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Results for "Ligang Sun"

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A New Kalman Filter Model for Nonlinear Systems Based on Ellipsoidal BoundingFeb 08 2018In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system. The main loop ... More
Pressure-induced lattice collapse in tetragonal phase and structural phase transition in single crystalline Fe1.05TeMay 20 2009Jul 20 2009We report studies of in-situ x-ray diffraction (XRD) and electronic properties on the single crystalline of Fe1.05Te compound under high pressure. The results demonstrated that the sample undergoes a pressure-induced lattice collapse in tetragonal phase ... More
The 3-colorability of planar graphs without cycles of length 4, 6 and 9Jun 15 2015In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.
Unions of 1-factors in $r$-graphsSep 06 2015The generalized Berge-Fulkerson conjecture states that every $r$-graph has $2r$ 1-factors such that each edge is contained in precisely two of them. This conjecture is shown to be equivalent to the statement that every $r$-graph can be covered by $2r-1$ ... More
Equation-free Dynamic Renormalization of a KPZ-type EquationMay 31 2005In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves ... More
Petersen cores and the oddness of cubic graphsJan 05 2015Let $G$ be a bridgeless cubic graph. Consider a list of $k$ 1-factors of $G$. Let $E_i$ be the set of edges contained in precisely $i$ members of the $k$ 1-factors. Let $\mu_k(G)$ be the smallest $|E_0|$ over all lists of $k$ 1-factors of $G$. If $G$ ... More
Two-Dimensional Diffusion in the Presence of Topological DisorderAug 29 2003How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite ... More
Monte Carlo Methods for Small Molecule High-Throughput ExperimentationJul 23 2001By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including Metropolis, three ... More
Reaction, Levy Flights, and Quenched DisorderJul 07 2001Aug 13 2002We consider the A + A --> emptyset reaction, where the transport of the particles is given by Levy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of reaction. With ... More
Strategies for High-Throughput, Templated Zeolite SynthesisAug 14 2002How best to design and redesign high-throughput experiments for zeolite synthesis is addressed. A model that relates materials function to chemical composition of the zeolite and the structure directing agent is introduced. Using this model, several Monte ... More
Face-degree bounds for planar critical graphsJan 05 2015Aug 24 2016The only remaining case of a well known conjecture of Vizing states that there is no planar graph with maximum degree 6 and edge chromatic number 7. We introduce parameters for planar graphs, based on the degrees of the faces, and study the question whether ... More
Disorder-Induced Time-Dependent Diffusion in ZeolitesDec 15 1999Apr 03 2000We suggest that disordered framework aluminums and non-framework cations can create a disordered electrostatic potential in zeolites that can lead to a discrepancy between diffusivities measured by microscopic and macroscopic experimental techniques. ... More
Cores, joins and the Fano-flow conjecturesJan 21 2016The Fan-Raspaud Conjecture states that every bridgeless cubic graph has three 1-factors with empty intersection. A weaker one than this conjecture is that every bridgeless cubic graph has two 1-factors and one join with empty intersection. Both of these ... More
Digital Makeup from Internet ImagesOct 16 2016We present a novel approach of color transfer between images by exploring their high-level semantic information. First, we set up a database which consists of the collection of downloaded images from the internet, which are segmented automatically by ... More
Choosability in signed planar graphsFeb 16 2015Sep 07 2015This paper studies the choosability of signed planar graphs. We prove that every signed planar graph is 5-choosable and that there is a signed planar graph which is not 4-choosable while the unsigned graph is 4-choosable. For each $k \in \{3,4,5,6\}$, ... More
A Perceptual Aesthetics Measure for 3D ShapesAug 17 2016While the problem of image aesthetics has been well explored, the study of 3D shape aesthetics has focused on specific manually defined features. In this paper, we learn an aesthetics measure for 3D shapes autonomously from raw voxel data and without ... More
Collective Multipole excitations of exotic nuclei in relativistic continuum random phase approximationSep 03 2013Journal of Combinatorial Theory, Series B, 98(1):173-225, 2008n exotic nuclei are studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum ... More
Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Aug 16 2016Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More
SPLZ: An Efficient Algorithm for Single Source Shortest Path Problem Using Compression MethodAug 11 2014Jan 11 2015Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing ... More
A Novel High-Pressure Monoclinic Metallic Phase of V2O3Dec 26 2013Vanadium sesquioxide, V2O3, is a prototypical metal-to-insulator system where, in temperature-dependent studies, the transition always coincides with a corundum-to-monoclinic structural transition. As a function of pressure, V2O3 follows the expected ... More
Different Particle Sizes Obtained from Static and Dynamic Laser Light ScatteringMay 31 2004Dec 08 2004Detailed investigation of static and dynamic laser light scattering has been attempted in this work both theoretically and experimentally based on dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) ... More
Note on K-stability of pairsAug 23 2011Nov 23 2012We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.
