Removable sets for continuous solutions of quasilinear elliptic equations

We show that sets of Hausdorff measure zero are removable for -Hölder continuous solutions to quasilinear elliptic equations similar to the -Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.

     

Nonlinear Cauchy-Riemann operators in

This paper has arisen from an effort to provide a comprehensive and unifying development of the -theory of quasiconformal mappings in . The governing equations for these mappings form nonlinear differential systems of the first order, analogous in many respects to the Cauchy-Riemann equations in the complex plane. This approach demands that one must work out certain variational integrals involving the Jacobian determinant. Guided by such integrals, we introduce two nonlinear differential operators, denoted by and , which act on weakly differentiable deformations of a domain .

Solutions to the so-called Cauchy-Riemann equations and are simply conformal deformations preserving and reversing orientation, respectively. These operators, though genuinely nonlinear, possess the important feature of being rank-one convex. Among the many desirable properties, we give the fundamental -estimate

In quest of the best constant , we are faced with fascinating problems regarding quasiconvexity of some related variational functionals. Applications to quasiconformal mappings are indicated.

     

Characterization of Certain Holomorphic Geodesic Cycles on Quotients of Bounded Symmetric Domains in terms of Tangent Subspaces

Let be an irreducible bounded symmetric domain and Aut() be a torsion-free discrete group of automorphisms, X /. We study the problem of algebro-geometric and differential-geometric characterizations of certain compact holomorphic geodesic cycles S X. We treat special cases of the problem, pertaining to a situation in which S is a compact holomorphic curve, and to the case where is a classical domain dual to the hyperquadric. In both cases we consider algebro-geometric characterizations in terms of tangent subspaces. As a consequence we derive effective pinching theorems where certain complex submanifolds S X are proven to be totally geodesic whenever their scalar curvatures are pinched between certain computed universal constants, independent of the volume of the submanifold S, giving new examples of the gap phenomenon for the characterization of compact holomorphic geodesic cycles.Research funded by a CERG grant from Research Grants Council of Hong Kong.     

L光滑拓扑空间中弱映射的强形式

在L光滑拓扑空间中给出了L光滑强不定映射、强不定开映射、强不定闭映射及L光滑强半连续映射、强半开闭映射，并讨论了它们的等价刻画和相互关系。     

素环上的交换映射

设R是一个环,F:R→R是一个映射.如果对所有的x∈R,有[F(x),x]=0成立,则称F是R上的交换映射.文章的主要结论为:设R是特征不为2的素环.如果存在一个非零广义导子:δR→R,使得映射x→[δ(x),x]在R上是可变换的且δ(I)∈Z(R),则δ在R上是可交换的.     

序映射的不动点定理

目的分析研究一类更广的序映射不动点问题。方法在序Banach空间中采用迭代序列方法。结果证明了序Banach空间中广义序映射的几个不动点定理。结论改进和推广了相应的序Banach空间中序映射的不动点定理。     

纹理映射技术

讨论了光照明模型对计算机真实感图形绘制的重要性 ,并深入讨论了纹理映射技术在计算机真实感图形绘制中的应用。     

凸度量空间中单值和集值映象的公共不动点定理(英文)

在单值映象与集值映象相容或次相容的条件下 ,讨论了完备凸度量空间中两个集值映象和一个单值映象的公共不动点的存在性 ,改进和推广了前人的有关结果     

模式识别在采矿中的应用

1 非线性映照法识别原理1.1特征向量选取特征向量的选取是模式识别工作的关键,首先,要求选取对分类贡献大而较少的(不破坏分类情况的最少特征量数)特征量数目,再者要求样本数和空间维数的比值要大于3.为此我们从表1的七个特征量中根据加权因子的大小作了初选。再据此通过各种组合逐步降维进行筛选.由七个特征量中筛选出分类效果最好的4个固有特征向量,即铅、锌、氧化钙+氧化镁和二氧化硅的分析数据.     

一类映象分歧点的存在性

该文将M.G.Grandall等人提出的结论中的参数空间(-1,1)推广为Banach空间A,dimN(F_x(0,0)=dim Y/R(F_x(0,0))=1推广为dimN(F_x(0,0))=dim Y/R(F_x(0,0))=n,给出了(0,0)∈X×A为非线性映象F:X×A→Y的分歧点的充分条件。