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Loop Current and Orbital Magnetism in Pyrite-Type $Ir_{3}Ch_{8}$ ($Ch=Se,Te$)Aug 21 2013Aug 23 2013We study the parent compound of the pyrite-type $Ir_{x}Ch_{2}$ iridium chalcogenide superconductors, $Ir_{0.75}Ch_{2}$ (or $Ir_{3}Ch_{8}$). While the lattice structure of the material is rather complicated, we show that the electron physics near the Fermi ... More

Magnetism in Quasi-One-Dimensional A$_2$Cr$_3$As$_3$ (A=K,Rb) superconductorsJan 02 2015Apr 21 2015We predict that the recently discovered quasi-one dimensional superconductors, A$_2$Cr$_3$As$_3$(A=K,Rb), possess strong frustrated magnetic fluctuations and are nearby a novel in-out co-planar magnetic ground state. The frustrated magnetism is very sensitive ... More

FeTe$_{1-x}$Se$_{x}$ monolayer films: towards the realization of high-temperature connate topological superconductivityJan 26 2017We performed angle-resolved photoemission spectroscopy studies on a series of FeTe$_{1-x}$Se$_{x}$ monolayer films grown on SrTiO$_{3}$. The superconductivity of the films is robust and rather insensitive to the variations of the band position and effective ... More

Mechanism for Odd Parity Superconductivity in Iron-Based SuperconductorsMar 11 2013Mar 15 2013Under the assumption that superconducting pairing is driven by local d-p hybridization, we show that the superconducting state in iron-based superconductors is classified as an odd parity s-wave spin-singlet pairing state in a single trilayer FeAs/Se, ... More

Electronic structure properties in the nematic phases of FeSeOct 14 2015We investigate the electronic structures of FeSe in the presence of different possible orders. We find that only ferro-orbital order (FO) and collinear antiferro-magnetism (C-AFM) can simultaneously induce splittings at $\Gamma$ and M. Bicollinear antiferro-magnetism ... More

Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe$_2$ mediated by mode-selective electron-phonon couplingJan 24 2019Quantum materials represent one of the most promising frontiers in the quest for faster, lightweight, energy efficient technologies. However, their inherent complexity and rich phase landscape make them challenging to understand or manipulate in useful ... More

Distinct surface and bulk charge density waves in ultrathin 1T-TaS2Mar 07 2016Nov 14 2016We employ low-frequency Raman spectroscopy to study the nearly commensurate (NC) to commensurate (C) charge density wave (CDW) transition in 1T-TaS2 ultrathin flakes protected from oxidation. We identify new modes originating from C phase CDW phonons ... More

Correlation between non-centrosymmetry and superconductivity in quasi-one-dimensional compounds A2Cr3As3 (A=K, Rb)Mar 05 2016Nov 07 2016Non-centrosymmetric superconductors, whose crystal structure is absent of inversion symmetry, have recently received special attentions due to the expectation of unconventional pairings and exotic physics associated with such pairings. The newly discovered ... More

Nematic orders and nematicity-driven topological phase transition in FeSeMar 07 2016We investigate nematic states in both bulk FeSe and FeSe thin films. It is found that their band structures and signature features that were observed in a variety of experiments can be perfectly explained by introducing the $d$-wave nematic orders that ... More

$g$-wave Pairing in BiS$_2$ SuperconductorsMar 24 2014Nov 03 2014Recent angle resolved photoemission spectroscopy(ARPES) experiments have suggested that BiS$_2$ based superconductors are at very low electron doping. Using random phase approximation(RPA) and functional renormalization group(FRG) methods, we find that ... More

Pairing Symmetry in Layered BiS$_2$ Compounds Driven by Electron-Electron CorrelationNov 23 2012Apr 17 2014We investigate the pairing symmetry of layered BiS$_2$ compounds by assuming that electron-electron correlation is still important so that the pairing is rather short range. We find that the extended s-wave pairing symmetry always wins over d-wave when ... More

Triplet $p_z$-wave pairing in quasi one dimensional A$_2$Cr$_3$As$_3$ superconductorsMar 23 2015Sep 19 2015We construct minimum effective models to investigate the pairing symmetry in the newly discovered quasi-one-dimensional superconductor K$_2$Cr$_3$As$_3$. We show that a minimum three-band model based on the $d_{z^2}$, $d_{xy}$ and $d_{x^2-y^2}$ orbitals ... More