Infinite Mixtures of Multivariate Gaussian ProcessesJul 26 2013This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture ... More
Independence of $\ell$ for the supports in the Decomposition TheoremDec 04 2015In this note, we prove a result on the independence of $\ell$ for the supports of irreducible perverse sheaves occurring in the Decomposition Theorem, as well as for the family of local systems on each support. It generalizes Gabber's result on the independence ... More
An exact axisymmetric spiral solution of incompressible 3D Euler equationsJan 29 2011Jul 31 2011Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler equations. The solution, ... More
Rank $n$ swapping algebra for the $\operatorname{PSL}(n, \mathbb{R})$ Hitchin componentNov 11 2014Oct 24 2015F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce ... More
A representation-theoretic proof of the branching rule for Macdonald polynomialsDec 01 2014We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal ... More
The Star of David RuleMay 09 2008In this note, a new concept called {\em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are ... More
Measures of Intermediate Entropies for Skew Product DiffeomorphismsJun 10 2009Jan 18 2010In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate entropies. ... More
Strichartz-type Estimates for Wave Equation for Normally Hyperbolic Trapped DomainsJul 20 2015We establish a mixed-norm Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega,g)$, for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is ... More
Virtual Domination of $3$-manifoldsJan 27 2014For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented $3$-manifold $N$, we will show that $M$ admits a finite cover $M'$, such that there exists a degree-$2$ map $f:M'\rightarrow N$, i.e. $M$ virtually $2$-dominates $N$.
W-Operators and Permutation GroupsOct 20 2016W-operators are differential operators on the polynomial ring. A special example of W-operators is the cut-and-join operator. We study the relation between W-operators and permutation groups. We find the W-operator $W([d])$ can be written as the sum of ... More
Dark Matter Searches in Jet plus Missing Energy in $\rm γp$ collision at CERN LHCJul 21 2014Aug 01 2014In this paper, we investigate the $\rm \gamma p$ photoproduction of jet plus missing energy signal to set limits on the couplings of the fermionic dark matter to the quarks at the LHC via the main reaction $\rm pp\rightarrow p\gamma p\rightarrow p \chi\chi ... More
Counting Hypergraphs in Data StreamsApr 28 2013We present the first streaming algorithm for counting an arbitrary hypergraph $H$ of constant size in a massive hypergraph $G$. Our algorithm can handle both edge-insertions and edge-deletions, and is applicable for the distributed setting. Moreover, ... More
Pluricanonical maps of varieties of Albanese fiber dimension twoNov 28 2012Feb 23 2014In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the 6-canonical map is birational. And we also show that the 5-canonical map is birational for any such variety with some geometric restrictions. ... More
Virtual Homological Torsion of Closed Hyperbolic 3-manifoldsSep 05 2013Jun 05 2014In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. ... More
On the Clifford theorem for surfacesMar 04 2012We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.
The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Oct 17 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... More
Universal central extensions of twisted forms of split simple Lie algebras over ringsNov 17 2010Nov 19 2010We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are obtained by ... More
On uniform estimate of complex elliptic equations on closed Hermitian manifoldsDec 16 2014Feb 10 2015In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed K\"ahler manifolds. ... More
On a class of fully nonlinear elliptic equations on closed Hermitian manifoldsOct 01 2013We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive $C^\infty$ {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed to launch ... More
A New Formula for the Inverse Wavelet TransformJun 20 2010Aug 30 2010Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
Shifted convolution sums of $GL_3$ cusp forms with $θ$-seriesSep 25 2015Sep 10 2016Let $A_f(1,n)$ be the normalized Fourier coefficients of a Hecke-Maass cusp form $f$ for $SL_3(\mathbb{Z})$ and $$ r_3(n)=\#\left\{(n_1,n_2,n_3)\in \mathbb{Z}^3:n_1^2+n_2^2+n_3^2=n\right\}. $$ Let $1\leq h\leq X$ and $\phi(x)$ be a smooth function compactly ... More
Direct images of bundles under Frobenius morphismsNov 13 2006Mar 31 2008Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded ... More
Suspicion on Engrafting HBT From Astronomy to Heavy Ion CollisionDec 13 2004Aug 19 2005HBT method in astronomy and heavy ion collision is contrasted in present article.Some differences are found and validity of using HBT in heavy ion collision is suspected.
