Characterizations of semiperfect and perfect rings

We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective coves are adapted from Azumaya's generalized projective covers

An analytic relation for the thickness of accretion flows

We take the vertical distribution of the radial and azimuthal velocity into account in spherical coordinates, and find that the analytic relation c_{s0}/(v_K \Theta) = [(\gamma -1)/(2\gamma)]^{1/2} is valid for both geometrically thin and thick accretion flows, where c_{s0} is the sound speed on the equatorial plane, v_K is the Keplerian velocity, \Theta is the half-opening angle of the flow, and \gamma is the adiabatic index.Comment: 4 pages, 2 figures, accepted by Science in China Series

Spectroscopy of broad absorption line quasars at 3≲z≲53\lesssim z \lesssim 5 -- I: evidence for quasar winds shaping broad/narrow emission line regions

We present an observational study of 22 broad absorption line quasars (BAL QSOs) at $3\lesssim z \lesssim5$ based on optical/near-IR spectroscopy, aiming to investigate quasar winds and their effects. The near-IR spectroscopy covers the \hb\ and/or \mgii\ broad emission lines (BELs) for these quasars, allowing us to estimate their central black hole (BH) masses in a robust way. We found that our BAL QSOs on average do not have a higher Eddington ratio than that from non-BAL QSOs matched in redshift and/or luminosity. In a subset consisting of seven strong BAL QSOs possessing sub-relativistic BAL outflows, we see the prevalence of large \civ-BEL blueshift ($\sim$3100 km s$^{-1}$) and weak \oiii\ emission (particularly the narrow \oiii$\lambda$5007 component), indicative of nuclear outflows affecting the narrow emission-line (NEL) regions. In another subset consisting of thirteen BAL QSOs having simultaneous observations of \mgii\ and \hb, we found a strong correlation between 3000~\AA\ and 5000~\AA\ monochromatic luminosity, consistent with that from non-BAL QSOs matched in redshift and luminosity; however, there is no correlation between \mgii\ and \hb\ in FWHM, likely due to nuclear outflows influencing the BEL regions. Our spectroscopic investigations offer strong evidence that the presence of nuclear outflows plays an important role in shaping the BEL/NEL regions of these quasars and possibly, regulating the growth of central supermassive black holes (SMBHs). We propose that BEL blueshift and BAL could be different manifestations of the same outflow system viewed at different sightlines and/or phases.Comment: 13 pages, 10 figures. Accepted for publication in Ap

Trojan Horse nanotheranostics with dual transformability and multifunctionality for highly effective cancer treatment.

Nanotheranostics with integrated diagnostic and therapeutic functions show exciting potentials towards precision nanomedicine. However, targeted delivery of nanotheranostics is hindered by several biological barriers. Here, we report the development of a dual size/charge- transformable, Trojan-Horse nanoparticle (pPhD NP) for delivery of ultra-small, full active pharmaceutical ingredients (API) nanotheranostics with integrated dual-modal imaging and trimodal therapeutic functions. pPhD NPs exhibit ideal size and charge for drug transportation. In tumour microenvironment, pPhD NPs responsively transform to full API nanotheranostics with ultra-small size and higher surface charge, which dramatically facilitate the tumour penetration and cell internalisation. pPhD NPs enable visualisation of biodistribution by near-infrared fluorescence imaging, tumour accumulation and therapeutic effect by magnetic resonance imaging. Moreover, the synergistic photothermal-, photodynamic- and chemo-therapies achieve a 100% complete cure rate on both subcutaneous and orthotopic oral cancer models. This nanoplatform with powerful delivery efficiency and versatile theranostic functions shows enormous potentials to improve cancer treatment

An ultra-luminous quasar with a twelve-billion-solar-mass black hole at redshift 6.30

So far, roughly 40 quasars with redshifts greater than z=6 have been discovered. Each quasar contains a black hole with a mass of about one billion solar masses ($10^9 M_\odot$). The existence of such black holes when the Universe was less than 1 billion years old presents substantial challenges to theories of the formation and growth of black holes and the coevolution of black holes and galaxies. Here we report the discovery of an ultra-luminous quasar, SDSS J010013.02+280225.8, at redshift z=6.30. It has an optical and near-infrared luminosity a few times greater than those of previously known z>6 quasars. On the basis of the deep absorption trough on the blue side of the Ly $\alpha$ emission line in the spectrum, we estimate the proper size of the ionized proximity zone associated with the quasar to be 26 million light years, larger than found with other z>6.1 quasars with lower luminosities. We estimate (on the basis of a near-infrared spectrum) that the black hole has a mass of $\sim 1.2 \times 10^{10} M_\odot$, which is consistent with the $1.3 \times 10^{10} M_\odot$ derived by assuming an Eddington-limited accretion rate.Comment: 24 pages, 4 figures plus 4 extended data figures, published in Nature on 26 February 201

Negaton and Positon solutions of the soliton equation with self-consistent sources

The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for $N$-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund transformation between two KdV equations with different degrees of sources and enable us to construct more general solutions with $N$ arbitrary $t$-dependent functions. By taking the special $t$-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of KdVES. Some properties of these solutions are discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge

An ultra-luminous quasar at z=5.363 with a ten billion solar mass black hole and a Metal-Rich DLA at z~5

We report the discovery of an ultra-luminous quasar J030642.51+185315.8 (hereafter J0306+1853) at redshift 5.363, which hosts a super-massive black hole (SMBH) with $M_{BH} = (1.07 \pm 0.27) \times10^{10}~M_\odot$. With an absolute magnitude $M_{1450}=-28.92$ and bolometric luminosity $L_{bol}\sim3.4\times10^{14} L_{\odot}$, J0306+1853 is one of the most luminous objects in the early Universe. It is not likely to be a beamed source based on its small flux variability, low radio loudness and normal broad emission lines. In addition, a $z=4.986$ Damped Ly$\alpha$ system (DLA) with $\rm [M/H]=-1.3\pm0.1$, among the most metal rich DLAs at $z \gtrsim 5$, is detected in the absorption spectrum of this quasar. This ultra-luminous quasar puts strong constraint on the bright-end of quasar luminosity function and massive-end of black hole mass function. It will provide a unique laboratory to the study of BH growth and the co-evolution between BH and host galaxy with multi-wavelength follow-up observations. The future high resolution spectra will give more insights to the DLA and other absorption systems along the line-of-sight of J0306+1853.Comment: 5 pages, 3 figures, accepted for publication in ApJ