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Novel Photovoltaic Phenomenon in Manganite/ZnO HeterostructureAug 30 2012In this paper, we report a novel photovoltaic phenomenon in a low cost manganite/ZnO p-n heterojunction grown on ITO glass substrate by pulsed laser depositon (PLD) under relative low growth temperature. The heterostructure ITO/La0.62Ca0.29K0.09MnO3(LCKMO)/ZnO/Al ... More

Random Distances Associated With Equilateral TrianglesJul 06 2012In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent triangles ... More

Gap theorem on Kähler manifold with nonnegative orthogonal bisectional curvatureAug 11 2017In this paper we prove a gap theorem for K\"ahler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for plurisubharmonic ... More

The distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equationsJun 06 2003We study the distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations.

A response to an article of Xu-Jia WangFeb 06 2013This is a response to the article arXiv:1212.3130v1 by Xu-Jia Wang, where he attempted to address a mathematical question we raised. We point out that, and explain why, the article is far from answering our objections. Moreover, we have more recently ... More

A generalized mass involving higher order symmetric function of the curvature tensorNov 15 2012Nov 16 2012We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is non-negative when the manifold is locally conformally flat and the $\sigma_k$ curvature vanishes at infinity. ... More

Harnack inequalities and Bôcher-type theorems for conformally invariant fully nonlinear degenerate elliptic equationsJun 27 2012Oct 19 2013We give a generalization of a theorem of B\^ocher for the Laplace equation to a class of conformally invariant fully nonlinear degenerate elliptic equations. We also prove a Harnack inequality for locally Lipschitz viscosity solutions and a classification ... More

Asymptotics of the gradient of solutions to the perfect conductivity problemNov 08 2018In the perfect conductivity problem of composite material, the gradient of solutions can be arbitrarily large when two inclusions are located very close. To characterize the singular behavior of the gradient in the narrow region between two inclusions, ... More

Asymptotics of the gradient of solutions to the perfect conductivity problemNov 08 2018Apr 04 2019In the perfect conductivity problem of composite material, the gradient of solutions can be arbitrarily large when two inclusions are located very close. To characterize the singular behavior of the gradient in the narrow region between two inclusions, ... More

Holographic Charged Fluid with Chiral Electric Separation EffectMar 22 2018Sep 26 2018Hydrodynamics with both vector and axial currents is under study within a holographic model, consisting of canonical $U(1)_V\times U(1)_A$ gauge fields in an asymptotically AdS$_5$ black brane. When gravitational back-reaction is taken into account, the ... More

Fourth order quasi-compact difference schemes for (tempered) space fractional diffusion equationsAug 27 2014The continuous time random walk (CTRW) underlies many fundamental processes in non-equilibrium statistical physics. When the jump length of CTRW obeys a power-law distribution, its corresponding Fokker-Planck equation has space fractional derivative, ... More

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutionsApr 27 2017Jun 08 2017We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles, parameterizing them as a four dimensional surface ... More

Positivity and boundedness preserving schemes for the fractional reaction-diffusion equationJan 14 2013In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes, and numerically ... More

A degree theory for second order nonlinear elliptic operators with nonlinear oblique boundary conditionsSep 08 2015In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence of solutions of certain nonlinear elliptic equations arising ... More

Existence and uniqueness to a fully non-linear version of the Loewner-Nirenberg problemApr 24 2018We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a problem considered ... More

Finding Theme Communities from Database Networks: from Mining to Indexing and Query AnsweringSep 23 2017Given a database network where each vertex is associated with a transaction database, we are interested in finding theme communities. Here, a theme community is a cohesive subgraph such that a common pattern is frequent in all transaction databases associated ... More

Mining Density Contrast SubgraphsFeb 18 2018Dense subgraph discovery is a key primitive in many graph mining applications, such as detecting communities in social networks and mining gene correlation from biological data. Most studies on dense subgraph mining only deal with one graph. However, ... More

