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Circular Flows in Planar GraphsDec 24 2018For integers $a\ge 2b>0$, a \emph{circular $a/b$-flow} is a flow that takes values from $\{\pm b, \pm(b+1), \dots, \pm(a-b)\}$. The Planar Circular Flow Conjecture states that every $2k$-edge-connected planar graph admits a circular $(2+\frac{2}{k})$-flow. ... More

Complementary Graphs with Flows Less Than ThreeMar 14 2019X. Hou, H.-J. Lai, P. Li and C.-Q. Zhang [J. Graph Theory 69 (2012) 464-470] showed that for a simple graph $G$ with $|V(G)|\ge 44$, if $\min\{\delta(G),\delta(G^c)\}\ge 4$, then either $G$ or its complementary graph $G^c$ has a nowhere-zero $3$-flow. ... More

Nowhere-zero $3$-flow of graphs with small independence numberJul 21 2017Tutte's $3$-flow conjecture states that every $4$-edge-connected graph admits a nowhere-zero $3$-flow. In this paper, we characterize all graphs with independence number at most $4$ that admit a nowhere-zero $3$-flow. The characterization of $3$-flow ... More

Anti-Ramsey number of paths in hypergraphsJan 18 2019The anti-Ramsey number of a hypergraph $\mathcal{H}$ is the smallest integer $c$ such that in any coloring of the edges of the $s$-uniform complete hypergraph on $n$ vertices with exactly $c$ colors, there is a copy of $\mathcal{H}$ whose edges have distinct ... More

Nowhere-zero $3$-flow and $\mathbb{Z}_3$-connectedness in Graphs with Four Edge-disjoint Spanning TreesOct 14 2016Given a zero-sum function $\beta : V(G) \rightarrow \mathbb{Z}_3$ with $\sum_{v\in V(G)}\beta(v)=0$, an orientation $D$ of $G$ with $d^+_D(v)-d^-_D(v)= \beta(v)$ in $\mathbb{Z}_3$ for every vertex $v\in V(G)$ is called a $\beta$-orientation. A graph $G$ ... More

Incorporating Structured Commonsense Knowledge in Story CompletionNov 01 2018The ability to select an appropriate story ending is the first step towards perfect narrative comprehension. Story ending prediction requires not only the explicit clues within the context, but also the implicit knowledge (such as commonsense) to construct ... More

Odd induced subgraphs in graphs with treewidth at most twoJul 16 2017A long-standing conjecture asserts that there exists a constant $c>0$ such that every graph of order $n$ without isolated vertices contains an induced subgraph of order at least $cn$ with all degrees odd. Scott (1992) proved that every graph $G$ has an ... More

Does a standalone, "cold" (low-thermal-noise), linear resistor exist without cooling?May 15 2018Classical ways of cooling require some of these elements: phase transition, compressor, non-linearity, valve, and/or switch. A recent example is the 2018 patent of Linear Technology Corporation; they utilize the shot noise of a diode to produce a standalone ... More

Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactificationsNov 15 2006Jan 01 2009We study the Chow groups and the Chow motives of the wonderful compactifications $Y_{\mathcal{G}}$ of arrangements of subvarieties. We prove a natural decomposition of the Chow motive of $Y_\mathcal{G}$, in particular of the Fulton-MacPherson configuration ... More

Hyperscaling Violating Solutions in Generalised EMD TheoryAug 10 2016Sep 01 2016This short note is devoted to deriving scaling but hyperscaling violating solutions in a generalised Einstein-Maxwell-Dilaton theory with an arbitrary number of scalars and vectors. We obtain analytic solutions in some special case and discuss the physical ... More

Phase transition for accessibility percolation on hypercubesFeb 26 2015Jun 02 2017In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d. uniform [0,1] random variables on vertices of a hypercube, and study whether there is a path connecting two vertices such that the values of these random variables ... More

Phase transition for accessibility percolation on hypercubesFeb 26 2015In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d.\ uniform random variables on vertices of a hypercube, and study whether there is a path (possibly with back steps) connecting two vertices such that the values of ... More

Wonderful compactification of an arrangement of subvarietiesNov 14 2006Jan 01 2009We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety $Y$ and certain collection $\mathcal{G}$ of subvarieties of $Y$, the wonderful compactification $Y_\mathcal{G}$ can be constructed ... More

Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrixJun 30 2011May 04 2012We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient ... More

Rank-based SLOCC classification for odd n qubitsJun 21 2011We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect ... More

SLOCC determinant invariants of order 2^{n/2} for even n qubitsJun 17 2011Feb 02 2012In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants ... More

Production and rescattering of strange baryons at SPS energies in a transport model with hadron potentialsOct 13 2010A mean-field potential version of the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is used to investigate the production of strange baryons, especially the $\Lambda$s and $\overline{\Lambda}$s, from heavy ion collisions at SPS energies. ... More

Query-focused Multi-document Summarization: Combining a Novel Topic Model with Graph-based Semi-supervised LearningDec 10 2012Dec 31 2013Graph-based semi-supervised learning has proven to be an effective approach for query-focused multi-document summarization. The problem of previous semi-supervised learning is that sentences are ranked without considering the higher level information ... More

Electromagnetic Force on a BraneSep 29 2016A fundamental assumption in the theory of brane world is that all matter and radiation are confined on the four-dimensional brane and only gravitons can propagate in the five-dimensional bulk spacetime. The brane world theory did not provide an explanation ... More

A Novel Algorithm for Compressive Sensing: Iteratively Reweighed Operator Algorithm (IROA)Mar 28 2009Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the sparsity-constraint optimization. ... More

Nonlinear differentiation equation and analytic function spacesOct 09 2015In this paper we consider the nonlinear complex differential equation $$(f^{(k)})^{n_{k}}+A_{k-1}(z)(f^{(k-1)})^{n_{k-1}}+\cdot\cdot\cdot+A_{1}(z)(f')^{n_{1}}+A_{0}(z)f^{n_{0}}=0, $$where $ A_{j}(z)$, $ j=0, \cdots, k-1 $, are analytic in the unit disk ... More

Model-Checking of Linear-Time Properties Based on Possibility MeasureMar 10 2012Sep 25 2016We study the LTL model-checking in possibilistic Kripke structure using possibility measure. First, the notion of possibilistic Kripke structure and the related possibility measure are introduced, then model-checking of reachability and repeated reachability ... More

Isomorphism between Differential and Moment Invariants under Affine TransformMay 20 2017May 24 2017The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or computer science ... More

Reflection Invariant and Symmetry DetectionMay 30 2017May 31 2017Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object recognition. And ... More

Higher cohomology of the pluricanonical bundle is not deformation invariantDec 01 2006Jan 16 2008In this paper, we compute the dimensions of the 1st and 2nd cohomology groups of all the pluricanonical bundles for Hirzebruch surfaces, and the dimensions of the 1st and 2nd cohomology groups of the second pluricanonical bundles for a blow-up of a projective ... More

Note on two results on the rainbow connection number of graphsOct 23 2011An edge-colored graph $G$, where adjacent edges may be colored the same, is rainbow connected if any two vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of a connected graph $G$ is the smallest ... More

The Lawson homology and Deligne-Beilinson cohomology for Fulton-MacPherson configuration spacesSep 28 2006In this paper, we compute the Lawson homology groups and Deligne-Beilinson cohomology groups for Fulton-MacPherson configuration spaces. The explicit formulas are given.

Some Numerical Results For Ito EquationJan 21 2013By the method of invariant manifold, we investigate the Ito equation numerically with high precision. By the numerical results, we can completely determine the form of analytic soliton solutions for the Ito equation. In fact, by the numerical data we ... More

Constraints and Soliton Solutions for the KdV Hierarchy and AKNS HierarchyNov 26 2010It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer ... More

Temperature dependence of thermal conductivity in 1D nonlinear latticesMar 22 2007We examine the temperature dependence of thermal conductivity of one dimensional nonlinear (anharmonic) lattices with and without on-site potential. It is found from computer simulation that the heat conductivity depends on temperature via the strength ... More

Fluctuation limits of the super-Brownian motion with a single point catalystNov 02 2009Oct 20 2014We prove a fluctuating limit theorem of a sequence of super-Brownian motions over $\mbb{R}$ with a single point catalyst. The weak convergence of the processes on the space of Schwarz distributions is established. The limiting process is an Ornstein-Uhlenbeck ... More

