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Results for "Fazhi Yang"

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A propagation matting method based on the Local Sampling and KNN Classification with adaptive feature spaceMay 03 2016Closed Form is a propagation based matting algorithm, functioning well on images with good propagation . The deficiency of the Closed Form method is that for complex areas with poor image propagation , such as hole areas or areas of long and narrow structures. ... More
Trust-aware Collaborative Denoising Auto-Encoder for Top-N RecommendationMar 06 2017May 08 2017Both feedback of ratings and trust relationships can be used to reveal users' tastes for improving recommendation performance, especially for cold users. However, both of them are facing data sparsity problem, which may severely degrade recommendation ... More
Observation of Majorana conductance plateau by scanning tunneling spectroscopyApr 12 2019Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits perfect ... More
Upper triangular matrices and Billiard ArraysAug 18 2015Jan 15 2016Fix a nonnegative integer $d$, a field $\mathbb{F}$, and a vector space $V$ over $\mathbb{F}$ with dimension $d+1$. Let $T$ denote an invertible upper triangular matrix in ${\rm Mat}_{d+1}(\mathbb{F})$. Using $T$ we construct three flags on $V$. We find ... More
Adaptive elastic net and Separate Selection from Least Squares for ultra-high dimensional regression modelsOct 14 2014This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy. Besides, we ... More
Research on Information Security Enhancement Approaches and the Applications on HCI SystemsFeb 02 2016With rapid development of computer techniques, the human computer interaction scenarios are becoming more and more frequent. The development history of the human-computer interaction is from a person to adapt to the computer to the computer and continually ... More
$L^2$ Forms and Ricci flow with bounded curvature on Complete Non-compact manifoldsSep 11 2005In this paper, we study the evolution of $L^2$ one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the $L^2$ norm of a smooth one form with compact support is non-increasing along the ... More
Decay of correlations for maximal measure of maps derived from Anosov: I: mostly contracting centerOct 03 2016It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables, assuming the ... More
Full quantum theory of control-not gate in ion-trap quantum computationNov 26 2015We investigate the exact effect on ion trap quantum computation after field quantization. First an exact expression of failure probability from field quantization after many CNOT operations in Cirac-Zoller scheme is given. It is proportional to operation ... More
The Heart-shaped Supernova Remnant 3C391 viewed in Multi-bandsMar 29 2007Using Chandra X-ray, Spitzer mid-IR, and 1.5 GHz radio data, we examine the spatial structure of SNR 3C391. The X-ray surface brightness is generally anti-correlative with the IR and radio brightness. The multiband data clearly exhibit a heart-shaped ... More
Narrow Band Chandra X-ray Analysis of Supernova Remnant 3C391May 02 2005We present the narrow-band and the equivalent width (EW) images of the thermal composite supernova remnant (SNR) 3C391 for the X-ray emission lines of elements Mg, Si, & S using the Chandra ACIS Observational data. These EW images reveal the spatial distribution ... More
On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equationMar 14 2019This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue waves are derived ... More
General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equationNov 16 2017Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves ... More
Further Results for Perron-Frobenius Theorem for Nonnegative Tensors IIApr 02 2011Nov 20 2012In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.
