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We generalize the determinant representation of the KP $\tau$ functions to the case of the 2D Toda $\tau$ functions. The generating functions for the weighted Hurwitz numbers are a parametric family of 2D Toda $\tau$ functions; for which we give a determinant representation of weighted Hurwitz numbers. Then we can get a finite-dimensional equation system for the weighted Hurwitz numbers $H^d_{G}(\sigma,\omega)$ with the same dimension $|\sigma|=|\omega|=n$. Using this equation system, we calculated the value of the weighted Hurwitz numbers with dimension $0,\,1,\,2$ and give a recursion formula to calculating the higher dimensional weighted Hurwitz numbers. For any given weighted generating function $G(z)$, the weighted Hurwitz number degenerates into the Hurwitz numbers when $d=0$. We get a matrix representation for the Hurwitz numbers. The generating functions of weighted paths in the Cayley graph of the symmetric group are a parametric family of 2D Toda $\tau$ functions; for which we obtain a determinant representation of weighted paths in the Cayley graph.

Recent observations have revealed a population of $\alpha$-element abundances enhanced giant stars with unexpected high masses ($\gtrsim$1 $M_\odot$) from asteroseismic analysis and spectroscopy. Assuming single-star evolution, their masses imply young ages ($\tau<6$Gyr) incompatible with the canonical Galactic chemical evolution scenario. Here we study the chemistry and kinematics of a large sample of such $\alpha$-rich, high-mass red giant branch (RGB) stars drawn from the LAMOST spectroscopic surveys. Using LAMOST and Gaia, we found these stars share the same kinematics as the canonical high-$\alpha$ old stellar population in the Galactic thick disk. The stellar abundances show that these high-$\alpha$ massive stars have $\alpha$- and iron-peak element abundances similar to those of the high-$\alpha$ old thick disk stars. However, a portion of them exhibit higher [(N+C)/Fe] and [Ba/Fe] ratios, which implies they have gained C- and Ba-rich materials from extra sources, presumably asymptotic giant branch (AGB) companions. The results support the previous suggestion that these RGB stars are products of binary evolution. Their high masses thus mimic "young" single stars, yet in fact they belong to an intrinsic old stellar population. To fully explain the stellar abundance patterns of our sample stars, a variety of binary evolution channels, such as, main-sequence (MS) + RGB, MS + AGB, RGB + RGB and RGB + AGB, are required, pointing to diverse formation mechanisms of these seemly rejuvenated cannibals. With this larger sample, our results confirm earlier findings that most, if not all, $\alpha$-rich stars in the Galactic disk seem to be old., Comment: 17 pages, 14 figures, 2 tables, accepted for publication in ApJ

The Kepler telescope has discovered over 4,000 planets (candidates) by searching ? 200,000 stars over a wide range of distance (order of kpc) in our Galaxy. Characterizing the kinematic properties (e.g., Galactic component membership and kinematic age) of these Kepler targets (including the planet (candidate) hosts) is the first step towards studying Kepler planets in the Galactic context, which will reveal fresh insights into planet formation and evolution. In this paper, the second part of the Planets Across the Space and Time (PAST) series, by combining the data from LAMOST and Gaia and then applying the revised kinematic methods from PAST I, we present a catalog of kinematic properties(i.e., Galactic positions, velocities, and the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 35,835 Kepler stars. Further analyses of the LAMOST-Gaia-Kepler catalog demonstrate that our derived kinematic age reveals the expected stellar activity-age trend. Furthermore, we find that the fraction of thin(thick) disk stars increases (decreases) with the transiting planet multiplicity (Np = 0, 1, 2 and 3+) and the kinematic age decreases with Np, which could be a consequence of the dynamical evolution of planetary architecture with age. The LAMOST-Gaia-Kepler catalog will be useful for future studies on the correlations between the exoplanet distributions and the stellar Galactic environments as well as ages., Comment: Accepted for publication in Astronomical Journal, 19 pages, 9 figures, 5 tables. The full data of the LAMOST-Gaia-Kepler kinematic catalog (Table 3) will be published with the journal. If you need to use the data, please contact us via the email (jwxie@nju.edu.cn, dg1826003@smail.nju.edu.cn)

