Results for "Weikun He"

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Random walks on linear groups satisfying a Schubert conditionMay 14 2019We study random walks on $\mathrm{GL}_d(\mathbb{R})$ whose proximal dimension $r$ is larger than $1$ and whose limit set in the Grassmannian $\mathrm{Gr}_{r,d}(\mathbb{R})$ is not contained any Schubert variety. These random walks, without being proximal, ... More
Discretized sum-product estimates in matrix algebrasNov 29 2016Oct 17 2017We generalize Bourgain's discretized sum-product theorem to matrix algebras.
Discretized Sum-Product Estimates in Matrix AlgebrasNov 29 2016We generalize Bourgain's discretized sum-product theorem to matrix algebras.
Orthogonal projections of discretized setsOct 02 2017May 09 2018We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of Hausdorff dimensions. ... More
Sum-product for real Lie groupsJun 17 2018We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-H\"older decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.
Sum-product for real Lie groupsJun 17 2018Feb 24 2019We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-H\"older decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.
Verification of Γ$_{7}$ symmetry assignment for the top valence band of ZnO by magneto-optical studies of the free A exciton stateNov 05 2012The circularly-polarized and angular-resolved magneto-photoluminescence spectroscopy was carried out to study the free A exciton 1S state in wurtzite ZnO at 5 K.
Unambiguous symmetry assignment for the top valence band of ZnO by magneto-optical studies of the free A-exciton stateJun 27 2007We studied the circular polarization and angular dependences of the magneto-photoluminescence spectra of the free A-exciton 1S state in wurtzite ZnO at T = 5 K. The circular polarization properties of the spectra clearly indicate that the top valence ... More
Joint Switch Upgrade and Controller Deployment in Hybrid Software-Defined NetworksMar 22 2019To improve traffic management ability, Internet Service Providers (ISPs) are gradually upgrading legacy network devices to programmable devices that support Software-Defined Networking (SDN). The coexistence of legacy and SDN devices gives rise to a hybrid ... More
A Unified 3D Mapping Framework using a 3D or 2D LiDAROct 30 2018Simultaneous Localization and Mapping (SLAM) has been considered as a solved problem thanks to the progress made in the past few years. However, the great majority of LiDAR-based SLAM algorithms are designed for a specific type of payload and therefore ... More
A data-driven linear-programming methodology for optimal transportOct 09 2017A data-driven formulation of the optimal transport problem is presented and solved using adaptively refined meshes to decompose the problem into a sequence of finite linear programming problems. Both the marginal distributions and their unknown optimal ... More
Optimal Monotone Drawings of TreesApr 13 2016A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists abpath P_{uw} in G that is monotone in some direction l_{uw}. (Namely, the order of the orthogonal projections of the vertices ... More
Transfer Learning Enhanced Common Spatial Pattern Filtering for Brain Computer Interfaces (BCIs): Overview and a New ApproachAug 08 2018The electroencephalogram (EEG) is the most widely used input for brain computer interfaces (BCIs), and common spatial pattern (CSP) is frequently used to spatially filter it to increase its signal-to-noise ratio. However, CSP is a supervised filter, which ... More
Modeling and Robust Attitude Controller Design for a Small Size HelicopterDec 20 2018This paper addresses the design and application controller for a small-size unmanned aerial vehicle (UAV). In this work, the main objective is to study the modeling and attitude controller design for a small size helicopter. Based on a non-simplified ... More
Spatial Filtering for Brain Computer Interfaces: A Comparison between the Common Spatial Pattern and Its VariantAug 08 2018The electroencephalogram (EEG) is the most popular form of input for brain computer interfaces (BCIs). However, it can be easily contaminated by various artifacts and noise, e.g., eye blink, muscle activities, powerline noise, etc. Therefore, the EEG ... More
Transfer Learning for Brain-Computer Interfaces: An Euclidean Space Data Alignment ApproachAug 08 2018Almost all EEG-based brain-computer interfaces (BCIs) need some labeled subject-specific data to calibrate a new subject, as neural responses are different across subjects to even the same stimulus. So, a major challenge in developing high-performance ... More
