The hybrid problems based on the streamline coordinates have to be solved in the image plane, which is composed of streamline and circumferential coordinates.

In the image plane, two special functions──pathline length function Y and energy function Ω──have been defined due to the fact that the control equations can be changed into conservative ones by space translation.

cross-section are constructed in the image plane (,), where is the path function which automatically satisfies the conservation of mass.

In order to probe the critical scaling law of the transition to chaos from quasiperi-odicity in a torus map, by starting with a pair of coupled circle maps.

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.

The research shows that unimodal map is similar to circle map.

The so called “hole induced coexistence of attractors” may occur in the discontinuous maps describing a kind of relaxation oscillators.