Topological Critical Materials of Ternary CompoundsJun 20 2018We review topological properties of two series of ternary compounds AMgBi (A=K, RB, Cs) and ABC with a hexagonal ZrBeSi type structure. The first series of materials AMgBi are predicted to be topological critical Dirac semimetals. The second series of ... More

Nodeless high-T$_c$ superconductivity in highly-overdoped monolayer CuO$_2$Apr 13 2018Nov 30 2018We study the electronic structure and superconductivity in CuO$_2$ monolayer grown recently on $d$-wave cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Density functional theory calculations indicate significant charge transfer across the interface ... More

Topological Characters in Fe(Te$_{1-x}$Se$_x$) thin filmsDec 10 2014We investigate topological properties in the Fe(Te,Se) thin films. We find that the single layer FeTe$_{1-x}$Se$_x$ has nontrivial $Z_2$ topological invariance which originates from the parity exchange at $\Gamma$ point of Brillouin zone. The nontrivial ... More

Experimental consequences of $p_z$-wave spin triplet superconductivity in A$_2$Cr$_3$As$_3$Jul 27 2015Aug 03 2015The experimental observable properties of the triplet $p_z$-wave pairing state, proposed by Wu {\em et al.} [arXiv:1503.06707] in quasi-one dimensional A$_2$Cr$_3$As$_3$ materials, are theoretically investigated. This pairing state is characterized by ... More

Hybrid Crystals of Cuprates and Iron-Based SuperconductorsJan 13 2016We propose two possible new compounds, Ba$_2$CuO$_2$Fe$_2$As$_2$ and K$_2$CuO$_2$Fe$_2$Se$_2$, which hybridize the building blocks of two high temperature superconductors, cuprates and iron-based superconductors. These compounds consist of square CuO$_2$ ... More

Bell inequality of frequency-bin entangled photon pairs with time-resolved detectionSep 08 2016Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as ... More

Magnetic ordering and multiferroicity in MnI$_2$Feb 09 2012Nov 24 2012Density-functional calculations are carried out to investigate incommensurate magnetic structures and ferroelectric polarization in newly discovered multiferroic material MnI$_2$. The exchange interactions among local moments on Mn are parameterized by ... More

Three-dimensional Critical Dirac semimetal in KMgBiJun 16 2016We predicted that AMgBi (A=K,Rb Cs), which have the same lattice structures as the 111 family of iron-based superconductors (Na/LiFeAs), are symmetry-protected Dirac semimetals located near the boundary of type-I and type-II Dirac semimetal phases. Doping ... More

Substrate-supported triplet superconductivity in Dirac semimetalsSep 11 2018Stimulated by the success of graphene and its emerging Dirac physics, the quest for versatile and tunable electronic properties in atomically thin systems has led to the discovery of various chemical classes of 2D compounds. In particular, honeycomb lattices ... More

Revisitation of superconductivity in K$_2$Cr$_3$As$_3$ based on the six-band modelDec 01 2015We investigate the pairing symmetry of the newly synthesized quasi-one-dimension K$_2$Cr$_3$As$_3$ superconductor based on the six-band model. We adopt standard random-phase-approximation to study the Hubbard-Hund model of the system. Our results confirm ... More

Unconventional superconductivity in a doped quantum spin Hall insulatorNov 05 2018A monolayer of jacutingaite (Pt$_2$HgSe$_3$) has recently been identified as a novel quantum spin Hall insulator. By first-principles calculations, we study its Fermiology in the doped regime and unveil a type-I and type-II van Hove singularity for hole ... More

Three-dimensional Critical Dirac semimetal in KMgBiJun 16 2016Dec 08 2016We predicted that AMgBi (A=K,Rb Cs), which have the same lattice structures as the 111 family of iron-based superconductors (Na/LiFeAs), are symmetry-protected Dirac semimetals located near the boundary of type-I and type-II Dirac semimetal phases. Doping ... More

$β$-CuI: a Dirac semimetal without surface Fermi arcsJan 17 2018Anomalous surface states with Fermi arcs are commonly considered to be a fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals, however, Fermi arcs of DSMs are not topologically protected. Using first-principles calculations, we predict ... More

