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A Simple Proof of a Conjecture of SimionSep 09 2008Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we present a simple ... More

Isoperimetric inequality, $Q$-curvature and $A_p$ weightsJun 07 2013A well known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature. In ... More

Michael-Simon inequalities for $k$-th mean curvaturesMay 14 2013This paper continues the study of Alexandrov-Fenchel inequalities for quermassintegrals for $k$-convex domains. It focuses on the application to the Michael-Simon type inequalities for $k$-curvature operators. The proof uses optimal transport maps as ... More

Isoperimetric inequality, finite total Q-curvature and quasiconformal mapApr 02 2010In this paper, we obtain the isoperimetric inequality on conformally flat manifold with finite total $Q$-curvature. This is a higher dimensional analogue of Li and Tam's result \cite{L-T} on surfaces with finite total Gaussian curvature. The main step ... More

Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equationDec 15 2017Jan 24 2019We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24, 22] and our new observations on the underlying wave structures of the equation ... More

Integrability of scalar curvature and normal metric on conformally flat manifoldsJul 14 2017On a manifold $(\mathbb{R}^n, e^{2u} |dx|^2)$, we say $u$ is normal if the $Q$-curvature equation that $u$ satisfies $(-\Delta)^{\frac{n}{2}} u = Q_g e^{nu}$ can be written as the integral form $u(x)=\frac{1}{c_n}\int_{\mathbb R^n}\log\frac{|y|}{|x-y|}Q_g(y)e^{nu(y)}dy+C$. ... More

Hawking-Moss Tunneling in Noncommutative Eternal InflationNov 28 2007The quantum behavior of noncommutative eternal inflation is quite different from the usual knowledge. Unlike the usual eternal inflation, the quantum fluctuation of noncommutative eternal inflation is suppressed by the Hubble parameter. Due to this, we ... More

Is Noncommutative Eternal Inflation Possible?Jun 05 2007Jun 21 2007We investigate the condition for eternal inflation to take place in the noncommutative spacetime. We find that the possibility for eternal inflation's happening is greatly suppressed in this case. If eternal inflation cannot happen in the low energy region ... More

Testing quantum gravity effects with latest CMB observationsApr 26 2014Jun 19 2014Inspired by quantum gravitational physics, the approach of non-commutative (NC) phase space leads to a modified dispersion relation of gravitational waves. This feature, if applied to the very early universe, gives rise to a modified power spectrum of ... More

Large Nonlocal Non-Gaussianity from a Curvaton BraneMay 02 2010Dec 01 2010We use a generalized delta N formalism to study the generation of the primordial curvature perturbation in the curvaton brane scenario inspired by stringy compactifications. We note that the non-Gaussian features, especially the trispectra, crucially ... More

The triangle-free graphs with rank 6Jan 03 2013Jan 05 2013The rank of a graph G is defined to be the rank of its adjacency matrix A(G). In this paper we characterize all connected triangle-free graphs with rank 6.

Maximum Estrada Index of Bicyclic GraphsApr 17 2012Let $G$ be a simple graph of order $n$, let $\lambda_1(G),\lambda_2(G),...,\lambda_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{\lambda_i(G)}$. In this paper we determine the unique ... More

The nullity of unicyclic signed graphsJul 02 2011In this paper we introduce the nullity of signed graphs, and give some results on the nullity of signed graphs with pendant trees. We characterize the unicyclic signed graphs of order n with nullity n-2; n-3; n-4; n-5 respectively.

Dual-Coding Theory and Connectionist Lexical SelectionMay 31 1994We introduce the bilingual dual-coding theory as a model for bilingual mental representation. Based on this model, lexical selection neural networks are implemented for a connectionist transfer project in machine translation. This lexical selection approach ... More

Variance Suppression: Balanced Training Process in Deep LearningNov 20 2018Nov 28 2018Stochastic gradient descent updates parameters with summation gradient computed from a random data batch. This summation will lead to unbalanced training process if the data we obtained is unbalanced. To address this issue, this paper takes the error ... More

Categories of vector spaces and GrassmanniansNov 08 2017We construct a new category of vector spaces which contains both the standard category of vector spaces and Grassmannians. Its space of objects classifies vector bundles, its space of morphisms classifies bundle isomorphisms, and it can be delooped to ... More

Dynamics of Bright Soliton in Optical FiberMay 12 2001The bright soliton in optical fiber is generally investigated via its spatial evolution in the time domain, where its waveform is considered in many studies. To be consistent with the well-established picture of the dynamics of solitons in other systems, ... More

