There are three flaws in the formula for simple commodity circulation "W-G-W"——also known as the formula for small commodity producers\' manufacture and management——and in the explanation summarized in the traditional political economics.

This paper deduced the universal formula of the alternating circuit of special cycle function by using the phase calculation,which made the calculation much easier.

By the methods of reducing order and Euler s eigenvalues,we obtain the general solution formula to one kind of systems of three dimensional second order ordinary differential equation with constant coefficients.

With the variable replacement method, general solution formulae were given to the linear differential systems with complex constant coefficients and that with a class of complex variable coefficients.

By reducing order and using Euler s eigenvalue method,the general solution formula to one kind of three-dimensional second-order ordinary differential equation groups with constant coefficients is obtained.

The paper provides an introduction of the accurate calculation of transition curve and the derivation of the general formula.

The article concludes a set of general formula of calculating curve coordinates.

Via deriving and analysing the general formula for ensuring the outer convex of planar earn profile, researched and solved the task of designing the minimum size translating flat-bottomed follower planar earn mechanism in accordance with the outer convex of earn profile and the allowable pressure angle.