Over 4,000 exoplanets have been identified and thousands of candidates are to be confirmed. The relations between the characteristics of these planetary systems and the kinematics, Galactic components, and ages of their host stars have yet to be well explored. Aiming to addressing these questions, we conduct a research project, dubbed as PAST (Planets Across Space and Time). To do this, one of the key steps is to accurately characterize the planet host stars. In this paper, the Paper I of the PAST series, we revisit the kinematic method for classification of Galactic components and extend the applicable range of velocity ellipsoid from about 100 pc to 1, 500 pc from the sun in order to cover most known planet hosts. Furthermore, we revisit the Age-Velocity dispersion Relation (AVR), which allows us to derive kinematic age with a typical uncertainty of 10-20% for an ensemble of stars. Applying the above revised methods, we present a catalog of kinematic properties (i.e. Galactic positions, velocities, the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 2,174 host stars of 2,872 planets by combining data from Gaia, LAMOST, APOGEE, RAVE, and the NASA exoplanet archive. The revised kinematic method and AVR as well as the stellar catalog of kinematic properties and ages lay foundation for future studies on exoplanets from two dimensions of space and time in the Galactic context., Comment: 26 pages, 20 figure, 10 tables, Accepted for publication in ApJ. The full data of the planet kinematic catalog (Table 10) will be published with the journal. If you need to use the data, please contact us via the email (jwxie@nju.edu.cn, dg1826003@smail.nju.edu.cn)

We present a data-driven method to estimate absolute magnitudes for O- and B-type stars from the LAMOST spectra, which we combine with {\it Gaia} parallaxes to infer distance and binarity. The method applies a neural network model trained on stars with precise {\it Gaia} parallax to the spectra and predicts $K_{\rm s}$-band absolute magnitudes $M_{Ks}$ with a precision of 0.25\,mag, which corresponds to a precision of 12\% in spectroscopic distance. For distant stars (e.g. $>5$\,kpc), the inclusion of constraints from spectroscopic $M_{Ks}$ significantly improves the distance estimates compared to inferences from {\it Gaia} parallax alone. Our method accommodates for emission line stars by first identifying them via PCA reconstructions and then treating them separately for the $M_{Ks}$ estimation. We also take into account unresolved binary/multiple stars, which we identify through deviations in the spectroscopic $M_{Ks}$ from the geometric $M_{Ks}$ inferred from {\it Gaia} parallax. This method of binary identification is particularly efficient for unresolved binaries with near equal-mass components and thus provides an useful supplementary way to identify unresolved binary or multiple-star systems. We present a catalog of spectroscopic $M_{Ks}$, extinction, distance, flags for emission lines, and binary classification for 16,002 OB stars from LAMOST DR5. As an illustration of the method, we determine the $M_{Ks}$ and distance to the enigmatic LB-1 system, where Liu et al. (2019) had argued for the presence of a black hole and incorrect parallax measurement, and we do not find evidence for errorneous {\it Gaia} parallax., Comment: 21 pages, 16 figures, submitted to ApJ Supplement. Comments are welcome

Standard stellar evolution model predicts a severe depletion of lithium (Li) abundance during the first dredge up process (FDU). Yet a small fraction of giant stars are still found to preserve a considerable amount of Li in their atmospheres after the FDU. Those giants are usually identified as Li-rich by a widely used criterion, A(Li) > 1.5 dex. A large number of works dedicated to searching for investigating this minority of the giant family, and the amount of Li-rich giants, has been largely expanded on, especially in the era of big data. In this paper, we present a catalog of Li-rich giants found from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey with Li abundances derived from a template-matching method developed for LAMOST low-resolution spectra.

