Results for "Zekun Lu"

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Dispersion of velocity gradients: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity provides a robust measure of magnetic field direction. In this paper, we use velocity centroids as the measures of velocity and propose a new way of studying media magnetization. ... More
Quantum Szilard engines with arbitrary spinFeb 02 2015The quantum Szilard engine (QSZE) is a conceptual quantum engine for understanding the fundamental physics of quantum thermodynamics and information physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE (SQSZE), and we systematically ... More
On the integrated squared error of the linear wavelet density estimatorOct 29 2012Linear wavelet density estimators are wavelet projections of the empirical measure based on independent, identically distributed observations. We study here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem. These results are proved ... More
Survey of Cognitive Radio Techniques in Wireless NetworkApr 29 2011In this report, I surveyed the cognitive radio technique in wireless networks. Researched several kinds of cognitive techniques about their advantages and disadvantages.
A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra NetworkJun 28 2016Jun 29 2016In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network. The development of the algorithms is based on the logarithmic cost and l0-norm constraint. To further overcome the ... More
Diffusion leaky LMS algorithm: analysis and implementationFeb 13 2016Jul 30 2016The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech ... More
An exact algorithm for the weighed mutually exclusive maximum set cover problemJan 24 2014In this paper, we introduce an exact algorithm with a time complexity of $O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover} problem, where $m$ is the number of subsets in the problem. This is an NP-hard motivated and abstracted ... More
An exact algorithm with the time complexity of $O^*(1.299^m)$ for the weighed mutually exclusive set cover problemFeb 23 2013In this paper, we will introduce an exact algorithm with a time complexity of $O^*(1.299^m)$ for the {\sc weighted mutually exclusive set cover} problem, where $m$ is the number of subsets in the problem. This problem has important applications in recognizing ... More
Farrell cohomology of low genus pure mapping class groups with puncturesJul 22 2002In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, `low genus' means g=1,2,3; and `pure mapping class groups with punctures' means the mapping class ... More
Observability Estimate and State Observation Problems for Stochastic Hyperbolic EquationsMay 03 2013Jun 09 2013In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. ... More
Deriving Abstract Semantics for Forward Analysis of Normal Logic ProgramsNov 06 1998The problem of forward abstract interpretation of {\em normal} logic programs has not been formally addressed in the literature although negation as failure is dealt with through the built-in predicate ! in the way it is implemented in Prolog. This paper ... More
Parametrizing Program Analysis by Lifting to Cardinal Power DomainsMay 25 2010A parametric analysis is an analysis whose input and output are parametrized with a number of parameters which can be instantiated to abstract properties after analysis is completed. This paper proposes to use Cousot and Cousot's Cardinal power domain ... More
Knowware: the third star after Hardware and SoftwareNov 27 2007This book proposes to separate knowledge from software and to make it a commodity that is called knowware. The architecture, representation and function of Knowware are discussed. The principles of knowware engineering and its three life cycle models: ... More
Two-Monopole Systems and the Formation of Non-Abelian CloudsJun 29 1998Nov 20 1998We study the energy density of two distinct fundamental monopoles in SU(3) and Sp(4) theories with an arbitrary mass ratio. Several special limits of the general result are checked and verified. Based on the analytic expression of energy density the coefficient ... More
A note on the holomorphic invariants of Tian-ZhuMay 26 2005In this paper, we compute the Tian-Zhu invariant on hypersurfaces of complex projective spaces.
Gradient estimates of the Yukawa couplingMay 26 2005The paper is related to the classification of special manifolds and projective special manifolds. One of the result of this paper is that, if the Weil-Petersson metric on a projective special manifold is complete, then the Hodge metrc and the Weil-Petersson ... More
A Note on the Analytic Families of Compact Submanifolds of Complex ManifoldsMay 26 2005In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).
Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear ProgrammingSep 29 2012In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$ minimization ... More
Smooth Optimization Approach for Sparse Covariance SelectionApr 04 2009In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply Nesterov's smooth optimization ... More
On the DDVV Conjecture and the Comass in Calibrated Geometry (II)Aug 21 2007In this paper, we proved P(n,3), which is an important part of the DDVV conjecture. The general case will be treated in the next version of the paper.
