球面和射影平面上不可分地图的色和

给出了球面和射影平面上带根不可分地图的色和方程,从色和方程导出了球面和射影平面上带根一般不可分地图、二部地图的计数函数方程. 利用色和理论,研究不同类地图的计数问题,得到了一种研究计数问题的新方法. 此外,还得到了一些计数显示表达式.     

射影平面和环面上奇异地图的色和

一个地图的每条边,若在同一面的边界上,则称它为奇异地图．由于含环的地图是不可着色的,本文所有地图均不含环．本文研究射影平面和环面上带根奇异地图的色和．     

关于双奇异平面地图的计数

本文讨论了带根双奇异平面地图的计数问题,提供了以根面次、度和内面数为参数及以根面次、奇异边数和自环数为参数的计数函数所满足的计数方程,并且导出了所有的计数显式.     

环面上一般有根地图的计数

这篇文章给出了环面上以内面个数，根面次和非根节点个数为参数的一般有根地图的计数方程，导出了以内面个数和非根节点个数为参数的这类地图的计数方程的精确解。作为推论，推出了以边数为参数的这类地图的个数，其近似解在文献[2]中已讨论。     

Klein瓶上的双奇异地图

一个地图的每条边如果不是环就是割边(即该边的两边是同一个面的边界)，则称之为双奇异地图，本文研究Klein瓶上带根双奇异地图的计数问题，得到了此类地图以边数、平面环数、手柄上本质环数和又帽上本质环数为参数的计数公式，并得到了部分计数显式。     

带根无环欧拉平面地图的计数(英文)

自20世纪60年代初Tutte的开创性工作以来,许多学者在带根地图的计数方面作了很多工作,但许多类无环地图的计数仍没有被处理.本文主要研究以根点次、非根点数和内面数为三个参数的带根无环欧拉平面地图的计数问题.     

带根单行平面地图的计数

提供了根点为一个奇点的带根单行平面地图以其边数、根点次和非根奇点次为参数的生成函数所满足的一些函数方程,并且导出了这些函数的显式,它们有两个是无和式.     

关于平面树色和方程结果的一个注记

这篇文章得到了有根平面树的节点剖分的色和方程. 导出了带无限多个参数的有根平面植树和平面树的色和方程的精确表达式. 作为直接推论可推出节点剖分的有根平面树的计数方程的精确结果 .     

关于平面地图的计数方程

本文介绍了在平面地图的计数中所出现的函数方程的若干类型和它们的解法.并提出了一些目前有待解决的问题.     

带根4-正则单行平面地图的计数(英文)

本文研究了带根4-正则单行平面地图的计数问题,并给出了以其非根点数和两个奇点次为三个参数的一些计数公式.     

The number of nonseparable maps on the projective plane

In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation.     

Dirichlet L-函数倒数的2k次加权均值

本文主要目的是利用经典的Ｋｌｏｏｓｔｅｒｍａｎｎ和估计及其解析方法研究Ｄｉｒｉｃｈ－ｌｅｔ Ｌ-函数倒数的 ２ｋ次加权均值,得到了一个较为精确的渐近公式．     

广义高阶Bernoulli数,Gauss和及广义Kloosterman和(英文)

利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式.     

Chromatic sums of nonseparable near-triangulations on the projective plane

In this paper, we study the chromatic sum functions of rooted nonseparable near-triangulations on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. Applying chromatic sum theory, the enumerating problem of different sorts maps can be studied, and a new method of enumeration can be obtained. Moreover, an asymptotic evaluation and some explicit expression of enumerating functions are also derived.     

Chromatic sums of biloopless nonseparable near-triangulations on the projective plane

In this paper, the chromatic sum functions of rooted biloopless nonseparable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.     

Computing Harmonic Maps and Conformal Maps on Point Clouds

We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic lattice to approximate its $\epsilon$-neighborhood. Then the harmonic map of the surface can be approximated by discrete harmonic maps on lattices. The conformal map, or the surface uniformization, is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant curvature. We propose algorithms and numerical examples for closed surfaces and topological disks. To the best of the authors' knowledge, our approach provides the first meshless method for computing harmonic maps and uniformizations of higher genus surfaces.     

A Note on the Game Chromatic Index of Graphs

In this note we prove that the game chromatic index χ _g ^′(G) of a graph G of arboricity k is at most Δ + 3k − 1. This improves a bound obtained by Cai and Zhu [J. Graph Theory 36 (2001), 144–155] for k-degenerate graphs. Tomasz Bartnicki: Research of the first author is supported by a PhD grant from Polish Ministry of Science and Higher Education N201 2128 33. Received: November 1, 2006. Final version received: December 22, 2007.