arXiv subjects
Publications and source records attributed to Yang Huang.
Let $A$ be a positive semidefinite $m\times m$ block matrix with each block $n$-square, then the following determinantal inequality for partial traces holds \[ (\mathrm{tr} A)^{mn} - \det(\mathrm{tr}_2 A)^n \ge \bigl| \det A - \det(\mathrm{tr}_1 A)^m \bigr|, \] where $\mathrm{tr}_1$ and $\mathrm{tr}_2$ stand for the first and second partial trace, respectively. This result improves a recent result of Lin [14].
A linear map $Φ:\mathbb{M}_n \to \mathbb{M}_k$ is called completely copositive if the resulting matrix $[Φ(A_{j,i})]_{i,j=1}^m$ is positive semidefinite for any integer $m$ and positive semidefinite matrix $[A_{i,j}]_{i,j=1}^m$. In this paper, we present some applications of the completely copositive maps $Φ(X)=(\mathrm{tr} X)I+X$ and $Ψ(X)= (\mathrm{tr} X)I-X$. Some new extensions about traces inequalities of positive semidefinite $3\times 3$ block matrices are included.
Let $ψ: G\to GL(V)$ and $φ:G \to GL (W)$ be representations of finite group $G$. A linear map $T: V\to W$ is called a morphism from $ψ$ to $φ$ if it satisfys $Tψ_g= φ_g T$ for each $g\in G$ and let $\mathrm{Hom}_G (ψ,φ)$ denote the set of all morphisms. In this paper, we make full stufy of the subspace $\mathrm{Hom}_G(ψ, φ)$. As byproducts, we include the proof of the first orthogonality relation and Schur's orthogonality relation.
The hot massive luminous blue variables (LBVs) represent an important evolutionary phase of massive stars. Here, we report the discovery of a new LBV -- LAMOST J0037+4016 in the distant outskirt of the Andromeda galaxy. It is located in the south-western corner (a possible faint spiral arm) of M31 with an unexpectedly large projection distance of $\sim$ 22 kpc from the center. The optical light curve shows a 1.2 mag variation in $V$ band and its outburst and quiescence phases both last over several years. The observed spectra indicate an A-type supergiant at epoch close to the outburst phase and a hot B-type supergiant with weak [Fe II] emission lines at epoch of much dimmer brightness. The near-infrared color-color diagram further shows it follows the distribution of Galactic and M31 LBVs rather than B[e] supergiants. All the existing data strongly show that LAMOST J0037+4016 is an LBV. By spectral energy distribution fitting, we find it has a luminosity ($4.42 \pm 1.64$)$\times 10^5$ $L_{\odot}$ and an initial mass $\sim 30$ $M_{\odot}$, indicating its nature of less luminosity class of LBV.
We initiate a systematic study of convex hypersurface theory and generalize the bypass attachment to arbitrary dimensions. We also introduce a new type of overtwisted object called the overtwisted orange which is middle-dimensional and contractible.
In the letter, we propose an anti-quantum-channel disturbance decoder for quantum key distribution (QKD). The decoder is based on a quarter-wave plate reflector-Michelson (Q-M) interferometer, with which the QKD system can be free of polarization disturbance caused by quantum channel and optical devices in the system. The theoretical analysis indicates that the Q-M interferometer is immune to polarization-induced signal fading and its corresponding operator is Pauli Matrix σ2, which naturally satisfies the anti-disturbance condition. A Q-M interferometer based time-bin phase encoding QKD setup is demonstrated and the experimental results show that the QKD setup works stably with a low quantum bit error rate and an average safe key rate about 7.34 kbps over 50.4 km standard optical fiber for two hours in the lab.
