We introduced the topological degree for the random multivalued A-proper mappings, usingit we obtained some random fixed points theorems.

As an application, the generalized topological degree theory for generalized A-proper mappings and some famous fixed point theorems can be extended.

Utilizing the properties of the topological degree for the A-proper mapping in the Probabilistic Metric Spaces,the paper studies the fixed point of nonlinear operator in the projection complete Z-P-S space,and some new results are obtained.

On the basis of Kwapisiz s semi-ordered space and abstract space, it discusses common fixed point problem of a kind of commuting mappings, extends the results of Zhang Shisheng.

Two definitions of dual function and complementary function are given from the viewpoint of one-to-one mapping of the truth table.

This paper discussed properties of images on locally separable metric spaces and gives some impotant related results.

It shows popular artistic charm due to three “images”: the restoration of the style of the original ethnic dance, a living folk cultural museum and the thriving of life consciousness, which are worthy of discussing and tasting.

Based on the analysis of the interrelationship betw ee n images and stylistic meaning,between images and contextual meaning,between ima ges and cultural meaning,this paper focuses on how to reproduce the images in th e process of translation.