Transfer Learning for Brain-Computer Interfaces: A Euclidean Space Data Alignment ApproachAug 08 2018Apr 02 2019Objective: This paper targets a major challenge in developing practical EEG-based brain-computer interfaces (BCIs): how to cope with individual differences so that better learning performance can be obtained for a new subject, with minimum or even no ... More
Real-time calibration and alignment of the LHCb RICH detectorsNov 01 2016In 2015, the LHCb experiment established a new and unique software trigger strategy with the purpose of increasing the purity of the signal events by applying the same algorithms online and offline. To achieve this, real-time calibration and alignment ... More
Geometric Progression-Free Sequences with Small Gaps IIMar 24 2015When $k$ is a constant at least $3$, a sequence $S$ of positive integers is called $k$-GP-free if it contains no nontrivial $k$-term geometric progressions. Beiglb\"ok, Bergelson, Hindman and Strauss first studied the existence of a $ $$k$-GP-free sequence ... More
Cross Number Invariants of Finite Abelian GroupsAug 18 2013Oct 31 2013The cross number of a sequence over a finite abelian group $G$ is the sum of the inverse orders of the terms of that sequence. We study two group invariants, the maximal cross number of a zero-sum free sequence over $G$, called $\mathsf{k}(G)$, introduced ... More
On the Classification of Universal Rotor-RoutersNov 06 2011The combinatorial theory of rotor-routers has connections with problems of statistical mechanics, graph theory, chaos theory, and computer science. A rotor-router network defines a deterministic walk on a digraph G in which a particle walks from a source ... More
On some partitions of an affine flag varietyOct 27 2009In this paper, we discuss some partitions of affine flag varieties. These partitions include as special cases the partition of affine flag variety into affine Deligne-Lusztig varieties and the affine analogue of the partition of flag varieties into $\cb_w(b)$ ... More
A Generalization of Lifting Non-proper Tropical IntersectionsJun 14 2016Let X and X' be closed subschemes of an algebraic torus T over a non-archimedean field. We prove the rational equivalence as tropical cycles, in the sense of Henning Meyer's graduate thesis, between the tropicalization of the intersection product of X ... More
A Lauricella hypergeometric series over finite fieldsOct 12 2016Oct 25 2016In this paper we introduce a finite field analogue of a Lauricella hypergeometric series. An integral formula for the Lauricella hypergeometric series and its finite field analogue are deduced. Transformation and reduction formulae and several generating ... More
Pruning Levy trees via an admissible family of branching mechanismsMar 03 2014By studying an admissible family of branching mechanisms introduced in Li (2014), we obtain a pruning procedure on L\'evy trees. Then we could construct a decreasing L\'evy-CRT-valued process $\{\T_t\}$ by pruning L\'evy trees and an analogous process ... More
A new way to deduce $ζ(1-k)=-B_k/k$Nov 22 2018Dec 18 2018In this paper, by introducing a new operation in the vector space of analytic functions, the author presents a method for derivating the well-known formula $\zeta(1-k)=-\frac{B_k}{k}$, where $\zeta$ denotes the Riemann zeta function and $B_k$ is the $k$-th ... More
A new treatment for some periodic Schrödinger operators II: the wave functionAug 18 2016Oct 20 2016Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wavefunctions are derived. This gives further evidence ... More
Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statisticsMar 29 2011Oct 27 2011The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless ... More
Frobenius splitting of projective toric bundlesApr 08 2014We give several mild conditions on a toric bundle on a nonsingular toric variety under which the projectivization of the toric bundle is Frobenius split.
Overcoming Barriers to Engagement with Educational Video Games for Self-Directed Learning: A Mixed-Methods Case StudySep 27 2017Research has established increased engagement and positive behavioral, attitudinal, and learning outcomes from educational games. Although engagement begets these benefits, there is a lack of research on how students engage with educational games, especially ... More
Character sheaves on certain spherical varietiesMay 07 2006We study a class of perverse sheaves on some spherical varieties which include the strata of the De Concini-Procesi completion of a symmetric variety. This is a generalization of the theory of (parabolic) character sheaves.
