1-quasiconformal mappings on a （2,2）-type quadric

This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.     

几类B值拟鞅空间上的原子分解

设1〈P≤2,0〈n≤1,X是P一致可光滑空间的Banach空间,则对每个X值拟鞅f=（fn）n≥0∈pHn^σ（X）存在分解fn=∑k∈Zμkαn^k（n≥0）,并且｜｜f｜｜pHα^σ（X）＋｜｜R（f）｜｜α～inf（∑k∈μk^a）^1/a,这里a^k=（an^k）n≥（k∈Z）是一列（1,α,∞;p）拟鞅原子,并且在L^1中收敛,sup k∈z｜｜a^k＊｜｜n〈∞,（μk）k∈Z∈la是非负实数列．对于拟鞅空间pHa^s（X）和qKn（x）成立类似的结果．此外,利用拟鞅原子分解定理,证明了几个拟鞅不等式．     

无记忆非拟 Newton 算法的导出和全局收敛性

In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.     

拟调和球的不存在性

证明了当N的万有覆盖上存在一个多项式增长的非负严格凸函数时,不存在从R~3到N的非平凡拟调和球.于是在dim M=3时推广了Eells-Sampson的定理.     

QUASILINEAR-ADDITIVE PROPERTIES AND APPLICATIONS

In this article, the authors study some basic properties of the so-called quasilinear- additive functions, and some applications to the special functions of quasiconformal analysis are specified.     

大气动力学方程组的半拉格朗日计算方案的数学研究

通过对大气动力学方程组的半拉格朗日方案的数学分析，得出主要结论如下：(1)说明了Robert的半拉格朗日方案并不是绝对稳定的，通过特征线理论和双曲拟线性方程组解的理论，进一步说明了Robert理论的不正确。(2)通过分析右端项沿轨道积分，给出了一个关于半拉格朗日方案成立的判据。该判据与CLF相仿。(3)根据浅水方程特征理论，发现半拉格朗日方案应包括沿轨道反向积分(大气中慢过程)和沿特征锥积分(大气中快过程)，而已有的方案仅含前一类。因此，今后有必要研究后一类的半拉格朗日方案并研究这两类过程之间的相互作用的计算问题。(4)即使研究沿轨道反向积分问题，其特征跟原方程组解直接有关，因此，不仅仅是一个常微分方程组的问题。而大气动力学方程组的经典解一般仅在小范围成立，并且一维、二维和三维间断均会出现。故大范围反向积分特征线一般是不可能的。     

非酯类拟除虫菊酯研究进展

从结构活性关系和合成方面综述了非酯类拟除虫菊酯的研究进展。