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Discretized sum-product estimates in matrix algebrasNov 29 2016Oct 17 2017We generalize Bourgain's discretized sum-product theorem to matrix algebras.

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 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.

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

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.

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

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

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

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

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

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

A Joint Optimization Approach of LiDAR-Camera Fusion for Accurate Dense 3D ReconstructionsJul 01 2019Fusing data from LiDAR and camera is conceptually attractive because of their complementary properties. For instance, camera images are higher resolution and have colors, while LiDAR data provide more accurate range measurements and have a wider Field ... More

An Analytic Expression of Performance Rate, Fitness Value and Average Convergence Rate for a Class of Evolutionary AlgorithmsNov 11 2015Feb 16 2016An important theoretical question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality of evolutionary algorithms in terms of the performance rate, which ... More

Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varietiesAug 25 2014Sep 24 2015In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties $X(\mu, b)_J$ for any tamely ramified group $G$ and its parahoric subgroup $P_J$. We show that $X(\mu, b)_J \neq \emptyset$ if and ... More

Cocenters of $p$-adic groups, I: Newton decompositionOct 15 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

Rotated sphere packing designsAug 12 2016We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled, rotated, translated ... More

On the cohomology ring of associated flag bundleOct 25 2016In this expository note, we survey the cohomology rings of flag bundles associated to vector bundles in terms of characteristic classes.

A New Framework for Ranking Vulnerabilities in the CloudsNov 23 2016Qualifying and ranking threat degrees of vulnerabilities in cloud service are known to be full of challenges. Although there have been several efforts aiming to address this problem, most of them are too simple or cannot be applied into cloud infrastructure. ... More

GKM graphs for odd dimensional manifolds with torus actionsAug 15 2016Oct 25 2016Let torus $T$ act on a 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 and $1$-dimensional ... More

Discretely decomposable restrictions of $(\mathfrak{g},K)$-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian typeAug 30 2018Let $(G,G')$ be a Klein four symmetric pair. If $\pi_K$ is a unitarizable simple $(\mathrm{g},K)$-module, the author shows some necessary conditions when $\pi_K$ is discretely decomposable as a $(\mathfrak{g}',K')$-module. In particular, if $G$ is an ... More

On Bilinear Maximal Bochner-Riesz OperatorsJul 12 2016We prove that the bilinear maximal Bochner-Riesz operator $T_*^\lambda$ is bounded from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ for appropriate $(p_1,p_2,p)$ when $\lambda>(4n+3)/5$.

Nonperturbative contribution to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Gribov-Levin-Ryskin equationApr 20 1999By studying the nonperturbative contribution to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Gribov-Levin-Ryskin equation, it is found that (i) the nonperturbative contribution suppresses the evolution rate at the low $Q^2$, small-x region; (ii) ... More

Educational game design: game elements for promoting engagementSep 27 2017Engagement in educational games, a recently popular academic topic, has been shown to increase learning performance, as well as a number of attitudinal factors, such as intrinsic interest and motivation. However, there is a lack of research on how games ... More

Possible Prescription to Avoid Chromomagnetic Instability in the g2SC and gCFL PhasesJun 07 2005Jun 12 2005This paper has been withdrawn.

A new understanding of $ζ(k)$Dec 16 2018Mar 12 2019In 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

Strong uniqueness for a class of singular SDEs for catalytic branching diffusionsSep 08 2008A new result for the strong uniqueness for catalytic branching diffusions is established, which improves the work of Dawson, D.A.; Fleischmann, K.; Xiong, J.[Strong uniqueness for cyclically symbiotic branching diffusions. Statist. Probab. Lett. 73, no. ... More

Classification of Compatible Parabolic Subalgebras for Complex Symmetric PairsMar 19 2014Mar 20 2014In this paper, we shall recall and arrange the relationship between hyperbolic elements and parabolic subalgebras at first. And then, we shall classify all the compatible parabolic subalgebras containing a $\tau$-stable Borel subalgebra for complex symmetric ... More

Reconstruction and Higher Dimensional GeometryNov 18 2005Jun 26 2006In this paper, we give a new proof on a Theorem of Tutte which says that the determinants of the adjacency matrices of two hypomorphic graphs are the same. We also study the lowest eigenvectors.

