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On Structure of cluster algebras of geometric type, II: Green's equivalences and paunched surfacesAug 18 2016Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a rooted cluster ... More

Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and $F$-polynomialsSep 20 2016Nov 26 2016In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we ... More

Beta-expansion and continued fraction expansion of real numbersMar 03 2016Let $\beta > 1$ be a real number and $x \in [0,1)$ be an irrational number. We denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $\beta$-expansion of $x$ ($n \in \mathbb{N}$). ... More

Understanding the charmed states recently observed by the LHCb and BaBar Collaborations in the quark modelJul 11 2014Sep 18 2014Comparing the expected spectroscopy in the relativistic quark model and the predicted strong decays in the $^3P_0$ model employing the realistic wave functions from the relativistic quark model with the measured properties of the LHCb and BaBar charmed ... More

On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphismsSep 03 2015Aug 18 2016Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing ... More

On representation rings in the context of monoidal categoriesJun 27 2014In general, representation rings are well-known as Green rings from module categories of Hopf algebras. In this paper, we study Green rings in the context of monoidal categories such that representations of Hopf algebras can be investigated through Green ... More

Categorification of sign-skew-symmetric cluster algebras and some conjectures on g-vectorsApr 25 2017Apr 26 2017Using the unfolding method given in \cite{HL}, we prove the conjectures on sign-coherence and a recurrence formula respectively of ${\bf g}$-vectors for acyclic sign-skew-symmetric cluster algebras. As a following consequence, the conjecture is affirmed ... More

Approximation orders of real numbers by $β$-expansionsMar 28 2016Jul 22 2016We prove that almost all real numbers (with respect to Lebesgue measure) are approximated by the convergents of their $\beta$-expansions with the exponential order $\beta^{-n}$. Moreover, the Hausdorff dimensions of sets of the real numbers which are ... More

A conjecture on $C$-matrices of cluster algebrasFeb 04 2017Nov 21 2017For a skew-symmetrizable cluster algebra $\mathcal A_{t_0}$ with principal coefficients at $t_0$, we prove that each seed $\Sigma_t$ of $\mathcal A_{t_0}$ is uniquely determined by its {\bf C-matrix}, which was proposed by Fomin and Zelevinsky in \cite{FZ3} ... More

The denominators of convergents for continued fractionsAug 03 2016For any real number $x \in [0,1)$, we denote by $q_n(x)$ the denominator of the $n$-th convergent of the continued fraction expansion of $x$ $(n \in \mathbb{N})$. It is well-known that the Lebesgue measure of the set of points $x \in [0,1)$ for which ... More

Limit theorems related to beta-expansion and continued fraction expansionJan 10 2016Let $\beta > 1$ be a real number and $x \in [0,1)$ be an irrational number. Denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $\beta$-expansion of $x$ ($n \in \mathbb{N}$). ... More

Complex Balancing Reconstructed to the Asymptotic Stability of Mass-action Chemical Reaction Networks with Conservation LawsMar 23 2017Nov 29 2018Motivated by the fact that the pseudo-Helmholtz function is a valid Lyapunov function for characterizing asymptotic stability of complex balanced mass action systems (MASs), this paper develops the generalized pseudo-Helmholtz function for stability analysis ... More

An extension of two-Higgs-doublet model and the excesses of 750 GeV diphoton, muon g-2 and $h\toμτ$Jan 19 2016Jan 21 2016In this paper we simultaneously explain the excesses of the 750 GeV diphoton, muon g-2 and $h\to \mu\tau$ in an extension of the two-Higgs-doublet model (2HDM) with additional vector-like fermions and a CP-odd scalar singlet ($P$) which is identified ... More

Double-peaked OI profile: a likely signature of the gaseous ring around KH 15DJun 11 2019KH 15D is a well-known spectroscopic binary because of its unique and dramatic photometric variability. The variability is explained by a circumbinary dust ring but the ring itself was never directly detected. We present a new interpretation of the double-peaked ... More