Search for Rare and Forbidden Decays D^+ --> h^pm e^mp e^+Aug 12 2005Nov 28 2005Using 0.8 million D^+D^- pairs collected with the CLEO-c detector at the psi(3770) resonance, we have searched for flavor-changing neutral current and lepton-number-violating decays of D^+ mesons to final states with dielectrons. We find no indication ... More
Topological Conjugacy of Non-hyperbolic Linear FlowsMar 13 2017The topological equivalence classification for linear flows on $\mathbb{R}^n$ had been completely solved by Kuiper and independently Ladis in 1973. However, Ladis' proof was published in a Russian journal which isn't easily available, Kuiper's proof is ... More
Evolve nondegenerate two formsOct 29 2015We introduce geometric flows on a compact almost complex manifold, with the aim to flow a nondegenerate two form to a symplectic two form. We discuss mainly two flows, $d^*d$-flow and $d^*d$-Ricci flow. Among others, we prove the uniqueness and short ... More
Scalar curvature and properness on Sasaki manifoldsFeb 11 2018We study (transverse) scalar curvature type equation on compact Sasaki manifolds, in view of recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of K\"ahler metrics with constant scalar curvature (csck) on compact K\"ahler manifolds. Following ... More
The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvatureMar 30 2011We show that Perelman's W-functional can be generalized to Sasaki-Ricci flow. When the basic first Chern class is positive, we prove a uniform bound on the scalar curvature, the diameter and a uniform $C^1$ bound for the transverse Ricci potential along ... More
Local solution and extension to the Calabi flowApr 06 2009Apr 19 2009We consider the local solution to the Calabi flow for C^\alpha initial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\infty sense. This can be viewed as obtaining ... More
Remarks on the existence of bilaterally symmetric extremal Kähler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$May 28 2007Jun 07 2007In this short note we show that the existence of bilaterally symmetric extremal K\"ahler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$.
Interaction energy and itinerant ferromagnetism in a strongly interacting Fermi gas in the absence of molecule formationMay 20 2014Nov 26 2014We investigate the interaction energy and the possibility of itinerant ferromagnetism in a strongly interacting Fermi gas at zero temperature in the absence of molecule formation. The interaction energy is obtained by summing the perturbative contributions ... More
Localization of equivariant cohomology rings of real GrassmanniansSep 20 2016Dec 19 2017We use localization method to understand the rational equivariant cohomology rings of real Grassmannians and oriented Grassmannians, then relate this to the Leray-Borel description which says the ring generators are equivariant Pontryagin classes, Euler ... More
Farthest-Point Heuristic based Initialization Methods for K-Modes ClusteringOct 09 2006The k-modes algorithm has become a popular technique in solving categorical data clustering problems in different application domains. However, the algorithm requires random selection of initial points for the clusters. Different initial points often ... More
Cocenter of $p$-adic groups, II: induction mapNov 21 2016In this paper, we study some relation between the cocenter $\bar H(G)$ of the Hecke algebra $H(G)$ of a connected reductive group $G$ over an nonarchimedean local field and the cocenter $\bar H(M)$ of its Levi subgroups $M$. Given any Newton component ... More
Cocenters of $p$-adic groups, I: Newton decompositionOct 15 2016Mar 08 2018In this paper, we introduce the Newton decomposition on a connected reductive $p$-adic group $G$. Based on it we give a nice decomposition of the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the usual conjugation ... More
Weakness in a Mutual Authentication Scheme for Session Initiation Protocol using Elliptic Curve CryptographyAug 20 2011The session initiation protocol (SIP) is a powerful signaling protocol that controls communication on the Internet, establishing, maintaining, and terminating the sessions. The services that are enabled by SIP are equally applicable in the world of mobile ... More
On regularity of complex Monge-Ampere equationFeb 25 2010Mar 02 2010We shall consider the regularity problem of solutions for complex Monge-Ampere equations. First we prove interior $C^2$ estimates of solutions in a bounded domain for complex Monge-Ampere equation with assumption of certain $L^p$ bound for Laplacian u, ... More
Localization of certain odd-dimensional manifolds with torus actionsAug 15 2016Feb 10 2018Let torus $T$ act on a compact smooth manifold $M$, if the equivariant cohomology $H^*_T(M)$ is a free module of $H^*_T(pt)$, then according to the Chang-Skjelbred Lemma, $H^*_T(M)$ can be determined by the $1$-skeleton $M_1$ consisting of fixed points ... More
Gradient Yamabe Solitons on Warped ProductsSep 11 2011The special nature of gradient Yamabe soliton equation which was first observed by Cao-Sun-Zhang\cite{CaoSunZhang} shows that a complete gradient Yamabe soliton with non-constant potential function is either defined on the Euclidean space with rotational ... More