Factorization of generalized theta functions at reducible caseApr 17 2000We proved the factorization of generalized theta functions when the curve has two irreducible components meeting at one node.
Topological Phases of Fermionic Ladders with Periodic Magnetic FieldsDec 14 2015In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting ... More
Two laws of large numbers for sublinear expectationsNov 18 2015In this paper, we consider the sublinear expectation on bounded random vari- ables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the no- tion of independence for ... More
A Transcendental Invariant of Pseudo-Anosov MapsSep 12 2012May 09 2013For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will ... More
A probabilistic approach to enumeration of Gessel walksMar 02 2009We consider Gessel walks in the plane starting at the origin $(0, 0)$ remaining in the first quadrant $i, j \geq 0$ and made of West, North-East, East and South-West steps. Let $F(m; n_1, n_2)$ denote the number of these walks with exact $m$ steps ending ... More
Finite dimensional representations of the rational Cherednik algebra for $G_4$Oct 29 2009In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group $G_4$. In particular, we classify the irreducible finite dimensional representations and compute their characters.
Investigation of Volume Phase Transition from the Different Properties of ParticlesNov 18 2005In this work, three different particle sizes: the static radius $R_{s}$, hydrodynamic radius $R_{h}$ and apparent hydrodynamic radius $ R_{h,app}$ obtained using the light scattering technique, are investigated for dilute poly-disperse homogenous spherical ... More
Zero entropy invariant measures for some skew product diffeomorphismsDec 15 2008In this paper we study some skew product diffeomorphisms with nonuniformly hyperbolic structure along fibers. We show that there is an invariant measure with zero entropy which has atomic conditional measures along fibers.
A probabilistic approach for enumeration of certain Young tableauxFeb 04 2013In this paper we establish an order statistics model of Young tableaux. Multiple integration over nested simplexes is applied to the enumeration of Young tableaux. A brief proof of Frobenius-Young's and Aitken's formulas is given. Partially standard Young ... More
Entropy and Ergodic Measures for Toral AutomorphismsMar 06 2011We show that for every linear toral automorphism, especially the non-hyperbolic ones, the entropies of ergodic measures form a dense set on the interval from zero to the topological entropy.
Necessity of numerical smoothnessJul 12 2012Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial smoothness indicators ... More
OPESCI-FD: Automatic Code Generation Package for Finite Difference ModelsMay 20 2016In this project, we introduce OPESCI-FD, a Python package built on symbolic mathematics to automatically generate Finite Difference models from a high-level description of the model equations. We investigate applying this framework to generate the propagator ... More
Tilt-stability, vanishing theorems for stable sheaves and applicationsSep 12 2016We study the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters. For a stable sheaf, we give some effective bounds of these parameters such that the stable sheaf is tilt-stable. ... More
Probe Anomalous $tqγ$ couplings through Single Top Photoproduction at the LHCFeb 08 2014Jul 17 2014In this work we study the constraints on the anomalous $tq\gamma$ ($q=u$, $c$) couplings by photon-produced leading single top production and single top jet associated production through the main reaction $pp\rightarrow p\gamma p\rightarrow pt\rightarrow ... More
The nonvanishing hypothesis at infinity for Rankin-Selberg convolutionsJul 20 2013Dec 02 2015We prove the nonvanishing hypothesis at infinity for Rankin-Selberg convolutions for $\GL(n)\times \GL(n-1)$.
Stability Criterion for Convolution-Dominated Infinite MatricesJul 22 2009Let $\ell^p$ be the space of all $p$-summable sequences on $\mathbb{Z}$. An infinite matrix is said to have $\ell^p$-stability if it is bounded and has bounded inverse on $\ell^p$. In this paper, a practical criterion is established for the $\ell^p$-stability ... More
Logarithmic heat projective operatorsSep 21 2000Let $f:\Cal C\to S$ be a flat family of curves over a smooth curve $S$ such that $f$ is smooth over $S_0=S\ssm\{s_0\}$ and $f^{-1}(s_0)=\Cal C_0$ is irreducible with one node. We have an associated family $\Cal M_{S_0}\to S_0$ of moduli spaces of semistable ... More
Degeneration of moduli spaces and generalized theta functionsJul 29 1999We prove a factorization theorem of generalized functions for moduli spaces of semistable parabolic bundles of any rank.
