拟对称的有界度圆填充逼近

拟对称集和拟圆周集是万有Teichm(u|¨)er空间中两个常用模型.对于任一个由K-拟圆周诱导的拟对称,应用有界度圆填充的方法,构造了其近似映射,并证明了这些近似映射一致收敛于该拟对称.     

R~d中无界子集的离散填充指标(I)(英文)

本文定义了 Rd 中无界集合上的几种离散填充指标 ,并得到了若干性质 .特别地 ,对任意给定的非空集合 A Rd 和任意正整数 m,dim( m )P (A) =d* im( m )P (A) =d～ im( m )P (A) =d～ im( m )P ((A) ) =dim( m )P ((A) ) =dim( 2 )P ((A) ) .     

关于无穷级半纯函数的填充圆

本文应用Ａｈｌｆｏｒｓ覆盖曲面理论，在一定条件下证明了无穷级半纯函数强性填充圆的存在性，从而部分地解决了李国平提出的一个猜想。     

Rd中无界子集的离散填充指标(Ⅰ)

本文定义了R^d中无界集合上的几种离散填充指标，并得到了若干性质，特别地，对任意给定的非空集合A属于R^d和任意正整数m，d^-imp^(m)(A)=dimp^(m)(A)=d^～imp^(m)(A^)=d^～imp^(m)（φ（A））=dimp^(m)(φ（A））=dimp^(2)(φ（A））。     

圆填充整体收敛速度估计

假设D是一个其边界为拟圆周的平面有界单连通区域,Pε是一个几乎填满D的半径为ε的正则六边形圆填充,则在单位圆盘U内存在一个组合等价于Pε的圆填充.众所周知,当ε → 0时,D内半径为ε的圆与U内对应的圆之间的离散规范化映射fε整体一致收敛于Riemann映射f:D→U.本文将给出这个整体收敛fε→f的速度估计.     

带跳跃非线性边界的p-Laplacian问题(英文)

利用Fadell与Rabinowitz提出的同调指标理论,研究了一类带不定权非线性边界的p-Laplacian特征值问题;更进一步,利用环绕定理,证明了一类带跳跃非线性边界的p-Laplacian问题非平凡解的存在性.     

刚性线夹杂与弹性圆夹杂的相互作用

本文将刚性线夹杂与弹性圆夹杂的相互作用，归为解一个标准的柯西型奇异积分方程，获得了刚性夹杂端点的应力强度因子及夹杂的界面应力．     

关于圆和椭圆逼近显示的最优算法(英文)

本文给出了一个逼近显示圆的新算法。该算法是通过相交多边形而不是内接多边形逼近圆。由于构造相交多边形时其面积等于圆面积 ,因此新算法是最优逼近。同时还推广到椭圆     

具有无界变差的连续函数研究进展

讨论了具有无界变差的连续函数的结构.首先按照局部结构和分形维数对连续函数进行了分类,给出了相应的例子.对这些具有无界变差的函数的性质进行了初步的讨论.对于新定义的奇异连续函数,给出了一个等价判别定理.基于奇异连续函数,又给出了局部分形函数和分形函数的定义.同时,分形函数又由奇异分形函数、非正则分形函数和正则分形函数组成.相应于不连续函数的情形也进行了简单的讨论.     

对合流形具有不动点集为RP(2n)■RP(2m)的维数

给定正整数n及m,m>n,本文讨论估计了以RP(2n)RP(2m)为不动点集的对合流形的维数.除个别情况外,我们获得了关于此维数问题的完整估计.     

The Densest Packing of 19 Congruent Circles in a Circle

Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n = 2,..., 16. In 1969 Pirl found the optimal packings for n 10, he also conjectured the dense configurations for 11 n 19. In 1994, Melissen provided a proof for n = 11. In this paper we exhibit the densest packing of 19 congruent circles in a circle with the help of a technique developed by Bateman and Erdös.     