The spin evolution of spin-3 $^{52}$Cr Bose-Einstein condensateAug 19 2009The spin evolution of a Bose-Einstein condensate starting from a mixture of two or three groups of $^{52}$Cr (spin-3) atoms in an optical trap has been studied theoretically. The initial state is so chosen that the system does not distinguish up and down. ... More
On the transverse scalar curvature of a compact Sasaki manifoldMay 20 2011We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in K\"ahler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant ... More
Minimal length elements in conjugacy classes of extended affine Weyl groupApr 23 2010We study the minimal length elements in an integral conjugacy class of a classical extended affine Weyl group and we show that these elements are quite "special" in the sense of Geck and Pfeiffer \cite{GP93}. We also discuss some application on extended ... More
Total positivity in the De Concini-Procesi compactificationOct 02 2003Mar 11 2004We study the nonnegative part \bar{G_{>0}} of the De Concini-Procesi compactification of a reductive algebraic group G, as defined by Lusztig. Using positivity properties of the canonical basis and parametrization of flag varieties, we will give an explicit ... More
A Link Representation for Gravity AmplitudesJul 17 2012We derive a link representation for all tree amplitudes in N=8 supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally ... More
Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups IJan 03 2011Mar 18 2013A Langlands parameter, in the Langlands dual group, can be decomposed into a product of a tempered parameter and a positive quasi-character. Fixing a tempered parameter, Arthur conjectured that positive quasi-characters corresponding to certain weighted ... More
Unitary Representations and Theta Correspondence for Type I Classical GroupsOct 23 2002In this paper, we prove that theta correspondence preserves unitarity under certain restrictions.
A Gluing Theorem for the Kapustin-Witten Equations with a Nahm PoleJul 19 2017In the present paper, we establish a gluing construction for the Nahm pole solutions to the Kapustin-Witten equations over manifolds with boundaries and cylindrical ends. Given two Nahm pole solutions with some convergence assumptions on the cylindrical ... More
The cocenter-representation dualityJun 30 2014Affine Hecke algebras arise naturally in the study of smooth representations of reductive $p$-adic groups. Finite dimensional complex representations of affine Hecke algebras (under some restriction on the isogeny class and the parameter function) has ... More
A new treatment for some periodic Schrödinger operators II: the wave functionAug 18 2016Sep 14 2016Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wavefunctions are derived. This gives further evidence ... More
A note on the maximal out-degree of Galton-Watson treesMar 07 2015In this note we consider both the local maximal out-degree and the global maximal out-degree of Galton-Watson trees. In particular, we show that the tail of any local maximal out-degree and that of the offspring distribution are asymptotically of the ... More
Gan-Gross-Prasad Conjecture for U(p,q)Aug 09 2015In this paper, we give a proof of the Gan-Gross-Prasad conjecture for discrete series of U(p,q).
Cocenters of $p$-adic groups, I: Newton decompositionOct 15 2016Nov 21 2016In this paper, we introduce the Newton decomposition on a connected reductive $p$-adic group $G$. Based on it we give a nice decomposition on the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the usual conjugation ... More
A new formula for $ζ(k)$Dec 16 2018Dec 18 2018In this paper, by introducing a new operation in the vector space of Laurent series, the author derived explicit series for the values of $\zeta$-funtion at positive integers, where $\zeta$ denotes the Riemann zeta function. The values of $\zeta(k),\ ... More
Existence and applications of Ricci flows via pseudolocalityOct 06 2016Oct 27 2017We prove the short-time existence of Ricci flows on complete manifolds with scalar curvature bounded below uniformly, Ricci curvature bounded below by a negative quadratic function, and with almost Euclidean isoperimetric inequality holds locally. In ... More
Villager's dilemmaMar 01 2009With deeper study of the Game Theory, some conditions of Prisoner's Dilemma is no longer suitable of games in real life. So we try to develop a new model-Villager's Dilemma which has more realistic conditions to stimulate the process of game. It is emphasize ... More
Quantum Optomechanics beyond LinearizationMar 09 2012Jun 06 2012The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum objects, for ... More
Square function characterization of weak Hardy spacesApr 27 2013Dec 09 2013We obtain a new square function characterization of the weak Hardy space $H^{p,\infty}$ for all $p\in(0,\iy)$. This space consists of all tempered distributions whose smooth maximal function lies in weak $L^p$. Our proof is based on interpolation between ... More