Unipotent Representations and Quantum InductionOct 23 2002Mar 02 2007In this paper, we construct certain unipotent representations for the real orthogonal group and the metaplectic group in the sense of Vogan. In particular, our results imply that there are irreducible unitary representations attached to each special nilpotent ... More

Theta Correspondence and Quantum InductionOct 23 2002Oct 24 2005In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or local theta ... More

Remarks on the extension of the Ricci flowJun 04 2012Jul 14 2012We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.

Lebesgue approximation of $(2,β)$-superprocessesJan 31 2012Feb 01 2012Let $\xi=(\xi_t)$ be a locally finite $(2,\beta)$-superprocess in $\RR^d$ with $\beta<1$ and $d>2/\beta$. Then for any fixed $t>0$, the random measure $\xi_t$ can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the $\varepsilon$-neighborhoods ... More

On the affineness of Deligne-Lusztig varietiesJul 02 2007We prove that the Deligne-Lusztig variety associated to minimal length elements in any $\d$-conjugacy class of the Weyl group is affine, which was conjectured by Orlik and Rapoport in \cite{OR}.

On Matrix-Valued Square Integrable Positive Definite FunctionsMay 01 2009Sep 09 2015In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on square integrable positive definite functions to matrix valued square integrable positive definite functions. We ... More

Discretely decomposable restrictions of $(\mathfrak{g},K)$-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian typeAug 30 2018Mar 22 2019Let $(G,G^\Gamma)$ be a Klein four symmetric pair. The author wants to classify all the Klein four symmetric pairs $(G,G^\Gamma)$ such that there exists at least one nontrivial unitarizable simple $(\mathfrak{g},K)$-module $\pi_K$ that is discretely decomposable ... More

Classification of Klein Four Symmetric Pairs of Holomorphic Type for $\mathrm{E}_{7(-25)}$Apr 10 2018The author classifies Klein four symmetric pairs of holomorphic type for the non-compact Lie group of Hermitian type $\mathrm{E}_{7(-25)}$, and applies the results to branching rules.

The $G$-stable pieces of the wonderful compactificationDec 15 2004Feb 01 2006Let $G$ be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification $\bar{G}$ of $G$ into finite many $G$-stable pieces, which were introduced by Lusztig. In this paper, we will investigate ... More

A sufficient condition for a finite-time $ L_2 $ singularity of the 3d Euler EquationSep 24 2002A sufficient condition is derived for a finite-time $L_2$ singularity of the 3d incompressible Euler equations, making appropriate assumptions on eigenvalues of the Hessian of pressure. Under this condition $\lim_{t \to T_*} \sup | \frac{D \o} {Dt} |_{L_2(\vO)} ... More

Suppression of blow-up in Parabolic-Parabolic Patlak-Keller-Segel via strictly monotone shear flowsOct 27 2017In this paper we consider the parabolic-parabolic Patlak-Keller-Segel models in $\mathbb{T}\times\mathbb{R}$ with advection by a large strictly monotone shear flow. Without the shear flow, the model is $L^1$ critical in two dimensions with critical mass ... More

A finite field analogue for Appell series F_3Apr 04 2017Dec 13 2017In this paper we introduce a finite field analogue for the Appell series F_3 and give some reduction formulae and certain generating functions for this function over finite fields.

On zeros of some entire functionsApr 11 2016Let \begin{equation*} A_{q}^{(\alpha)}(a;z) = \sum_{k=0}^{\infty} \frac{(a;q)_{k} q^{\alpha k^2} z^k} {(q;q)_{k}}, \end{equation*} where $\alpha >0,~0<q<1.$ In a paper of Ruiming Zhang, he asked under what conditions the zeros of the entire function $A_{q}^{(\alpha)}(a;z)$ ... 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

Fast and Rigorous DC Solution in Finite Element Method for Integrated Circuit AnalysisApr 24 2015Large scale circuit simulation, such as power delivery network analysis, has become increasingly challenge in the VLSI design verification flow. Power delivery network can be simulated by both SPICE-type circuit-based model and eletromagnetics-based model ... More

Equivariant cohomology rings of the real flag manifoldsOct 25 2016Jan 11 2019We give Leray-Borel-type descriptions for the mod-$2$ and the rational equivariant cohomology rings of the real and the oriented flag manifolds under the canonical torus or 2-torus actions.

On W_2 lifting of Frobenius of Algebraic SurfacesSep 03 2013We completely decide which minimal algebraic surfaces in positive characteristics allow a lifting of their Frobenius over the trucated witt rings of lengh 2.