Variational characterizations of $ξ$-submanifolds in the Eulicdean space $\bbr^{m+p}$Dec 29 2016$\xi$-submanifold in the Euclidean space $\bbr^{m+p}$ is a natural extension of the concept of self-shrinker to the mean curvature flow in $\bbr^{m+p}$. It is also a generalization of the $\lambda$-hypersurface defined by Q.-M. Cheng et al to arbitrary ... More

On the Lagrangian angle and the Kähler angle of immersed surfaces in the complex plane $\bbc^2$Nov 09 2015In this paper, we discuss the Lagrangian angle and the K\"ahler angle of immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in $\mathbb C^2$ than Lagrangian surfaces, ... More

Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formulaOct 11 2010Jun 24 2012This article studies the Lie algebra $Diff(K\Gamma)$ of derivations on the path algebra $K\Gamma$ of a quiver $\Gamma$ and the Lie algebra on the first Hochschild cohomology group $H^1(K\Gamma)$. We relate these Lie algebras to the algebraic and combinatorial ... More

Global $W^{2,δ}$ estimates for singular fully nonlinear elliptic equations with $L^n$ right hand side termsSep 14 2017We establish in this paper \emph{a priori} global $W^{2,\delta}$ estimates for singular fully nonlinear elliptic equations with $L^n$ right hand side terms. The method is to slide paraboloids and barrier functions vertically to touch the solution of the ... More

$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$Sep 09 2009Let $I$ be the ideal generated by alternating polynomials in two sets of $n$ variables. Haiman proved that the $q,t$-Catalan number is the Hilbert series of the graded vector space $M(=\bigoplus_{d_1,d_2}M_{d_1,d_2})$ spanned by a minimal set of generators ... More

Solutions for Toda systems on Riemann surfacesApr 19 2005Aug 26 2005In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems.

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.

Dirichlet forms and polymer models based on stable processesMay 01 2019In this paper, we are concerned with polymer models based on $\alpha$-stable processes, where $\alpha\in (\frac{d}{2},d\wedge 2)$ and $d$ stands for dimension. They are attached with a delta potential at the origin and the associated Gibbs measures are ... More

Pseudo Sequence based 2-D hierarchical reference structure for Light-Field Image CompressionDec 21 2016In this paper, we present a novel pseudo sequence based 2-D hierarchical reference structure for light-field image compression. In the proposed scheme, we first decompose the light-field image into multiple views and organize them into a 2-D coding structure ... More

Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classificationAug 11 2013We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local operations and classical ... More

Implicit Asymptotic Preserving Method for Linear Transport EquationsFeb 01 2016The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the speed of light, ... More

Towards Label Imbalance in Multi-label Classification with Many LabelsApr 05 2016In multi-label classification, an instance may be associated with a set of labels simultaneously. Recently, the research on multi-label classification has largely shifted its focus to the other end of the spectrum where the number of labels is assumed ... More

Quantum Criticality and DBI Magneto-resistanceAug 08 2016Sep 01 2016We use the DBI action from string theory and holography to study the magneto-resistance at quantum criticality with hyperscaling violation. We find and analyze a rich class of scaling behaviors for the magneto-resistance. A special case describes the ... More

Network analysis of the state space of chaotic map in digital domainOct 28 2014Nov 04 2014Complex dynamics of chaotic maps under an infinite-precision mathematical framework have been well known. The case in a finite-precision computer remains to be further explored. Previous work treated a digital chaotic map as a black box and gave different ... More

Novel Algorithm for Sparse Solutions to Linear Inverse Problems with Multiple MeasurementsMay 20 2009In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly sparse recovery ... More

Beat the Rayleigh limit: OAM based super-resolution diffraction tomographyJun 27 2013This letter is the first to report that a super-resolution imaging beyond the Rayleigh limit can be achieved by using classical diffraction tomography (DT) extended with orbital angular momentum (OAM), termed as OAM based diffraction tomography (OAM-DT). ... More

The neighbor-scattering number can be computed in polynomial time for interval graphsMar 17 2006Neighbor-scattering number is a useful measure for graph vulnerability. For some special kinds of graphs, explicit formulas are given for this number. However, for general graphs it is shown that to compute this number is NP-complete. In this paper, we ... More

Effects of alpha particles on the angular momentum loss from the SunJun 07 2006The classic Weber-Davis model of the solar wind is reconsidered by incorporating alpha particles and by allowing the solar wind to flow out of the equatorial plane in an axisymmetrical configuration. In the ion momentum equations of the solar wind, the ... More

Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soupsMay 14 2016Aug 29 2016We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical ... More

A New Unified Theory of Electromagnetic and Gravitational InteractionsNov 04 2015Mar 30 2016In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations ... More

Radioactive $γ$-Ray Emissions from Neutron Star MergersAug 29 2018Jan 20 2019Gravitational waves and electromagnetic radiations from a neutron star merger were discovered on 17 August 2017. Multiband observations of the optical transient have identified brightness and spectrum features broadly consistent with theoretical predictions. ... More

Variational Neural Networks: Every Layer and Neuron Can Be UniqueOct 14 2018The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural ... More

The Politics of AttentionOct 26 2018Jan 20 2019We develop an equilibrium theory of attention and politics. In a spatial model of electoral competition where candidates have varying policy preferences, we examine what kinds of political behaviors capture voters' limited attention and how this concern ... More

Characters and patterns of communities in networksJan 14 2013In this paper, we propose some new notions to characterize and analyze the communities. The new notions are general characters of the communities or local structures of networks. At first, we introduce the notions of internal dominating set and external ... More

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

Towards extremely high-resolution broad-band flat-field spectrometer in 'water window'Aug 19 2018The optical design of a novel spectrometer is present, combining a cylindrically convex pre-mirror with a cylindrically concave VLS grating (both in meridional) to deliver a resolving power of 100,000-200,000 in 'water window' (2-5nm). More remarkably, ... More

MB-tensors and MB0-tensorsNov 24 2014Dec 01 2014The class of MB(MB0)-tensors, which is a generation of B(B0)-tensors and quasi-double B(B0)-tensors, is proposed. And we prove that an even order symmetric MB(MB0)-tensor is positive (semi-)definite. This provides a positive answer for the conjecture ... More

Double B-tensor and quasi-double B-tensorAug 11 2014In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors and show that ... More

Monochromatic disconnection: Erdős-Gallai-type problems and product graphsApr 18 2019For an edge-colored graph $G$, we call an edge-cut $M$ of $G$ monochromatic if the edges of $M$ are colored with a same color. The graph $G$ is called monochromatically disconnected if any two distinct vertices of $G$ are separated by a monochromatic ... More

Uniqueness of positive bound states to Schrodinger systems with critical exponentsAug 02 2007We prove the uniqueness for the positive solutions of the following elliptic systems: \begin{eqnarray*} \left\{\begin{array}{ll} - \lap (u(x)) = u(x)^{\alpha}v(x)^{\beta} - \lap (v(x)) = u(x)^{\beta} v(x)^{\alpha} \end{array} \right. \end{eqnarray*} Here ... More

Global existence of weak solutions for quantum MHD equationsMay 07 2018In this paper, we consider the quantum MHD equations with both the viscosity coefficient and the magnetic diffusion coefficient are depend on the density. we prove the global existence of weak solutions and perform the lower planck limit in a 3-dimensional ... More

Optimal Deployment of Drone Base Stations for Cellular Communication by Network-based LocalizationSep 19 2018Drone base stations can assist cellular networks in a variety of scenarios. To serve the maximum number of users in an area without apriori user distribution information, we proposed a two-stage algorithm to find the optimal deployment of drone base stations. ... More

Two-sample Test of Community Memberships of Weighted Stochastic Block ModelsNov 30 2018Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the ... More

Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebrasJan 09 2019Rota-Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing ... More

On the B-twisted topological sigma model and Calabi-Yau geometryFeb 27 2014We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the target manifold ... More

The isospin dependent nucleon-nucleon inelastic cross section in the nuclear mediumOct 04 2016A theoretical calculation on the energy-, density-, and isospin-dependent nucleon-nucleon (NN) inelastic cross section $\sigma^*_{NN\rightarrow N\Delta}$, based on the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck microscopic transport theory, ... More

Effects of non-WKB Alfven waves on a multicomponent solar wind with differential ion flowApr 10 2008We present multicomponent solar wind models self-consistently incorporating the contribution from dissipationless, monochromatic, finite-wavelength (non-WKB), hydromagnetic, toroidal Alfv\'en waves, which are coupled to the flow only through the ponderomotive ... More

