几个关于Mercier恒等式的推广

本文建立了几个包含Gauss二项系数的恒等式，这些结果推广了几个Mercier的结果。

Generalizations of Several Identities Related to Mercier's

The purpose of this paper is to establish sev eral identities containing Gaussian binomial coefficient. These results generali ze several Mercier's results. Key words:Gaussian binomial coefficient; identity; the functio n A(T,T 2,...,T n)culating eige nvalues of auto-correlation matrix of the physical control force of actuators. T he optimization algorithm calculating the optimal actuator placement is then put forward via the minimization of an energy criterion, which is chosen as the con trol index. Numerical examples show the effectiveness of the proposed method.