Theoretical prediction of the half-metallicity in one-dimensional Cr2NO2 nanoribbonsDec 27 2016One-dimensional Cr2NO2 nanoribbons cutting from the oxygen-passivated Cr2NO2 MXene are investigated by using density functional theory. The wide nanoribbons have ferromagnetic ground states and are half-metals, independent of their chirality. The half-metallic ... More

Multi-Stream InflationMar 12 2009Jul 24 2009We propose a "multi-stream" inflation model, which is a double field model with spontaneous breaking and restoration of an approximate symmetry. We calculate the density perturbation and non-Gaussianity in this model. We find that this model can have ... More

The inviscid limit to a contact discontinuity for the compressible Navier-Stokes-Fourier system using the relative entropy methodMay 28 2015We consider the zero heat conductivity limit to a contact discontinuity for the mono-dimensional full compressible Navier-Stokes-Fourier system. The method is based on the relative entropy method, and do not assume any smallness conditions on the discontinuity, ... More

Operator-scaling Gaussian random fields via aggregationDec 19 2017We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In our model, each copy of the random field in the aggregation is built from two correlated one-dimensional random walks, each ... More

Fractional Poincaré inequality with finite total $Q$-curvatureJan 01 2016In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.

On locally conformally flat manifolds with finite total $Q$-curvatureDec 31 2015In this paper, we focus our study on the ends of a locally conformally flat complete manifold with finite total $Q$-curvature. We prove that for such a manifold, the integral of the $Q$-curvature equals an integral multiple of a dimensional constant $c_n$, ... More

Fermi Study of gamma-ray Millisecond Pulsars: the Spectral Shape and Pulsed 25--200 GeV Emission from J0614-3329Apr 29 2016We report our analysis of the Fermi Large Area Telescope data for 39 millisecond pulsars (MSPs) listed in the second $\gamma$-ray pulsar catalog. Spectra of the pulsars are obtained. We fit the spectra with a function of a power law with exponential cutoff, ... More

Quantum UV/IR Relations and Holographic Dark Energy from Entropic ForceJan 25 2010Mar 30 2010We investigate the implications of the entropic force formalism proposed by Verlinde. We show that an UV/IR relation proposed by Cohen et al, as well as an uncertainty principle proposed by Hogan can be derived from the entropic force formalism. We show ... More

Geometric realization and its variantsApr 01 2018In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.

Separable functions: symmetry, monotonicity, and applicationsSep 15 2018In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functions. We first study the axial symmetry and monotonicity of separable functions ... More

An approximation of the $e$-invariant in the stable homotopy categoryJul 11 2017Oct 17 2017In their construction of the topological index for flat vector bundles, Atiyah, Patodi and Singer associate to each flat vector bundle a particular $\mathbb{C/Z}$-$K$-theory class. This assignment determines a map, up to weak homotopy, from $K_{a}\mathbb{C}$, ... More

Coherent Point Drift Networks: Unsupervised Learning of Non-Rigid Point Set RegistrationJun 07 2019Jun 11 2019Given new pairs of source and target point sets, standard point set registration methods often repeatedly conduct the independent iterative search of desired geometric transformation to align the source point set with the target one. This limits their ... More

Fat realization and Segal's classifying spaceOct 10 2017In this paper, we give a new proof of a well-known theorem due to tom Dieck that the fat realization and Segal's classifying space of an internal category in the category of topological spaces are homotopy equivalent.

Multilinear singular and fractional integral operators on weighted Morrey spacesMar 19 2013In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

Towards the physical vacuum of cosmic inflationJul 18 2015There have been long debates about the initial condition of inflationary perturbations. In this work we explicitly show the decay of excited states during inflation via interactions. For this purpose, we note that the folded shape non-Gaussianity can ... More

On random linear dynamical systems in a Banach space. I. Multiplicative Ergodic Theorem and Krein-Rutmann type TheoremsJul 02 2015For linear random dynamical systems in a separable Banach space $X$, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-$k$, which present a (quasi)-equivalence relation between the measurably co-invariant ... More

Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvatureNov 11 2016In this paper, we study contact forms on the three- dimensional Heisenberg manifold with its standard CR structure. We discover that the $Q'$-curvature, introduced by Branson, Fontana and Morpurgo [BFM13] on the CR three-sphere and then generalized to ... More

Transversality for Cyclic Negative Feedback SystemsDec 04 2014Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in the category of monotone dynamical systems in the sense of Hirsch. Our ... More

On the log-convexity of combinatorial sequencesFeb 28 2006Nov 27 2006This paper is devoted to the study of the log-convexity of combinatorial sequences. We show that the log-convexity is preserved under componentwise sum, under binomial convolution, and by the linear transformations given by the matrices of binomial coefficients ... More