The perturbation mechanism of the Galactic disk has puzzled us for a long time. The imprints from perturbations provide important diagnostics on the disk formation and evolution. Here we try to constrain when the vertical perturbation took place in the disk by tracking the phase mixing history. Firstly, we clearly depict the spiral structures of radial ($v_R$) and azimuthal ($v_{\phi}$) velocities in the phase space of the vertical position and velocity ($z$-$v_z$) with 723,871 LAMOST-Gaia combined stars. Then, we investigate the variation of the spirals with stellar age ($\tau$) by dividing the sample into seven stellar age bins. Finally, we find that the spirals explicitly exist in all the bins, even in the bin of $\tau<0.5$\,Gyr, except for the bin of $\tau>6.0$\,Gyr. This constrains the vertical perturbation probably starting no later than 0.5\,Gyr ago. But we can not rule out whether the young stars ($\tau<0.5$\,Gyr) inherit the oscillations from the perturbed ISM where they born from. This study provides some important observational evidences to understand the disk perturbation mechanisms, even the formation and evolution of our Galaxy., Comment: 7 pages, 4 figures, accepted for publication in ApJL

In this paper, we report the discovery of a new late-B type unbound hyper-runaway star (LAMOST-HVS4) from the LAMOST spectroscopic surveys. According to its atmospheric parameters, it is either a B-type main sequence (MS) star or a blue horizontal branch (BHB) star. Its Galactocentric distance and velocity are 30.3 +/- 1.6 kpc and 586 +/- 7 km/s if it is an MS star, and they are 13.2 +/- 3.7 kpc and 590 +/- 7 km/s if a BHB star. We track its trajectories back, and find that the trajectories intersect with the Galactic disk and the Galactic center lies outside of the intersection region at the 3 sigma confidence level. We investigate a number of mechanisms that could be responsible for the ejection of the star, and find that it is probably ejected from the Galactic disk by supernova explosion or multiple-body interactions in dense young stellar clusters., Comment: 7 pages, 3 figures, accepted by AJ

We present extensive spectroscopic observations of supernova remnant (SNR) S147 collected with the Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST). The spectra were carefully sky-subtracted taking into account the complex filamentary structure of S147. We have utilized all available LAMOST spectra toward S147, including sky and stellar spectra. By measuring the prominent optical emission lines including H{\alpha}, [NII]{\lambda}6584, and [SII]{\lambda}{\lambda}6717,6731, we present maps of radial velocity and line intensity ratio covering the whole nebula of S147 with unprecedented detail. The maps spatially correlated well with the complex filamentary structure of S147. For the central 2 deg of S147, the radial velocity varies from -100 to 100 km/s and peaks between ~ 0 and 10 km/s. The intensity ratios of H{\alpha}/[SII]{\lambda}{\lambda}6717,6731, [SII]{\lambda}6717/{\lambda}6731 and H{\alpha}/[NII]{\lambda}6584 peak at about 0.77, 1.35 and 1.48, respectively, with a scatter of 0.17, 0.19 and 0.37, respectively. The intensity ratios are consistent with the literature values. However, the range of variations of line intensity ratios estimated here and representative of the whole nebula, are larger than previously estimated., Comment: 19 pages, 13 figures, 3 tables, accepted for publication in RAA

In this work, we present a catalog of 2651 carbon stars from the fourth Data Release (DR4) of the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST). Using an efficient machine-learning algorithm, we find out these stars from more than seven million spectra. As a by-product, 17 carbon-enhanced metal-poor (CEMP) turnoff star candidates are also reported in this paper, and they are preliminarily identified by their atmospheric parameters. Except for 176 stars that could not be given spectral types, we classify the other 2475 carbon stars into five subtypes including 864 C-H, 226 C-R, 400 C-J, 266 C-N, and 719 barium stars based on a series of spectral features. Furthermore, we divide the C-J stars into three subtypes of CJ( H), C-J(R), C-J(N), and about 90% of them are cool N-type stars as expected from previous literature. Beside spectroscopic classification, we also match these carbon stars to multiple broadband photometries. Using ultraviolet photometry data, we find that 25 carbon stars have FUV detections and they are likely to be in binary systems with compact white dwarf companions., Comment: 72 pages, 23 figures. accepted by ApJS, lal@nao.cas.cn