Nitride has been drawing much attention due to its wide range of applications in optoelectronics and remains plenty of room for materials design and discovery. Here, a large set of nitrides have been designed, with their band gap and alignment being studied by first-principles calculations combined with machine learning. Band gap and band offset against wurtzite GaN accurately calculated by the combination of screened hybrid functional of HSE and DFT-PBE were used to train and test machine learning models. After comparison among different techniques of machine learning, when elemental properties are taken as features, support vector regression (SVR) with radial kernel performs best for predicting both band gap and band offset with prediction root mean square error (RMSE) of 0.298 eV and 0.183 eV, respectively. The former is within HSE calculation uncertainty and the latter is small enough to provide reliable predictions. Additionally, when band gap calculated by DFT-PBE was added into the feature space, band gap prediction RMSE decreases to 0.099 eV. Through a feature engineering algorithm, elemental feature space based band gap prediction RMSE further drops by around 0.005 eV and the relative importance of elemental properties for band gap prediction was revealed. Finally, band gap and band offset of all designed nitrides were predicted and two trends were noticed that as the number of cation types increases, band gap tends to narrow down while band offset tends to go up. The predicted results will be a useful guidance for precise investigation on nitride engineering.
With the photometric data from the SDSS survey, the spectroscopic data from the SDSS/SEGUE and the LAMOST surveys, and the astrometric data from the Gaia DR2, we have identified 71 highly-probable member stars of the GD-1 cold stellar stream spread along almost its entire length (i.e. from 126 to 203 degree in Right Ascension). With the accurate spectroscopic (i.e. metallicity and line-of-sight velocity) and astrometric (i.e. proper motions) information, the position-velocity diagrams, i.e. $ϕ_{1}$-$μ_α$, $ϕ_{1}$-$μ_δ$ and $ϕ_{1}$-${v_{\rm gsr}}$, of the GD-1 stream are well mapped. The stream has an average metallicity [Fe/H] $= -1.95 \pm 0.23$. The rich information of member stars of the stream now available allow one not only to model its origin, but also to place strong constraints on the mass distribution and the gravitational potential of the Milky Way.
We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this theory will get spontaneously scalarized into a non-Kerr black hole.
We present 22\,901 OB spectra of 16\,032 stars identified from LAMOST DR5 dataset. A larger sample of OB candidates are firstly selected from the distributions in the spectral line indices space. Then all 22\,901 OB spectra are identified by manual inspection. Based on a sub-sample validation, we find that the completeness of the OB spectra reaches about $89\pm22$\% for the stars with spectral type earlier than B7, while around $57\pm16$\% B8--B9 stars are identified. The smaller completeness for late B stars is lead to the difficulty to discriminate them from A0--A1 type stars. The sub-classes of the OB samples are determined using the software package MKCLASS. With a careful validation using 646 sub-samples, we find that MKCLASS can give fairly reliable sub-types and luminosity class for most of the OB stars. The uncertainty of the spectral sub-type is around 1 sub-type and the uncertainty of the luminosity class is around 1 level. However, about 40\% of the OB stars are failed to be assigned to any class by MKCLASS and a few spectra are significantly misclassified by MKCLASS. This is likely because that the template spectra of MKCLASS are selected from nearby stars in the solar neighborhood, while the OB stars in this work are mostly located in the outer disk and may have lower metallicity. The rotation of the OB stars may also be responsible for the mis-classifications. Moreover, we find that the spectral and luminosity classes of the OB stars located in the Galactic latitude larger than 20$^\circ$ are substantially different with those located in latitude smaller than 20$^\circ$, which may either due to the observational selection effect or hint a different origin of the high Galactic latitude OB stars.
We present a catalog of stellar age and mass estimates for a sample of 640\,986 red giant branch (RGB) stars of the Galactic disk from the LAMOST Galactic Spectroscopic Survey (DR4). The RGB stars are distinguished from the red clump stars utilizing period spacing derived from the spectra with a machine learning method based on kernel principal component analysis (KPCA). Cross-validation suggests our method is capable of distinguishing RC from RGB stars with only 2 per cent contamination rate for stars with signal-to-noise ratio (SNR) higher than 50. The age and mass of these RGB stars are determined from their LAMOST spectra with KPCA method by taking the LAMOST - $Kepler$ giant stars having asteroseismic parameters and the LAMOST-TGAS sub-giant stars based on isochrones as training sets. Examinations suggest that the age and mass estimates of our RGB sample stars with SNR $>$ 30 have a median error of 30 per cent and 10 per cent, respectively. Stellar ages are found to exhibit positive vertical and negative radial gradients across the disk, and the age structure of the disk is strongly flared across the whole disk of $6<R<13$\,kpc. The data set demonstrates good correlations among stellar age, [Fe/H] and [$α$/Fe]. There are two separate sequences in the [Fe/H] -- [$α$/Fe] plane: a high--$α$ sequence with stars older than $\sim$\,8\,Gyr and a low--$α$ sequence composed of stars with ages covering the whole range of possible ages of stars. We also examine relations between age and kinematic parameters derived from the Gaia DR2 parallax and proper motions. Both the median value and dispersion of the orbital eccentricity are found to increase with age. The vertical angular momentum is found to fairly smoothly decrease with age from 2 to 12\,Gyr, with a rate of about $-$50\,kpc\,km\,s$^{-1}$\,Gyr$^{-1}$. A full table of the catalog is public available online.
Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding and cryptography. In this paper, lattice reduction technique is adopted to Gibbs sampler for lattice Gaussian sampling. Firstly, with respect to lattice Gaussian distribution, the convergence rate of systematic scan Gibbs sampling is derived and we show it is characterized by the Hirschfeld-Gebelein-Rényi (HGR) maximal correlation among the multivariate of being sampled. Therefore, lattice reduction is applied to formulate an equivalent lattice Gaussian distribution but with less correlated multivariate, which leads to a better Markov mixing due to the enhanced convergence rate. Then, we extend the proposed lattice-reduction-aided Gibbs sampling to lattice decoding, where the choice of the standard deviation for the sampling is fully investigated. A customized solution that suits for each specific decoding case by Euclidean distance is given, thus resulting in a better trade-off between Markov mixing and sampler decoding. Moreover, based on it, a startup mechanism is also proposed for Gibbs sampler decoding, where decoding complexity can be reduced without performance loss. Simulation results based on large-scale MIMO detection are presented to confirm the performance gain and complexity reduction.
Density functional theory (DFT) based calculations have been conducted to draw a broad picture of pressure induced band structure evolution in various phases of organic and inorganic halide perovskite materials. Under a wide range of pressure applied, distinct band structure behaviors including magnitude change of band gap, direct-indirect/indirect-direct band gap transitions and CBM/VBM shifts, have been observed between organic and inorganic perovskites among different phases. Through atomic and electronic structure calculations, band gap narrowing/widening has been rationalized through crystal orbitals coupling transformations; direct-indirect mutual transitions were explained based on structural symmetry evolution; different VBM/CBM shifts behaviors between organic and inorganic perovskites were analyzed focusing on orientation and polarity of molecules/atoms outside the octahedrals. These results provide a comprehensive guidance for further experimental investigations on pressure engineering of perovskite materials.
Wireless power transfer and backscatter communications have emerged as promising solutions for energizing and communicating with power limited devices. Despite some progress in wirelessly powered backscatter communications, the focus has been concentrated on backscatter and energy harvester. Recently, significant progress has been made on the design of transmit multisine waveform, adaptive to the Channel State Information at the transmitter (CSIT), in point-to-point backscatter system. In this paper, we leverage the work and study the design of transmit multisine waveform in a multiuser backscatter system, made of one transmitter, one reader and multiple tags active simultaneously. We derive an efficient algorithm to optimize the transmit waveform so as to identify the tradeoff between the amount of energy harvested at the tags and the reliability of the communication, measured in terms of Signal-to-Interference-plus-Noise Ratio (SINR) at the reader. Performance with the optimized waveform based on linear and nonlinear energy harvester (EH) models are studied. Numerical results demonstrate the benefits of accounting for the energy harvester nonlinearity, multiuser diversity, frequency diversity and multisine waveform adaptive to the CSIT to enlarge the SINR-energy region.