1+1-dimensional p-wave superconductors from intersecting D-branesMay 08 2012Oct 31 2012In this work we explore 1+1 dimensional p-wave superconductors using the probe D-brane construction. Specifically, we choose three intersecting D-brane models: D1/D5, D2/D4 and D3/D3 systems. According to the dilaton running behavior, we denote the former ... More

Power vs. Spectrum 2-D Sensing in Energy Harvesting Cognitive Radio NetworksFeb 13 2015Energy harvester based cognitive radio is a promising solution to address the shortage of both spectrum and energy. Since the spectrum access and power consumption patterns are interdependent, and the power value harvested from certain environmental sources ... More

A Tractable Approach to Dynamic Network Dimensioning Based on the Best-cell ConfigurationApr 18 2017Spatial distributions of other cell interference (OCIF) and interference to own-cell power ratio (IOPR) with reference to the distance between a mobile and its serving base station (BS) are modeled for the down-link reception of cellular systems based ... More

Multi-View Region Adaptive Multi-temporal DMM and RGB Action RecognitionApr 12 2019Human action recognition remains an important yet challenging task. This work proposes a novel action recognition system. It uses a novel Multiple View Region Adaptive Multi-resolution in time Depth Motion Map (MV-RAMDMM) formulation combined with appearance ... More

Energy Efficient Resource Allocation for Time-Varying OFDMA Relay Systems with Hybrid Energy SuppliesApr 04 2016Apr 06 2016This paper investigates the energy efficient resource allocation for orthogonal frequency division multiple access (OFDMA) relay systems, where the system is supplied by the conventional utility grid and a renewable energy generator equipped with a storage ... More

Local gradient estimates of solutions to some conformally invariant fully nonlinear equationsMay 20 2006Aug 21 2007This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.

ReCoSa: Detecting the Relevant Contexts with Self-Attention for Multi-turn Dialogue GenerationJul 09 2019In multi-turn dialogue generation, response is usually related with only a few contexts. Therefore, an ideal model should be able to detect these relevant contexts and produce a suitable response accordingly. However, the widely used hierarchical recurrent ... More

Some Liouville theorems and applicationsSep 14 2006We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical ... More

Conformally invariant fully nonlinear elliptic equations and isolated singularitiesApr 29 2005Jun 10 2005We study solutions to conformally invariant equations with isolated singularties.

Degenerate conformally invariant fully nonlinear elliptic equationsApr 29 2005May 24 2005We establish Liouville type theorems for degenerate conformally invariant equations.

Holographic superconductors with $z=2$ Lifshitz scalingOct 31 2012We use gauge/gravity duality to explore strongly coupled superconductors with dynamical exponent $z=2$. In the probe limit we numerically establish background solutions for the matter fields and plot the condensate versus the dimensionless temperature. ... More

Asymptotic behavior of solutions to the $σ_k$-Yamabe equation near isolated singularitiesNov 02 2009$\sigma_k$-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In an earlier work YanYan Li proved that an admissible solution with an isolated singularity at $0\in \mathbb R^n$ to the $\sigma_k$-Yamabe equation ... More

Gradual Machine Learning for Entity ResolutionOct 29 2018Jun 14 2019Usually considered as a classification problem, entity resolution (ER) can be very challenging on real data due to the prevalence of dirty values. The state-of-the-art solutions for ER were built on a variety of learning models (most notably deep neural ... More

Shear driven formation of nano-diamonds at sub-gigapascals and 300 KMay 29 2018The transformation pathways of carbon at high pressures are of broad interest for synthesis of novel materials and for revealing the Earth's geological history. We have applied large plastic shear on graphite in rotational anvils to form hexagonal and ... More

Architectural Support for Global Smart SpacesJun 24 2010A GLObal Smart Space (GLOSS) provides support for interaction amongst people, artefacts and places while taking account of both context and movement on a global scale. Crucial to the definition of a GLOSS is the provision of a set of location-aware services ... More