Real-Variable Characterizations Of Hardy Spaces Associated With Bessel OperatorsFeb 07 2011Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0, \infty), dm_\lambda)$ ... More
Bound-preserving discontinuous Galerkin method for compressible miscible displacement in porous mediaJul 18 2017In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the $i$th component ... More
Transformations between nonlocal and local integrable equationsApr 30 2017Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable equations can ... More
Decay of correlations for maximal measure of maps derived from AnosovOct 03 2016Oct 23 2017It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables, assuming the ... More
Existence and nondegeneracy of ground states in critical free boundary problemsMay 06 2014Mar 17 2015Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. The corresponding study of higher critical points was recently initiated in Jerison and Perera [30, 31]. In particular, the existence ... More
Local Hardy Spaces of Musielak-Orlicz Type and Their ApplicationsAug 13 2011Jun 28 2012Let $\phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S. Rychkov). In this ... More
Geometric Measure of non-Commuting Simultaneous Measurement based on K-Means ClusteringDec 13 2018Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The rationality of our ... More
Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticityAug 04 2018Jan 04 2019We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor can be uniquely ... More
The Inverse Problem for the Dirichlet-to-Neumann map on Lorentzian manifoldsJul 29 2016Sep 27 2016We consider the Dirichlet-to-Neumann map $\Lambda$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric $g$, a magnetic field $A$ and a potential $q$. We show that we can recover the jet of $g,A,q$ on the boundary ... More
Botnets Drilling Away Privacy InfrastructureDec 20 2015In this paper, we explore various technologies and their roles in subverting the privacy infrastructure of the Internet. We also provide mitigation techniques on the attack vectors the technologies provide, and assess the overall severity of these threats. ... More
On some properties of nonnegative weakly irreducible tensorsNov 03 2011Mar 13 2012In this paper, we mainly focus on how to generalize some conclusions from nonnegative irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and important lemma is proven using new tools. First, we give the definition of stochastic ... More
Application of EOS-ELM with binary Jaya-based feature selection to real-time transient stability assessment using PMU dataSep 08 2018Recent studies show that pattern-recognition-based transient stability assessment (PRTSA) is a promising approach for predicting the transient stability status of power systems. However, many of the current well-known PRTSA methods suffer from excessive ... More
Musielak-Orlicz Hardy Spaces Associated with Operators and Their ApplicationsJan 26 2012Jun 29 2012Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a nonnegative self-adjoint operator in $L^2(\mathcal{X})$ satisfying the Davies-Gaffney estimates. Let $\varphi:\,\mathcal{X}\times[0,\infty)\to[0,\infty)$ be a function such that $\varphi(x,\cdot)$ ... More
Real-variable Characterizations of Orlicz-Hardy Spaces on Strongly Lipschitz Domains of $\mathbb{R}^n$Jul 17 2011Let $\Omega$ be a strongly Lipschitz domain of $\mathbb{R}^n$, whose complement in $\mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (\Omega)$ with the Dirichlet boundary condition, and the heat semigroup ... More
Boundedness of Linear Operators via Atoms on Hardy Spaces with Non-doubling MeasuresJun 07 2009Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear operator $T$ ... More
Thermo and photoacoustic Tomography with variable speed and planar detectorsMay 03 2016We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propose ... More
Multiwave tomography with reflectors: Landweber's iterationMar 23 2016Apr 19 2016We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the step size for ... More
Atomic and Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators on Spaces of Homogeneous TypeAug 30 2018Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ whose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth function $\varphi:\ \mathcal{X}\times[0,\infty) ... More
A note on the geometric simplicity of the spectral radius of nonnegative irreducible tensorsJan 13 2011Mar 13 2012We prove that the spectral radius of even order nonnegative irreducible tensors is real geometrically simple. In the case when the order of the tensor is odd, or in the complex field, some conditions are given to guarantee the geometric simplicity of ... More