The Gursky-Streets equationsJul 15 2017Gursky-Streets introduced a formal Riemannian metric on the space of conformal metrics in a fixed conformal class of a compact Riemannian four-manifold in the context of the $\sigma_2$-Yamabe problem. The geodesic equation of Gursky-Streets' metric is ... More
On the convergence of the Calabi flowMar 12 2013Suppose there is a constant scalar curvature metric on a compact Kahler manifold without holomorphic vector field. We prove that the Calabi flow, if it is assumed to exist for all time with bounded Ricci curvature, will converge to the constant scalar ... More
Matone's relation of N=2 super Yang-Mills and spectrum of Toda chainMar 20 2011Apr 13 2011In N=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation < Tr\phi^2 >. This relation has been proved to hold for Omega deformed theories too, using localization ... More
On Calabi's extremal metric and propernessJan 23 2018In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar K\"ahler metric on a compact K\"ahler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates ... More
An Iterative Regression Approach for Face Pose Estimation from RGB ImagesSep 10 2017This paper presents a iterative optimization method, explicit shape regression, for face pose detection and localization. The regression function is learnt to find out the entire facial shape and minimize the alignment errors. A cascaded learning framework ... More
Combinatorial approach to Mathieu and Lamé equationsAug 01 2011Jul 27 2015Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the Lam\'{e} equation. ... More
The Donaldson equationOct 22 2008In this short note, we solve a Dirichlet problem for a fully nonlinear elliptic equation. The operator is introduced by S. Donaldson and it is relevant to the geometry of the space of volume forms.
Measurement of Absolute Hadronic Branching Fractions of D Mesons and e^+e^- --> D barD Cross Sections at E_cm = 3773 MeVApr 01 2005Apr 21 2006Using 55.8 pb^-1 of e^+e^- collisions recorded at the psi(3770) resonance with the CLEO-c detector at CESR, we determine absolute hadronic branching fractions of charged and neutral D mesons using a double tag technique. Among measurements for three D^0 ... More
Work function of α-Fe_{2}O_{3} : a DFT calculationSep 14 2017The work functions of (001) and (00 -1) surfaces of {\alpha}-Fe_{2}O_{3} are investigated with density functional theory and symmetry slab model. These two surfaces are found to be almost nonpolarized and their work functions are 6.10 eV and 5.49 eV respectively. ... More
A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPANov 15 2014Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This paper confirms ... More
Measurement of directed flow of $D^{0}$ and $\bar{D^{0}}$ mesons in 200 GeV Au+Au collisions at RHIC using the STAR detectorJan 17 2019Charm quarks, owing to their large mass, are produced predominantly in the initial hard scatterings in heavy-ion collisions, and therefore can be a valuable tool for studying the early time dynamics of these collisions. The rapidity-odd directed flow ... More
Scattering of quasiparticle of spin-triplet pairs in diffusive superconductor-ferromagnetic nanowire-superconductor junctionMar 11 2011We analyze the proximity effect of superconductor/ferromagnet nanostructures and point out that the scattering of quasiparticle of spin-triplet pairs by local magnetic moments leads to large resistance peak slightly below the superconducting transition ... More
Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theoriesJul 12 2010Nov 10 2010QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential $\mu_{\text B}$ and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose ... More
Certain actions of finitely generated groups on higher dimensional noncommutative toriMay 12 2015We study certain actions of finitely generated abelian groups on higher dimensional noncommutative tori. Given a dimension $d$ and a finitely generated abelian group $G$, we apply a certain function to detect whether there is a simple noncommutative $d$-torus ... More
New Examples and Non-examples of Mori Dream Spaces when Blowing up Toric SurfacesMar 02 2017Jun 19 2017We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori Dream Spaces. For some of these toric surfaces, the question whether the blow-up is a Mori Dream Space is equivalent to countably ... More
A subalgebra of 0-Hecke algebraApr 11 2009Let $(W, I)$ be a finite Coxeter group. In the case where $W$ is a Weyl group, Berenstein and Kazhdan in \cite{BK} constructed a monoid structure on the set of all subsets of $I$ using unipotent $\chi$-linear bicrystals. In this paper, we will generalize ... More
Minimal length elements in some double cosets of Coxeter groupsNov 02 2006We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig's $G$-stable pieces and the generalization of $G$-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements ... More
Normality and Cohen-Macaulayness of local models of Shimura varietiesFeb 19 2012Sep 10 2013We prove that in the unramified case, local models of Shimura varieties with Iwahori level structure are normal and Cohen Macaulay.
