Enhanced Photocatalytic Properties of PET Filaments Coated with Ag-N Co-Doped TiO2 Nanoparticles Sensitized with Disperse Blue Dyes

In this study, the effects of disperse blue dye-sensitization on the photocatalytic properties of the Ag-N co-doped TiO2 nanoparticles loaded on polyethylene terephthalate (PET) filaments are investigated under visible light irradiation. The microstructure and photocatalytic properties of the as-synthesized TiO2 nanocomposites, as well as the as-prepared PET filaments, are systematically characterized. The photocatalytic performance of the PET filaments coated with the Ag-N co-doped TiO2 nanoparticles sensitized with disperse blue dyes is evaluated via its capacity of photo-degrading methyl orange (MO) dyes under visible light irradiation. It is found that the holes are the predominant reactive radical species and the hydroxyl and superoxide radicals play a subordinate role in the photocatalytic reaction process. The reaction rate constant of the photocatalytic composite filaments is nearly 4.0 times higher than that of the PET filaments loaded solely with TiO2 nanoparticles. The resultant photocatalytic composite filaments are evident to be capable of repeatedly photo-degrading MO dyes without losing its photocatalytic activity significantly

Microlensing of Sub-parsec Massive Binary Black Holes in Lensed QSOs: Light Curves and Size-Wavelength Relation

Sub-parsec binary massive black holes (BBHs) are long anticipated to exist in many QSOs but remain observationally elusive. In this paper, we propose a novel method to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSO hosts a sub-parsec BBH in its center, it is expected that the BBH is surrounded by a circum-binary disk, each component of the BBH is surrounded by a small accretion disk, and a gap is opened by the secondary component in between the circum-binary disk and the two small disks. Assuming such a BBH structure, we generate mock microlensing light curves for some QSO systems that host BBHs with typical physical parameters. We show that microlensing light curves of a BBH QSO system at the infrared-optical-UV bands can be significantly different from those of corresponding QSO system with a single massive black hole (MBH), mainly because of the existence of the gap and the rotation of the BBH (and its associated small disks) around the center of mass. We estimate the half-light radii of the emission region at different wavelengths from mock light curves and find that the obtained half-light radius vs. wavelength relations of BBH QSO systems can be much flatter than those of single MBH QSO systems at a wavelength range determined by the BBH parameters, such as the total mass, mass ratio, separation, accretion rates, etc. The difference is primarily due to the existence of the gap. Such unique features on the light curves and half-light radius-wavelength relations of BBH QSO systems can be used to select and probe sub-parsec BBHs in a large number of lensed QSOs to be discovered by current and future surveys, including the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS), the Large Synoptic Survey telescope (LSST) and Euclid.Comment: 18 pages, 17 figures, accepted for publication in the Astrophysical Journa

Ergodicity for the GI/G/1GI/G/1-type Markov Chain

Ergodicity is a fundamental issue for a stochastic process. In this paper, we refine results on ergodicity for a general type of Markov chain to a specific type or the $GI/G/1$-type Markov chain, which has many interesting and important applications in various areas. It is of interest to obtain conditions in terms of system parameters or the given information about the process, under which the chain has various ergodic properties. Specifically, we provide necessary and sufficient conditions for geometric, strong and polynomial ergodicity, respectively.Comment: 16 page