Propagation of non-WKB Alfven waves in a multicomponent solar wind with differential ion flowFeb 14 2007Mar 27 2007The propagation of dissipationless, hydromagnetic, non-WKB, purely toroidal Alfv\'en waves in a realistic background three-fluid solar wind with axial symmetry and differential proton-alpha flow is investigated. The wave equations are derived from standard ... More

Kazhdan-Lusztig polynomials and drift configurationsJun 09 2010Oct 04 2010The coefficients of the Kazhdan-Lusztig polynomials $P_{v,w}(q)$ are nonnegative integers that are upper semicontinuous on Bruhat order. Conjecturally, the same properties hold for $h$-polynomials $H_{v,w}(q)$ of local rings of Schubert varieties. This ... More

The Primary Design of the RidgetronMay 27 2016The ridgetron is used to accelerate the intense beam for the electron irradiation. According to the electromagnetic field simulation, the extend electrode should be cancelled to increase the shunt impedence. The method of parameter sweeping with constraint ... More

Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit statesJan 11 2012Oct 26 2012We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to ... More

The Isospin Distribution of Fragments in Reactions 96Ru+96Ru, 96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at Beam Energy 400 AMeVNov 21 2002The isospin distribution of particles and fragments in collisions 96Ru+96Ru, 96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at beam energy 400 AMeV is studied with isospin dependent QMD model. We find that the rapidity distribution of differential neutron-proton ... More

Uniform regularity for linear kinetic equations with random input based on hypocoercivityDec 05 2016In this paper we study the effect of randomness in kinetic equations that preserve mass. The analysis is carried out in a general setting, with the regularity result not depending on the specific form of the collision term, the probability distribution ... More

Meta-path Augmented Response GenerationNov 02 2018We propose a chatbot, namely Mocha to make good use of relevant entities when generating responses. Augmented with meta-path information, Mocha is able to mention proper entities following the conversation flow.

Electrodynamics on Cosmological ScalesAug 26 2015Feb 29 2016Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge, ... More

Bijection between Conjugacy Classes and Irreducible Representations of Finite Inverse SemigroupsAug 28 2012In this paper we show that the irreducible representations of a finite inverse semigroup $S$ over an algebraically closed field $F$ are in bijection with the conjugacy classes of $S$ if the characteristic of $F$ is zero or a prime number that does not ... More

Finite time blowup of generalized Euler ODE in matrix geometryFeb 11 2015In this paper, we study the finite time blowup of the generalized Euler ODE in the matrix geometry. We can extend Sullivan's result which is about the finite time blowup result of initial invertible linear operators to singular linear operators. we can ... More

Semi-dynamic shortest-path tree algorithms for directed graphs with arbitrary weightsMar 05 2019Given a directed graph $G$ with arbitrary real-valued weights, the single source shortest-path problem (SSSP) asks for, given a source $s$ in $G$, finding a shortest path from $s$ to each vertex $v$ in $G$. A classical SSSP algorithm detects a negative ... 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.

Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varietiesJan 20 2010We study Hilbert-Samuel multiplicity for points of Schubert varieties in the complete flag variety, by Groebner degenerations of the Kazhdan-Lusztig ideal. In the covexillary case, we give a positive combinatorial rule for multiplicity by establishing ... More

The asymptotic number of occurrences of a subtree in trees with bounded maximum degree and an application to the Estrada indexMay 07 2010Let $\mathcal {T}^{\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\Delta$. Suppose that every tree in $\mathcal {T}^{\Delta}_n$ is equally likely. For any given subtree $H$, we show that ... More

The asymptotic value of Randic index for treesMar 25 2010Let $\mathcal{T}_n$ denote the set of all unrooted and unlabeled trees with $n$ vertices, and $(i,j)$ a double-star. By assuming that every tree of $\mathcal{T}_n$ is equally likely, we show that the limiting distribution of the number of occurrences ... More

The asymptotic values of the general Zagreb and Randić indices of trees with bounded maximum degreeApr 11 2010Let $\mathcal {T}^{\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\Delta$. Suppose that every tree in $\mathcal {T}^{\Delta}_n$ is equally likely. We show that the number of vertices of ... More

Hardness results on generalized connectivityMay 04 2010Let $G$ be a nontrivial connected graph of order $n$ and let $k$ be an integer with $2\leq k\leq n$. For a set $S$ of $k$ vertices of $G$, let $\kappa (S)$ denote the maximum number $\ell$ of edge-disjoint trees $T_1,T_2,...,T_\ell$ in $G$ such that $V(T_i)\cap ... More