First Smart SpacesJul 01 2010This document describes the Gloss software currently implemented. The description of the Gloss demonstrator for multi-surface interaction can be found in D17. The ongoing integration activity for the work described in D17 and D8 constitutes our development ... More

A priori bounds for co-dimension one isometric embeddingsJul 23 1998We prove a priori bounds for the trace of the second fundamental form of a $C^4$ isometric embedding into $R^{n+1}$ of a metric $g$ of non-negative sectional curvature on $S^n$, in terms of the scalar curvature, and the diameter of $g$. These estimates ... More

Compactness of solutions to the Yamabe problem. IINov 01 2004We study compactness of solutions to the Yamabe problem on Riemannian manifolds which are not locally conformally flat.

A general Liouville type theorem for some conformally invariant fully nonlinear equationsJan 21 2003We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamicsSep 10 2014Mar 09 2015In ref. \cite{1406.7222}, we reported a construction of all order linearized fluid dynamics with strongly coupled $\mathcal{N}=4$ super-Yang-Mills theory as underlying microscopic description. The linearized fluid/gravity correspondence makes it possible ... More

A geometric problem and the Hopf Lemma. IIJan 29 2006Feb 03 2006A classical result of A.D. Alexandrov states that a connected compact smooth $n-$dimensional manifold without boundary, embedded in $\Bbb R^{n+1}$, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of $M$ ... More

Regularity of the distance function to the boundaryOct 26 2005Let $\Omega$ be a domain in a smooth complete Finsler manifold, and let $G$ be the largest open subset of $\Omega$ such that for every $x$ in $G$ there is a unique closest point from $\partial \Omega$ to $x$ (measured in the Finsler metric). We prove ... More

Text Matching as Image RecognitionFeb 20 2016Matching two texts is a fundamental problem in many natural language processing tasks. An effective way is to extract meaningful matching patterns from words, phrases, and sentences to produce the matching score. Inspired by the success of convolutional ... More

CDAS: A Crowdsourcing Data Analytics SystemJun 30 2012Some complex problems, such as image tagging and natural language processing, are very challenging for computers, where even state-of-the-art technology is yet able to provide satisfactory accuracy. Therefore, rather than relying solely on developing ... More

Further results on Liouville type theorems for some conformally invariant fully nonlinear equationsJan 22 2003We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

Elementary n-Lie algebrasNov 16 2005Nov 19 2005In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras, we also give the relations between elementary n-algebras and E-algebras.

Learning Cross-lingual Distributed Logical Representations for Semantic ParsingJun 14 2018With the development of several multilingual datasets used for semantic parsing, recent research efforts have looked into the problem of learning semantic parsers in a multilingual setup. However, how to improve the performance of a monolingual semantic ... More

On the Hopf LemmaSep 21 2007Sep 28 2007The Hopf Lemma for second order elliptic operators is proved to hold in domains with $C^{1,\alpha}$, and even less regular, boundaries. It need not hold for $C^1$ boundaries. Corresponding results are proved for second order parabolic operators.

Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equationsApr 20 2016We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal ... More

A sharp Sobolev inequality on Riemannian manifoldsJan 24 2002Let (M,g) be a smooth compact Riemannian manifold without boundary of dimension n>=6. We prove that {align*} \|u\|_{L^{2^*}(M,g)}^2 \le K^2\int_M\{|\nabla_g u|^2+c(n)R_gu^2\}dv_g +A\|u\|_{L^{2n/(n+2)}(M,g)}^2, {align*} for all u\in H^1(M), where 2^*=2n/(n-2), ... More

Starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic spaceMay 08 2005We study the existence of starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space.

All Order Linearized Hydrodynamics from Fluid/Gravity CorrespondenceJun 27 2014Nov 02 2014Using fluid/gravity correspondence, we determine the (linearized) stress energy tensor of $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling with all orders in derivatives of fluid velocity included. We find that the dissipative effects are fully ... More

The rigidity of hypersurface in Euclidean spaceOct 18 2016In the present paper, we revisit the rigidity of hypersurfaces in Euclidean space. We highlight Darboux equation and give new proof of rigidity of hypersurfaces by energy method and maximal principle.

