Abstract: In IEEE 802.11 networks, it is well known that the
traditional time-domain contention often leads to low channel
utilization. The first frequency-domain contention scheme, the time to
frequency (T2F), has recently been proposed to improve the channel
utilization and has attracted a great deal of attention. In this paper, we
present the latest research progress on the weighed frequency-domain
contention. We compare the basic ideas, work principles of these
related schemes and point out their differences. This paper is very
useful for further study on frequency-domain contention.
Abstract: In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.
Abstract: We investigate the planar quasi-septic non-analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The system could be changed into an analytic system by two transformations, with the help of computer algebra system MATHEMATICA, the conditions of uniform isochronous center are obtained.