Notes on Chern's Affine Bernstein ConjectureApr 04 2011There were two famous conjectures on complete affine maximal surfaces, one due to E. Calabi, the other to S.S. Chern. Both were solved with different methods about one decade ago by studying the associated Euler-Lagrange equation. Here we survey two proofs ... More

Molecular Environment of the Supernova Remnant IC 443: Discovery of the Molecular Shells Surrounding the RemnantMay 28 2014We have carried out 12CO, 13CO, and C18O observations toward the mixed morphology supernova remnant (SNR) IC 443. The observations cover a 1.5*1.5 deg^2 area and allow us to investigate the overall molecular environment of the remnant. Some northern and ... More

Discovery of a pre-existing molecular filament associated with supernova remnant G127.1+0.5Jul 24 2014We performed millimeter observations in CO lines toward the supernova remnant (SNR) G127.1+0.5. We found a molecular filament at 4--13 km s$^{-1}$ consisting of two distinct parts: a straight part coming out of the remnant region and a curved part in ... More

Random Continued fractions: Lévy constant and Chernoff-type estimateJan 10 2016Given a stochastic process $\{A_n, n \geq 1\}$ taking values in natural numbers, the random continued fractions is defined as $[A_1, A_2, \cdots, A_n, \cdots]$ analogue to the continued fraction expansion of real numbers. Assume that $\{A_n, n \geq 1\}$ ... More

Nucleon pole contribution in the $pp\to ppK^+K^-$ reaction below the $φ$ meson thresholdApr 28 2014Sep 18 2014Nucleon pole contribution in the $pp\to ppK^+K^-$ reaction below the threshold of the production of the $\phi$ meson is studied within the effective Lagrangian approach. It is assumed that the $K^- p$ final state originates from the decay of the hyperons ... More

Phase matched second harmonic generation in an on-chip lithium niobate microresonator fabricated by femtosecond laserSep 09 2015Dec 26 2015Nonlinear optical processes in whispering gallery mode (WGM) microresonators have attracted much attention. Owing to the strong confinement of light in a small volume, a WGM microresonator can dramatically boost the strength of light field, thereby promoting ... More

CO~($J = 1-0$) Observations of a Filamentary Molecular Cloud in the Galactic Region Centered at $l = 150\arcdeg, b = 3.5\arcdeg$Mar 04 2017Mar 24 2017We present large-field (4.25~$\times$~3.75 deg$^2$) mapping observations toward the Galactic region centered at $l = 150\arcdeg, b = 3.5\arcdeg$ in the $J = 1-0$ emission line of CO isotopologues ($^{12}$CO, $^{13}$CO, and C$^{18}$O), using the 13.7 m ... More

Monolithic integration of a high-quality factor lithium niobate microresonator with a free-standing membrane waveguide using femtosecond laser assisted ion beam writing (FLAIBW)Jan 19 2017We demonstrate integrating a high quality factor lithium niobate microdisk resonator with a free-standing membrane waveguide. Our technique is based on femtosecond laser direct writing which produces the pre-structure, followed by focused ion beam milling ... More

On-chip electro-optic tuning of a lithium niobate microresonator with integrated in-plane microelectrodesNov 11 2016We demonstrate electro-optic tuning of an on-chip lithium niobate microresonator with integrated in-plane microelectrodes. First two metallic microelectrodes on the substrate were formed via femtosecond laser process. Then a high-Q lithium niobate microresonator ... More

Fabrication of high quality factor lithium niobate double-disk using a femtosecond laserOct 20 2017We demonstrate fabrication of a high quality factor lithium niobate double-disk whispering-gallery microcavity using femtosecond laser assisted ion beam milling. Using this method, two vertically stacked 30-um-diameter disks with a 200-nm-gap are fabricated. ... More

