Rota-Baxter operators on Witt and Virasoro algebras

The homogeneous Rota-Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang-Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.Comment: 28 page

CSD: Discriminance with Conic Section for Improving Reverse k Nearest Neighbors Queries

The reverse $k$ nearest neighbor (R$k$NN) query finds all points that have the query point as one of their $k$ nearest neighbors ($k$NN), where the $k$NN query finds the $k$ closest points to its query point. Based on the characteristics of conic section, we propose a discriminance, named CSD (Conic Section Discriminance), to determine points whether belong to the R$k$NN set without issuing any queries with non-constant computational complexity. By using CSD, we also implement an efficient R$k$NN algorithm CSD-R$k$NN with a computational complexity at $O(k^{1.5}\cdot log\,k)$. The comparative experiments are conducted between CSD-R$k$NN and other two state-of-the-art RkNN algorithms, SLICE and VR-R$k$NN. The experimental results indicate that the efficiency of CSD-R$k$NN is significantly higher than its competitors

Quantum Hall Effects in a Non-Abelian Honeycomb Lattice

We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall effects in honeycomb optical lattice when the internal valley degrees of freedom enlarge.Comment: 7 pages, 6 figure

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