We present a sample of quasars discovered in the area of Galactic Anti-Center (GAC) of $150^{\circ} \leq l \leq 210^{\circ}$ and $|b| \leq 30^{\circ}$, based on the LAMOST Data Release 3 (DR3). The sample contains 151 spectroscopically confirmed quasars. Among them 80 are newly discovered with the LAMOST. All those quasars are very bright, with $i$ magnitudes peaking around 17.5\, mag. All the newly quasars are discovered serendipitously, targeted originally with the LAMOST as stars of bluer colours, except for a few targeted as variable, young stellar object candidates. This bright quasar sample at low Galactic latitudes will help fill the gap in the spatial distribution of known quasars near the Galactic disk that are used to construct astrometric reference frame for the purpose of accurate proper motion measurements, for example, Gaia. They are also excellent tracers to probe the kinematics and chemistry of the interstellar medium of the Milky Way disk and halo via absorption line spectroscopy., Comment: 4 pages, 1 figure, Accepted for publication in Research in Astronomy and Astrophysics Letter

Using the shuffle structure of the graphs, we introduce a new kind of the Hopf algebraic structure for tagged graphs with, or without loops. Like a quantum group structure, its product is non-commutative. With the help of the Hopf algebraic structure, after taking account symmetry of the tagged graphs, we reconstruct the topological recursion on spectral curves proposed by B. Eynard and N. Orantin, which includes the one-loop equations of various matrix integrals as special cases., Comment: Substantially improved version: We discussed on tagged graphs instead of unlabelled graphs; the definition of coproduct is changed; Section 5 is rewritten. One of main results on the relationships between coproduct and topological recursion is more specific and essential; title and abstract changed accordingly; v1 26 pages; v2 28pages

The discovery of pure spinor formalism makes the computation of superstring scattering amplitudes possible. In this paper, we will illustrate how computer algebra system Cadabra is used in computing the supersymmetric amplitude in pure spinor formalism and provide the source code that computes the tree-level massless 5-gluon amplitude., Comment: 23 pages,3 figure.v1-v5:comments are added, several mistakes are corrected, some references are added

Asteroseismology allows for deriving precise values of surface gravity of stars. The accurate asteroseismic determinations now available for large number of stars in the Kepler fields can be used to check and calibrate surface gravities that are currently being obtained spectroscopically for a huge numbers of stars targeted by large-scale spectroscopic surveys, such as the on-going Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Galactic survey. The LAMOST spectral surveys have obtained a large number of stellar spectra in the Kepler fields. Stellar atmospheric parameters of those stars have been determined with the LAMOST Stellar Parameter Pipeline at Peking University (LSP3), by template matching with the MILES empirical spectral library. In the current work, we compare surface gravities yielded by LSP3 with those of two asteroseismic samples - the largest sample from Huber et al. (2014) and the most accurate sample from Hekker et al. (2012, 2013). We find that LSP3 surface gravities are in good agreement with asteroseismic values of Hekker et al. (2012, 2013), with a dispersion of about 0.2 dex. Except for a few cases, asteroseismic surface gravities of Huber et al. (2014) and LSP3 spectroscopic values agree for a wide range of surface gravities. However, some patterns of differences can be identified upon close inspection. Potential ways to further improve the LSP3 spectroscopic estimation of stellar atmospheric parameters in the near future are briefly discussed. The effects of effective temperature and metallicity on asteroseismic determinations of surface gravities for giant stars are also discussed., Comment: Accepted for Publication in RAA

