This pa- per defines L-fuzzy rough approximation operator based on residuated lattice in axiomatic approach,and presents the simplest for- mulas of the axiom sets charactering the L-fuzzy rough approximation operators.

To develop a more reliable program, two checking methods about program’s varification of correctness are studied, such as Dijkstra’s weakest pre-predicate transformer and Hoare’s axiomatic approach.

From the history of the development of geometry,axiomatic method has undergone two stages.

In the situation of the enlargement of college students,combining the background of basic educational reform with the research situation of Elementary Geometry Research,the article brings forward guiding ideology and program of integrating this curriculum,of emphasizing the integration of advanced and elementary geometry,emphasizing axiomatic methods and geometric transformation.

This paper intends to discuss an axiomatic method for the definition of determinant and prove that the deterninant defined by the aniomatic method and the determinant defined by the tradictional method equivalent,and discuss some teaching problems on the definition of determinant.

The article proves sine rule and that vertical line of a line crosses its slant lines are both equivalent for the parallel axiom (Euclid) on the combined axiom; the sequence axiom; the repeatability axiom; the continuity axiom (the axiom system of Hilbert), so they are equivalent for each other .