Simultaneous generation of four-wave mixing and stimulated Raman scattering in coupled lithium niobate microdisks mediated by second harmonic generationMar 30 2018High quality lithium niobate thin film microresonators provide an ideal platform for on-chip nonlinear optics applications. However, the phase matching condition for efficient parametric process sets a high requirement for fabrication control. Here we ... More

Highly-efficient second and third harmonic generation in a monocrystalline lithium niobate microresonatorAug 12 2018Nonlinear optics in whispering-gallery-mode (WGM) microresonators have attracted much attention. Owing to strong confinement of the light in a small volume, a WGM microresonator can dramatically boost the strength of light field, giving rise to enhancement ... More

A note on Rényi's "record" problem and Engel's seriesJul 11 2016Jul 27 2016In 1973, Williams introduced two interesting discrete Markov processes, namely $C$-processes and $A$-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes ... More

On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheaterNov 18 2014We report on fabrication of a microtoroid resonator of high-quality (high-Q) factor integrated with an on-chip microheater. Both the microresonator and microheater are fabricated using femtosecond laser three-dimensional (3D) micromachining. The microheater, ... More

A large-scale survey of CO and its isotopologues toward the Rosette molecular cloudAug 28 2018Sep 04 2018Using the PMO-13.7m millimeter telescope at Delingha in China, we have conducted a large-scale simultaneous survey of $^{12}$CO, $^{13}$CO, and C$^{18}$O J=1-0 emission toward the Rosette molecular cloud (RMC) region with a sky coverage of 3.5 $\times$ ... More

Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and $F$-polynomialsSep 20 2016In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we ... More

The one-loop on-shell renormalization of some vertexes in MSSMMay 21 2013Jun 06 2013The on-shell renormalization scheme for the electroweak theory is well studied in the standard model(SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model(MSSM) is still unknown. In MSSM, we study the on-shell ... More

Predicting missing links and their weights via reliable-route-based methodAug 05 2014Link prediction aims to uncover missing links or predict the emergence of future relationships according to the current networks structure. Plenty of algorithms have been developed for link prediction in unweighted networks, with only a very few of them ... More

Fabrication of a microresonator-fiber assembly maintaining a high-quality factor by CO2 laser weldingSep 18 2015We demonstrate fabrication of a microtoroid resonator of a high-quality (high-Q) factor using femtosecond laser three-dimensional (3D) micromachining. A fiber taper is reliably assembled to the microtoroid using CO2 laser welding. Specifically, we achieve ... More

Nucleon resonances in the $γp \to φK^+ Λ$ reaction near thresholdDec 19 2014Nov 26 2015We investigate the $\gamma p \to \phi K^+ \Lambda$ reaction near threshold within an effective Lagrangian approach and the isobar model. Various nucleon resonances caused by the $\pi$ and $\eta$ meson exchanges and background contributions are considered. ... More

Interaction between the Supernova Remnant HB 3 and the Nearby Star-Forming Region W3Sep 13 2016We performed millimeter observations in CO lines toward the supernova remnant (SNR) HB 3. Substantial molecular gas around -45 km s^-1 is detected in the conjunction region between the SNR HB 3 and the nearby W3 complex. This molecular gas is distributed ... More

The Wigner Solution and QCD Phase Transitions in a Modified PNJL ModelNov 16 2013By employing some modification to the widely used two-flavor Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, we discuss the Wigner solution of the quark gap equation at finite temperature and zero quark chemical potential beyond the chiral limit, ... More

The near threshold $π^- p \to ηn$ reaction in an effective Lagrangian approachDec 20 2013The near threshold $\pi^- p \to \eta n$ reaction is studied within an effective Lagrangian approach and the isobar model. By considering the contributions from $s$- and $u$-channel nucleon pole and $N^{*}(1535)$ resonance, the total and differential cross ... More

The Distant Outer Gas Arm Between l=35d and l=45dAug 19 2016The Galactic plane has been mapped from l=34.75d to 45.25d and b=-5.25d to 5.25d in the CO (J=1-0) emission with the 13.7 m telescope of the Purple Mountain Observatory. The unbiased survey covers a large area of 100 square degrees sampled every 30" with ... More

