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, ...

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., ...

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...

http://dx.doi.org/10.1016/j.cie.2014.05.012 0360-8352/ 2014 Elsevier Ltd. All rights reserved. q This manuscript was processed by Area Editor Hans Kellerer. ⇑ Corresponding author. Address: Department of Industrial Management, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan. Tel.: +886 2 2737 6337. E-mail address: [email protected] (C....

Recently, Tsai et al., Liao et al. and Li et al. each proposed a multi-server authentication protocol. They claimed their protocols are secure and can withstand various attacks. However, we found some security loopholes in each of their schemes, for example, both Tsai et al.’s and Liao et al.‘s schemes suffers from server spoofing attack by an insider server. Li et al.s’ suffers from the lost s...

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa–Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu & Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & ...

Wei-keng Liao Northwestern University 1.