On the Rigidity of Horizontal SlicesMay 26 2005In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.
On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau ThreefoldsMay 26 2005Jun 02 2005In this paper, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized Calabi-Yau threefold. The symmetricity of the Yukawa coupling is also studied. In the last section of this paper, ... More
On the Lower Order Terms of the Asymptotic Expansion of ZelditchNov 21 1998Jan 31 1999In this paper, we computed the first three coefficients of the asymptotic expansion of Zelditch. We also proved that in general, the $k$-th coefficient is a polynomial of the curvature and its derivative of weight $k$.
GRBS: Standard Model & BeyondJan 03 2001There have been great and rapid progresses in the field of $\gamma$-ray bursts since BeppoSAX and other telescopes discovered their afterglows in 1997. In this talk, the main observational facts of $\gamma$-ray bursts and their afterglows, and the standard ... More
What do $γ$-ray bursts look like?Feb 08 2000There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct ... More
Symplectic fixed points and Lagrangian intersections on weighted projective spacesJan 12 2006In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also true if each weight ... More
Synthesis of Self-assembled Iron Silicon Oxide Nanowires onto Single-crystalline Si(100)Jul 30 2013Iron silicon oxide nanowire has been synthesized by putting single crystalline Si(100) wafer into ammonium iron sulfate, hydrogen peroxide, and triethylamine solution heated to from 70 to 100 degree in the air. The prepared iron silicon oxide nanowires ... More
Periodic motion of a charge on a manifold in the magnetic fieldsMay 24 1999May 25 2000In this paper we prove the existence of a periodic motion of a charge on a large class of manifolds under the action of the magnetic fields. Our methods also give a class of closed manifolds whose cotangent bundle contain no the closed exact Lagrangian ... More
Semantic Information Measure with Two Types of Probability for Falsification and ConfirmationSep 26 2016Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional ... More
Form factor description of the non-collinear Compton scattering tensorJul 10 1997Aug 08 1997We present a parameterization of the non-collinear (virtual) Compton scattering tensor in terms of form factors, in which the Lorentz tensor associated with each form factor possesses manifest electromagnetic gauge invariance. The main finding is that ... More
Symmetry analysis of the hadronic tensor for the semi-inclusive pseudoscalar meson leptoproduction from an unpolarized nucleon targetJun 16 1995Sep 09 1995By examining the symmetry constraints on the semi-inclusive pseudoscalar particle production in unpolarized inelastic lepton-hadron scattering, we present a complete, exact Lorentz decomposition for the corresponding hadronic tensor. As a result, we find ... More
Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone BosonsMar 14 2016Jun 06 2016We propose a Clifford algebra based model, which treats both gravity and Yang-Mills interactions as gauge fields. There are two sectors of boson fields as electroweak and Majorana bosons. The electroweak boson sector induces fermion masses via spontaneous ... More
An invariance principle for stochastic heat equations with periodic coefficientsMay 13 2015In this paper we investigate the asymptotic behaviors of solution $u(t, \cdot)$ of a stochastic heat equation with a periodic nonlinear term. Such equation appears related to the dynamical sine-Gordon model. We consider the reversible case and extend ... More
The splitting lemmas for nonsmooth functionals on Hilbert spacesFeb 10 2011Nov 07 2012The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least $C^2$-smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for ... More
Exact Controllability for Stochastic Schrodinger EquationsApr 26 2013This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the standard duality ... More
Sequence Training and Adaptation of Highway Deep Neural NetworksJul 07 2016Jul 28 2016Highway deep neural network (HDNN) is a type of depth-gated feedforward neural network, which has shown to be easier to train with more hidden layers and also generalise better compared to conventional plain deep neural networks (DNNs). Previously, we ... More
Constructing a weak subset of a random setFeb 11 2016The tree forcing method given by (Liu 2015) enables the cone avoiding of strong enumeration of a given tree, within a subset or co-subset of an arbitrary given set, provided the given tree does not admit computable strong enumeration. Using this result, ... More