Gradient Estimates for Parabolic Systems from Composite MaterialMay 07 2011Jul 05 2012In this paper we derive $W^{1,\infty}$ and piecewise $C^{1,\alpha}$ estimates for solutions, and their $t-$derivatives, of divergence form parabolic systems with coefficients piecewise H\"older continuous in space variables $x$ and smooth in $t$. This ... More

Flux-approximation limits of solutions to the Brio system with two independent parametersJan 05 2019By the flux-approximation method, we study limits of Riemann solutions to the Brio system with two independent parameters. The Riemann problem of the perturbed system is solved analytically, and four kinds of solutions are obtained constructively. It ... More

Towards Green Shipping with Integrated Fleet Deployment and Bunker ManagementDec 15 2014The vast majority of world trade is carried by the sea shipping industry and petroleum is still the major energy source. To reduce greenhouse gas emissions, it is an urgent need for both industry and government to promote green shipping. To move shipping ... More

Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on Kähler manifoldsApr 27 2010In this paper we study the heat equation (of Hodge-Laplacian) deformation of $(p, p)$-forms on a K\"ahler manifold. After identifying the condition and establishing that the positivity of a $(p, p)$-form solution is preserved under such an invariant condition ... More

Partial results on extending the Hopf LemmaOct 02 2009In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a very partial ... More

Giant Two-Photon Absorption in Monolayer MoS2Mar 08 2015Oct 10 2015Strong two-photon absorption (TPA) in monolayer MoS2 is demonstrated in contrast to saturable absorption (SA) in multilayer MoS2 under the excitation of femtosecond laser pulses in the near infrared region. MoS2 in the forms of monolayer single crystal ... More

Comparison principles for some fully nonlinear subelliptic equations on the Heisenberg groupNov 27 2018In this paper, we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form $\nabla^{2}_{H}\psi+L(\cdot,\psi,\nabla_{H}\psi)$ on the Heisenberg group, which include the CR invariant operators.

Compactness of conformal metrics with constant $Q$-curvature. IJun 02 2015Jan 15 2019We study compactness for nonnegative solutions of the fourth order constant $Q$-curvature equations on smooth compact Riemannian manifolds of dimension $\ge 5$. If the $Q$-curvature equals $-1$, we prove that all solutions are universally bounded. If ... More

On some conformally invariant fully nonlinear equations, Part II: Liouville, Harnack and YamabeMar 25 2004The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem. ... More

Linearly resummed hydrodynamics in a weakly curved spacetimeFeb 27 2015We extend our study of all-order linearly resummed hydrodynamics in a flat space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature $\mathcal{N}=4$ super-Yang-Mills theory at strong ... More

Existence and nonexistence to exterior Dirichlet problem For Monge-Ampère equationApr 01 2018We consider the exterior Dirichlet problem for Monge-Amp\`ere equation with prescribed asymptotic behavior. Based on earlier work by Caffarelli and the first named author, we complete the characterization of the existence and nonexistence of solutions ... More

Hop Doubling Label Indexing for Point-to-Point Distance Querying on Scale-Free NetworksMar 04 2014May 02 2014We study the problem of point-to-point distance querying for massive scale-free graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a hop-doubling ... More

A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature boundDec 03 2012We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions when the associated ... More

A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundaryNov 17 2009In this paper we establish existence and compactness of solutions to a general fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.