The CIV Baldwin effect in QSOs from Seventh Data Release of the Sloan Digital Sky SurveySep 16 2012Using the properties of SDSS DR7 QSOs catalog from Shen et al., the Baldwin effect, its slope evolution, the underlying drive for a large sample of 35019 QSOs with reliable spectral analysis are investigated. We find that the Baldwin effect exists in ... More

A model study of the chiral phase diagram of QCDApr 11 2014In this paper we study the chiral phase transition of QCD at finite temperature and density by using the rank-2 confining separable gluon propagator model in the framework of Dyson-Schwinger Equations. The critical end point is located at (T_CEP, {\mu}_CEP) ... More

Explaining 750 GeV diphoton excess from top/bottom partner cascade decay in two-Higgs-doublet model extensionJan 04 2016Mar 24 2016In this paper, we interpret the 750 GeV diphoton excess in the Zee-Babu extension of the two-Higgs-doublet model by introducing a top partner ($T$)/bottom partner ($B$). In the alignment limit, the 750 GeV resonance is identified as the heavy CP-even ... More

Temperature dependence of the plastic scintillator detector for DAMPEDec 11 2016The Plastic Scintillator Detector (PSD) is one of the main sub-detectors in the DArk Matter Particle Explorer (DAMPE) project. It will be operated over a large temperature range from -$10$ to $30^{\circ}$C, so the temperature effect of the whole detection ... More

Complete Affine K$\ddot{a}$hler ManifoldsAug 16 2010Oct 19 2010In this paper we prove that for a complete, connected and oriented K\"{a}ler affine manifold $(M,G)$ of dimension $n,$ if it is K\"ahler affine Ricci flat or the K$\ddot{a}$hler affine scalar curvature $S\equiv0,$ ($n\leq 5$), then the universal covering ... More

Millimeter Spectral Line Mapping Observations Toward Four Massive Star Forming HII RegionsDec 08 2016We present spectral line mapping observations toward four massive star-forming regions (Cepheus A, DR21S, S76E and G34.26+0.15), with the IRAM 30 meter telescope at 2 mm and 3 mm bands. Totally 396 spectral lines from 51 molecules, one helium recombination ... More

L1188: a promising candidate of cloud-cloud collision triggering the formation of the low- and intermediate-mass starsJan 13 2017We present a new large-scale (4 square degrees) simultaneous $^{12}$CO, $^{13}$CO, and C$^{18}$O ($J$=1$-$0) mapping of L1188 with the PMO 13.7-m telescope. Our observations have revealed that L1188 consists of two nearly orthogonal filamentary molecular ... More

Study of dark matter in the extended BLMSSMJan 21 2019Mar 26 2019There are strong evidences for existence of dark matter in some experiments at present. However, the question is that we do not have a reasonable explanation for dark matter in the framework of the Standard Model(SM) of particle physics. It is necessary ... More

Real-time Electrical Tuning of an Optical Spring on a Monolithically Integrated Ultrahigh Q Lithium Nibote MicroresonatorDec 31 2018Cavity optomechanics, the study of the interplay between light and mechanical properties of matter, has triggered a wide range of groundbreaking researches from cavity quantum electrodynamics, label free single molecule detection to the creation of phonon ... More

Poisson Vector Graphics (PVG) and Its Closed-Form SolverJan 16 2017This paper presents Poisson vector graphics, an extension of the popular first-order diffusion curves, for generating smooth-shaded images. Armed with two new types of primitives, namely Poisson curves and Poisson regions, PVG can easily produce photorealistic ... More

A SiO J = 5 - 4 Survey Toward Massive Star Formation RegionsMay 21 2019We performed a survey in the SiO $J=5\rightarrow4$ line toward a sample of 199 Galactic massive star-forming regions at different evolutionary stages with the SMT 10 m and CSO 10.4 m telescopes. The sample consists of 44 infrared dark clouds (IRDCs), ... More

