The backwater regions of the free vibration of sliding systems with linear, hardening or softening restoring force are analyzed comprehensively; relevant analytical solutions are obtained; the continuity and regularity of these solutions changing with the system parameters are demonstrated.

The analytic formulas for the backwater region and phase trajectories of the free vibration are derived, and the variation laws of the length of the standstill region, the phase trajectory and the remaining displacement are analyzed by numerical calculations.

Aiming at the above,the following strategy is suggested: adding the tracking and replacing mechanism to every searching node;counting the stagnation times of a node at a certain station in its searching route;if the times oversteps the allowable value,a new node randomly arises in the solution space to replace the stagnating one for improving the searching efficiency.

Aiming at the stagnation exists in the cooperative particle swarm optimization,presents a new kind of the cooperative particle swarm optimization algorithm based on particle s spatial extension.

But conventional differential evolution algorithm has a problem of stagnation that can stop the algorithm convergence.

There is a question of being at a standstill of Chinese soybean production in recent years.

External factors are the cause of thirty years standstill of sociology of education in Chinese mainland, but what is more important is the conflict between two different types of sociology of education and the wrong understanding of the conflict.