Observability transition in real networksJul 25 2016We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function of the fraction ... More
Finite Heat conduction in 2D LatticesJul 30 2001This paper gives a 2D hamonic lattices model with missing bond defects, when the capacity ratio of defects is enough large, the temperature gradient can be formed and the finite heat conduction is found in the model. The defects in the 2D harmonic lattices ... More
Multiwave tomography in a closed domain: averaged sharp time reversalDec 29 2014Feb 05 2015We study the mathematical model of multiwave tomography including thermo and photoacoustic tomography with a variable speed for a fixed time interval $[0,T]$. We assume that the waves reflect from the boundary of the domain. We propose an averaged sharp ... More
A Parallel Best-Response Algorithm with Exact Line Search for Nonconvex Sparsity-Regularized Rank MinimizationNov 13 2017In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms ... More
A Unified Successive Pseudo-Convex Approximation FrameworkJun 16 2015Apr 07 2016In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of successively ... More
$(N,q)$-Laplacian problems with critical Trudinger-Moser nonlinearitiesNov 09 2014Oct 29 2015We obtain nontrivial solutions of a $(N,q)$-Laplacian problem with a critical Trudinger-Moser nonlinearity in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical nonlinearities, ... More
$N$-Laplacian problems with critical Trudinger-Moser nonlinearitiesJun 24 2014Jan 03 2016We prove existence and multiplicity results for a $N$-Laplacian problem with a critical exponential nonlinearity that is a natural analog of the Brezis-Nirenberg problem for the borderline case of the Sobolev inequality. This extends results in the literature ... More
Accurate atomic quantum defects from particle-particle random phase approximationOct 26 2015The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect theory to (a) separate errors due to approximate ionization potentials, ... More
A Hierarchical Butterfly LU Preconditioner for Two-Dimensional Electromagnetic Scattering Problems Involving Open SurfacesJan 31 2019This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect electrically ... More
Singularites in the Bousseneq equation and in the generalized KdV equationAug 16 2001In this paper, two kinds of the exact singular solutions are obtained by the improved homogeneous balance (HB) method and a nonlinear transformation. The two exact solutions show that special singular wave patterns exists in the classical model of some ... More
Existence and mass concentration of pseudo-relativistic Hartree equationApr 12 2017In this paper, we investigate the constrained minimization problem \begin{equation}\label{eq:0.1} e(a):=\inf_{\{u\in \mathcal{H},\|u\|_2^2=1\}}E_a(u), \end{equation} where the energy functional \begin{equation} \label{eq:0.2} E_a(u)=\int_{\mathbb{R}^3}(u\sqrt{-\Delta+m^2}\,u+Vu^2)\,dx ... More
Weighted Local Orlicz-Hardy Spaces with Applications to Pseudo-differential OperatorsJul 17 2011Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orlicz-Hardy space $h^{\Phi}_{\omega}(\mathbb{R}^n)$ via the local ... More
Orlicz-Hardy Spaces Associated with Divergence Operators on Unbounded Strongly Lipschitz Domains of $\mathbb{R}^n$Jul 15 2011Jun 29 2012Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and $\Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,\infty)$ of upper type 1 and of strictly critical lower type $p_{\Phi}\in(n/(n+1),1]$. ... More
Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators Satisfying Gaussian EstimatesMar 16 2016Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\,\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that $\varphi(x,\cdot)$ ... More
On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Aug 03 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More
On asymptotic dynamics for $L^2$ critical generalized KdV equations with a saturated perturbationSep 16 2016In this paper, we consider the $L^2$ critical gKdV equation with a saturated perturbation: $$\partial_t u+(u_{xx}+u^5-\gamma u|u|^{q-1})_x=0,$$ where $q>5$ and $0<\gamma\ll1$. For any initial data $u_0\in H^1$, the corresponding solution is always global ... More
Spacecraft Attitude and Reaction Wheel Desaturation Combined Control MethodMar 31 2016Nov 10 2016Two popular types of spacecraft actuators are reaction wheels and magnetic torque coils. Magnetic torque coils are particularly interesting because they can be used for both attitude control and reaction wheel momentum management (desaturation control). ... More
Blocks of defect of p-solvable groupsJan 14 2015Let $p$ be a prime such that $p \geq 5$. Let $G$ be a finite $p$-solvable group and let $p^a$ be the largest power of $p$ dividing $\chi(1)$ for an irreducible character $\chi$ of $G$, we show that $|G:F(G)|_p \leq p^{5.5a}$. Let $G$ be a finite $p$-solvable ... More