Isospin Effects of the Critical Behavior in the Lattice Gas ModelApr 21 1999Isospin effects of the critical phenomena were studied via Xe isotopes in the frame of lattice gas model. All the critical temperatures for four Xe isotopes are close to 5.5 MeV at the same freeze-out density of about 0.39 $\rho_0$. The critical values ... More

Deep Portrait Image Completion and ExtrapolationAug 23 2018General image completion and extrapolation methods often fail on portrait images where parts of the human body need to be recovered - a task that requires accurate human body structure and appearance synthesis. We present a two-stage deep learning framework ... More

Molecular clouds in the extreme outer Galaxy between $l=34.75^{\circ}$ to $45.25^{\circ}$Feb 28 2017We present the result of an unbiased CO survey in Galactic range of 34.75$^{\circ}\leq$l$\leq$ 45.25$^{\circ}$ and -5.25$^{\circ}\leq$b$\leq$ 5.25$^{\circ}$, and velocity range beyond the Outer arm. A total of 168 molecular clouds (MCs) are identified ... More

Diffusion entropy analysis on the stride interval fluctuation of human gaitAug 21 2006In this paper, the diffusion entropy technique is applied to investigate the scaling behavior of stride interval fluctuations of human gait. The scaling behavior of the stride interval of human walking at normal, slow and fast rate are similar; with the ... More

A New Look at T Tauri Star Forbidden Lines: MHD Driven Winds from the Inner DiskOct 08 2018Magnetohydrodynamic (MHD) and photoevaporative winds are thought to play an important role in the evolution and dispersal of planet-forming disks. We report the first high-resolution ($\Delta v\sim$6\kms) analysis of [S II] $\lambda$4068, [O I] $\lambda$5577, ... More

Three-dimensional laser printing of macro-scale glass objects at a micro-scale resolutionFeb 11 2019Three-dimensional (3D) printing has allowed for production of geometrically complex 3D objects with extreme flexibility, which is currently undergoing rapid expansions in terms of materials, functionalities, as well as areas of application. When attempting ... More

Low-loss Lithium Niobate on Insulator (LNOI) Waveguides of a 10 cm-length and a Sub-nanometer Surface RoughnessOct 06 2018We develop a technique for realizing lithium niobate on insulator (LNOI) waveguides of a multi-centimeter-length with a propagation loss as low as 0.027 dB/cm. Our technique relies on patterning a chromium (Cr) thin film coated on the top surface of LNOI ... More

A large area plastic scintillation detector with 4-corner-readoutAug 23 2015Aug 26 2015A 760 $\times$ 760 $\times$ 30 mm$^3$ plastic scintillation detector viewed by photomultiplier tubes (PMTs) from four corners has been developed, and the detector has been tested with cosmic rays and $\gamma$ rays. A position-independent effective time ... More

Near-threshold $η$ production in $pp$ collisionsJan 26 2015May 01 2015We study near-threshold $\eta$ meson production in $pp$ collisions within an effective Lagrangian approach combined with the isobar model, by allowing for the various intermediate nucleon resonances due to the $\pi$, $\eta$, and $\rho$-meson exchanges. ... More

Quantum Tomography of the Photon-Plasmon Conversion Process in a Metal Hole ArrayApr 24 2019In the past decades, quantum plasmonics has become an active area due to its potential applications in on-chip plasmonic devices for quantum information processing. However, the fundamental physical process, i.e., how a quantum state of light evolves ... More

Asteroseismic based estimation of the surface gravity for the LAMOST giant starsNov 02 2014May 10 2015Asteroseismology is one of the most accurate approaches to estimate the surface gravity of a star. However, most of the data from the current spectroscopic surveys do not have asteroseismic measurements, which is very expensive and time consuming. In ... More

