In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs) on Z d , known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time 0 all particles are sleeping, except f...

For a nonlinear optimal control problem with state constraints, we give conditions under which the optimal control depends Lipschitz continuously in the L2 norm on a parameter. These conditions involve smoothness of the problem data, uniform independence of active constraint gradients, and a coercivity condition for the integral functional. Under these same conditions, we obtain a new nonoptima...

Selecting a partial set of sensor nodes for execution and still maintaining the system sensing coverage is an important issue in wireless sensor networks. The previous research was concentrated on the location-aware sensor networks but little attention has been devoted to the location-free environments. This paper describes an approach to determining active nodes for full coverage without locat...