A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z)

In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. Firstly, a vector matroid is defined over F(z). Secondly, the full rank conditions of [sI-A|B] are derived in terms of the concept related to matroid theory, such as rank, base and union. Then the sufficient condition for the linear system and composite system over F(z) to be structurally controllable is obtained. Finally, this paper gives several examples to demonstrate that the married-theoretic approach is simpler than other existing approaches

The short-time behavior of kinetic spherical model with long-ranged interactions

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m_{0} quenched from a very high temperature to T < T_{c} is solved. In the short-time regime, the bulk order increases with a power law in both the critical and phase-ordering dynamics. To the latter dynamics, a power law for the relative order m_{r} ~ -t^{-k} is found in the intermediate time-regime. The short-time scaling relation of small m_{0} are generalized to an arbitrary m_{0} and all the time larger than t_{mic}. The characteristic functions $\phi (b,m_{0})$ for the scaling of m_{0} and $\epsilon (b,T')$ for T'=T/T_{c} are obtained. The crossover between scaling regimes is discussed in detail.Comment: 22 pages, 3 figure