Antifactor of regular bipartite graphsNov 30 2015This problem is NP-complete in general, but for the case when no prescription contains two consecutive gaps, Lov\'asz gave a structural description, and Cornu\'ejols gave a polynomial algorithm. However, results on $H$-factors are known only in some special ... More
A Polymorphic Groundness Analysis of Logic ProgramsOct 31 1998A polymorphic analysis is an analysis whose input and output contain parameters which serve as placeholders for information that is unknown before analysis but provided after analysis. In this paper, we present a polymorphic groundness analysis that infers ... More
Rationale awareness for quality assurance in iterative human computation processesApr 16 2012Human computation refers to the outsourcing of computation tasks to human workers. It offers a new direction for solving a variety of problems and calls for innovative ways of managing human computation processes. The majority of human computation tasks ... More
Shape Variables for the Doubly-Charmed B DecaysJun 08 1996We propose to use the hadronic shape variables to test the assumption of ``local duality'' in the doubly-charmed B decays, $B\rightarrow X_{c\bar c s}$. We compute these shape variables at leading order in parton model, and discuss how they can be compared ... More
Uniform bounds of base change conductors and link with the generalized Szpiro conjectureNov 02 2012Mar 11 2014The difference between the Faltings height of an abelian variety $A$ defined over a number field $k$ and its stable height is measured by the so-called base change conductor. In this paper, we give a uniform bound of the base change conductor in terms ... More
Avoid Internal Loops in Steady State Flux Space SamplingOct 18 2012As a widely used method in metabolic network studies, Monte-Carlo sampling in the steady state flux space is known for its flexibility and convenience of carrying out different purposes, simply by alternating constraints or objective functions, or appending ... More
Analytical correlation of routing table length index and routing path length index in hierarchical routing modelApr 13 2008In Kleinrock and Kamoun's paper, the inverse relation of routing table length index and routing path length index in hierarchical routing model is illustrated. In this paper we give the analytical correlation of routing table length index and routing ... More
Virtual moduli cycles and Gromov-Witten invariants of noncompact symplectic manifoldsJun 17 2003May 03 2006This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get solutions of ... More
Inverse curvature flow in anti-de Sitter-Schwarzschild manifoldSep 30 2016In this paper, we consider the inverse hessian quotient curvature flow with star-shaped initial hypersurface in anti-de Sitter-Schwarzschild manifold. We prove that the solution exists for all time, and the second fundamental form converges to identity ... More
Introduction to bulk metallic glass composite and its recent applicationsFeb 28 2011Bulk metallic glass (BMG) materials are hot topics in recent years, not to mention BMG matrix composites, which further improve the magnetic and mechanical properties of BMG materials. BMG and BMG matrix materials are fast developing and promising materials ... More
Sequential Convex Programming Methods for A Class of Structured Nonlinear ProgrammingOct 10 2012Oct 31 2016In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in ... More
Adaptive First-Order Methods for General Sparse Inverse Covariance SelectionApr 04 2009In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum likelihood estimation ... More
On the Geometry of Classifying Spaces and Horizontal SlicesMay 26 2005In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let $U$ be a neighborhood of the moduli space. Then we know the universal covering space $V$ of $U$ is a smooth manifold. Suppose $D$ is the classifying ... More
A Note on Special Kahler ManifoldsMay 26 2005We proved a conjecture of D. Freed that there are no non-trivial complete special Kaehler manifolds.
Inflation in the Generalized Inverse Power Law ScenarioNov 02 2013We propose a single field inflationary model by generalizing the inverse power law potential from the intermediate model. We study the implication of our model on the primordial anisotropy of cosmological microwave background radiation. Specifically, ... More
A Study on the Amount of Random Graph GroupiesJan 13 2013In 1980, Ajtai, Komlos and Szemer{\'e}di defined "groupie": Let $G=(V,E)$ be a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\in V$, let $r(v)$ denote the sum of the degrees of the vertices adjacent to $v$. We say $v\in V$ is a {\it groupie}, if $\frac{r(v)}{\deg(v)}\geq\frac{e}{n}.$ ... More
On the passibility of a short-lived free Dirac particleMay 01 1998A time-decaying Dirac equation is suggested. For a free particle with rest mass about 0.5GeV, the live-time is about 10**(-25) second in the rest frame.
