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.     

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.     

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.     

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.     

近场声压法在定位柴油机故障中的应用

在柴油机的故障诊断中，常采用多个传感器测取柴油机的多个信号，如：振动信号，油压信号等进行分析判断各缸工作状况，所需设备复杂，数据处理繁杂。而本文提出了只用一个声压传感器就可定位并分析各缸的工况，较之以往的方法简单易行。     

关于R(Ax)闭的连续算子族Ax的Moore-Penrose广义逆Ax+连续的充要条件

设X是拓扑空间,A_x,闭值域R(A_x)为X→B(H)的连续映射,我们知道:即使在dim(H)有限的情况下,M.-P.逆A_x⁺:也不一定连续,A_x⁺连续的充要条件,对现代分析和应用数学的一些研究是很重要的,本文给出了,在一般拓扑空间X、局部紧拓扑空间X、A_x为Fredholm算子族等情况下,A_x⁺为连续的充分必要条件。     

关于算子─（△—ia）~2＋Ⅴ的性质（Ⅰ）

关于算子─（△—ia）￣２＋Ⅴ的性质（Ⅰ）余开奇，马吉薄（南京航空航天大学数理力学系，２１００１６）（南京大学数学系，２１０００８）关键词自伴算子，本质自扩张，Ｓｃｈｒｏｄｉｕｇｅｒ算子．分类号ＡＭｓ（１９９１）４７Ｆ０５，４７Ｂ８０／ＣＣＬＯ１７７．...     

有关M.S.Berger问题的注记

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 真包含 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.     

均分散胶体的研究──Ⅷ．草酸钛酰钡均分散颗粒的制备、组成及应用

本文提出了制备草酸钛酰钡均分散颗粒的优选条件．对此条件下制备的均分散颗粒进行了化学分析、ＴＧＡ、ＩＲ分析并确定了其化学组成．将此种颗粒灼烧成氧化物后，基本上可保留原形貌．用ＢａＯ·ＴｉＯ２均分微颗粒与Ｙ２Ｏ３均分散颗粒烧制成ＢａＴｉＯ３均分散陶瓷，以达到控制陶瓷超微结构均匀的目的．     

学生上台演示 教学效果良好

在普通化学课教学中,我们采取学生上台演示试验的做法,效果较好。具体做法是课前选择两位同学,在任课教师指导下把演示试验做成功,再到课堂上做给大家看。例如,为了讲磷的氢化物,我们在课前让学生自己动手制备好Ca_3P_2,盛在试管里置于干燥器中备用。在课堂上讲到PH_3时,他们便将盛有Ca_3P_2的试管投入装有水的缸中,于是一个个气泡升到水面,接着火光一闪一闪,一个个烟圈冉冉上升,