Packings of the complete directed graph with m-circuits

A packing of the complete directed symmetric graph DKv with m-circuits, denoted by(v,m)-DCP, is defined to he a family of are-disjoint m-circuits of DK, such that any one arc of DKv occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m-circults in such a packing. The packing problem is to determine the value P(v,m) for everyinteger v ≥ m. In this paper, the problem is reduced to the case m 6 ≤v≤2m-[(4m-3的平方极) 1/2],for any fixed even integer m≥4,In particular,the values of P（v,m） are completely determined for m=12,14 and 16.     

单位圆内无限级拟亚纯映射的充满圆

本文研究了单位圆内无限级拟亚纯映射的充满圆，证明了单位圆内存在充满圆序列；Borel点邻域内存在充满圆序列．     

On Large Lattice Packings of Spheres

The packing density of large lattice packings of spheres in Euclidean E ^d measured by the parametric density depends on the parameter and on the shape of the convex hull P of the sphere centers; in particular on the isoperimetric coefficient of P and on the second term in the Ehrhart polynomial of the lattice polytope P. We show in E ^d , d 2, that flat or spherelike polytopes generate less dense packings, whereas polytopes with suitably chosen large facets generate dense packings. This indicates that large lattice packings in E ³ of high parametric density may be good models for real crystals.     

单位圆内无限级代数体函数的Borel点

应用Ahlfors覆盖曲面的几何方法,证明了单位圆内无限级代数体函数的Borel点的存在性.将Valiron关于无限级Borel方向存在性的结果推广到了单位圆内.     

Rotation Numbers of Discontinuous Orientation-Preserving Circle Maps

We extend a few well-known results about orientation preserving homeomorphisms of the circle to orientation preserving circle maps, allowing even an infinite number of discontinuities. We define a set-valued map associated to the lift by filling the gaps in the graph, that shares many properties with continuous functions. Using elementary set-valued analysis, we prove existence and uniqueness of the rotation number, periodic limit orbit in the case when the latter is rational, and Cantor structure of the unique limit set when the rotation number is irrational. Moreover, the rotation number is found to be continuous with respect to the set-valued extension if we endow the space of such maps with the Haussdorff topology on the graph. For increasing continuous families of such maps, the set of parameter values where the rotation number is irrational is a Cantor set (up to a countable number of points).     

Rigidity of Noncompact Finsler Manifolds

For a Euclidean space or a Minkowski space, we change the metric in a compact subset and show that the resulting Finsler manifold is isometric to the original standard space under certain conditions. We assume that the mean tangent curvature vanishes and the metric satisfies some curvature conditions or have no conjugate points.     

Rigidity of higher elliptic genera

We prove some general rigidity theorems for both elliptic and higher elliptic genera under a natural condition on the first equivariant Pontrjagin classes. We also obtain the vanishing of some higher elliptic genera.Both authors are supported in part by NFS     

Rigidity of Conformal Iterated Function Systems

The paper extends the rigidity of the mixing expanding repellers theorem of D. Sullivan announced at the 1986 IMC. We show that, for a regular conformal, satisfying the Open Set Condition, iterated function system of countably many holomorphic contractions of an open connected subset of a complex plane, the Radon–Nikodym derivative d/dm has a real-analytic extension on an open neighbourhood of the limit set of this system, where m is the conformal measure and is the unique probability invariant measure equivalent with m. Next, we introduce the concept of nonlinearity for iterated function systems of countably many holomorphic contractions. Several necessary and sufficient conditions for nonlinearity are established. We prove the following rigidity result: If h, the topological conjugacy between two nonlinear systems F and G, transports the conformal measure m _F to the equivalence class of the conformal measure m _G , then h has a conformal extension on an open neighbourhood of the limit set of the system F. Finally, we prove that the hyperbolic system associated to a given parabolic system of countably many holomorphic contractions is nonlinear, which allows us to extend our rigidity result to the case of parabolic systems.