Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This paper discusses an algebraic framework to study such questions. The systems discussed here are given by mappings on an affine space over a finite field, whose...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Aerosol particles in the atmosphere are important participants in the formation of cloud droplets and have significant impact on cloud albedo and global climate. According to the Köhler theory which describes the nucleation and the equilibrium growth of cloud droplets, the surface tension of an aerosol droplet is one of the most important factors that determine the critical supersaturation of d...