Color-Kinematics Duality and Sudakov Form Factor at Five LoopsOct 07 2016Using color-kinematics duality, we construct for the first time the full integrand of the five-loop Sudakov form factor in N=4 super-Yang-Mills theory, including non-planar contributions. This result also provides a first manifestation of the color-kinematics ... More
Troisième groupe de cohomologie non ramifiée des torseurs universels sur les surfaces rationnellesSep 16 2016Let $k$ a field of characteristic zero. Let $X$ be a smooth, projective, geometrically rational $k$-surface. Let $\mathcal{T}$ be a universal torsor over $X$ with a $k$-point et $\mathcal{T}^c$ a smooth compactification of $\mathcal{T}$. There is an open ... More
Approximation forte pour les variétés avec une action d'un groupe linéaireApr 12 2016Oct 21 2016Let $G$ be a connected linear algebraic group over a number field. Let $U \hookrightarrow X$ be a $G$-equivariant open embedding of a $G$-homogeneous space with connected stabilizers into a smooth $G$-variety. We prove that $X$ satisfies strong approximation ... More
Axions and Dark MatterSep 02 2015Sep 10 2015Dark matter particles constitute $23\%$ of the total energy density of our universe and their exact properties are still unclear besides that they must be very cold and weakly interacting with the standard model particles. Many beyond standard model theories ... More
Projective spectrum in Banach algebrasApr 02 2008For a tuple $A=(A_0, A_1, ..., A_n)$ of elements in a unital Banach algebra ${\mathcal B}$, its {\em projective spectrum} $p(A)$ is defined to be the collection of $z=[z_0, z_1, ..., z_n]\in \pn$ such that $A(z)=z_0A_0+z_1A_1+... +z_nA_n$ is not invertible ... More
Booster High-level RF Frequency Tracking Improvement Via Bias-Curve OptimizationJan 06 2005It is important to improve the frequency tracking between the RF drive and the cavity field for the purpose of reducing longitudinal phase oscillations and increasing the effective accelerating voltage. And this is especially beneficial for Booster running ... More
Modular curvature for toric noncommutative manifoldsOct 15 2015Jun 25 2016A general question behind this paper is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80s. It has only recently begun (2014) to be comprehended via the intensive study of modular ... More
New link invariants and Polynomials (I), oriented caseApr 13 2010May 09 2011Given any oriented link diagram, two types of new knot invariants are constructed. They satisfy some generalized skein relations. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of those rings define new ... More
Adaptive Accelerated Gradient Converging Methods under Holderian Error Bound ConditionNov 23 2016In this paper, we focus our study on the convergence of (proximal) gradient methods and accelerated (proximal) gradient methods for smooth (composite) optimization under a H\"{o}lderian error bound (HEB) condition. We first show that proximal gradient ... More
The KPZ Equation, Non-Equilibrium Solutions, and Weak Universality for Long-Range InteractionsOct 05 2018Nov 02 2018We study the weak KPZ universality problem by extending the KPZ universality results for random, microscopic fields known as the density fluctuation field developed by Goncalves-Jara \cite{GJ16}, Goncalves-Jara-Sethuraman \cite{GJS15} and Gubinelli-Perkowski ... More
Partially-PT-symmetric optical potentials with all-real spectra and soliton families in multi-dimensionsDec 12 2013Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial directions. However, ... More
Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equationsMar 23 2012Bifurcations of solitary waves are classified for the generalized nonlinear Schr\"odinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary ... More
Tortoise coordinate and Hawking effect in a dynamical Kerr black holeMar 04 2010Hawking effect from a dynamical Kerr black hole is investigated using the improved Damour-Ruffini method with a new tortoise coordinate transformation. Hawking temperature of the black hole can be obtained point by point at the event horizon. It is found ... More
Dynamic Point-Formation in Dielectric FluidsMar 31 2003We use boundary-integral methods to compute the time-dependent deformation of a drop of dielectric fluid immersed in another dielectric fluid in a uniform electric field E. Steady state theory predicts, when the permittivity ratio, \beta, is large enough, ... More
Tangent spaces to motivic cohomology groupsNov 23 2013Sep 14 2016BY using Green-Griffiths' results on tangent spaces to algebraic cycles [4], we study the tangent space to $CH^{2}(X,1)$, where $X$ is a nonsingular projective curve over a field $k$ of characteristic $0$.
