Describe the boundedness of the operator-valued martingale transforms,and as an application the p-uniform smoothness and q-uniform convexity of Banach spaces are characterized by the boundedness of martingale transform operators.

By using the property of supporting functionals,the paper obtain a characterization of uniform smoothness.

We define the TC modulus of convexity and smoothness of Banach spaces and characterize uniform convexity and uniform smoothness.

This paper pointed out the importance of accurately evaluation the test result of the average trajectory consistency, analyzed the shortcoming that exist in the currently in effect test evaluation method of home and abroad, put forward a new test evaluation method that coherent with the demand of fighting and training.

Weighted average-consensus for networks of multi-agent with time-delays;