Classification of Extremely Red Objects in the Hubble Ultra Deep FieldFeb 16 2009In this paper we present a quantitative study of the classification of Extremely Red Objects (EROs). The analysis is based on the multi-band spatial- and ground-based observations (HST/ACS-$BViz$, HST/NICMOS-$JH$, VLT-$JHK$) in the Hubble Ultra Deep Field ... More

Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystalDec 13 2015Jan 11 2016We experimentally demonstrate the orbital angular momentum (OAM) conversion by the coupled nonlinear optical processes in a quasi-periodically poled LiTaO3 crystal. In such crystal, third-harmonic generation (THG) is realized by the coupled second-harmonic ... More

Quantum and Thermal Transitions Out of the Pair-Supersolid Phase of Two-Species Bosons in LatticeMar 26 2012Jun 15 2012We investigate two-species bosons in a two-dimensional square lattice by quantum Monte Carlo method. We show that the inter-species attraction and nearest-neighbor intra-species repulsion results in the pair-supersolid phase, where a diagonal solid order ... More

High-order sideband effect with two-level atoms in a shaken optical latticeApr 05 2018The system of cold two-level atoms inside an optical lattice potential has been used to simulate various models encountered in fundamental and condensed-matter physics. When the optical lattice is periodically shaken, some interesting dynamical effects ... More

Magnetic Chains Created by Polymer-Induced Assembly of Hollow Cobalt NanoparticlesSep 09 2005Magnetic chains of hollow cobalt nanoparticles (450-750 nm) have been synthesized by using poly(vinyl pyrrolidone) (PVP) as a template in an ethylene glycol solution. In this process, CoCl2.6H2O was reduced by N2H4.H2O in the presence of PVP. All of the ... More

Little Higgs theory confronted with the LHC Higgs dataJan 01 2013Jan 14 2013We confront the little Higgs theory with the LHC Higgs search data (up to 17 fb$^{-1}$ of the combined 7 and 8 TeV run). Considering some typical models, namely the littlest Higgs model (LH), the littlest Higgs model with T-parity (LHT-A and LHT-B) and ... More

Higgs and Z-boson FCNC decays correlated with B-meson decays in littlest Higgs model with T-parityJul 28 2008In the littlest Higgs model with T-parity (LHT) new flavor-changing interactions between mirror fermions and the Standard Model (SM) fermions can induce various FCNC decays for B-mesons, Z-boson and Higgs boson. Since all these decays induced in the LHT ... More

Top quark FCNC decays and productions at LHC in littlest Higgs model with T-parityMar 31 2009In the littlest Higgs model with T-parity (LHT) the newly introduced mirror quarks have flavor-changing couplings with the Standard Model (SM) quarks and may enhance the flavor-changing neutral-current (FCNC) top quark interactions which are extremely ... More

Learning a Multi-Modal Policy via Imitating Demonstrations with Mixed BehaviorsMar 25 2019We propose a novel approach to train a multi-modal policy from mixed demonstrations without their behavior labels. We develop a method to discover the latent factors of variation in the demonstrations. Specifically, our method is based on the variational ... More

B-Meson Wave Function through A Comparative Analysis of the $B\to π$, $K$ Transition Form FactorsAug 02 2008Dec 23 2008The properties of the B-meson light-cone wave function up to next-to-leading order Fock state expansion have been studied through a comparative study of the $B\to \pi$, $K$ transition form factors within the $k_T$ factorization approach and the light-cone ... More

Star-forming content of the giant molecular filaments in the Milky WayNov 06 2018Observations have discovered numerous giant molecular filaments (GMFs) in the Milky Way. However, their role in the Galactic star formation and Galaxy-scale evolution of dense gas is still unknown. We investigate systematically the star-forming content ... More

Re-visiting the extended Schmidt law: the important role of existing stars in regulating star formationJan 03 2018We revisit the proposed extended Schmidt law (Shi et al. 2011) which points that the star formation efficiency in galaxies depends on the stellar mass surface density, by investigating spatially-resolved star formation rates (SFRs), gas masses and stellar ... More