Random Distances Associated with HexagonsJun 11 2011In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent hexagons sharing a ... More

Random Distances Associated with RhombusesJun 07 2011Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations research, etc. ... More

Coherent perfect absorber and laser in purely imaginary conjugate metamaterialsAug 07 2017Conjugate metamaterials, in which the permittivity and the permeability are complex conjugates of each other, possess the elements of loss and gain simultaneously. By employing a conjugate metamaterial with a purely imaginary form, we propose a mechanism ... More

Dielectrophoretically Assembled Polymer Nanowires for Gas SensingFeb 26 2007We measured the electronic properties and gas sensing response of nanowires containing segments of poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS) that were synthesized using anodic aluminum oxide (AAO) membranes. The nanowires have ... More

Compactness of conformal metrics with constant $Q$-curvature. IJun 02 2015Jun 17 2015We establish compactness for nonnegative solutions of the fourth order constant $Q$-curvature equations on smooth compact Riemannian manifolds of dimension $\ge 5$. If the $Q$-curvature equals $-1$, we prove that all solutions are universally bounded. ... More

A Liouville type theorem for some conformally invariant fully nonlinear equationsDec 30 2002We establish a Liouville type theorem for some conformally invariant fully nonlinear equations

A fully nonlinear version of the Yamabe problem and a Harnack type inequalityDec 02 2002We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations.

Compactness of solutions to the Yamabe problem. IIIDec 12 2006For a sequence of blow up solutions of the Yamabe equation on non-locally confonformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates ... More

Monge-Ampère equation with bounded periodic dataJun 06 2019We consider the Monge-Amp\`ere equation $\det(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is a positive bounded periodic function. We prove that $u$ must be the sum of a quadratic polynomial and a periodic function. For $f\equiv 1$, this is the classic result ... More

Holographic Magnetized Chiral Density WaveJul 01 2018We explore the end point of the helical instability in finite density, finite magnetic field background discussed by Kharzeev and Yee [1]. The nonlinear solution is obtained and identified with the (magnetized) chiral density wave phase in literature. ... More

A geometric problem and the Hopf Lemma. IJul 13 2005This, and its sequel, concern some variations of a classical theorem of A.D. Alexandrov and teh Hopf Lemma.

A Deep Architecture for Semantic Matching with Multiple Positional Sentence RepresentationsNov 26 2015Matching natural language sentences is central for many applications such as information retrieval and question answering. Existing deep models rely on a single sentence representation or multiple granularity representations for matching. However, such ... More

Gas Sensing Properties of Single Conducting Polymer Nanowires and the Effect of TemperatureAug 23 2008Nov 19 2008We measured the electronic properties and gas sensing responses of template-grown poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS)-based nanowires. The nanowires have a "striped" structure (gold-PEDOT/PSS-gold), typically 8um long (1um-6um-1um ... More

Some multi-valued solutions to Monge-Ampere equationsMay 06 2005We construct several types of multi-valued solutions to the Monge-Ampere equation in higher dimensions.

Upper triangular matrices and Billiard ArraysAug 18 2015Jan 15 2016Fix a nonnegative integer $d$, a field $\mathbb{F}$, and a vector space $V$ over $\mathbb{F}$ with dimension $d+1$. Let $T$ denote an invertible upper triangular matrix in ${\rm Mat}_{d+1}(\mathbb{F})$. Using $T$ we construct three flags on $V$. We find ... More

A Nonlinear Elliptic PDE with Two Sobolev-Hardy Critical ExponentsFeb 21 2011In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents, \label{0.1} {& \Delta u + \lambda\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \text{in} \Omega, & u=0 \qquad \text{on} \Omega, where ... More

Collective benefits in traffic during mega events via the use of information technologiesJul 27 2016Information technologies today can inform each of us about the best alternatives for shortest paths from origins to destinations, but they do not contain incentives or alternatives that manage the information efficiently to get collective benefits. To ... More

Optical Limiting and Theoretical Modelling of Layered Transition Metal Dichalcogenide NanosheetsMar 08 2015Oct 10 2015Nonlinear optical property of transition metal dichalcogenide (TMDC) nanosheet dispersions, including MoS2, MoSe2, WS2, and WSe2, was performed by using Z-scan technique with ns pulsed laser at 1064 nm and 532 nm. The results demonstrate that the TMDC ... More

