In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...

In this paper, the researchers have investigated a Concatenated Robot Move (CRM) sequence problem and Minimal Part Set (MPS) schedule problem with different setup times for two-machine robotic cell. They have focused on simultaneous solving of CRM sequence and MPS schedule problems with different loading and unloading times. They have applied a Simulated Annealing (SA) algorithm to provide a go...

We present two solutions to the firing synchronization problem on the ring, an 8-state minimal-time solution and a 6-state non-minimal-time solution. Both solutions use fewer states than the previous best-known minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We ...

the main goal of this note is to introduce another second-order differenceequation where every nontrivial solution is of minimal period 5, namelythe difference equation:xn+1 =1 + xn−1xnxn−1 − 1, n = 1, 2, 3, . . .with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

⎯It is well known that the solution set of fuzzy relational equations with max-product composition can be determined by the maximum solution and a finite number of minimal solutions. There exists an analytic expression for the maximum solution and it can be yielded easily, but finding the complete set of minimal solutions is not trivial. In this paper we first provide a necessary condition for ...