Harmonic mappings of the Sierpinski gasket to the circle

Harmonic mappings from the Sierpinski gasket to the circle are described explicitly in terms of boundary values and topological data. In particular, all such mappings minimize energy within a given homotopy class. Explicit formulas are also given for the energy of the mapping and its normal derivatives at boundary points.

     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

关于有界域的逆紧映照

本文对近20年来多复变函数的一个发展迅速的数学热门分支－逆紧映照作了一个回顾和整理。这是作者继续从事此方向研究的先声，也希望本文能为有志于此的研究者提供一些便利。本文从经典的结果开始，通过对逆紧映照在边界上的开拓及分支点的分布的讨论，详细地阐述了这些年来关于逆紧映照何时成为双全纯映照的若干结果。最后，对近年来关于逆紧映照另外的一些工作进行了简单的介绍。     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

On the Stability of Bifurcation Diagrams of Vanishing Flattening Points

On a smooth surface in Euclidean 3-space, we consider vanishing curves whose projections on a given plane are small circles centered at the origin. The bifurcations diagram of a parameter-dependent surface is the set of parameters and radii of the circles corresponding to curves with degenerate flattening points. Solving a problem due to Arnold, we find a normal form of the first nontrivial example of a flattening bifurcation diagram, which contains one continuous invariant.     

Fixed point theorems under the interior condition

We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.

     

两类拟共形映射的掩盖定理

In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。