The study of neutron spectra in water bath from Pb target irradiated by 250MeV/u protonsSep 05 2014The spallation neutrons were produced by the irradiation of Pb with 250 MeV protons. The Pb target was surrounded by water which was used to slow down the emitted neutrons. The moderated neutrons in the water bath were measured by using the resonance ... More

On fully nonlinear CR invariant equations on the Heisenberg groupOct 30 2010In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author (2003). We ... More

Precision Higgs Physics at CEPCOct 21 2018Mar 04 2019The discovery of the Higgs boson with its mass around 125 GeV by the ATLAS and CMS Collaborations marked the beginning of a new era in high energy physics. The Higgs boson will be the subject of extensive studies of the ongoing LHC program. At the same ... More

Some remarks on singular solutions of nonlinear elliptic equations. IApr 18 2009The paper concerns singular solutions of nonlinear elliptic equations.

Travel Time Estimation without Road Networks: An Urban Morphological Layout Representation ApproachJul 08 2019Travel time estimation is a crucial task for not only personal travel scheduling but also city planning. Previous methods focus on modeling toward road segments or sub-paths, then summing up for a final prediction, which have been recently replaced by ... More

A geometric characterization of a sharp Hardy inequalityMar 28 2011Jun 01 2011In this paper, we prove that the distance function of an open connected set in $\mathbb R^{n+1}$ with a $C^{2}$ boundary is superharmonic in the distribution sense if and only if the boundary is {\em weakly mean convex}. We then prove that Hardy inequalities ... More

Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentumDec 26 2007May 30 2008We extend the validity of Dain's angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a twist potential. ... More

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. I. One singularitySep 26 2016We classify all $(-1)-$homogeneous axisymmetric no swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, ... More

Gradient resummation for nonlinear chiral transport: an insight from holographyJul 30 2018Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as $U(1)_V\times U(1)_A$ Maxwell-Chern-Simons theory in Schwarzschild-$AdS_5$. In presence of weak constant background electromagnetic ... More

Gradient estimates for solutions of the Lamé system with partially infinite coefficients in dimensions greater than twoJan 28 2016We establish upper bounds on the blow-up rate of the gradients of solutions of the Lam\'{e} system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system ... More

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. I. One singularitySep 26 2016Jun 09 2017We classify all $(-1)-$homogeneous axisymmetric no swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, ... More

Symmetry and Asymmetry: The Method of Moving SpheresMar 27 2007We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory, we obtain ... More

Selfishness need not be badDec 20 2017This article studies the user selfish behavior in non-atomic congestion games (NCG). We prove that the price of anarchy of general NCGs tends to 1 as number of users tends to infinity. This generalizes a recent result in the literature. Although our result ... More

Modeling Conceptual Characteristics of Virtual Machines for CPU Utilization PredictionNov 01 2018Cloud services have grown rapidly in recent years, which provide high flexibility for cloud users to fulfill their computing requirements on demand. To wisely allocate computing resources in the cloud, it is inevitably important for cloud service providers ... More

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two singularitiesJan 24 2019All $(-1)$-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a four dimensional ... More

Singular Behavior of an Electrostatic--Elastic Membrane System with an External PressureFeb 11 2019We analyze nonnegative solutions of the nonlinear elliptic problem $\Delta u=\frac{\lambda f(x)}{u^2}+P$, where $\lambda>0$ and $P\geq0$, on a bounded domain $\Omega$ of $\mathbb{R}^N$ ($N\geq 1$) with a Dirichlet boundary condition. This equation models ... More

Hypersurfaces of Prescribed Curvature MeasureMar 11 2011We consider the corresponding Christoffel-Minkowski problem for curvature measures. The existence of star-shaped $(n-k)$-convex bodies with prescribed $k$-th curvature measures ($k>0$) has been a longstanding problem. This is settled in this paper through ... More