Staggered FeSe Monolayer on SrTiO$_3$ (110) surfaceJan 15 2016We investigate the electronic and magnetic properties of FeSe monolayer on the anisotropic SrTiO$_3$ (110) surface. With compressive strain along $[1\bar{1}0]$ direction from the substrate, the monolayer FeSe possesses a staggered bipartite iron lattice ... More

$d+id$ chiral superconductivity in a triangular lattice from trigonal bipyramidal complexesJan 08 2018We model the newly predicted high-$T_c$ superconducting candidates constructed by corner-shared trigonal bipyramidal complexes with an effective three-orbital tight-banding Hamiltonian and investigate the pairing symmetry of their superconducting states ... More

Topological phase in non-centrosymmetric material NaSnBiNov 05 2016We predict that a non-centrosymmetric material NaSnBi locates in a three-dimensional non-trivial topological phase under ambient pressure based on first-principle calculations. By deriving the effective model around $\Gamma$ point, we find that the topological ... More

The effect of As-Chain layers in CaFeAs$_2$Feb 19 2014The new discovered iron-based superconductors have chain-like As layers. These layers generate an additional 3-dimensional hole pocket and cone-like electron pockets. The former is attributed to the Ca $d$ and As1 $p_z$ orbitals and the latter are attributed ... More

CaFeAs$_2$: a Staggered Intercalation of Quantum Spin Hall and High Temperature SuperconductivityMay 25 2014Mar 03 2015We predict that CaFeAs$_2$, a newly discovered iron-based high temperature (T$_c$) superconductor, is a staggered intercalation compound that integrates topological quantum spin hall (QSH) and superconductivity (SC). CaFeAs$_2$ has a structure with staggered ... More

Topological Vortex Phase Transitions in Iron-Based SuperconductorsJan 10 2019We study topological vortex phases in iron-based superconductors. Besides the previously known vortex end Majorana zero modes (MZMs) phase stemming from the existence of a three dimensional (3D) strong topological insulator state, we show that there is ... More

Direct observation of multiple topological phases in the iron-based superconductor Li(Fe,Co)AsMar 02 2018Topological insulators/semimetals and unconventional iron-based superconductors have attracted major attentions in condensed matter physics in the past 10 years. However, there is little overlap between these two fields, although the combination of topological ... More

Visualizing Band Offsets and Edge States in Bilayer-Monolayer Transition Metal Dichalcogenides Lateral HeterojunctionDec 05 2015Semiconductor heterostructures are fundamental building blocks for many important device applications. The emergence of two-dimensional semiconductors opens up a new realm for creating heterostructures. As the bandgaps of transition metal dichalcogenides ... More

Origin of the pressure-dependent T$_c$ valley in superconducting simple cubic phosphorusDec 18 2017Motivated by recent experiments, we investigate the pressure-dependent electronic structure and electron-phonon (\emph{e-ph}) coupling for simple cubic phosphorus by performing first-principle calculations within the full potential linearized augmented ... More

Dense network of one-dimensional mid-gap metallic modes in monolayer MoSe2 and their spatial undulationsJul 22 2014We report the observation of a dense triangular network of one-dimensional (1D) metallic modes in a continuous and uniform monolayer of MoSe2 grown by molecular-beam epitaxy. High-resolution transmission electron microscopy and scanning tunneling microscopy ... More

Distinct surface and bulk charge density waves in ultrathin 1T-TaS2Mar 07 2016We employ low-frequency Raman spectroscopy to study the nearly commensurate (NC) to commensurate (C) charge density wave (CDW) transition in 1T-TaS2 ultrathin flakes protected from oxidation. We identify new modes that originate from C phase CDW phonons ... More

Positive correlation between non-centrosymmetry and superconductivity in quasi-one-dimensional compounds A2Cr3As3 (A=K, Rb)Mar 05 2016Non-centrosymmetric superconductors, whose crystal structure is absent of inversion symmetry, have recently received special research attentions due to the expectation of unconventional pairings and exotic physics associated with such pairings. However, ... More

High-throughput investigation of tunable superconductivity in FeSe filmsJul 03 2018There is an ongoing debate about the relative importance of structural change versus doping charge carriers on the mechanism of superconductivity in Fe-based materials. Elucidating this issue is a major challenge since it would require a large number ... More

