CONTINUITY OF GENERALIZED INVERSES OF LINEAR OPERATORS IN BANACH SPACES AND ITS APPLICATIONS

The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.     

原子Boolean格代数的导子

设L是Banach空间X上的原子Boolean子空间格,δ是algL的任一导子,则存在X中的一个稠定线性算子T,使得δ（A）＝AT—TA（A∈algL）在T的定义域D（T）上成立．另外,如果L还是一个有限格,并且对L的任一原子L,L＋L＇闭,则δ是连续的和内的．     

Banach空间中闭线性算子广义预解式存在定理

在Banach空间中研究闭线性算子广义逆扰动问题和广义预解式存在性问题.给出了闭线性算子广义逆在T-有界扰动下的一些稳定特征,这些特征推广了在有界线性算子情形、闭线性算子有界扰动情形以及闭线性算子保值域或保核空间情形的一些已知结果.以此为基础,得到了闭线性算子广义预解式存在的一些充要条件及其广义预解式的显式表达式.作为应用,给出了闭Fredholm算子和闭半-Fredholm算子的广义预解式存在性特征.     

稳定同位素标记1,4-二氢吡啶类药剂的5,6-位及其取代基碳的合成

l,4-二氢吡啶结构是许多生物活性物以及药物分子的重要骨架,同时也是非常重要的有机合成中间体.当前并没有一种适用的方法用于13C标记1,4-二氢吡啶的合成.提供了一种13C标记1,4-二氢吡啶的合成方法以13C2-乙酸钠为标记原料,经磷酸酸化得到13C2-乙酸,羰基二咪唑酰化13C2-乙酸得到13C2-N-乙酰咪唑,随...     

A Note on a Problem of M. S. Berger

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U (?)E→ F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x)=y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.     

叠氮两端桥连的双核席夫碱铜(Ⅱ)配合物的合成、晶体结构、热稳定性和磁性研究

利用三齿席夫碱配体5-(乙基甲基氨基)-2-[(2-吗啉-4-乙亚胺基)甲基]苯酚(HL)和叠氮化钠以及醋酸铜在甲醇中反应制备了一个新的具有二重轴对称性的叠氮配体两端桥连的双核铜(Ⅱ)配合物[Cu2L2(μ1,3-N3)2]。利用元素分析、红外光谱和X-射线单晶衍射表征了该配合物的结构。配合物的晶体以正交晶系P21212空间群结晶,其晶体学参数a=0.974 6(1),b=1.378 4(2),c=1.504 1(2)nm,V=2.023 3(5)nm3,Z=2,R1=0.063 8,wR2=0.166 8。本文还研究了该配合物的热稳定性和磁性。     

Banach空间中非Lipschitzian交换非线性拓扑半群的遍历理论

本文在满足opial条件或存在Frechet可微范数的一致凸Banach空间中,给出了非Lipschitzian交换拓扑半群的遍历收敛定理及弱收敛定理.     

Banach流形上一类非线性方程的解集的结构

设f是两个Ck(k≥1)Banach流形M和N之间的C1映射.由f定义M上的一个三重指标(M(x),Mc(x),Mr(x)),用此三重指标刻画了f的局部精细点.同时当y是f的广义正则值时,获得原像f-1(y)中含xo的连通分支是M中一个具有维数为M(xo)的C1Banach子流形.特别地,给出非线性方程f(x)=y的孤立解的一个特征.     

A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS

In this article the concept of local conjugation of a C1 mapping between two Banach manifolds is introduced. Then a rank theorem for nonlinear semi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis.     

关于Moore-Penrose逆T+连续性的一个注

设X为拓扑空间.H1和H2为Hilbert空间,T(·)为X到B(H1,H2)的连续映射.本文主要利用Tikhonov正则化算子给出了Moore-Penrose逆T x连续的充分必要条件.这个结果在计算数学中是很重要的.