• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.263-267
• /
• 2014

We study the growth rate of $H^1$ Sobolev norm of the solutions to Gross-Neveu and Thirring equations. A well-known result is the double exponential rate. We show that the $H^1$ Sobolev norm grows at most an exponential rate exp($ct^2$).

• Publications of The Korean Astronomical Society
• /
• v.30 no.2
• /
• pp.587-589
• /
• 2015

We present the results from analysis of the Hilbert-Huang transform (HHT) for the 4 Hz quasi-periodic oscillations (QPO) around the black hole X-ray binary XTE J1550-564. The resultant Hilbert spectra demonstrate that the QPO is composed of a series of intermittent signals appearing occasionally. From the analysis of the HHT, we further found the distribution of the lifetimes for the intermittent oscillations and the distribution for the time intervals with no significant signal (the break time). The mean lifetime is 1.45 s and 90% of the oscillation segments have lifetimes less than 3.1 s whereas the mean break time is 0.42 s and 90% of break times are less than 0.73 s. We conclude that the intermittent feature of the QPO could be explained by the Lense-Thirring precession model and rules out interpretations of continual frequency modulation.