Estimated Depth Map Helps Image ClassificationSep 20 2017We consider image classification with estimated depth. This problem falls into the domain of transfer learning, since we are using a model trained on a set of depth images to generate depth maps (additional features) for use in another classification ... More

Separating Current from Potential Sweep Method of Electrochemical Kinetics for SupercapacitorsFeb 27 2017We briefly elaborate the concept of electrochemical kinetics firstly, and introduce a method to separate current from potential sweep method of electrochemical kinetics for supercapacitors. The current in CV curves has been separated by equating the intercepts ... More

Proof of the Pólya conjectureNov 05 2014Nov 09 2014In this paper, we study lower bounds for higher eigenvalues of the Dirichlet eigenvalue problem of the Laplacian on a bounded domain $\Omega$ in $\mathbb{R}^n$. It is well known that the $k$-th Dirichlet eigenvalue $\lambda_k$ obeys the Weyl asymptotic ... More

Hypersurfaces with null higher order anisotropic mean curvatureDec 09 2011Jun 20 2013Given a positive function $F$ on $\mathbb S^n$ which satisfies a convexity condition, for $1\leq r\leq n$, we define for hypersurfaces in $\mathbb{R}^{n+1}$ the $r$-th anisotropic mean curvature function $H_{r; F}$, a generalization of the usual $r$-th ... More

Spin-Current Shot Noise in Mesoscopic ConductorsJul 17 2006In this paper, we present a method to investigate the spin-current shot noise in mesoscopic conductors, by using scattering matrix theory and Green's function technique. We first derive a general expression for the spin-current noise at zero-frequency ... More

Sharp estimate of lower bound for the first eigenvalue in the Laplacian operator on compact Riemannian manifoldsOct 21 2012The aim of this paper is give a simple proof of some results in \cite{Jun Ling-2006-IJM} and \cite{JunLing-2007-AGAG}, which are very deep studies in the sharp lower bound of the first eigenvalue in the Laplacian operator on compact Riemannian manifolds ... 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

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.

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.

Mislearning from Censored Data: The Gambler's Fallacy in Optimal-Stopping ProblemsMar 21 2018Nov 21 2018I study endogenous learning dynamics for people expecting systematic reversals from random sequences -- the "gambler's fallacy." Biased agents face an optimal-stopping problem, such as managers conducting sequential interviews. They are uncertain about ... 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

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

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 $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$.

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

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

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

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

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

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

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

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

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

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

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

Unitary Representations and Heisenberg Parabolic SubgroupMay 28 2010Mar 27 2011In this paper, we study the restriction of an irreducible unitary representation $\pi$ of the universal covering $\widetilde{Sp}_{2n}(\mb R)$ to a Heisenberg maximal parabolic group $\tilde P$. We prove that if $\pi|_{\tilde P}$ is irreducible, then $\pi$ ... More

Discontinuous Superprocesses with Dependent Spatial MotionJul 01 2008We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the particles are ... 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

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

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

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

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

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

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

Local convergence of critical random trees and continuous-state branching processesMar 03 2015Aug 09 2015We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random trees, we show that random trees conditioned to have large functional ... More

Conditioning Galton-Watson trees on large maximal out-degreeDec 05 2014We propose a new way to condition random trees, that is, condition random trees to have large maximal out-degree. Under this new conditioning, we show that conditioned critical Galton-Watson trees converge locally to size-biased trees with a unique infinite ... More

A new treatment for some periodic Schrödinger operatorsDec 21 2014Sep 14 2016We revise some aspects of the asymptotic solution for the eigenvalues for Schr\"odinger operators with periodic potential, from the perspective of the Floquet theory. In the context of classical Floquet theory, when the periodic potential can be treated ... More

Zero-sum Subsequences of Length kq over Finite Abelian p-GroupsMar 24 2015For a finite abelian group $G$ and a positive integer $k$, let $s_{k}(G)$ denote the smallest integer $\ell\in\mathbb{N}$ such that any sequence $S$ of elements of $G$ of length $|S|\geq\ell$ has a zero-sum subsequence with length $k$. The celebrated ... More

Mesoscopic linear statistics of Wigner matrices of mixed symmetry classMar 28 2018May 10 2018We prove a central limit theorem for the mesoscopic linear statistics of $N\times N$ Wigner matrices $H$ satisfying $\mathbb{E}|H_{ij}|^2=1/N$ and $\mathbb{E} H_{ij}^2= \sigma /N$, where $\sigma \in [-1,1]$. We show that on all mesoscopic scales $\eta$ ... More