Topological Symmetries of R^3, IIMar 10 2016If a fintie group G acts topologically and faithfully on R^3, then G is a subgroup of O(3)
Convergence of Coalescing Nonsimple Random Walks to the Brownian WebJan 10 2005The Brownian Web (BW) is a family of coalescing Brownian motions starting from every point in space and time $\R\times\R$. It was first introduced by Arratia, and later analyzed in detail by T\'{o}th and Werner. More recently, Fontes, Isopi, Newman and ... More
Model actions for almost reduced groups on UHF algebrasSep 24 2014For any countable discrete group $G$ with a reduced abelian subgroup of finite index, we construct an action $\alpha$ of $G$ on the universal UHF algebra $\Qq$ using an infinite tensor product of permutation representations of $G$ and show that these ... More
The general $J$-flowsJul 31 2015We study the general $J$-flows. We use Moser iteration to obtain the uniform estimate.
Physical Angular Momentum Separation for QEDAug 18 2016We study the non-uniqueness problem of the gauge-invariant angular momentum separation for the case of QED, which stems from the recent controversy concerning the proper definitions of the orbital angular momentum and spin operator of the individual parts ... More
Covering a cubic graph by 5 perfect matchingsJan 13 2016Feb 29 2016Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we show that Berge Conjecture holds for two classes of cubic graphs, cubic graphs with a circuit ... More
Traces of intertwiners for quantum affine sl_2 and Felder-Varchenko functionsAug 17 2015Dec 06 2015We show that the traces of $U_q(\widehat{\mathfrak{sl}}_2)$-intertwiners of Etingof-Schiffmann-Varchenko valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction ... More
Laguerre and Jacobi analogues of the Warren processOct 05 2016We define Laguerre and Jacobi analogues of the Warren process. That is, we construct local dynamics on a triangular array of particles so that the projections to each level recover the Laguerre and Jacobi eigenvalue processes of K\"onig-O'Connell and ... More
Virtual homological eigenvalue and mapping torus of pseudo-Anosov mapsAug 25 2016In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a finite cover which has a homological eigenvalue with modulus greater than $1$, then the monodromy of any fibered structure of any finite cover of $M_{\phi}$ has this property.
On Noether approach in the cosmological model with scalar and gauge fields: symmetries and the selection ruleApr 18 2015In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given ... More
Decomposition Theorem for Perverse sheaves on Artin stacks over finite fieldsSep 22 2010Mar 11 2012We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.
L-series of Artin stacks over finite fieldsAug 22 2010Mar 28 2011We reprove the Lefschetz trace formula for stacks (in the context of derived categories and the six operations for stacks developed by Laszlo and Olsson), and give the meromorphic continuation of L-series (in particular, zeta functions) of Artin stacks ... More
Axisymmetrically Tropical Cyclone-like Vortices with Secondary CirculationsSep 07 2013The secondary circulation of the tropical cyclone (TC) is related to its formation and intensification, thus becomes very important in the studies. The analytical solutions have both the primary and secondary circulation in a three-dimensionally nonhydrostatic ... More
Identify the diapycnical eddy diffusivities by salt fingers and turbulence with vertical microstructure measurementsJun 23 2014Diapycnical eddy diffusivities are formulated from physical relations according to a simple fact that the different formulas are identical for the same parameter. It is found that the dispassion ratio \Gamma is a crucial parameter. When it is above a ... More
Morphological Structures of Planetary NebulaeNov 30 2009Since various structural components of planetary nebulae manifest themselves differently, a combination of optical, infrared, submm, and radio techniques is needed to derive a complete picture of planetary nebulae. The effects of projection can also make ... More
Character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groupsJun 20 2016We determine the character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groups ${^3}D_4(q^3)$.
Eisenstein integrals for theta stable parabolic subalgebrasMar 25 2004Nov 28 2004Let $G$ be a connected semisimple Lie group with a finite center, with a maximal compact subgroup $K$. There are two general methods to construct representations of $G$, namely, ordinary parabolic induction and cohomological parabolic induction. We define ... More
A refined error analysis for fixed-degree polynomial optimization over the simplexDec 20 2013Aug 17 2014We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this paper, we revisit ... More
Exponential Decay of Lebesgue NumbersFeb 02 2010Nov 20 2010We study the exponential rate of decay of Lebesgue numbers of open covers in topological dynamical systems. We show that topological entropy is bounded by this rate multiplied by dimension. Some corollaries and examples are discussed.
