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It has been more than 30 years since the enigmatic 21 {\mu}m emission feature was first discovered in protoplanetary nebulae (PPNs). Although dozens of different dust carrier candidates have been proposed, there is as yet no widely accepted one. We present the results of molecular observations toward 21{\mu}m objects using the 10m Submillimeter Telescope of Arizona Radio Observatory at the 1.3 mm band and the 13.7 m telescope of Purple Mountain Observatory at the 3mm band, aiming to investigate whether the gas-phase environments of these unusual sources have some peculiarities compared to normal PPNs. We detect 31 emission lines belonging to seven different molecular species, most of which are the first detection in 21 {\mu}m PPNs. The observations provide clues on the identification of the 21 {\mu}m feature. We report a correlation study between the fractional abundance of gas-phase molecules and the strengths of the 21 {\mu}m emission. Our study shows that given the small sample size, the 21 {\mu}m feature has weak or no correlations with the gas-phase molecules. Future radio observations of high spatial and spectral resolution toward a large sample are desirable to elucidate the 21 {\mu}m emission phenomena., Comment: 40 pages, 10 figures, 11 tables, accepted for publication in The Astronomical Journal

We present a study of molecular outflows using six molecular lines (including 12CO/13CO/C18O/HCO+(J = 1-0) and SiO/CS(J = 2-1)) toward nine nearby high-mass star-forming regions with accurate known distances. This work is based on the high-sensitivity observations obtained with the 14-m millimeter telescope of Purple Mountain Observatory Delingha (PMODLH) observatory. The detection rate of outflows (including 12CO, 13CO, HCO+, and CS) is 100\%. However, the emission of SiO was not detected for all sources. The full line widths ($\Delta V$) at 3$\sigma$ above the baseline of these molecular lines have the relationship $\Delta V_{\rm ^{12}CO} > \Delta V_{\rm HCO^{+}} > \Delta V_{\rm CS} \approx \Delta V_{\rm ^{13}CO} > \Delta V_{\rm ^{18}CO}$. 12CO and HCO+ can be used to trace relatively high-velocity outflows, while 13CO and CS can be employed to trace relatively low-velocity outflows. The dynamical timescales of the 13CO and CS outflows are longer than those of the 12CO and HCO+ outflows. The mechanical luminosities, masses, mass-loss rates and forces of all outflows (including 12CO, 13CO, HCO+, and CS) are correlated with the bolometric luminosities of their central IRAS sources., Comment: 35 pages, 17 figures, 9 tables, accepted for publication in ApJS

We performed a multi-wavelength observation toward LkHa 101 embedded cluster and its adjacent 85arcmin*60arcmin region. The LkHa 101 embedded cluster is the first and only one significant cluster in California molecular cloud (CMC). These observations have revealed that the LkHa 101 embedded cluster is just located at the projected intersectional region of two filaments. One filament is the highest-density section of the CMC, the other is a new identified filament with a low-density gas emission. Toward the projected intersection, we find the bridging features connecting the two filaments in velocity, and identify a V-shape gas structure. These agree with the scenario that the two filaments are colliding with each other. Using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we measured that the RRL velocity of the LkHa 101 H II region is 0.5 km/s, which is related to the velocity component of the CMC filament. Moreover, there are some YSOs distributed outside the intersectional region. We suggest that the cloud-cloud collision together with the fragmentation of the main filament may play an important role in the YSOs formation of the cluster., Comment: 6 pages, 5 figures, accepted for publication in ApJL

The electronic density of state and optical properties of the SI methane hydrates with three different configurations are calculated by first-principle, including (abbreviated as cI, similarly hereinafter), each cage is fully filled with only one methane molecule; (cII), only one of the small cage lacks its unique methane molecule; (cIII), only one large cage lacks its unique methane molecule. The results show that the hydrate is most stable in the cI due to its perfect structure, the cII is less stable, whereas the cIII is least stable owing to its larger structural distortion after the loss of methane. On the contrary, loss of a methane from cII causes negligible deformation. The electronic density of states and the energy band gap of the cII is almost the same with those of cI, differing obviously with those of cIII. Methane hydrate is only responsive to light in the ultraviolet region, revealing their similar properties, regardless of their structural discrepancies, or/and the different ratios of water and methane molecules, 46/8=5.75 versus 46/7=6.57. Our calculations demonstrate that the lack of one methane in the cII causes negligible influence to the lattice structure and therefore to the electronic and optical properties in comparison with the cI, whereas the lack of one methane in the cIII can cause detectable changes. These results might provide valuable reference to the industrial exploration.

Let $\mathbb{N}$ denote the set of all nonnegative integers and $A$ be a subset of $\mathbb{N}$. Let $h\geq2$ and let $r_h(A,n)=\sharp \{ (a_1,\ldots,a_h)\in A^{h}: a_1+\cdots+a_h=n\}.$ The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently large integers $n$. An asymptotic basis $A$ of order $h$ is minimal if no proper subset of $A$ is an asymptotic basis of order $h$. Recently, Chen and Tang resoved a problem of Nathanson on minimal asymptotic bases of order $h$. In this paper, we generalized this result to $g$-adic representations.