Another finite field analogue for Appell series F_{1}Sep 26 2017In this paper we introduce another finite field analogue for Appell series F_{1} and obtain certain reduction formulae and a generating function for this analogue.
A study on the relation between linguistics-oriented and domain-specific semanticsDec 07 2010In this paper we dealt with the comparison and linking between lexical resources with domain knowledge provided by ontologies. It is one of the issues for the combination of the Semantic Web Ontologies and Text Mining. We investigated the relations between ... More
Future Reactor ExperimentsOct 28 2013The measurement of the neutrino mixing angle $\theta_{13}$ opens a gateway for the next generation experiments to measure the neutrino mass hierarchy and the leptonic CP-violating phase. Future reactor experiments will focus on mass hierarchy determination ... More
Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTsNov 02 2017Jan 08 2019The R\'enyi entanglement entropy (REE) of the states excited by local operators in two-dimensional irrational conformal field theories (CFTs), especially in Liouville field theory (LFT) and $\mathcal{N}=1$ super-Liouville field theory (SLFT), has been ... More
Some useful lemmas on the edge Szeged indexMay 17 2018Jun 05 2018The edge Szeged index of a graph $G$ is defined as $Sz_{e}(G)=\sum\limits_{uv\in E(G)}m_{u}(uv|G)m_{v}(uv|G)$, where $m_{u}(uv|G)$ (resp., $m_{v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to ... More
A one-dimensional diffusion model for overloaded queues with customer abandonmentDec 16 2013We use an Ornstein--Uhlenbeck (OU) process to approximate the queue length process in a $GI/GI/n+M$ queue. This one-dimensional diffusion model is able to produce accurate performance estimates in two overloaded regimes: In the first regime, the number ... More
Stabilizing the Richardson Algorithm by Controlling ChaosJun 11 1996By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the ... More
On a semilinear elliptic systems in Hyperbolic spaceJun 18 2012In this paper, we consider systems of semilinear elliptic equations \displaystyle -\Delta_{\mathbb{H}^{N}}u=|v|^{p-1}v, \displaystyle -\Delta_{\mathbb{H}^{N}}v=|u|^{q-1}u, in the whole of Hyperbolic space $\mathbb{H}^{N}$. We establish decay estimates ... More
On large deviation rates for sums associated with Galton-Watson processesFeb 05 2015Aug 28 2015Given a super-critical Galton-Watson process $\{Z_n\}$ and a positive sequence $\{\epsilon_n\}$, we study the limiting behaviors of $P(S_{Z_n}/Z_n\geq\epsilon_n)$ and $P(S_{Z_n}/m^n\geq\epsilon_n) $ with sums $S_{n}$ of i.i.d. random variables $X_i$ and ... More
Branching Laws of Generalized Verma Modules for Non-symmetric Polar PairsOct 21 2013Apr 06 2014We give branching formulas from $so(7,\mathbb{C})$ to $\mathfrak{g}_2$ for generalized Verma modules attached to $\mathfrak{g}_2$-compatible parabolic subalgebras of $so(7,\mathbb{C})$, and branching formulas from $\mathfrak{g}_2$ to $sl(3,\mathbb{C})$ ... More
Generalized matrix coefficients of Unitary RepresentationsJul 28 2013Sep 09 2015This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the results are ... More
Fleming-Viot Processes in an EnvironmentNov 04 2009We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on real line ... More
Entanglement of heterogeneous free fermion chainsDec 14 2016Jul 25 2018We calculate the ground state entanglement entropy between two heterogeneous parts of a free fermion chain. The two parts could be XX chains with different parameters or an XX half chain connected with a quantum Ising half chain. It is shown that logarithmic ... More
Knowledge Reduction and Discovery based on Demarcation InformationMay 27 2004Knowledge reduction, includes attribute reduction and value reduction, is an important topic in rough set literature. It is also closely relevant to other fields, such as machine learning and data mining. In this paper, an algorithm called TWI-SQUEEZE ... More
On sharp lower bound of the spectral gap for a Schrödinger operator and some related resultsJul 02 2014In this paper, we give an easy proof of the main results of Andrews and Clutterbuck's paper [J. Amer. Math. Soc. 24 (2011), no. 3, 899--916], which gives both a sharp lower bound for the spectral gap of a Schr\"oinger operator and a sharp modulus of concavity ... More
Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equationsJan 16 2014Dec 08 2014The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint ... More