问题，指出等距曲线逼近的关键在于参数速度的逼近，并用两种方式来实现它。

The results are much better than the other approaches'. Then we give another method for approximating offset curves. The circle is first approximated by regular polygon within some tolerance. The exact offset curve is then approximated by the convolution of the regular polygon with a B-spline curve or a NURBS curve having the same degree.

与此同时作者从基圆的正多边形逼近出发，通过求解包络的技巧给出了等距曲线逼近的另一个算法，可整体估计误差，所得的等距逼近曲线为与基曲线同次数的B样条或NURBS曲线，克服了国际上现有同类算法中逼近曲线次数几倍于基曲线次数的缺陷。

The purpose of this dissertation is to study a principle or method to describe and analyze the complex problems with high gradients arising from practical engineering. The main contents cover:1. The Bezier function was introduced to approximate high gradient functions, and a suitable coupled function was derived. Some detail numerical results show that the Bezier-based function is dominant over other combination function such as polynominal and trigonometric series, when to describe a high gradient function.

针对工程中大量存在的高梯度问题进行函数逼近的研究，引入Bezier函数对高梯度问题进行函数逼近，构成以Bezier函数为主的复合逼近函数，数值考证表明：与常规多项式插值函数的逼近及"幂／三角"复合函数的逼近相比，基于Bezier函数的逼近函数对高梯度问题的描述具有明显优势。

Direct and inverse theorems of approximation by this kind of operators are discussed, and the Jackson—type integral estimation of approximation and Steckin — Marchaud inequality of weak type of uniform approximation for these operators are obtained.

讨论了一元Bernstein型算子的逼近正逆定理，建立了该算子逼近的Jackson型积分估计式和一致逼近的弱Steckin-Marchaud型不等式。

In this paper, a region approximation idea that means using a "fat curve" with a width to approximate the offset curve is proposed, and a complete set of algorithms to approximate offset curve using disk Bézier curve are given and implemented. In the algorithms, the optimal and uniform approximate curve of the offset curve as the central curve of the Disk Bézier curve is found by using Remez method, and then the upper optimal and uniform approximation principle is proposed to compute the error radius function of the Disk Bézier curve. Thus, the whole Disk Bézier curve can be obtained. In the end of this paper, the approximate effect of the Disk Bézier curve is not only analyzed and assessed, but also some specific examples are provided.

提出用一条带宽度的"胖曲线"来逼近上述等距曲线的区域逼近思想，并建立与实现了圆域Bézier曲线等距逼近的整套算法，包括应用Remez方法求出等距曲线的最佳一致逼近曲线作为圆域Bézier曲线的中心曲线，提出上控最佳一致逼近的原理求出圆域Bézier曲线的误差半径函数，以及确定整条圆域Bézier曲线，最后还对该圆域Bézier逼近的效果做了分析和考核，并给出了一些具体实例。

In practice, the offset curve usually is approximated by lower degree rational polynomial cur ve in order to have the unified expression of data structure and geometric algor ithm in the commercial modeling systems.

通过用双圆弧逼近表示 NURBS( non- uniform rational B- spline)曲线及其 offset，并利用双圆弧逼近的特有性质，把 offset的双圆弧逼近转化为原曲线的双圆弧逼近，简化了问题的求解。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。