带形状参数控制的三次B样条曲线曲面的光顺

三次B样条曲线是一种广泛应用于计算机辅助几何设计中的非常重要的曲线.本文在以曲线的最小应变能作为衡量曲线光顺性的基础上,采用带调节控制参数的方法分别对三次B样条曲线和双三次B样条曲面进行了光顺处理.由所提供的方法以及实例可以看出,本方法可在曲线曲面光顺的基础上通过修改参数大小以达到控制曲线曲面形状的目的,且修改后的点的位置与原坏点的距离是由参数的大小控制决定的,这样就使得我们的光顺处理可以控制在数据测量的误差范围内.     

STUDY OF THE SMOOTH DEGREE OF THE CLOSED C-B（E）ZIER AND B-TYPE SPLINE CURVE

本文研究了与多边形相切的样条曲线的构造方法和基本属性问题,给出了曲线光顺度的一般定义和计算方法.利用该方法对分段C-Bézier曲线、4-5-5-4次交错B-样条曲线和3阶B样条曲线的光顺度进行计算,获得了3阶B样条曲线最为光顺的结果.     

C-Bézier和B-型样条闭曲线光滑性研究

本文研究了与多边形相切的样条曲线的构造方法和基本属性问题,给出了曲线光顺度的一般定义和计算方法.利用该方法对分段C-Bézier曲线、4-5-5-4次交错B-样条曲线和3阶B样条曲线的光顺度进行计算,获得了3阶B样条曲线最为光顺的结果.     

关于隐函数样条的凸性分析

本文讨论由隐函数样条F(x)=αg~h(x)-(1-α)f(x)=0,x∈R~(?),0<α<1定义的函数(Functional spline)的凸性,得到:1)当 g(x)=l_0(x),f(x)=multiply from j to k l_j(x),其中,l_j(x)=sum from i=1 to n a_(ij)x_i+b_j 是线性的,且 (?)(x)≥0围成区域Ω,那么在Ω内,当 h>k 时,F(x)=αg~h(x)-(1-α)f(x)=0是凸的;2)在 R~2内,若 f(x,y)=0,g(x,y)=0定义两条凸曲线,那么隐函数样条不一定是凸的.但可以构造 f_1,g_1,使得 f_1与 f 定义同一条曲线,g_1与 g 也定义同一条曲线,而这时的隐函数样条是凸的.本文还给出了一个凸样条的充分条件.     

在共振点附近的一类二阶泛函微分方程的解析解

在复域C内研究一类包含未知函数迭代的二阶微分方程x″(z)=G(z,x(z),x~2(z),…,x~m(z))解析解的存在性.通过Schr(?)der变换,即x(z)=y(αy~(-1)(z)),把这类方程转化为一种不含未知函数迭代的泛函微分方程α~2y″(αz)y″(z)-αy′(αz)y″(z)= (y′(z))~3G(y(z),y(αz),…,y(α~mz)),并给出它的局部可逆解析解.本文不仅讨论了双曲型情形0<|α|<1和共振的情形(α是一个单位根),而且还在Brjuno条件下讨论了共振点附近的情形(即单位根附近).     

基于样条的高阶矩阵微分方程近似解

矩阵微分方程经常出现在许多物理模型和工程技术模型中.利用矩阵样条构造形如{y(p)(x)=Ap-1(x)y(p-1)(x)+Ap-2(x)y(p-2)(x)+…+A1(x)y(1)(x)+A0(x)y(x)+B0(x),y(a)=ya,…,y(p-1)(a)=y(p-1)a,x∈[a,b];Ai(x),B0(x)∈C4[a,b],0≤i≤p-烅烄烆1的高阶矩阵线性微分方程初值问题的数值解.给出实现算法和数值解的近似误差估计以及数值实例.先将高阶矩阵微分方程转化为一阶矩阵微分方程,然后利用三次矩阵样条求出一阶矩阵线性微分方程的数值解,从而解决高阶微分方程问题.     

带有面积约束的B样条曲线拟合方法

1984年刘鼎元等给出了B样条曲线的光顺拟合方法,本文在其基础上处理了带有面积约束的B样条曲线拟合问题。它来源于船舶线型设计:设计者往往先确定横剖面面积曲线,再设计线型。因而,在横剖面的光顺拟合中,就要求各站的横剖面面积保持不变。本文用B样条参数曲线表达拟合曲线,导出了曲线与坐标轴所围面积的表达式,目标函数由偏离的平方和、二阶导数平方和以及Lagrange乘子与面积公式的乘积所组成。     

用广义交互确认方法选择良好参数进行多元多项式散乱数据自然样条光顺

1．简介多元样条函数在多元逼近中发挥很大作用，已有数量相当多的综合报告和研究论文正式发表，就在1996年6月在法国召开的第三届国际曲线与曲面会议上便有不少多元样条方面的报告，不过总的感觉是仍然缺乏对噪声数据特别是散乱数据的有效光顺方法．李岳生、崔锦泰、关履泰、胡日章等讨论广义调配样条与张量积函数，并用希氏空间样条方法处理多元散乱数据样条插值与光顺，提出多元多项式自然样条，推广了相应一元的结果．我们知道，在样条光顺中有一个如何选择参数的问题，用广义交互确认方法（generalizedcross－validation，以下简称GC…     

曲线与其曲率圆

设一条曲线的方程为y=f(x).该曲线在点M(x_0,y_0)处的曲率圆在切点附近的一支曲线方程设为y=g(x),并设f(x)在x=x_0附近有三阶连续导数,且f″(x_0)≠0.将f(x)-g(x)在x=x_0处展开为二阶泰勒公式(注意到 f(x_0)=g(x_0),f′(x_0)=g′(x_0)及f″(x_o)=g″(x_0):     

曲线C都是一个函数的图像理解

正2009年上海高考理科数学试卷14题:将函数y=4+6x-x2-2(x∈[0,6])的图像绕坐标原点逆时针方向旋转角θ(0≤θ≤α),得到曲线C.若对于每一个旋转角θ,曲线C都是一个     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.