On the Wassertein distance for a martingale central limit theorem

We prove an upper bound on the Wassertein distance between normalized martingales and the standard normal random variable, which extends a result of R\"ollin [Statist. Probabil. Lett. 138 (2018) 171-176]. The proof is based on a method of Bolthausen [Ann. Probab. 10 (1982) 672-688]

A Hubble Space Telescope Imaging Study of Four FeLoBAL Quasar Host Galaxies

We study the host galaxies of four Iron Low-Ionization Broad Absorption-line Quasars (FeLoBALs) using Hubble Space Telescope imaging data, investigating the possibility that they represent a transition between an obscured AGN and an ordinary optical quasar. In this scenario, the FeLoBALs represent the early stage of merger-triggered accretion, in which case their host galaxies are expected to show signs of an ongoing or recent merger. Using PSF subtraction techniques, we decompose the images into host galaxy and AGN components at rest-frame ultraviolet and optical wavelengths. The ultraviolet is sensitive to young stars, while the optical probes stellar mass. In the ultraviolet we image at the BAL absorption trough wavelengths so as to decrease the contrast between the quasar and host galaxy emission. We securely detect an extended source for two of the four FeLoBALs in the rest-frame optical; a third host galaxy is marginally detected. In the rest-frame UV we detect no host emission; this constrains the level of unobscured star formation. Thus, the host galaxies have observed properties that are consistent with those of non-BAL quasars with the same nuclear luminosity, i.e., quiescent or moderately starforming elliptical galaxies. However, we cannot exclude starbursting hosts that have the stellar UV emission obscured by modest amounts of dust reddening. Thus, our findings also allow the merger-induced young quasar scenario. For three objects, we identify possible close companion galaxies that may be gravitationally interacting with the quasar hosts.Comment: 33 pages, 15 figures. Accepted for publication in MNRA

A Sample of Quasars with Strong Nitrogen Emission Lines from the Sloan Digital Sky Survey

We report on 293 quasars with strong NIV] lambda 1486 or NIII] lambda 1750 emission lines (rest-frame equivalent width > 3 \AA) at 1.7 < z < 4.0 selected from the Sloan Digital Sky Survey (SDSS) Fifth Data Release. These nitrogen-rich (N-rich) objects comprise ~1.1% of the SDSS quasars. The comparison between the N-rich quasars and other quasars shows that the two quasar subsets share many common properties. We also confirm previous results that N-rich quasars have much stronger Lya and NV lambda 1240 emission lines. Strong nitrogen emission in all ionization states indicates high overall nitrogen abundances in these objects. We find evidence that the nitrogen abundance is closely related to quasar radio properties. The radio-loud fraction in the NIII]-rich quasars is 26% and in the NIV]-rich quasars is 69%, significantly higher than ~8% measured in other quasars with similar redshift and luminosity. Therefore, the high nitrogen abundance in N-rich quasars could be an indicator of a special quasar evolution stage, in which the radio activity is also strong.Comment: 8 pages, 4 figures; accepted by ApJ (ApJ June 10, 2008, v680 n1 issue

Metamaterial-based polarization control plate for producing incoherent laser irradiation

We present a metamaterial-based random polarization control plate to produce incoherent laser irradiation by exploiting the ability of metamaterial in local polarization manipulation of beam upon transmission via tuning its local geometry. As a proof-of-principle, we exemplify this idea numerically in a simple optical system using a typical L-shaped plasmonic metamaterial with locally varying geometry, from which the desired polarization distribution can be obtained. The calculating results illustrate that this scheme can effectively suppress the speckle contrast and increase irradiation uniformity, which has potential to satisfy the increasing requirements for incoherent laser irradiation.Comment: 5 pages, 6 figure

Hubble Advanced Camera for Surveys Observations of the z=6.42 Quasar SDSS 1148+5251: A Leak in the Gunn-Peterson Trough

The Hubble Advanced Camera for Surveys has been used to obtain a narrow-band image of the weak emission peak seen at lambda=7205 A in the Gunn-Peterson Ly beta absorption trough of the highest redshift quasar, SDSS J1148+5251. The emission looks perfectly point-like; there is no evidence for the intervening galaxy that we previously suggested might be contaminating the quasar spectrum. We derive a more accurate astrometric position for the quasar in the two filters and see no indication of gravitational lensing. We conclude that the light in the Ly beta trough is leaking through two unusually transparent, overlapping windows in the IGM absorption, one in the Ly beta forest at z ~ 6 and one in the Ly alpha forest at z ~ 5. If there are significant optical depth variations on velocity scales small compared with our spectral resolution (~150 km/s), the Ly alpha trough becomes more transparent for a given Ly beta optical depth. Such variations can only strengthen our conclusion that the fraction of neutral hydrogen in the IGM increases dramatically at z>6. We argue that the transmission in the Ly beta trough is not only a more sensitive measure of the neutral fraction than is Ly alpha, it also provides a less biased estimator of the neutral hydrogen fraction than does the Ly alpha transmission.Comment: Submitted to the Astronomical Journa