An analytic expression for the intensity of the central point in Fresnel′s circular aperture diffraction was derived using the methods of vector map and integration respectively.

In this paper, the essential problems about the transformation matrix of B-spline bases the conditions of existence, the analytic representation and the computational formulas of the transformation matrix arc studied, and the results in those aspects are given.

Based on the permeability curves of fractured sandstone reservoir, the analytical expression of the water-flooding curve of fractured sandstone reservoir is derived,and the curve is mapped.

Based on the traditional method of making geometrical chart,the analytical expressions of deformation compatibility equation of statically indeterminate truss is obtained in this paper.

And an analytical expression between the safety factor and the sliding radius,soil parameters and sliding toe coordinates was also obtained.

The analytic expression of the two controlling variables and the two controlled variables is deduced.

It gives the analytic expression of the intersection line and the formula of calculating a specific point coordination and provides a basic material for 2D graphic software.

In addition, the main electric coupling coefficients are named, which have an approximate analytic expression.