Generalized virtual braid groups, quasi-shuffle product and quantum groupsNov 14 2013We introduce in this paper the generalized virtual braid group on n strands GVB_n, generalizing simultaneously the braid groups and their virtual versions. A Mastumoto-Tits type section lifting shuffles in a symmetric group S_n to the monoid associated ... More

A Borel-Weil-Bott type theorem of quantum shuffle algebrasAug 28 2012We prove in this paper a Borel-Weil-Bott type theorem for the coHochschild homology of a quantum shuffle algebra associated with quantum group datum taking coefficients in some well-chosen bicomodules, which can be looked as an analogue of equivariant ... More

On a Question of Arveson about Ranks of Hilbert modulesApr 25 2001It's well known that the functional Hilbert space over the unit ball in $B_{d} \in C^d$, with kernel function $K(z,w)=\frac{1}{1-z_{1}w_{1}-... -z_{d}w_{d}}$, admits a natural $A(B_{d})$-module structure. We show the rank of a nonzero submodule is infinity ... More

Wasserstein-2 bounds in normal approximation under local dependenceJul 16 2018Jan 21 2019We obtain a general bound for the Wasserstein-2 distance in normal approximation for sums of locally dependent random variables. The proof is based on an asymptotic expansion for expectations of second-order differentiable functions of the sum. We apply ... More

Bijective proofs of character evaluations using trace forest of the jeu de taquinMar 22 2014Irreducible characters in the symmetric group are of special interest in combinatorics. They can be expressed either combinatorially with ribbon tableaux, or algebraically with contents. In this paper, these two expressions are related in a combinatorial ... More

Construct holomorphic invariants in Čech cohomology by a combinatorial formulaDec 21 2018Dec 25 2018In this paper, we give a combinatorial formula for the \v{C}ech cocycles representing the power sums of the Chern roots of a holomorphic vector bundle over a complex manifold. By an observation motivation by author's previous paper, we also construct ... More

A geometric criterion for prescribing residues and some applicationsAug 02 2018Dec 24 2018An old theorem of Weil and Kodaira says that for a compact K\"ahler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this paper, we generalize ... More

On a multi-particle Moser-Trudinger InequalityJan 16 2004We verify a conjecture of Gillet-Soul\'{e}. We prove that the determinant of the Laplacian on a line bundle over $\mathbb{CP}^{1}$ is always bounded from above. This can also be viewed as a multi-particle generalization of the Moser-Trudinger Inequality. ... More

On the scattering operators for ACHE metrics of Bergman type on strictly pseudoconvex domainsAug 13 2015Feb 26 2017The scattering operators associated to an ACHE metric of Bergman type on a strictly pseudovonvex domain are a one-parameter family of CR-conformally invariant pseudodifferntial operators of Heisenberg class with respect to the induced CR structure on ... More

Pressure rigidity of three dimensional contact Anosov flowsMar 10 2005We study the cohomological pressure introduced by R.Sharp (defined by using topological pressures of certain potentials of Anosov flows). In particular, we get the rigidity in the case that this pressure coincides with the metrical entropy, generalising ... More

Smooth rigidity of uniformly quasiconformal Anosov flowsMar 10 2005We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of volume-preserving ... More

A universal error bound in the CLT for counting monochromatic edges in uniformly colored graphsAug 03 2014Let $\{G_n: n\geq 1\}$ be a sequence of simple graphs. Suppose $G_n$ has $m_n$ edges and each vertex of $G_n$ is colored independently and uniformly at random with $c_n$ colors. Recently, Bhattacharya, Diaconis and Mukherjee (2013) proved universal limit ... More

Composition series for GKZ-systemsMay 15 2018In this paper, we find a composition series of GKZ-systems with semisimple successive quotients. We also study the composition series of the corresponding perverse sheaves and compare these two composition series under the Riemann-Hilbert correspondence. ... More

