Connection between closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation

It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation. Some discussion was made about the factorization of a 1D Schr\"{o}dinger equation.Comment: 14 pages, no figure

Characterizing Some Gaia Alerts with LAMOST and SDSS

Gaia is regularly producing Alerts on objects where photometric variability has been detected. The physical nature of these objects has often to be determined with the complementary observations from ground-based facilities. We have compared the list of Gaia Alerts (until 20181101) with archival LAMOST and SDSS spectroscopic data. The date of the ground-based observation rarely corresponds to the date of the Alert, but this allows at least the identification of the source if it is persistent, or the host galaxy if the object was only transient like a supernova. A list of Gaia Nuclear Transients from Kostrzewa-Rutkowska et al. (2018) has been included in this search also. We found 26 Gaia Alerts with spectra in LAMOST+SDSS labelled as stars (12 with multi-epoch spectra). A majority of them are CVs. Similarly 206 Gaia Alerts have associated spectra labelled as galaxies (49 with multi-epoch spectra). Those spectra were generally obtained on a date different from the Alert date, are mostly emission-line galaxies, leading to the suspicion that most of the Alerts were due to a SN. As for the GNT list, we found 55 associated spectra labelled as galaxies (13 with multi-epoch spectra). In two galaxies, Gaia17aal and GNTJ170213+2543, was the date of the spectroscopic observation close enough to the Alert date: we find a trace of the SN itself in their LAMOST spectrum, both classified here as a type Ia SN. The GNT sample has a higher proportion of AGNs, suggesting that some of the detected variations are also due to the AGN itself. Similar for Quasars, we found 30 Gaia Alerts but 68 GNT cases have single epoch quasar spectra, while 12 plus 23 have multi-epoch spectra. For ten out of these 35, their multi-epoch spectra show appearance or disappearance of the broad Balmer lines and also variations in the continuum, qualifying them as "Changing Look Quasars".Comment: Accepted for publication in APSS, 14 pages, 8 figures, 2 table

Selective Combining for Hybrid Cooperative Networks

In this study, we consider the selective combining in hybrid cooperative networks (SCHCNs scheme) with one source node, one destination node and $N$ relay nodes. In the SCHCN scheme, each relay first adaptively chooses between amplify-and-forward protocol and decode-and-forward protocol on a per frame basis by examining the error-detecting code result, and $N_c$ ($1\leq N_c \leq N$) relays will be selected to forward their received signals to the destination. We first develop a signal-to-noise ratio (SNR) threshold-based frame error rate (FER) approximation model. Then, the theoretical FER expressions for the SCHCN scheme are derived by utilizing the proposed SNR threshold-based FER approximation model. The analytical FER expressions are validated through simulation results.Comment: 27 pages, 8 figures, IET Communications, 201

Supramolecular control over self-assembly and double thermoresponsive behavior of an amphiphilic block copolymer

A poly(ethylene glycol)-b-poly[N, N-dimethylacrylamide-ran-2-acrylamidoethyl nonanoate] (PEG-b-P(DMA-AAEN)) block copolymer has been demonstrated to show double thermoresponsive behavior in aqueous solution in the presence of hydroxypropylated cyclodextrin (HPCD). The polymer itself is insoluble in water due to the presence of hydrophobic alkyl chain, however, with the presence of HPCD, fully dissolution of the polymer could be obtained indicating the formation of host-guest interaction between HPCD and the alkyl chain. The clear solution of HPCD/polymer complex showing a first thermoresponsiveness during heating and led to the formation of small micelles stabilized by PEG chains and DMA segments. Upon further heating of the aqueous solution, the small micelles aggregated and formed multimicellar aggregates. The reported double thermoresponsive behavior may provide a new strategy of designing smart polymeric systems, which can find broad applications in the fabrication of smart materials