Homotopical theory of periodic points of periodic homeomorphisms on closed surfaces

In this work we show that the Wecken theorem for periodic points holds for periodic homeomorphisms on closed surfaces, which therefore completes the periodic point theory in such a special case. Using it we derive the set of homotopy minimal periods for such homeomorphisms. Moreover we show that the results hold for homotopically periodic self-maps of closed surfaces. This let us to re-formulate our results as a statement on properties of elements of finite order in the group of outer automorphisms of the fundamental group of a surface with non-positive Euler characteristic.     

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.     

《微积分中值定理间点的关系》注记

微分中值定理的结论是在开区间内至少存在一点使得某个等式成立,不妨把这样的点称为微分点;积分中值定理的结论也是在开区间内至少存在一点使得某个等式成立,不妨把这样的点称为积分点.本文讨论这两类点之间是否有关系,以及关系如何的问题,指出相关文献所提供的若干个结论中,有不只一个存在错误.     

闭集与闭区间上连续函数的性质

本文首先分析了闭集与闭区间上连续函数的联系,随之在此基础上证明了闭区间上连续函数常用的一些性质     

Closed fractal interpolation surfaces

Based on the construction of bivariate fractal interpolation surfaces, we introduce closed spherical fractal interpolation surfaces. The interpolation takes place in spherical coordinates and with the transformation to Cartesian coordinates a closed surface arises. We give conditions for this construction to be valid and state some useful relations about the Hausdorff and the Box counting dimension of the closed surface.     

三维空间型中闭曲面和测地球面的比较

本文建立关于三维空间型中的可定向闭曲面的某些公式.引入积分绝对平均曲率来描述可定向闭曲面的平均弯曲程度.在此意义上,可定向闭曲面可以与作为包含该闭曲面的凸的测地球的边界测地球面进行比较,这种比较能用于说明空间型自身的某些属性     

Random fixed points of asymptotically nonexpansive random operators on unbounded domains

The aim of this paper is to prove some random fixed point theorems for asymptotically nonexpansive random operator defined on an unbounded closed and starshaped subset of a Banach space.      

The Relative Maximum Genus of a Graph

A relative embedding of a graph in a surface with respect to a set of closed walks is one where each of the prescribed closed walks bounds a face of the embedding In the special case where the set of closed walks is empty, this amounts to the usual concept of a graph embedding. We present a formula for the maximum (orientable) genus of the surface on which a graph has a relative embedding with respect to a set of closed walks.     

Bridge position and the representativity of spatial graphs

In this paper, we consider closed surfaces which contain spatial graphs. In the case that a closed surface is a 2-sphere, we show that the 2-sphere can be isotoped so that it intersects a bridge sphere for the spatial graph in a single loop. In the case that a closed surface is not a 2-sphere, we define an invariant of a spatial graph by counting the number of intersection of a compressing disk for the closed surface and the spatial graph. By using this invariant, we give a lower bound for the bridge number of a spatial graph.     

三维体积计算中的等参变换法

利用散度定理将体积计算转化为闭曲面上的积分,对曲面进行三角形网格剖分.构造等参变换,建立任一空间三角形与标准三角形的1-1对应关系,推导出空间三角形上的曲面积分表达式.引入了简单四面体的有向体积概念,最后得多面体体积计算公式.     

简单曲面的顶点对应算法及其关键帧动画实现

本文利用曲面参数化的思想设计了３维关键帧动画中的顶点对应简化算法．在这个基础上，本文把Ｓｅｄｅｒｂｅｒｇ关于２维闭曲线帧插值的方法推广到３维闭曲面帧插值，并进行了大量的动画编程实践．试验表明，本文的方法对许多简单曲面都有较好的插值效果．     

On a class of inequality problems with lack of compactness

In this paper we prove the existence of at least one solution for a variational-hemivariational inequality on a closed and convex set without using critical point theory. We apply a version of the well-known theorem of Knaster-Kuratowski-Mazurkiewicz. The obtained results can be applied to Schrödinger type problems and to problems with radially symmetric functions.     

No optimal 1‐planar graph triangulates any nonorientable closed surface

Suzuki [Discrete Math. 310 (2010), 6–11] proved that for any orientable closed surface F² other than the sphere, there exists an optimal 1‐planar graph which can be embedded on F² as a triangulation. However, for nonorientable closed surfaces, the existence of such graphs is unknown. In this article, we prove that no optimal 1‐planar graph triangulates a nonorientable closed surface.     

鞍点集的结构

本文对两人零和对策给出了其鞍点集是凸的或闭的充分条件。     

Analytic solutions of initial-boundary-value problems of transient conduction using symmetries

Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and closed form solutions is carried out for a physical problem of heat conduction in a semi-infinite solid bar made of AISI 304 stainless steel.     

Circle action with prescribed number of fixed points

Given any two positive integers k and n, this paper is concerned with the existence of a circle action on a closed, smooth orientable n-dimensional manifold with precisely k isolated fixed points. We first show that this existence problem can be reduced to that of an n-dimensional manifold with exactly three fixed points. Then by using a rigidity result, we determine possible weights on these three fixed points when n = 4.     

On the integral invariants of a closed ruled surface

Summary In this paper, it is shown that the dual integral invariant of a closed ruled surface, the dual angle of pitch, corresponds to the dual spherical surface area described by the dual spherical indicatrix of the closed ruled surface. So, new geometric interpretations of the real angle of pitch and the real pitch of a closed ruled surface, and some results are given.     

Estimate and monotonicity of the first eigenvalue under the Ricci flow

In this paper, we first derive a monotonicity formula for the first eigenvalue of on a closed surface with nonnegative scalar curvature under the (unnormalized) Ricci flow. We then derive a general evolution formula for the first eigenvalue under the normalized Ricci flow. As an application, we obtain various monotonicity formulae and estimates for the first eigenvalue on closed surfaces.     

Extreme points of the closed convex hull of composition operators

We study the extreme points of the closed convex hull of the set of all composition operators on the space of bounded analytic functions and the disk algebra.     

不动点集为F=U_(i=1)~mRP_i(1)×HP_i(n)的对合

(M,T)是一个在r维光滑闭流形M上的不平凡光滑对合,它的不动点集为F．本文给出了F=U(i=1)~m RPi(1)×HPi(n)时对合的协边类,其中HP(n)表示n维四元数射影空间．