Room Temperature Continuous-wave Excited Biexciton Emission in CsPbBr3 NanocrystalsApr 17 2018Biexcitons are a manifestation of many-body excitonic interactions crucial for quantum information and quantum computation in the construction of coherent combinations of quantum states. However, due to their small binding energy and low transition efficiency, ... More

Bell inequality of frequency-bin entangled photon pairs with time-resolved detectionSep 08 2016Oct 12 2016Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as ... More

Topological Dirac semimetal phase in the iron-based superconductor Fe(Te,Se)Mar 02 2018Topological Dirac semimetals (TDSs) exhibit bulk Dirac cones protected by time reversal and crystal symmetry, as well as surface states originating from non-trivial topology. While there is a manifold possible onset of superconducting order in such systems, ... More

Multiple topological states in iron-based superconductorsSep 25 2018Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant fields, even ... More

The $k$-tuple Prime Difference ChampionOct 30 2017Jan 03 2018Let $D_{k}$ be a set with $k$ distinct elements of integers such that $d_{1}<d_{2}<\cdots<d_{k}$. We say $D_{k}^{*}$ is a $k$-tuple prime difference champion ($k$-tuple PDC) for primes $\le x$ if the set $D_{k}^{*}$ is the most probable differences among ... More

Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusionMar 30 2017This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various ... More

High-throughput investigation of tunable superconductivity in FeSe filmsJul 03 2018Mar 11 2019There is an ongoing debate about the relative importance of structural change versus doping charge carriers on the mechanism of superconductivity in Fe-based materials. Elucidating this issue is a major challenge since it would require a large number ... More

Blow-up criterion of classical solutions for the incompressible nematic liquid crystal flowsOct 15 2012Jun 08 2016In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at a finite ... More

Higher rank rigidity for Berwald spacesOct 15 2015Oct 16 2015We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected reversible Berwald space of finite volume and bounded nonpositive flag curvature with rank at least 2 ... More

A Scheme to Classify Topological Property of Band Insulator Based On One-band U(1) Chern NumberFeb 28 2011Topological insulator(TI) is a phase of matter discovered recently. Kane and Mele proposed this phase is distinguished from the ordinary band insulator by a Z2 topological invariant.2 Several authors have try to related this Z2 invariant to Chern numbers. ... More

On Solutions of Three Quasi-Geostrophic ModelsDec 10 2000Dec 12 2000We consider the 2D quasi-geostrophic model and its two different regularizations. Global regularity results are established for the regularized models with subcritical or critical indices. The proof of Onsager's conjecture concerning weak solutions of ... More

The selforganization phenomenon in Rayleigh-Benard convection: a hydrodynamics analysisNov 19 2010The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is well studied. Here we review results from the investigation of this system as well as a number of related and novel numerical ... More

Equilibrium Value Method for the Proof of QIP=PSPACEApr 02 2010Mar 12 2011We provide an alternative proof of \class{QIP}=\class{PSPACE} to the recent breakthrough result. Unlike solving some semidefinite programs that captures the computational power of quantum interactive proofs, our method starts with one \class{QIP}-Complete ... More

Gravitational Shielding Effects in Gauge Theory of GravityJul 23 2003In 1992, E.E.Podkletnov and R.Nieminen find that, under certain conditions, ceramic superconductor with composite structure has revealed weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's ... More

A New Electroweak Model Without Higgs BosonFeb 04 1998Jul 02 1998In this paper, we try to construct an electroweak model which avoids using Higgs mechanism. We simultaneously introduce two sets of gauge bosons so as to keep the masses of gauge bosons $W^{\pm}$ and $Z$ non-zero without using Higgs mechanism. In order ... More

Renormalizable Quantum Gauge General RelativitySep 08 2003The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational gauge symmetry. ... More

Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge TheoryFeb 03 2003In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitational gauge interactions is discussed. SU(N) gauge interactions and gravitational gauge interactions are formulated on the similar basis and are unified ... More

A Note on Spectral Analysis for ${\rm GL}_2$: IIOct 02 2016Oct 17 2016We generalize Zagier's work on regularized integral to the adelic setting and to smooth Eisenstein series, guided by a spectral analytic viewpoint. We prove a singular case of the triple product formula for non rapidly decreasing functions constructed ... More

