Analyses of mean and turbulent motion in the tropics with the use of unequally spaced data

Wind velocities from 25 km to 60 km over Ascension Island, Fort Sherman and Kwajalein for the period January 1970 to December 1971 are analyzed in order to achieve a better understanding of the mean flow, the eddy kinetic energy and the Eulerian time spectra of the eddy kinetic energy. Since the data are unequally spaced in time, techniques of one-dimensional covariance theory were utilized and an unequally spaced time series analysis was accomplished. The theoretical equations for two-dimensional analysis or wavenumber frequency analysis of unequally spaced data were developed. Analysis of the turbulent winds and the average seasonal variance and eddy kinetic energy of the turbulent winds indicated that maximum total variance and energy is associated with the east-west velocity component. This is particularly true for long period seasonal waves which dominate the total energy spectrum. Additionally, there is an energy shift for the east-west component into the longer period waves with altitude increasing from 30 km to 50 km

On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits

In this paper, we construct grammian-like quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Through continuum limits of this non-Abelian Hirota-Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative differential-difference equations ending with the noncommutative KP equation. For each of these systems the quasideterminant solutions are constructed as well.Comment: 9 pages, 1 figur

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Resolving the decades-long transient FIRST J141918.9+394036: an orphan long gamma-ray burst or a young magnetar nebula?

Ofek (2017) identified FIRST J141918.9+394036 (hereafter FIRST J1419+3940) as a radio source sharing similar properties and host galaxy type to the compact, persistent radio source associated with the first known repeating fast radio burst, FRB 121102. Law et al. (2018) showed that FIRST J1419+3940 is a transient source decaying in brightness over the last few decades. One possible interpretation is that FIRST J1419+3940 is a nearby analogue to FRB 121102 and that the radio emission represents a young magnetar nebula (as several scenarios assume for FRB 121102). Another interpretation is that FIRST J1419+3940 is the afterglow of an `orphan' long gamma-ray burst (GRB). The environment is similar to where most such events are produced. To distinguish between these hypotheses, we conducted radio observations using the European VLBI Network at 1.6 GHz to spatially resolve the emission and to search for millisecond-duration radio bursts. We detect FIRST J1419+3940 as a compact radio source with a flux density of $620 \pm 20\ \mathrm{\mu Jy}$ (on 2018 September 18) and a source size of $3.9 \pm 0.7\ \mathrm{mas}$ (i.e. $1.6 \pm 0.3\ \mathrm{pc}$ given the angular diameter distance of $83\ \mathrm{Mpc}$). These results confirm that the radio emission is non-thermal and imply an average expansion velocity of $(0.10 \pm 0.02)c$. Contemporaneous high-time-resolution observations using the 100-m Effelsberg telescope detected no millisecond-duration bursts of astrophysical origin. The source properties and lack of short-duration bursts are consistent with a GRB jet expansion, whereas they disfavor a magnetar birth nebula.Comment: 8 pages, 4 figures, accepted for publication in ApJ