New Computational Result on Harmonious TreesJun 17 2011Oct 31 2012Graham and Sloane proposed in 1980 a conjecture stating that every tree has a harmonious labelling, a graph labelling closely related to additive base. Very limited results on this conjecture are known. In this paper, we proposed a computational approach ... More

Discretized normal approximation by Stein's methodNov 14 2011Jul 04 2014We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of i.i.d. Bernoulli ... More

Quantum groups, q-Boson algebras and quantized Weyl algebrasApr 01 2010Sep 13 2010We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category $\mathcal{O}(B_q)$ ... More

$AF$ Embedding of Crossed Products of Certain Graph $C^*$-Algebras by Quasi-free ActionsOct 26 2005We introduce the labelling map and the quasi-free action of a locally compact abelian group on a graph $C^*$-algebra of a row-finite directed graph. Some necessary conditions for embedding the crossed product to an $AF$ algebra are discussed, and one ... More

Dedekind η-function and quantum groupsMay 02 2012Aug 10 2015We realize some powers of Dedekind $\eta$-function as traces on quantum coordinate algebras.

The Fredholm index of a pair of commuting operatorsAug 02 2005This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a method to calculate ... More

On orbit equivalence of quasiconformal Anosov flowsMar 10 2005In this article, we give a quasi-final classification of quasiconformal Anosov flows. We deduce a very interesting differentable rigidity result for the orbit foliations of hyperbolic manifold of dimension at least three.

Geometric Anosov flows of dimension five with smooth distributionsMar 10 2005We classify five dimensional Anosov flows with smooth decomposition which are in addition transversely symplectic. Up to finite covers and a special time change, we find exectly the suspensions of symplectic hyperbolic automorphisms of four dimensional ... More

A Faster Structured-Tag Word-Classification MethodOct 25 1996Several methods have been proposed for processing a corpus to induce a tagset for the sub-language represented by the corpus. This paper examines a structured-tag word classification method introduced by McMahon (1994) and discussed further by McMahon ... More

Approximate Converse TheoremMar 28 2012We present an approximate converse theorem which measures how close a given set of irreducible admissible unramified unitary generic local representations of GL(n) is to a genuine cuspidal representation. To get a formula for the measure, we introduce ... More

Quantum cluster algebras from unpunctured triangulated surfaces: arbitrary coefficients and quantizationJul 18 2018Jan 08 2019We study quantum cluster algebras from unpunctured surfaces with arbitrary coefficients and quantization. We first give a new proof of the Laurent expansion formulas for commutative cluster algebras from unpunctured surfaces, we then give the quantum ... More

Two-nucleon excitation from $p$ to $sd$ shell in $^{12,14}$CFeb 01 2016The effect of the two-nucleon excitation from $p$ to $sd$ shell is discussed in $^{12}$C and $^{14}$C in the frame work of shell model. The recently suggested shell-model Hamiltonian YSOX provides an suitable tool to investigate the $2~\hbar\omega$ excitation ... More

Intrinsic basis-independent quantum coherence measureJan 18 2017Oct 22 2017Quantum coherence is a key resource in quantum information processing scenarios, and quantifying coherence is an important task for both quantum foundation and quantum technology. However, until now, all most of coherence measures are basis-dependent ... More

The Link between Magnetic Fields and Filamentary Clouds: Bimodal Cloud Orientations in the Gould BeltOct 23 2013The orientations of filamentary molecular clouds in the Gould Belt and their local ICM (inter-cloud media) magnetic fields are studied using near-infrared dust extinction maps and optical stellar polarimetry data. These filamentary clouds are a few-to-ten ... More

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VI. Velocity-resolved Reverberation Mapping of H$β$ LineFeb 05 2016In the sixth of the series of papers reporting on a large reverberation mapping (RM) campaign of active galactic nuclei (AGNs) with high accretion rates, we present velocity-resolved time lags of H$\beta$ emission lines for nine objects observed in the ... More