The velocity and angular momentum of a free Dirac electronApr 22 1998It is shown that, in Dirac theory, there is a spatial velocity of a free electron which commutes with the Hamiltonian, so it is a conserved quantity of the motion. Furthermore, there is a spatial orbital angular momentum which also commutes with the Hamiltonian ... More
High-frequency limit of the Maxwell-Landau-Lifshitz system in the diffractive optics regimeFeb 16 2012Feb 17 2012We study semilinear Maxwell-Landau-Lifshitz systems in one space dimension. For highly oscillatory and prepared initial data, we construct WKB approximate solutions over long times $O(1/\e)$. The leading terms of the WKB solutions solve cubic Schr\"odinger ... More
Subjective Information Measure and Rate Fidelity TheoryMay 24 2007Using fish-covering model, this paper intuitively explains how to extend Hartley's information formula to the generalized information formula step by step for measuring subjective information: metrical information (such as conveyed by thermometers), sensory ... More
On the degenerated Arnold-Givental conjectureJun 01 2008Aug 20 2008This paper has been withdrawn by author due to an error in the proof.
The $\hatΓ$-genus and a regularization of an $S^1$-equivariant Euler classApr 17 2008Aug 28 2008We show that a new multiplicative genus, in the sense of Hirzebruch, can be obtained by generalizing a calculation due to Atiyah and Witten. We introduce this as the $\hat{\Gamma}$-genus, compute its value for some examples and highlight some of its interesting ... More
SYZ Mirror Symmetry of Hitchin's Moduli Spaces Near Singular Fibers IAug 18 2012We study hyperkahler metrics and hyperholomorphic connections of Hitchin's moduli spaces after Gaiotto, Moore and Neitzke. Their construction via the twistor technique produces intricate wall crossing behaviors. For certain four dimensional Hitchin's ... More
Backward stochastic Volterra integral equations associated with a Levy process and applicationsJun 30 2011Mar 10 2016In this paper, we study a class of backward stochastic Volterra integral equations driven by Teugels martingales associated with an independent L\'{e}vy process and an independent Brownian motion (BSVIELs). We prove the existence and uniqueness as well ... More
Remark on the kinematics of the one-photon production in electron-proton scatteringMay 26 1997Aug 01 1997I clarify the mistakes in the original version hep-ph/9705427 about the phase space factor for the one-photon production in electron-proton scattering and confirm that the earlier result given by Kroll, Sch\"urmann and Guichon is right.
Equivariant Morse inequalities and applicationsMay 15 2012In this paper, we prove equivariant Morse inequalities via Bismut-Lebeau's analytic localization techniques. As an application, we obtain Morse inequalities on compact manifold with nonempty boundary by applying equivariant Morse inequalities to the doubling ... More
Asynchronous Physical-layer Network CodingMay 16 2011Jun 05 2011A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as ... More
DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth GradientsJun 20 2016Jul 17 2016We propose DoReFa-Net, a method to train convolutional neural networks that have low bitwidth weights and activations using low bitwidth parameter gradients. In particular, during backward pass, parameter gradients are stochastically quantized to low ... More
Reducts of the random bipartite graphJan 10 2011Aug 18 2011Let $\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\Gamma$ that preserve sides. We classify the ... More
On stable hypersurfaces with constant mean curvature in Euclidean spacesDec 14 2012In this paper, we derive curvature estimates for strongly stable hypersurfaces with constant mean curvature immersed in $\mathbb{R}^{n+1}$, which show that the locally controlled volume growth yields a globally controlled volume growth if $\partial M=\emptyset$. ... More
On an example of δ-Koszul algebrasSep 17 2011The main purpose of this paper is to study a concrete example of $\delta$-Koszul algebras, which is related to three questions raised by Green and Marcos in [3].
