The variability of the Crab Nebula in radio: No radio counterpart to gamma-ray flares

We present new Jansky Very Large Array (VLA) radio images of the Crab Nebula at 5.5 GHz, taken at two epochs separated by 6 days about two months after a gamma-ray flare in 2012 July. We find no significant change in the Crab's radio emission localized to a region of <2 light-months in radius, either over the 6-day interval between our present observations or between the present observations and ones from 2001. Any radio counterpart to the flare has a radio luminosity of <~ $2 \times 10^{-4}$ times that of the nebula. Comparing our images to one from 2001, we do however find changes in radio brightness, up to 10% in amplitude, which occur on decade timescales throughout the nebula. The morphology of the changes is complex suggesting both filamentary and knotty structures. The variability is stronger, and the timescales likely somewhat shorter, nearer the centre of the nebula. We further find that even with the excellent uv~coverage and signal-to-noise of the VLA, deconvolution errors are much larger than the noise, being up to 1.2% of peak brightness of the nebula in this particular case.Comment: Accepted to MNRAS; 13 pages, 6 figure

Linear Precoding for Broadcast Channels with Confidential Messages under Transmit-Side Channel Correlation

In this paper, we analyze the performance of regularized channel inversion (RCI) precoding in multiple-input single-output (MISO) broadcast channels with confidential messages under transmit-side channel correlation. We derive a deterministic equivalent for the achievable per-user secrecy rate which is almost surely exact as the number of transmit antennas and the number of users grow to infinity in a fixed ratio, and we determine the optimal regularization parameter that maximizes the secrecy rate. Furthermore, we obtain deterministic equivalents for the secrecy rates achievable by: (i) zero forcing precoding and (ii) single user beamforming. The accuracy of our analysis is validated by simulations of finite-size systems.Comment: to appear IEEE Communications Letter

Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table

Dust-to-gas ratio, XCOX_{\rm CO} factor and CO-dark gas in the Galactic anticentre: an observational study

We investigate the correlation between extinction and H~{\sc i} and CO emission at intermediate and high Galactic latitudes (|b|>10\degr) within the footprint of the Xuyi Schmidt Telescope Photometric Survey of the Galactic anticentre (XSTPS-GAC) on small and large scales. In Paper I (Chen et al. 2014), we present a three-dimensional dust extinction map within the footprint of XSTPS-GAC, covering a sky area of over 6,000\,deg$^2$ at a spatial angular resolution of 6\,arcmin. In the current work, the map is combined with data from gas tracers, including H~{\sc i} data from the Galactic Arecibo L-band Feed Array H~{\sc i} survey and CO data from the Planck mission, to constrain the values of dust-to-gas ratio $DGR=A_V/N({\rm H})$ and CO-to-$\rm H_2$ conversion factor $X_{\rm CO}=N({\rm H_2})/W_{\rm CO}$ for the entire GAC footprint excluding the Galactic plane, as well as for selected star-forming regions (such as the Orion, Taurus and Perseus clouds) and a region of diffuse gas in the northern Galactic hemisphere. For the whole GAC footprint, we find $DGR=(4.15\pm0.01) \times 10^{-22}$\,$\rm mag\,cm^{2}$ and $X_{\rm CO}=(1.72 \pm 0.03) \times 10^{20}$\,$\rm cm^{-2}\,(K\,km\,s^{-1})^{-1}$. We have also investigated the distribution of "CO-dark" gas (DG) within the footprint of GAC and found a linear correlation between the DG column density and the $V$-band extinction: $N({\rm DG}) \simeq 2.2 \times 10^{21} (A_V - A^{c}_{V})\,\rm cm^{-2}$. The mass fraction of DG is found to be $f_{\rm DG}\sim 0.55$ toward the Galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and CO-traced molecular gas in the same region. This result is consistent with the theoretical work of Papadopoulos et al. but much larger than that expected in the $\rm H_2$ cloud models by Wolfire et al.Comment: 11 pages, 7 figures, accepted for publication in MNRA

Directionality and complexity of L1 transfer in L2 acquisition: Evidence from L2 Chinese discourse

Abstract First language (L1) transfer is a common phenomenon in second language (L2) acquisition. However, it will be argued in this article that although there are indeed pervasive influences of learners’ L1 in L2 acquisition, L1 transfer is not everywhere and it can be directional. We compare data from Chang’s (2001b. Discourse effects on the second language acquisition of English and Chinese dative structures. Honolulu: University of Hawai’i at Manoa PhD dissertation, 2004. Discourse effects on EFL learners’ production of dative constructions. Journal of Kaohsiung University of Applied Sciences 33. 145–169.) studies of Chinese-speaking learners of English with data of our study of English-speaking learners of Chinese to examine whether their L2 English discourse and L2 Chinese discourse are equally influenced by their L1 discourse rules. We focus on learners’ answers to wh-questions with a double object construction or a prepositional object construction. The results demonstrate that L1 transfer takes place in Chinese-speaking learners’ L2 English discourse but not in English-speaking learners’ L2 Chinese discourse. This directionality of L1 transfer is accounted for on the basis of computational complexity of linguistic structures involved and on an economical consideration.</jats:p

Spectroscopic Observations of Planetary Nebulae in the Northern Spur of M31

We present spectroscopy of three planetary nebulae (PNe) in the Northern Spur of the Andromeda Galaxy (M31) obtained with the Double Spectrograph on the 5.1 m Hale Telescope at the Palomar Observatory. The samples are selected from the observations of Merrett et al. Our purpose is to investigate formation of the substructures of M31 using PNe as a tracer of chemical abundances. The [O III] 4363 auroral line is detected in the spectra of two objects, enabling temperature determinations. Ionic abundances are derived from the observed collisionally excited lines, and elemental abundances of nitrogen, oxygen, and neon as well as sulphur and argon are estimated. Correlations between oxygen and the alpha-element abundance ratios are studied, using our sample and the M31 disk and bulge PNe from the literature. In one of the three PNe, we observed relatively higher oxygen abundance compared to the disk sample in M31 at similar galactocentric distances. The results of at least one of the three Northern Spur PNe might be in line with the proposed possible origin of the Northern Spur substructure of M31, i.e. the Northern Spur is connected to the Southern Stream and both substructures comprise the tidal debris of the satellite galaxies of M31.Comment: 5 tables, 17 figures; accepted for publication in Ap