Dirac cohomology and Euler-Poincar\'e pairing for weight modules

Let $\mathfrak{g}$ be a reductive Lie algebra over $\mathbb{C}$. For any simple weight module of $\mathfrak{g}$ with finite-dimensional weight spaces, we show that its Dirac cohomology is vanished unless it is a highest weight module. This completes the calculation of Dirac cohomology for simple weight modules since the Dirac cohomology of simple highest weight modules was carried out in our previous work. We also show that the Dirac index pairing of two weight modules which have infinitesimal characters agrees with their Euler-Poincar\'{e} pairing. The analogue of this result for Harish-Chandra modules is a consequence of the Kazhdan's orthogonality conjecture which was settled by the first named author and Binyong Sun

Kinematic properties of the dual AGN system J0038+4128 based on long-slit spectroscopy

The study of kiloparsec-scale dual active galactic nuclei (AGN) will provide important clues to understand the co-evolution between the host galaxies and their central supermassive black holes undergoing a merging process. We present long-slit spectroscopy of the J0038$+$4128, a kiloparsec-scale dual AGN candidate discovered by Huang et al. recently, using the Yunnan Faint Object Spectrograph and Camera (YFOSC) mounted on Li-Jiang 2.4-m telescope at Yunnan observatories. From the long-slit spectra, we find that the average relative line-of-sight (LOS) velocity between the two nuclei (J0038$+$4128N and J0038$+$4128S) is about 150 km s$^{-1}$. The LOS velocities of the emission lines from the gas ionized by the nuclei activities and of the absorption lines from stars governed by the host galaxies for different regions of the J0038$+$4128 exhibit the same trend. The same velocities trend indicates that the gaseous disks are co-rotating with the stellar disks in this ongoing merge system. We also find several knots/giant HII regions scattered around the two nuclei with strong star formation revealed by the observed line ratios from the spectra. Those regions are also detected clearly in HST $F336W/U$-band and HST $F555W/V$-band images.Comment: 12 pages, 5 figures, 3 tables, Research in Astronomy and Astrophysics accepte

Implications for B→ηKB \to \eta K and B→Glueball+KB \to Glueball + K Modes from Observed Large B→η′K+XB\to \eta' K+X

The unexpectedly large branching ratios for $B\to \eta' K (\eta' X_s)$ decays could be of gluonic origin. We study the implications for $B\to \eta K (\eta X_s)$ and $P K (PX_s)$, where $P$ is the pseudoscalar glueball. In the mechanism proposed by Fritzsch, large branching ratios are predicted for these modes. The $B\to \eta K$ rate is barely within the experimental limit, and $B\to P K$, $PX_s$ could be at the 0.1% and 1% level, respectively. Smaller but less definite results are found for the mechanism of $g^* \to \eta' g$ via the gluon anomaly.Comment: 11 pages, revtex, no fig

UAV Placement for Real-time Video Acquisition: A Tradeoff between Resolution and Delay

Recently, UAVs endowed with high mobility, low cost, and remote control have promoted the development of UAV-assisted real-time video/image acquisition applications, which have a high demand for both transmission rate and image resolution. However, in conventional vertical photography model, the UAV should fly to the top of ground targets (GTs) to capture images, thus enlarge the transmission delay. In this paper, we propose an oblique photography model, which allows the UAV to capture images of GTs from a far distance while still satisfying the predetermined resolution requirement. Based on the proposed oblique photography model, we further study the UAV placement problem in the cellular-connected UAV-assisted image acquisition system, which aims at minimizing the data transmission delay under the condition of satisfying the predetermined image resolution requirement. Firstly, the proposed scheme is first formulated as an intractable non-convex optimization problem. Then, the original problem is simplified to obtain a tractable suboptimal solution with the help of the block coordinate descent and the successive convex approximation techniques. Finally, the numerical results are presented to show the effectiveness of the proposed scheme. The numerical results have shown that the proposed scheme can largely save the transmission time as compared to the conventional vertical photography model.Comment: submitted to ieee for possible publication. arXiv admin note: text overlap with arXiv:2006.14438 by other author