We present empirical metallicity-dependent calibrations of effective temperature against colours for dwarfs of luminosity classes IV and V and for giants of luminosity classes II and III, based on a collection from the literature of about two hundred nearby stars with direct effective temperature measurements of better than 2.5 per cent. The calibrations are valid for an effective temperature range 3,100 - 10,000 K for dwarfs of spectral types M5 to A0 and 3,100 - 5,700 K for giants of spectral types K5 to G5. A total of twenty-one colours for dwarfs and eighteen colours for giants of bands of four photometric systems, i.e. the Johnson ($UBVR_{\rm J}I_{\rm J}JHK$), the Cousins ($R_{\rm C}I_{\rm C}$), the Sloan Digital Sky Survey (SDSS, $gr$) and the Two Micron All Sky Survey (2MASS, $JHK_{\rm s}$), have been calibrated. Restricted by the metallicity range of the current sample, the calibrations are mainly applicable for disk stars ([Fe/H]$\,\gtrsim\,-1.0$). The normalized percentage residuals of the calibrations are typically 2.0 and 1.5 per cent for dwarfs and giants, respectively. Some systematic discrepancies at various levels are found between the current scales and those available in the literature (e.g. those based on the infrared flux method IRFM or spectroscopy). Based on the current calibrations, we have re-determined the colours of the Sun. We have also investigated the systematic errors in effective temperatures yielded by the current on-going large scale low- to intermediate-resolution stellar spectroscopic surveys. We show that the calibration of colour ($g-K_{\rm s}$) presented in the current work provides an invaluable tool for the estimation of stellar effective temperature for those on-going or upcoming surveys., Comment: 28 pages, 19 figures, 8 tables, accepted for publication in MNRAS

Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a $W_{1+\infty}$ constraint of the partition function of $r$-spin intersection numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function. The $W_{1+\infty}$ constraint completely determines the Schur polynomials expansion of the Hodge partition function., Comment: 51 pages, 1 figure

We report a detailed investigation of the bulk motions of the nearby Galactic stellar disk, based on three samples selected from the LSS-GAC DR2: a global sample containing 0.57 million FGK dwarfs out to $\sim$ 2 kpc, a local subset of the global sample consisting $\sim$ 5,400 stars within 150 pc, and an anti-center sample containing $\sim$ 4,400 AFGK dwarfs and red clump stars within windows of a few degree wide centered on the Galactic anti-center. The global sample is used to construct a three-dimensional map of bulk motions of the Galactic disk from the solar vicinity out to $\sim$ 2 kpc with a spatial resolution of $\sim$ 250 pc. Typical values of the radial and vertical components of bulk motion range from $-$15 km s$^{-1}$ to 15 km s$^{-1}$, while the lag behind the circular speed dominates the azimuthal component by up to $\sim$ 15 km s$^{-1}$. The map reveals spatially coherent, kpc-scale stellar flows in the disk, with typical velocities of a few tens km s$^{-1}$. Bending- and breathing-mode perturbations are clearly visible, and vary smoothly across the disk plane. Our data also reveal higher-order perturbations, such as breaks and ripples, in the profiles of vertical motion versus height. From the local sample, we find that stars of different populations exhibit very different patterns of bulk motion. Finally, the anti-center sample reveals a number of peaks in stellar number density in the line-of-sight velocity versus distance distribution, with the nearer ones apparently related to the known moving groups. The "velocity bifurcation" reported by Liu et al. (2012) at Galactocentric radii 10--11 kpc is confirmed. However, just beyond this distance, our data also reveal a new triple-peaked structure., Comment: 27 pages, 17 figures, Accepted for publication in a special issue of Research in Astronomy and Astrophysics on LAMOST sciences