Entropy DistanceMar 01 2013Apr 29 2013Motivated by the approach of random linear codes, a new distance in the vector space over a finite field is defined as the logarithm of the "surface area" of a Hamming ball with radius being the corresponding Hamming distance. It is named entropy distance ... More
Equidistribution of expanding translates of curves and Diophantine approximation on matricesSep 23 2018Oct 16 2018We study the general problem of equidistribution of expanding translates of an analytic curve by an algebraic diagonal flow on the homogeneous space $G/\Gamma$ of a semisimple algebraic group $G$. We define two families of algebraic subvarieties of the ... More
Consistency of cross validation for comparing regression proceduresMar 20 2008Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for kernel smoothing). ... More
Livšic Measurable Rigidity Theorem for \mathcal{C}^1 Generic Volume-preserving SystemsOct 31 2014In this paper, we prove that for $\mathcal{C}^1$ generic volume-preserving Anosov diffeomorphisms of a compact Riemannian manifold, Liv\v{s}ic measurable rigidity theorem holds. We also prove that for $\mathcal{C}^1$ generic volume-preserving Anosov flows ... More
Intelligent Processing in Vehicular Ad hoc Networks: a SurveyMar 28 2019The intelligent Processing technique is more and more attractive to researchers due to its ability to deal with key problems in Vehicular Ad hoc networks. However, several problems in applying intelligent processing technologies in VANETs remain open. ... More
Fine-tune BERT for Extractive SummarizationMar 25 2019BERT, a pre-trained Transformer model, has achieved ground-breaking performance on multiple NLP tasks. In this paper, we describe BERTSUM, a simple variant of BERT, for extractive summarization. Our system is the state of the art on the CNN/Dailymail ... More
Emergent Commensurability from Hilbert Space Truncation in Fractional Quantum Hall FluidsDec 31 2018Jan 18 2019We show that model states of fractional quantum Hall fluids at all experimentally detected plateau can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation motivated from physical local measurements. ... More
Recent Development in Analog Computation - A Brief OverviewApr 02 2015The recent development in analog computation is reviewed in this paper. Analog computation was used in many applications where power and energy efficiency is of paramount importance. It is shown that by using innovative architecture and circuit design, ... More
An Efficient Dispatcher for Large Scale GraphProcessing on OpenCL-based FPGAsJun 03 2018High parallel framework has been proved to be very suitable for graph processing. There are various work to optimize the implementation in FPGAs, a pipeline parallel device. The key to make use of the parallel performance of FPGAs is to process graph ... More
On the classification of certain hypersurfaces in CP^4Sep 19 2006In this paper the singular hypersurfaces in $\mathbb{C}\mathrm{P}^4$ of degree $d$ with an isolated singularity are studied. If the singularity is of type $A_{2k+1}$, under the condition $d<(k+5)/2$, a classification of such hypersurfaces upto homeomorphism ... More
Analysis of Markovian Competitive Situations using Nonatomic GamesOct 23 2015Apr 02 2017For dynamic situations where the evolution of a player's state is influenced by his own action as well as other players' states and actions, we show that equilibria derived for nonatomic games (NGs) can be used by their large finite counterparts to achieve ... More
A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite CounterpartsOct 23 2015Jun 22 2016We show that equilibria of a sequential semi-anonymous nonatomic game (SSNG) can be adopted by players in corresponding large but finite dynamic games to achieve near-equilibrium payoffs. Such equilibria in the form of random state-to-action rules are ... More
Bifurcation of limit cycles from a quadratic global center with two switching linesOct 07 2018In this paper, we generalize the Picard-Fuchs equation method to study the bifurcation of limit cycles of perturbed differential systems with two switching lines. We obtain the detailed expression of the corresponding first order Melnikov function which ... More
A new nonlocal nonlinear Schroedinger equation and its soliton solutionsJul 05 2018A new integrable nonlocal nonlinear Schroedinger (NLS) equation with clear physical motivations is proposed. This equation is obtained from a special reduction of the Manakov system, and it describes Manakov solutions whose two components are related ... More
Dirac Composite Fermion - A Particle-Hole SpinorNov 22 2017Jan 10 2018The particle-hole (PH) symmetry at half-filled Landau level requires the relationship between the flux number N_phi and the particle number N on a sphere to be exactly N_phi - 2(N-1) = 1. The wave functions of composite fermions with 1/2 "orbital spin", ... More
On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag CurvatureFeb 14 2013Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(\alpha,\beta)$-metrics which are locally projectively flat with constant flag curvature ... More
On a Class of Singular Douglas and Projectively flat Finsler MetricsFeb 14 2013Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of singular Finsler metrics defined by a Riemann metric $\alpha$ and 1-form $\beta$ and characterize ... More
Affine Actions and the Yang-Baxter EquationJul 12 2016In this paper, the relations between the Yang-Baxter equation and affine actions are explored in detail. In particular, we classify solutions of the Yang-Baxter equations in two ways: (i) by their associated affine actions of their structure groups on ... More
Virtual harmonyOct 23 2015This article serves a few purposes. First of all, it reviews polyfold--Kuranishi correspondence I ( and previews and samples some results from four papers I have been preparing. It is also a written-up and expanded version ... More
Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1Mar 31 20121.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral is the only possible candidate to enhance a path with ... More
Stably weakly shadowing transitive sets and dominated splittingsMar 10 2010We prove that for any $C^1$-stably weakly shadowing transitive set $\Lambda$, either $\Lambda$ is a sink or a source, or $\Lambda$ admits a dominated splitting.