The Functor $A^{\min}$ for $(p-1)$-cell Complexes and $\EHP$ SequencesFeb 04 2010Let $X$ be a co-$H$-space of $(p-1)$-cell complex with all cells in even dimensions. Then the loop space $\Omega X$ admits a retract $\bar A^{\min}(X)$ that is the evaluation of the functor $\bar A^{\min}$ on $X$. In this paper, we determine the homology ... More

Power sums of Hecke's eigenvalues and applicationJun 28 2008We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi's recent results on higher order symmetric powers. As an application, we improve Kohnen, Lau & Shparlinski's lower bound for the number of Hecke eigenvalues ... More

The average exponent of elliptic curves modulo $p$Jun 26 2012Let $E$ be an elliptic curve defined over ${\mathbb Q}$. For a prime $p$ of good reduction for $E$, denote by $e_p$ the exponent of the reduction of $E$ modulo $p$. Under GRH, we prove that there is a constant $C_E\in (0, 1)$ such that $$ \frac{1}{\pi(x)} ... More

Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearityOct 15 2012Nov 21 2012In this paper, we consider the nonlinear fractional Schr\"odinger equations with Hartree type nonlinearity. We obtain the existence of standing waves by studying the related constrained minimization problems by applying the concentration-compactness principle. ... More

The Cauchy problem for the Pavlov equation with large dataJan 23 2015The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a nonlinear Riemann-Hilbert ... More

Biologically Inspired Hierarchical Model for Feature Extraction and LocalizationApr 14 2006Feature extraction and matching are among central problems of computer vision. It is inefficent to search features over all locations and scales. Neurophysiological evidence shows that to locate objects in a digital image the human visual system employs ... More

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann EquationSep 13 2014Oct 16 2015We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier ... More

Local Wellposedness of Viscous Surface Wave without Surface TensionJun 10 2012Dec 06 2014We consider an incompressible viscous flow without surface tension in a finite- depth domain of three dimension, with free top boundary. This system is governed by a Naiver-Stokes equation in a moving domain and a transport equation for the top boundary. ... More

Bias Correction for Regularized Regression and its Application in Learning with Streaming DataMar 15 2016We propose an approach to reduce the bias of ridge regression and regularization kernel network. When applied to a single data set the new algorithms have comparable learning performance with the original ones. When applied to incremental learning with ... More

Stability analysis for a class of nonlinear time-changed systemsFeb 23 2016This paper investigates the stability of a class of differential systems time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized It\^o formula ... More

Observational Evidence for Young Radio Galaxies are Triggered by Accretion Disk InstabilityJul 13 2009The bolometric luminosities and black hole (BH) masses are estimated by various methods for a sample of young radio galaxies with known ages. We find that the ages are positively correlated with the bolometric luminosities in these young radio galaxies, ... More

Physical foundation of the mathematical concepts in the nonstandard analysis theory of turbulenceJan 18 2006The physical foundation of the main mathematical concepts in the nonstandard analysis theory of turbulence are presented and discussed. The basic fact is that there does not exist the absolute zero fluid-volume. Therefore, the corresponding physical object ... More

Regularity Structure, Vorticity Layer and Convergence Rates of Inviscid Limit of Free Surface Navier-Stokes Equations with or without Surface TensionAug 25 2016In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes equations ... More

Non-local correction to the energy-momentum tensor for $φ^{3}$ theory in six dimensionsMay 07 2015Oct 05 2015Applying the background field method, we construct by explicit computation the leading-order non-local quantum correction to the on-shell effective action for $\phi^3$ theory in six dimensions. We then use the resulting action to obtain the non-local ... More

Profitable Bayesian implementation in one-shot mechanism settingsDec 26 2018Jan 26 2019In the mechanism design theory, a designer would like to implement a desired social choice function which specifies her favorite outcome for each possible profile of all agents' types. In a standard one-shot mechanism, the agents interact only once and ... More

Two Error Bounds of Imperfect Binary SearchOct 31 2017Suppose we know that an object is in a sorted table and we want to determine the index of that object. To achieve this goal we could perform a binary search. However, suppose it is time-consuming to determine the relative position of that object to any ... More

Improve SAT-solving with Machine LearningOct 30 2017In this project, we aimed to improve the runtime of Minisat, a Conflict-Driven Clause Learning (CDCL) solver that solves the Propositional Boolean Satisfiability (SAT) problem. We first used a logistic regression model to predict the satisfiability of ... More