Quasi-Koszulity and minimal Horseshoe LemmaSep 17 2011In this paper, the criteria for minimal Horseshoe Lemma to be true are given via quasi-$\delta$-Koszul modules, which are the nongraded version of $\delta$-Koszul modules first introduced by Green and Marcos in 2005. Moreover, some applications of minimal ... More
On uniform estimates for Laplace equation in balls with small holesMar 03 2015Oct 06 2015In this paper, we consider the Dirichlet problem of the three-dimensional Laplace equation in the unit ball with a shrinking hole. The problem typically arises from homogenization problems in domains perforated with tiny holes. We give an almost complete ... More
Higher-order resonances and instability of high-frequency WKB solutionsDec 11 2013Oct 20 2015This paper focuses on the destabilizing role of resonances in high-frequency WKB solutions. Specifically, we study higher-order resonances associated with higher-order harmonics generated by nonlinearities. We give examples of systems and solutions for ... More
Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge WeightsJul 07 2013Let $G$ be a graph and $\mathcal {S}$ be a subset of $Z$. A vertex-coloring $\mathcal {S}$-edge-weighting of $G$ is an assignment of weight $s$ by the elements of $\mathcal {S}$ to each edge of $G$ so that adjacent vertices have different sums of incident ... More
$\mathsf{RT}_2^2$ does not imply $\mathsf{WKL}_0$Feb 11 2016We prove that $\mathsf{RCA}_0+\mathsf{RT}_2^2\not\rightarrow \mathsf{WKL}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not of PA-degree.
Successful High Power Acceleration of the HSC Type Injector for Cancer Therapy in IMPMar 25 2015A Hybrid single cavity (HSC) linac, which is formed by combining a radio frequency quadrupole (RFQ) structure and a drift tube (DT) structure into one interdigital-H (IH) cavity, is fabricated and assembled as a proof of principle (PoP) type injector ... More
Walsh Sampling with Incomplete Noisy SignalsJan 30 2016With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources as well. Under ... More
Statics and field-driven dynamics of transverse domain walls in biaxial nanowires under uniform transverse magnetic fieldsDec 17 2015Mar 26 2016In this work, we report analytical results on transverse domain wall (TDW) statics and field-driven dynamics in quasi one-dimensional biaxial nanowires under arbitrary uniform transverse magnetic fields (TMFs) based on the Landau-Lifshitz-Gilbert equation. ... More
Asymptotic structure of self-shrinkersOct 16 2016We show that each end of a noncompact self-shrinker in $\mathbb{R}^3$ of finite topology is smoothly asymptotic to either a regular cone or a self-shrinking round cylinder.
Observability Estimate for Stochastic Schroedinger EquationsJun 04 2012May 03 2013In this paper, we establish a boundary observability estimate for stochastic Schr\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic Schr\"{o}dinger-like operator. ... More
On crown-free families of subsetsJun 27 2012The crown $\Oh_{2t}$ is a height-2 poset whose Hasse diagram is a cycle of length $2t$. A family $\F$ of subsets of $[n]:=\{1,2..., n\}$ is {\em $\Oh_{2t}$-free} if $\Oh_{2t}$ is not a weak subposet of $(\F,\subseteq)$. Let $\La(n,\Oh_{2t})$ be the largest ... More
Transport through the single-molecular dots in an external irradiationMar 18 2003Apr 03 2003We present a fully nonequilibrium calculation of the low-temperature transport properties of a single molecular quantum dot coupled to local phonon mode when an ac field is applied to the gate. The resonant behavior is shown in the time-averaged differential ... More
Planar lower envelope of monotone polygonal chainsDec 20 2014Jul 04 2015A simple linear search algorithm running in $O(n+mk)$ time is proposed for constructing the lower envelope of $k$ vertices from $m$ monotone polygonal chains in 2D with $n$ vertices in total. This can be applied to output-sensitive construction of lower ... More
Singularity categories of some 2-CY-tilted algebrasSep 18 2015Mar 31 2016We define a class of finite-dimensional Jacobian algebras, which are called (simple) polygon-tree algebras, as a generalization of cluster-tilted algebras of type $\D$. They are $2$-CY-tilted algebras. Using a suitable process of mutations of quivers ... More
Some applications of recollements to Gorenstein projective modulesDec 02 2014We apply the technique of recollement to study the Gorenstein projective modules. First, we construct a recollement of defect Gorenstein categories for the upper triangular matrix algebras. Then we use the defect Gorenstein category to give a categorical ... More