A new compact class of open sets under Hausdorff distance and shape optimizationMar 20 2010Aug 16 2010In this paper we obtain a new class of open sets, and we prove the class is compact under the Hausdorff distance, then we prove the existence of solutions of some shape optimization for elliptic equations.
Recent Development of QCD Factorization for B-> M1 M2Mar 09 2010After briefly introducing the framework of QCD factorization for B-> M1 M2 in the language of the Soft-Collinear Effective Theory, we firstly address the recent efforts on higher-order radiative corrections in QCD factorization. Then we discuss some phenomenologies ... More
A note on antimagic orientations of even regular graphsNov 05 2018Motivated by the conjecture of Hartsfield and Ringel on antimagic labelings of undirected graphs, Hefetz, M\"{u}tze, and Schwartz initiated the study of antimagic labelings of digraphs in 2010. Very recently, it has been conjectured in [Antimagic orientation ... More
On a general theorem for additive Levy processesJul 12 2007We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
A deformation of Penner's simplicial coordinateNov 07 2010Jul 15 2011We produce a one-parameter family of coordinates $\{\Psi_h\}_{h\in\mathbb{R}}$ of the decorated Teichm\"{u}ller space of an ideally triangulated punctured surface $(S,T)$ with negative Euler characteristic, which is a deformation of Penner's simplicial ... More
Explicit Realization of Hopf Cyclic Cohomology Classes of Bicrossed Product Hopf AlgebrasNov 02 2015We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\cH=\big( \cU(\Fg_1) \acr \cR(G_2) \big)^{\cop}$ constructed from a matched pair of Lie groups $G_1$ and $G_2$, on a convolution algebra $\cA=C_c^{\ify}(G_1)\rtimes ... More
A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated PolynomialsJul 29 2007Apr 22 2010The main result of this paper is to calculate the Batalin-Vilkovisky structure of $HH^*(C^*(\mathbf{K}P^n;R);C^*(\mathbf{K}P^n;R))$ for $ \mathbf{K}=\mathbb{C}$ and $\mathbb{H}$, and $R=\mathbb{Z}$ and any field; and shows that in the special case when ... More
A Decomposition of Complex Monge-Ampere MeasuresFeb 20 2007We prove one decomposition theorem of complex Monge-Ampere measures of plurisubharmonic functions in connection with their pluripolar sets.
Toric Fano manifolds with nef tangent bundlesJun 18 2015In this note we prove that any toric Fano manifold with nef tangent bundle is a product of projective spaces. In particular, it implies that Campana-Peternell conjecture hold for toric manifolds.
Convex domain which tiles space by translation,with multiplicitySep 12 2018Sep 17 2018This paper shows that a multiple translative tile in the plane must be a multiple lattice tile.
Solar models with new low-metal abundancesMar 05 2016In the last decade, the photospheric abundances of the Sun had been revised several times by many observers. The standard solar models (SSM) constructed with the new low-metal abundances disagree with helioseismic results and detected neutrino fluxes. ... More
A gluing construction of collapsing Calabi-Yau metrics on K3 fibred 3-foldsSep 21 2018We use the gluing method to give a refined description of the collapsing Calabi-Yau metrics on Calabi-Yau 3-folds admitting a Lefschetz K3 fibration.
Harnack Inequality and Applications for SDEs Driven by $G$-Brownian motionAug 27 2018We establish Harnack inequality and shift Harnack inequality for stochastic differential equation driven by $G$-Brownian motion. As applications, the uniqueness of invariant linear expectations and estimates on the $\sup$-kernel are investigated, where ... More