Monochromatic $k$-edge-connection colorings of graphsOct 28 2018A path in an edge-colored graph $G$ is called monochromatic if any two edges on the path have the same color. For $k\geq 2$, an edge-colored graph $G$ is said to be monochromatic $k$-edge-connected if every two distinct vertices of $G$ are connected by ... More

Global $W^{2,δ}$ estimates for a type of singular fully nonlinear elliptic equationsSep 14 2017We obtain global $W^{2,\delta}$ estimates for a type of singular fully nonlinear elliptic equations where the right hand side term belongs to $L^\infty$. The main idea of the proof is to slide paraboloids from below and above to touch the solution of ... More

Associated Production of Neutral Higgs Boson with Squark Pair in the Minimal Supersymmetric Standard Model with Explicit CP Violation at the CERN LHCJan 18 2006Apr 09 2006We investigate the associated production of neutral Higgs boson with squark pair in the minimal supersymmetric standard model with and without explicit CP violation, respectively. We show that the dominant productions in both cases are always ones of ... More

Constraining fast radio burst progenitors with gravitational lensingMar 31 2014May 14 2014Fast Radio Bursts (FRBs) are new transient radio sources discovered recently. Because of the angular resolution restriction in radio surveys, no optical counter part has been identified yet so it is hard to determine the progenitor of FRBs. In this paper ... More

Connection Sensitive Attention U-NET for Accurate Retinal Vessel SegmentationMar 13 2019We develop a connection sensitive attention U-Net(CSAU) for accurate retinal vessel segmentation. This method improves the recent attention U-Net for semantic segmentation with four key improvements: (1) connection sensitive loss that models the structure ... More

Dynamic Fair Division Problem with General ValuationsFeb 14 2018Apr 18 2018In this paper, we focus on how to dynamically allocate a divisible resource fairly among n players who arrive and depart over time. The players may have general heterogeneous valuations over the resource. It is known that the exact envy-free and proportional ... More

Primary visual cortex as a saliency map: parameter-free prediction of behavior from V1 physiologyNov 02 2014It has been hypothesized that neural activities in the primary visual cortex (V1) represent a saliency map of the visual field to exogenously guide attention. This hypothesis has so far provided only qualitative predictions and their confirmations. We ... More

Isospin effect on nuclear stopping in intermediate energy Heavy Ion CollisionsNov 21 2002By using the Isospin Dependent Quantum Molecular Dynamics Model (IQMD), we study the dependence of nuclear stopping Q_{ZZ}/A and R in intermediate energy heavy ion collisions on system size, initial N/Z, isospin symmetry potential and the medium correction ... More

Holographic Competition of Phases and SuperconductivitySep 30 2015Jan 13 2016We use a holographic theory to model and study the competition of four phases: an antiferromagnetic phase, a superconducting phase, a metallic phase and a striped phase, using as control parameters temperature and a doping-like parameter. We analyse the ... More

Criteria For Superfluid Instabilities of Geometries with Hyperscaling ViolationJun 08 2016We examine the onset of superfluid instabilities for geometries that exhibit hyperscaling violation and Lifshitz-like scaling at infrared and intermediate energy scales, and approach AdS in the ultraviolet. In particular, we are interested in the role ... More

Zero-sum and nonzero-sum differential games without Isaacs conditionJul 17 2015In this paper we study the zero-sum and nonzero-sum differential games with not assuming Isaacs condition. Along with the partition $\pi$ of the time interval $[0,T]$, we choose the suitable random non-anticipative strategy with delay to study our differential ... More

The Crossover-Distance for ISI-Correcting Decoding of Convolutional Codes in Diffusion-Based Molecular CommunicationsDec 29 2018In diffusion based molecular communication, the intersymbol interference (ISI) is an important reason for system performance degradation, which is caused by the random movement, out-of-order arrival and indistinguishability of the moleclues. In this paper, ... More

Two-Step Many-Objective Optimal Power Flow Based on Knee Point-Driven Evolutionary AlgorithmDec 04 2018To coordinate the economy, security and environment protection in the power system operation, a two-step many-objective optimal power flow (MaOPF) solution method is proposed. In step 1, it is the first time that knee point-driven evolutionary algorithm ... 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.