In this work, we report new quasars discovered in the vicinity fields of the Andromeda (M31) and Triangulum (M33) galaxies with the LAMOST (Large Sky Area Multi-Object Fiber Spectroscopic Telescope, also named Guoshoujing Telescope) during the 2013 observational season, the second year of Regular Survey. In total, 1330 new quasars are discovered in an area of $\sim$133 deg$^2$ around M31 and M33. With $i$ magnitudes ranging from 14.79 to 20.0, redshifts from 0.08 to 4.85, the 1330 new quasars represent a significant increase of the number of identified quasars in the vicinity fields of M31 and M33. Up to the moment, there are in total 1870 quasars discovered by LAMOST in this area (see also Huo et al. 2010, 2013). The much enlarged sample of known quasars in this area can potentially be utilized to construct a precise astrometric reference frame for the measurement of the minute proper motions of M31, M33 and the associated substructures, vital for the understanding of the formation and evolution of M31, M33 and the Local Group of galaxies.Meanwhile, amongst the sample, there are in total 45, 98 and 225 quasars with $i$ magnitudes brighter than 17.0, 17.5 and 18.0 respectively. In the aforementioned brightness bins, 15, 35 and 84 quasars are reported here for the first time, 6, 21 and 81 are reported in Huo et al. (2010, 2013), while 0, 1 and 6 are from the Sloan Digital Sky Survey, and 24, 41 and 54 are from the NED database. These bright quasars provide an invaluable sample for the kinematics and chemistry study of the interstellar/intergalactic medium of the Local Group., Comment: 12 pages, 6 figures, Accepted for publication in a special issue of Research in Astronomy and Astrophysics on LAMOST sciences

Using a sample of over 70, 000 red clump (RC) stars with $5$-$10$% distance accuracy selected from the LAMOST Spectroscopic Survey of the Galactic Anti-center (LSS-GAC), we study the radial and vertical gradients of the Galactic disk(s) mainly in the anti-center direction, covering a significant disk volume of projected Galactocentric radius $7 \leq R_{\rm GC} \leq 14$ kpc and height from the Galactic midplane $0 \leq |Z| \leq 3$ kpc. Our analysis shows that both the radial and vertical metallicity gradients are negative across much of the disk volume probed, and exhibit significant spatial variations. Near the solar circle ($7 \leq R_{\rm GC} \leq 11.5$ kpc), the radial gradient has a moderately steep, negative slope of $-0.08$ dex kpc$^{-1}$ near the midplane ($|Z| < 0.1$ kpc), and the slope flattens with increasing $|Z|$. In the outer disk ($11.5 < R_{\rm GC} \leq 14$ kpc), the radial gradients have an essentially constant, much less steep slope of $-0.01$ dex kpc $^{-1}$ at all heights above the plane, suggesting that the outer disk may have experienced an evolution path different from that of the inner disk. The vertical gradients are found to flatten largely with increasing $R_{\rm GC}$. However, the vertical gradient of the lower disk ($0 \leq |Z| \leq 1$ kpc) is found to flatten with $R_{\rm GC}$ quicker than that of the upper disk ($1 < |Z| \leq 3$ kpc). Our results should provide strong constraints on the theory of disk formation and evolution, as well as the underlying physical processes that shape the disk (e.g. gas flows, radial migration, internal and external perturbations)., Comment: 24 pages, 12 figures, 1 table, Accepted for publication in a special issue of Research in Astronomy and Astrophysics on LAMOST sciences

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra., Comment: 1+16 pages, several types corrected, a little modification

We present new quasars discovered in the vicinity of the Andromeda and Triangulum galaxies with the LAMOST during the 2010 and 2011 observational seasons. Quasar candidates are selected based on the available SDSS, KPNO 4 m telescope, XSTPS optical, and WISE near infrared photometric data. We present 509 new quasars discovered in a stripe of ~135 sq. deg from M31 to M33 along the Giant Stellar Stream in the 2011 pilot survey datasets, and also 17 new quasars discovered in an area of ~100 sq. deg that covers the central region and the southeastern halo of M31 in the 2010 commissioning datasets. These 526 new quasars have i magnitudes ranging from 15.5 to 20.0, redshifts from 0.1 to 3.2. They represent a significant increase of the number of identified quasars in the vicinity of M31 and M33. There are now 26, 62 and 139 known quasars in this region of the sky with i magnitudes brighter than 17.0, 17.5 and 18.0 respectively, of which 5, 20 and 75 are newly-discovered. These bright quasars provide an invaluable collection with which to probe the kinematics and chemistry of the ISM/IGM in the Local Group of galaxies. A total of 93 quasars are now known with locations within 2.5 deg of M31, of which 73 are newly discovered. Tens of quasars are now known to be located behind the Giant Stellar Stream, and hundreds behind the extended halo and its associated substructures of M31. The much enlarged sample of known quasars in the vicinity of M31 and M33 can potentially be utilized to construct a perfect astrometric reference frame to measure the minute PMs of M31 and M33, along with the PMs of substructures associated with the Local Group of galaxies. Those PMs are some of the most fundamental properties of the Local Group., Comment: 26 pages, 6 figures, AJ accepted

