线性多边形链的彩虹路连通性(英文)

假定G是一个非平凡的连通图,对G的边全部着上颜色,相邻的边可以着相同的颜色.用数字表示颜色,并假定c:E(G)→{1,2,…,k,k∈N}是G的一种着色方式.G中的一条道路P称为是一条彩虹路,如果P所经过的边的颜色各不相同.如果图G的任意两点间都有一条彩虹路,则称G是彩虹路连通的.使得图G为彩虹路连通所使用的最少颜色数k称为G的彩虹路连通数.本文计算了线性多边形链图的彩虹路2～连通度和线性偶数边多边形链图的彩虹路连通数.     

双圆封闭折线一类特例研究

杨之先生在其名著[1 ] 中倡导研究的“双圆多边形”是指既有外接圆又有内切圆的多边形 .仿此 ,我们给出下面的定义　若一条封闭折线的顶点都在一个圆上 ,每条边都与另一个圆相切 ,则称该折线为双圆封闭折线 .相应地 ,若它的边数为 n,环数为 k,则称为 n边 k环双圆封闭折线 .图 1     

欧拉公式的证明与应用

欧拉研究多面体时，得到了一个著名的欧拉公式：V＋F-E=2，其中V表示简单多面体的“顶点数”，F表示“面数”，E表示“棱数”，若将简单多面体去掉一个面，并将其余各面拉开压缩到该面所在平面，便得到平面内多边形的“点数、面数与线数”的三者关系：V＋F-E=1．这里的V表示“点数”，F表示“面数”，E表示“棱（线段）数”．     

任意次有理Bezier曲线／面对其控制多边形／网格的整体或局部逼近

本文给出一种利用权因子构造整体或局部逼近控制多边形／网格的有理Ｂｅｚｉｅｒ曲线／面的方法,该法适用于任意次数的有理Ｂｅｚｉｅｒ曲线／面、任意的控制多边形／网络,权因子的选择和逼近度的估计都只依赖于一个参数ｗ．当ｗ→＋∞时,相应的曲线／面可按预定要求整体或局部地逼近其控制多边形／网络,逼近阶为ｏ（１／ｗ）。     

正多边形控制的曲线段及其性质

本文给出了由多边形控制曲线段的方法，并依据多边长的延长量的性质，讨论了相应曲线段的性质，并给出了数值例子和对应图象，文末还给出了以曲线段为切线多边形的B－样条曲线方程和以曲线段端点为插值点的插值函数。     

有趣的多边形数

分析 本题首先可以通过观察题目给出的前几个多边形数,分析寻找其中的规律,然后猜想和归纳出第n个k边形数N（n,k）（k≥3）的表达式,进而计算出N（10,24）的值．     

平行四边形的内切椭圆

类似于多边形的内切圆,可以如下定义多边形的内切椭圆：与一个多边形的各边都相切且位于该多边形内部的椭圆称为该多边形的内切椭圆．文[1]、[2]利用仿射变换对三角形的内切椭圆的存在性和性质进行了深入的研究,那么四边形的内切椭圆是否存在？特别地,文[3]利用仿射变换,将椭圆变换为圆,给出了平行四边形内切椭圆的一种几何作法（问题43）．笔者尝试用初等方法研究平行四边形的内切椭圆的一些简单几何性质和作图问题．     

中心对称多边形外接圆周上点的性质

笔者发现 ,中心对称的多边形外接圆周上的点具有如下性质 :中心对称多边形的每组对边上关于它的外接圆的对称点到过外接圆周上任一点的切线的距离之和为定值 .即命题 1　设中心对称的多边形Ａ1Ａ2 …Ａ2ｎ(ｎ≥ 2 )的外接圆Ｏ的半径为Ｒ ,ｌ为过圆周上任一点Ｐ的切线 .Ｍｉ 与Ｍｉ′为第ｉ组(ｉ=1 ,2 ,… ,ｎ)对边上关于圆心Ｏ的对称点 ,且Ｍｉ 与Ｍｉ′到ｌ的距离分别为ＭｉＮｉ 与Ｍｉ′·Ｎｉ′ ,则∑ｎｉ=1(ＭｉＮｉ+Ｍｉ′·Ｎｉ′) =2ｎＲ为定值 .分析 :不失一般性 ,当ｎ =2时 ,即对中心对称的四边形的情况给出证明 .图 1　命题 1图证…     

平面整点正n边形（n≠4）不存在的一个证明

平面整点正ｎ边形（ｎ≠４）不存在的一个证明刘国栋（广东惠州大学数学系５１６０１５）我们把平面直角坐标系中横坐标和纵坐标都是整数的点，称为整点，如果一个平面多边形的所有顶点都是整点，那么称这个多边形为平面整点多边形．本文将用一种简洁的方法证明了Ｐｉｃｋ...     

一种构造三次PH曲线的几何方法

通过给出始末两点以及对应的切线与弦线,利用三次PH曲线控制多边形的边与角之间的几何关系,通过加入辅助线,用几何方法求出控制多边形的弦长,从而构造出满足初始条件的控制多边形.在此基础上求出满足条件的三次PH曲线,并给出了数值实例.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].