Minimizing Embedding Distortion with Weighted Bigraph Matching in Reversible Data HidingDec 18 2017For a required payload, the existing reversible data hiding (RDH) methods always expect to reduce the embedding distortion as much as possible, such as by utilizing a well-designed predictor, taking into account the carrier-content characteristics, and/or ... More

An Introduction to the Discharging MethodNov 07 2017In this survey essay, I explore the application of the discharging method in graph theory, including the selection of charging rules and discharging rules, and the general characteristics of the discharging method. As examples, I will prove some lemmas ... More

A Note on Spectral Analysis in Automorphic Representation Theory for ${\rm GL}_2$: IIOct 02 2016Oct 17 2017We generalize Zagiers work on regularized integral to the singular case in the adelic setting. We develop necessary tools of treating various singular cases of regularized triple product formulas, which appear naturally in the work of Michel and Venkatsh ... More

Subconvex bounds for compact toric integralsApr 07 2016Jul 11 2018We generalize our method for subconvex bounds for $\mathrm{GL}_2 \times \mathrm{GL}_1$ to the setting of the Waldspurger's formula for compact torical integrals. We address the two major difficulties: one is the lack of split places with small norm, the ... More

Polychromatic Arm Exponents for the Critical Planar FK-Ising modelApr 22 2016Jan 13 2018Schramm Loewner Evolution (SLE) is a one-parameter family of random planar curves introduced by Oded Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical lattice models. This is the only possible process with ... More

Boundary Arm Exponents for SLENov 27 2015Jul 19 2016We derive boundary arm exponents and interior arm exponents for SLE$(\kappa)$. Combining with the possible convergence of critical lattice models to SLE, these exponents would give the corresponding alternating half-plane arm exponents and alternating ... More

Maximum Margin Clustering for State Decomposition of Metastable SystemsDec 31 2014When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most ... More

Optimal stopping under g_ΓexpectationMay 11 2011In this paper, we solve the existence problem of optimal stopping problem under some kind of nonlinear expectation named g_\Gamma expectation which was recently introduced in Peng, S.G. and Xu, M.Y. [8]. Our method based on our preceding work on the continuous ... More

Simplified Khovanov-Rozansky Chain Complexes of Open 2-braidsNov 15 2011Jun 25 2012Motivated by the works of Krasner [arXiv:0801.4018] and Lobb [arXiv:1103.1412], we simplify the Khovanov-Rozansky chain complexes of open 2-braids. As an application, we show that, for a knot containing a "long" 2-braid, the sl(N) Rasmussen invariant ... More

Electronic structure study of double perovskites $A_{2}$FeReO$_{6}$ (A=Ba,Sr,Ca) and Sr$_{2}M$MoO$_{6}$ (M=Cr,Mn,Fe,Co) by LSDA and LSDA+UJul 23 2001We have implemented a systematic LSDA and LSDA+U study of the double perovskites $A_{2}$FeReO$_{6}$ (A=Ba,Sr,Ca) and Sr$_{2}$$M$MoO$_{6}$ (M=Cr,Mn,Fe,Co) for understanding of their intriguing electronic and magnetic properties. The results suggest a ferrimagnetic ... More

On the justification of applying quantum strategies to the Prisoners' Dilemma and mechanism designJul 08 2010The Prisoners' Dilemma is perhaps the most famous model in the field of game theory. Consequently, it is natural to investigate its quantum version when one considers to apply quantum strategies to game theory. There are two main results in this paper: ... More

On amending the Maskin's sufficiency theorem by using complex numbersApr 29 2010Apr 17 2012The Maskin's theorem is a fundamental work in the theory of mechanism design. In this paper, we will propose a self-enforcing agreement by which agents can fight a bad social choice rule which satisfies monotonicity and no-veto if an additional condition ... More

Equivariant colored sl(N)-homology for linksFeb 15 2010Feb 28 2011We construct an equivariant colored sl(N)-homology for links, which generalizes both the colored sl(N)-homology defined by the author and the equivariant sl(N)-homology defined by Krasner. The construction is a straightforward generalization of that of ... More