Using the "standard pair" technique of paring stars of almost nil and high extinction but otherwise of almost identical stellar parameters from the SDSS, and combing the SDSS, GALEX, 2MASS and WISE photometry ranging from the far UV to the mid-IR, we have measured dust reddening in the FUV-NUV, NUV-u, u-g, g-r, r-i, i-z, z-J, J-H, H-Ks, Ks-W1 and W1-W2 colors for thousands of Galactic stars. The measurements, together with the E(B-V) values given by Schlegel et al. (1998), allow us to derive the observed, model-free reddening coefficients for those colors. The results are compared with previous measurements and the predictions of a variety of Galactic reddening laws. We find that 1) The dust reddening map of Schlegel et al. (1998) over-estimates E(B-V) by about 14 per cent, consistent with the recent work of Schlafly et al. (2010) and Schlafly & Finkbeiner (2011); 2) All the new reddening coefficients, except those for NUV-u and u-g, prefer the R(V) = 3.1 Fitzpatrick reddening law rather than the R(V) = 3.1 CCM and O'Donnell (O'Donnell 1994) reddening laws. Using the Ks-band extinction coefficient predicted by the R(V) = 3.1 Fitzpatrick law and the observed reddening coefficients, we have deduced new extinction coefficients for the FUV, NUV, u, g, r, i, z, J, H, W1 and W2 passbands. We recommend that the new reddening and extinction coefficients should be used in the future and an update of the Fitzpatrick reddening law in the UV is probably necessary. We stress however that the FUV- and NUV-band coefficients should be used with caution given their relatively large measurement uncertainties. Finally, potential applications of the "standard pair" technique with the LAMOST Galactic surveys are discussed., Comment: 13 pages, 9 figures, accepted to MNRAS

In this paper we generalize certain results concerning quantum affine algebra $U_{q}(\hat{sl_{2}})$ at the critical level to the corresponding elliptic case $E_{q,p}(\hat{sl_2})$. Using the Wakimoto realization of the algebra $E_{q,p}(\hat{sl_2})$, we construct the central elements of it at the critical level. It turns out that the so called Drinfeld conjecture originally proposed for Kac-Moody algebras also holds for the elliptic quantum algebras., Comment: 12 pages

The free-field representations of the $D(2,1;\a)$ current superalgebra and the corresponding energy-momentum tensor are constructed. The related screening currents of the first kind are also presented., Comment: Latex file, 10 pages

We construct a realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for any given level $k$ in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization of the quantum affine algebra $U_{q}(\hat{sl_N})$. We also construct a family of screening currents, which commute with the currents of $U_{q,p}(\hat{sl_N})$ up to total q-differences. And we give explicit twisted expressions for the type $I$ and the type $II$ vertex operators of $U_{q,p}(\hat{sl_N})$ by twisting the known results of the type $I$ vertex operators of the quantum affine algebra $U_{q}(\hat{sl_N})$ and the new results of the type $II$ vertex operators of $U_{q}(\hat{sl_N})$ we obtained in this paper., Comment: 28 pages

A realization of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ for any given level $k$ is constructed in terms of three free boson fields and their accompanying twisted partners. It can be viewed as the elliptic deformation of Wakimoto realization. Two screening currents are constructed; they commute or anti-commute with $U_{q,p}(\widehat{sl_2})$ modulo total q-differences. The free fields realization for two types vertex operators nominated as the type $I$ and the type $II$ vertex operators are presented. The twisted version of the two types vertex operators are also obtained. They all play crucial roles in calculating correlation functions., Comment: 23 pages

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate $gl(2|2)$ current superalgebra at general level $k$. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented., Comment: LaTex file 11 pages