A Generalized Information Formula as the Bridge between Shannon and PopperJul 24 2007A generalized information formula related to logical probability and fuzzy set is deduced from the classical information formula. The new information measure accords with to Popper's criterion for knowledge evolution very much. In comparison with square ... More
On Weyl's embedding problem in Riemannian manifoldsAug 26 2016We consider a priori estimates of the Weyl's embedding problem of $(\mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, \bar g)$. We establish the mean curvature estimate under natural geometric assumption. Together with a recent work ... More
Recent developments of the DDVV ConjectureAug 23 2007In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
A Correlator Formula for Quantum Sheaf CohomologyNov 30 2015For a class of monadic deformations of the tangent bundles over nef-Fano smooth projective toric varieties, we study the correlators using quantum sheaf cohomology. We prove a summation formula for the correlators, confirming a conjecture by McOrist and ... More
On the Futaki Invariants of Complete IntersectionsMay 26 2005In this paper, we give an explicit formula for the Futaki invariants of complete intersections. The result is new in the case where the variety is smooth or has orbifold singularities.
On the lower bound estimates of sections of the canonical bundle over a Riemann surfaceNov 05 1999In this paper, we give some estimates of the sum of the square norm of the sections of the pluricanonical bundles over a Riemann surface with genus greater than 2 and Gauss curvature (-1). Using these estimate, we give a uniform estimate of the corona ... More
Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli SpacesOct 17 2010Apr 20 2011We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to physicists Gaiotto, Moore and Neitzke. ... More
$L^p$-solutions of Reflected Backward Doubly Stochastic Differential EquationsDec 29 2009Jan 14 2010In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz coefficients.
Accessing directly the strange quark content of the proton at HERAAug 15 1995Nov 20 1995We investigate a double-spin asymmetry for the semi-inclusive $\Lambda$ hyperon production in the longitudinally deep inelastic lepton-proton scattering, the sign of which can provide us with important information about the strange quark helicity distribution ... More
Splitting lemmas for the Finsler energy functional on the space of $H^1$-curvesNov 12 2014May 04 2016We establish the splitting lemmas (or generalized Morse lemmas) for the energy functionals of Finsler metrics on the natural Hilbert manifolds of $H^1$-curves around a critical point or a critical $\R^1$ orbit of a Finsler isometry invariant closed geodesic. ... More
The splitting lemmas for nonsmooth functionals on Hilbert spaces II. The case at infinityNov 06 2012Jan 25 2015We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow methods our proof ... More
A Thom-Smale-Witten theorem on manifolds with boundaryMay 21 2012Given a smooth compact manifold with boundary, we show that the subcomplex of the deformed de Rham complex consisting of eigenspaces of small eigenvalues of the Witten Laplacian is canonically isomorphic to the Thom-Smale complex constructed by Laudenbach. ... More
Theta correspondence and the Prasad conjecture for SL(2)Feb 06 2018We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of SL(2) over a nonarchimedean quadratic field extension E/F. Then we will verify the Prasad conjecture for SL(2). With a similar ... More
Sequential Convex Programming Methods for A Class of Structured Nonlinear ProgrammingOct 10 2012In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in ... More
Harmonic map heat flow with rough boundary dataOct 16 2010Let $B_1$ be the unit open disk in $\Real^2$ and $M$ be a closed Riemannian manifold. In this note, we first prove the uniqueness for weak solutions of the harmonic map heat flow in $H^1([0,T]\times B_1,M)$ whose energy is non-increasing in time, given ... More
Reducts of the Generalized Random Bipartite GraphJul 20 2011Let \Gamma be the generalized random bipartite graph that has two sides Rl and Rr with edges for every pair of vertices between R1 and Rr but no edges within each side, where all the edges are randomly colored by three colors P1; P2; P3. In this paper, ... More