A Family of Transverse Link HomologiesAug 14 2013Apr 07 2014We define a homology $\mathcal{H}_N$ for closed braids by applying Khovanov and Rozansky's matrix factorization construction with potential $ax^{N+1}$. Up to a grading shift, $\mathcal{H}_0$ is the HOMFLYPT homology defined in arXiv:math/0505056. We demonstrate ... More

A Tractable Approach to Dynamic Network Dimensioning Based on the Best-cell ConfigurationApr 18 2017Spatial distributions of other cell interference (OCIF) and interference to own-cell power ratio (IOPR) with reference to the distance between a mobile and its serving base station (BS) are modeled for the down-link reception of cellular systems based ... More

Recent results for STAR $\sqrt{s_{NN}}=4.9$ GeV Al+Au and $\sqrt{s_{NN}}=4.5$ GeV Au+Au Fixed-Target CollisionsJul 18 2018Oct 24 2018We present recent results from Al(beam)+Au(target) collisions at $\sqrt{s_{NN}}=4.9$ GeV and Au+Au collisions at $\sqrt{s_{NN}}=4.5$\kern 0.16667em GeV from the STAR fixed-target (FXT) program. We report transverse mass spectra of protons, $K^0_S$ and ... More

A metric sphere not a quasisphere but for which every weak tangent is EuclideanJun 07 2018We show that for all $n \geq 2$, there exists a doubling linearly locally contractible metric space $X$ that is topologically a $n$-sphere such that every weak tangent is isometric to $\R^n$ but $X$ is not quasisymmetrically equivalent to the standard ... More

Systematic Noise: Micro-movements in Equity Options MarketsAug 23 2017Equity options are known to be notoriously difficult to price accurately, and even with the development of established mathematical models there are many assumptions that must be made about the underlying processes driving market movements. As such, the ... More

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: homogeneous relaxation and transport coefficientsOct 07 2018A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and ... More

Betti Numbers of the HOMFLYPT HomologyMar 21 2017Apr 04 2018In arXiv:math/0508510, Rasmussen observed that the Khovanov-Rozansky homology of a link is a finitely generated module over the polynomial ring generated by the components of this link. In the current paper, we study the module structure of the middle ... More

Virtual Abelian varieties of $\mathrm{GL}_2$-typeJul 11 2015Sep 28 2017This paper studies a class of Abelian varieties that are of $\mathrm{GL}_2$-type and with isogenous classes defined over a number field $k$ (i.e., $k$-virtual). We treat both cases when their endomorphism algebras are (1) a totally real field $K$ or (2) ... More

Positivity-Preserving Analysis of Numerical Schemes for Ideal MagnetohydrodynamicsFeb 07 2018May 16 2018Numerical schemes provably preserving the positivity of density and pressure are highly desirable for MHD, but the rigorous positivity-preserving (PP) analysis remains challenging. The difficulties mainly arise from the intrinsic complexity of the MHD ... More

On regular configurations and disjoint cycles in shift graphsSep 30 2007Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are discussed, including ... More

A non-local one-phase free boundary problem from obstacle to cavitationOct 10 2018We consider a one-phase free boundary problem of the minimizer of the energy \[ J_{\gamma}(u)=\frac{1}{2}\int_{(B_1^{n+1})^+}{y^{1-2s}|\nabla u(x,y)|^2dxdy}+\int_{B_1^{n}\times \{y=0\}}{u^{\gamma}dx}, \] with constants $0<s,\gamma<1$. It is an intermediate ... More

Subsets of colossally abundant numbersMar 08 2019Let $G(n)=\sigma (n)/(n \log \log n )$. Robin made hypothesis that $G(n)<e^\gamma$ for all integer $n>5040$. This article divides all colossally abundant numbers in to three disjoint subsets CA1, CA2 and CA3, and shows that Robin hypothesis is true if ... More

Properties of counterexample to Robin hypothesisJan 16 2019Feb 14 2019Let $G(n)=\sigma (n)/(n \log \log n )$. Robin made hypothesis that $G(n)<e^\gamma$ for all integer $n>5040$. If there exists counterexample to Robin hypothesis, then there must exist finite number of counterexamples $n>5040$ such that $G(n)$ attains largest ... More

Equivariant Holomorphic Morse Inequalities II: Torus and Non-Abelian Group ActionsFeb 15 1996Jun 22 1998We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kahler manifolds and show the necessity of the Kahler condition. For torus actions, there is ... More