Mott-Hubbard Scenario for the Metal-Insulator Transition in the Two Dimensional Electron GasAug 01 2006By comparing the responses to an in-plane magnetic field near the metal-insulator transition (MIT), we find that the observed MIT in Si MOSFETs can be described by the non-perturbative Mott-Hubbard scenario. Interrelations between independent measurables ... More
A Simulation and Modeling of Access Points with Definition LanguageApr 06 2013Apr 11 2013This submission has been withdrawn by arXiv administrators because it contains fictitious content and was submitted under a pseudonym, which is against arXiv policy.
Arithmetic genus of integral space curvesMay 23 2016We give an estimation for the arithmetic genus of an integral space curve, which are not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for $\mathbb{P}^3$ proved by Macri.
Large Extra Dimension effects through Light-by-Light Scattering at the CERN LHCJun 16 2014Jul 31 2014Observing light-by-light scattering at the Large Hadron Collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the ... More
Dual pairs and contragredients of irreducible representationsMar 08 2009Dec 08 2009Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient of $\pi$ is ... More
Almost linear Nash groupsOct 30 2013Nov 21 2013A Nash group is said to be almost linear if it has a Nash representation with finite kernel. Structures and basic properties of these groups are studied.
Cohomologically induced distinguished representations and cohomological test vectorsNov 11 2011Jan 30 2015Let $G$ be a real reductive group, and let $\chi$ be a character of a reductive subgroup $H$ of $G$. We construct $\chi$-invariant linear functionals on certain cohomologically induced representations of $G$, and show that these linear functionals do ... More
NonLERFness of arithmetic hyperbolic manifold groupsAug 17 2016We will show that, for any noncompact arithmetic hyperbolic $m$-manifold with $m\geq 4$, and any compact arithmetic hyperbolic $m$-manifold with $m\geq 5$ which is not a $7$-dimensional arithmetic hyperbolic manifold defined by octonions, its fundamental ... More
A note on simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass $L$-functionsSep 10 2016In this note, we prove that given a Hecke-Maass cusp form $f$ for $SL_2(\mathbb{Z})$ and a sufficiently large integer $q=q_1q_2$ with $q_j\asymp \sqrt{q}$ being prime numbers for $j=1,2$, there exists a primitive Dirichlet character $\chi$ of conductor ... More
Localized nonlinear functional equations and two sampling problems in signal processingApr 09 2013Let $1\le p\le \infty$. In this paper, we consider solving a nonlinear functional equation $$f(x)=y,$$ where $x, y$ belong to $\ell^p$ and $f$ has continuous bounded gradient in an inverse-closed subalgebra of ${\mathcal B}(\ell^2)$, the Banach algebra ... More
Libcint: An efficient general integral library for Gaussian basis functionsDec 01 2014An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library can handle arbitrary integral expressions on top of $\mathbf{p}$, $\mathbf{r}$ and $\sigma$ ... More
Wiener's Lemma for Infinite Matrices IIJan 09 2010In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of ${\mathcal B}(\ell^q_w)$, the algebra of all bounded linear operators on the weight ... More
Towards Shockingly Easy Structured Classification: A Search-based Probabilistic Online Learning FrameworkMar 29 2015There are two major approaches for structured classification. One is the probabilistic gradient-based methods such as conditional random fields (CRF), which has high accuracy but with drawbacks: slow training, and no support of search-based optimization ... More
Demosaicing and Superresolution for Color Filter Array via Residual Image Reconstruction and Sparse RepresentationSep 29 2012Jul 04 2013A framework of demosaicing and superresolution for color filter array (CFA) via residual image reconstruction and sparse representation is presented.Given the intermediate image produced by certain demosaicing and interpolation technique, a residual image ... More
Conformally invariant scaling limits in planar critical percolationNov 02 2009Oct 21 2011This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site percolation on ... More
Why are there strong radio AGNs in the center of "non-cool core" clusters?Oct 05 2009Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGNs also exist in "noncool core" clusters, which brings up the question whether ... More
Every BCG with a strong radio AGN has an X-ray cool core: is the cool core - noncool core dichotomy too simple?Apr 13 2009Sep 20 2009Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGN also exist in "noncool core" clusters, which brings up the question whether ... More
Confining the light wave by using non-Euclidean transformation opticsFeb 03 2013Sep 24 2013A new way to understand why some inhomogeneous dielectric medium can be used for confining the light wave has been given by using non-Euclidean transformation optics. We show that special inhomogeneous dielectric medium, which corresponds to a dip in ... More