in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

We study rectangular Vandermonde matrices V with N+1 rows and s irregularly spaced nodes on the unit circle, in cases where some of are “clustered” together – elements inside each cluster being separated by at most h?1N, clusters from other least ??1N. show that any pair column subspaces corresponding to two different nearly orthogonal: minimal principal angle between them is most?2?c1N??c2Nh, ...

The steady states of an isotone electric system are described by function with respect to the componentwise order. When there states, we highlight a dominant state and study its domain attraction for fixed point iteration method.