anti-lock braking system (abs) which is a nonlinear and time variant system may not be easily controlled by classic control methods. this is due to the fact that classic linear controllers are just capable of controlling a specific plant in small region of state space. to overcome this problem, a more powerful control technique must be employed for complex nonlinear plants. fuzzy controllers ar...

In this paper, we study countably compact fuzzy sets using the definition of C. K. Wong [10] and obtain its several properties. 1. Introduction The concept of fuzzy set and fuzzy set operations were first introduced by L. A. Zadeh [11] in1965. Several other mathematicians studied fuzzy sets in various areas in mathematics. Firstly, C. L. Chang [2] in 1968 developed the theory of fuzzy topologic...

We investigate the zero-forcing number for triangle-free graphs. We improve upon the trivial bound, δ ≤ Z(G) where δ is the minimum degree, in the triangle-free case. In particular, we show that 2δ− 2 ≤ Z(G) for graphs with girth of at least 5, and this can be further improved when G has a small cut set. Lastly, we make a conjecture that the lower bound for Z(G) increases as a function of the g...

We present a counterexample to a lower bound for power domination number given in Liao, Power domination with bounded time constraints, J. Comb. Optim., in press 2014. We also define the power propagation time and make connections between the power domination propagation ideas in Liao and the (zero forcing) propagation time in Hogben et al, Propagation time for zero forcing on a graph, Discrete...

In this paper a number of pilot-based channel estimation techniques are investigated for a multiple antenna system using the zero-forcing algorithm. The techniques are tested in typical indoor and outdoor (vehicular) channels. Performance results are presented in terms of bit error rate, mean squared error and data throughput. It is found that different pilot strategies offer the best performan...