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...

Standard estimates of the dimension of the attractor of the 2D Navier–Stokes equations are given in terms of a dimensionless Grashof number that measures the total amount of energy injected into the flow. However, this result takes no account of whether the forcing is concentrated at large or small scales. By a simple modification of the usual argument, this paper provides a bound that is linea...

Spatial periodic forcing of pattern-forming systems is an important, but lightly studied, method of controlling patterns. It can be used to control the amplitude and wave number of one-dimensional periodic patterns, to stabilize unstable patterns, and to induce them below instability onset. We show that, although in one spatial dimension the forcing acts to reinforce the patterns, in two dimens...

We present a counterexample to a lower bound for the power domination number given in Liao, Power domination with bounded time constraints, J. Comb. Optim. 31 (2016): 725–742. We also define the power propagation time, using 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 Appl. Math., ...

5 We present a counterexample to a lower bound for power domination number given in Liao, Power 6 domination with bounded time constraints, J. Comb. Optim., in press 2014. We also define the power 7 propagation time and make connections between the power domination propagation ideas in Liao and the 8 (zero forcing) propagation time in Hogben et al, Propagation time for zero forcing on a graph, ...

It is known that the zero forcing number of a graph an upper bound for maximum nullity (see [AIM Minimum Rank - Special Graphs Work Group (F. Barioli, W. Barrett, S. Butler, Cioab$\breve{\text{a}}$, D. Cvetkovi$\acute{\text{c}}$, Fallat, C. Godsil, Haemers, L. Hogben, R. Mikkelson, Narayan, O. Pryporova, I. Sciriha, So, Stevanovi$\acute{\text{c}}$, H. van der Holst, K. Vander Meulen, and A. Wan...

Openand closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angles of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge, and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in pha...