This study expands the coverage and improves the homogeneity of the distribution of MILES template stars in the parameter space, as well as extends the wavelength coverage of the template spectra to the far red beyond the Ca\,{\sc{ii}} triplet. To achieve this we have carried out a major observational campaign using the OMR long-slit spectrograph mounted on the NAOC 2.16\,m telescope and the YFOSC long-slit spectrograph mounted on the YNAO 2.4\,m telescope. The original sample is based on the MILES library, supplemented by 918 stars selected from PASTEL database. In total, 822 OMR and 1,324 YFOSC spectra, covering respectively the wavelength ranges $λλ$3800--5180 and $λλ$5150--9000, have been collected and reduced. The spectra have a mean resolution FWHM (full-width at half-maximum) of $\sim 3.3$\,Å and are wavelength- and flux-calibrated to an accuracy of $\sim 20$\,km\,s$^{-1}$ and $\sim 5$\,per\,cent, respectively. The spectra are further corrected for systematic errors in the wavelength calibration to an accuracy of $\sim 4$\,km\,s$^{-1}$ by cross-correlating with the theoretical spectra. Almost all the spectra have an average signal to noise ratio (SNR) better than 100 per pixel. Combined with the MILES spectra, there are now 1,731, 1,542, 1,324 and 1,273 stars with spectra covering respectively $λλ$3800--5180, $λλ$3800--7500, $λλ$5150--9000 and $λλ$3800--9000. This paper describes our template star selection, the observation and data reduction, and presents the reduced spectra collected hitherto.
It is known that a massive charged scalar field can trigger a superradiant instability in the background of a Kerr-Newman black hole. In this paper, we present a numerical study of such an instability by using the continued fraction method. It is shown that for given a black hole, the unstable scalar mode with a specific azimuthal index $m$ only occurs in a finite region in the parameter space of the scalar field. The maximum mass of the scalar cloud is exactly the upper bound of the mass of the unstable modes. We show that due to the electromagnetic interaction between the scalar field and the Kerr-Newman black hole, the growth rate of the instability can be $15.7\%$ larger than that of a scalar field in Kerr spacetime of the same rotation parameter. In addition, we find a maximum value of the growth rate $τ^{-1}=1.788\times 10^{-7}M^{-1}$, which is about $4\%$ larger than that in the Kerr case.
We study the photon's motion around a black hole in the presence of a plasma whose density is a function of the radius coordinate by a renewed ray-tracing algorithm and investigate the influence of the plasma on the shadow of the black hole. The presence of plasma affects not only the size but also the shape of black hole shadow. Furthermore, the influence of plasma on trajectories of photons depends on the frequency of photon. For the high-frequency photons, the influence is negligible, on the contrary, the trajectories of low-frequency photons is affected significantly by the plasma. Interestingly, it is also found that the black hole image would take on a multi-ring structure due to the presence of plasma.
We present a detailed determination and analysis of 3D stellar mass distribution of the Galactic disk for mono-age populations using a sample of 0.93 million main-sequence turn-off and subgiant stars from the LAMOST Galactic Surveys. Our results show (1) all stellar populations younger than 10\,Gyr exhibit strong disk flaring, which is accompanied with a dumpy vertical density profile that is best described by a $sech^n$ function with index depending on both radius and age; (2) Asymmetries and wave-like oscillations are presented in both the radial and vertical direction, with strength varying with stellar populations; (3) As a contribution by the Local spiral arm, the mid-plane stellar mass density at solar radius but 400--800\,pc (3--6$^\circ$) away from the Sun in the azimuthal direction has a value of $0.0594\pm0.0008$\,$M_\odot$/pc$^3$, which is 0.0164\,$M_\odot$/pc$^3$ higher than previous estimates at the solar neighborhood. The result causes doubts on the current estimate of local dark matter density; (4) The radial distribution of surface mass density yields a disk scale length evolving from $\sim$4\,kpc for the young to $\sim$2\,kpc for the old populations. The overall population exhibits a disk scale length of $2.48\pm0.05$\,kpc, and a total stellar mass of $3.6(\pm0.1)\times10^{10}$\,$M_\odot$ assuming $R_{\odot}=8.0$\,kpc, and the value becomes $4.1(\pm0.1)\times10^{10}$\,$M_\odot$ if $R_{\odot}=8.3$\,kpc; (5) The disk has a peak star formation rate ({\rm SFR}) changing from 6--8\,Gyr at the inner to 4--6\,Gyr ago at the outer part, indicating an inside-out assemblage history. The 0--1\,Gyr population yields a recent disk total {\rm SFR} of $1.96\pm0.12$\,$M_\odot$/yr.