In the paper, the author applies the extended hyperbolic function and extended triangle function to the cyclic function and the cyclic powers series and so on.

It is proposed in this article that small towns should be dynamically planned,and the circulative accumulation is an important inner motive force for small towns development.

The relation between the two-dimensional cyclic convolution and the discrete reconstruction convolution is educed.

This paper proposes a new algorithm for the computation of Discrete Cosine Transform (DCT) with odd prime length using cyclic or skew cyclic convolutions.

Convolution is converted to cyclic convolution,and also FFT is employed to calculate cyclic convolution.

The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals.

Routh and Chaplygin equations for variable mass nonlinear nonholonomic system in noninertial reference frame are extended,and the cyclic integral and its condition of existence for the system are given.

In this paper, the D Alembert-Lagrange principle and the generalized chaplygin s equation for variable mass weakly nonholonomio systems moving relative to noninertial reference frame are established at first, and then the generalized energy integral and the generalized cyclic integral of the dynamical equations in the case of one-order approximation for the systems above are studied and presented.