Searching for $γ$-Ray Pulsars among Fermi Unassociated Sources: 2FGL J1906.5+0720Feb 26 2014Jul 04 2014We report the results from our analysis of the \textit{Fermi} Large Area Telescope data of the \textit{Fermi} unassociated source 2FGL J1906.5$+$0720, which is a high-ranked candidate pulsar. In order to better study our target, we first update the ephemeris ... More

Search for gamma-ray emission from four accreting millisecond pulsars with Fermi/LATNov 27 2012Apr 08 2013We report our search for \gamma-ray emission in the energy range from 100 MeV to 300 GeV from four Accreting Millisecond Pulsars (AMPs), SAX J1808.4-3658, IGR J00291+5934, XTE J1814-338, and XTE J0929-314. The data are from four-year observations carried ... More

Discovery of Gamma-Ray Orbital Modulation in the Black Widow PSR J1311-3430Feb 17 2015Apr 15 2015We report our discovery of orbitally modulated $\gamma$-ray emission from the black widow system PSR J1311-3430. We analyze the \textit{Fermi} Large Area Telescope data during the offpulse phase interval of the pulsar, and find the orbital modulation ... More

Fermi Observation of the transitional pulsar binary XSS J12270-4859Nov 13 2014Because of the disappearance of its accretion disk since the time period around 2012 November--December, XSS J12270-4859 has recently been identified as, in addition to PSR J1023+0038, another transitional millisecond pulsar binary. We have carried out ... More

Theoretical Prediction of the Robust Intrinsic Half-Metallicity in Ni2N MXene with Different Types of Surface TerminationsMay 16 2017Bare and surface-passivated Fe2N, Co2N, and Ni2N MXene were investigated by using density functional theory. Fe2N(OH)2, Fe2NO2, Co2NO2, Ni2NF2, Ni2N(OH)2, and Ni2NO2 are intrinsic half-metals, while other structures have antiferromagnetic ground states. ... More

From N M2's to N D2'sJul 09 2008May 06 2009In this short note, we reduce the N=6, U(N)xU(N) Chern-Simons gauge theories to N=8, U(N) Yang-Mills gauge theories. This process corresponds to recovering the world-volume theory of N D2-branes from that of N M2-branes in an intermediate energy range. ... More

Simplicial Waldhausen categories and topological $K$-theoryMay 15 2017Jan 23 2018Utilizing simplicial Waldhausen theory, we prove that the geometric realization of the topologized category of bounded chain complexes over complex numbers (resp. real numbers) is an infinite loop space that represents connective complex (resp. real) ... More

The likely Fermi detection of GRO J1008-57:hint for gamma-ray production in neutron-star X-ray binariesFeb 03 2019In our search for gamma-ray emission from Be X-ray binaries from analysis of the data obtained with the Large Area Telescope (LAT) on board the Fermi Gamma-Ray Space Telescope, we find likely detection of GRO J1008-57. The binary has an orbital period ... More

Massive Fields as Systematics for Single Field InflationMar 13 2017Jul 05 2017During inflation, massive fields can contribute to the power spectrum of curvature perturbation via a dimension-5 operator. This contribution can be considered as a bias for the program of using $n_s$ and $r$ to select inflation models. Even the dimension-5 ... More

The least eigenvalues of signless Laplacian of non-bipartite graphs with pendant verticesAug 20 2012In this paper we determine the graph whose least eigenvalue of signless Laplacian attains the minimum or maximum among all connected non-bipartite graphs of fixed order and given number of pendant vertices. Thus we obtain a lower bound and an upper bound ... More

Non-Commutativity, Teleology and GRB Time DelayApr 07 2009Apr 14 2009We propose a model in which an energy-dependent time delay of a photon originates from space-time non-commutativity, the time delay is due to a noncommutative coupling between dilaton and photon. We predict that in our model, high energy photons with ... More

The F-theory geometry with most flux vacuaNov 10 2015Nov 29 2015Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold ${\cal M}_{\rm max}$ gives rise to ${\cal O} (10^{272,000})$ F-theory flux vacua, and that the sum total of the numbers of flux ... More

A unified approach to polynomial sequences with only real zerosSep 09 2005Nov 27 2006We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, ... More

Convergence rate and concentration inequalities for Gibbs sampling in high dimensionOct 16 2014The objective of this paper is to study the Gibbs sampling for computing the mean of observable in very high dimension - a powerful Markov chain Monte Carlo method. Under the Dobrushin's uniqueness condition, we establish some explicit and sharp estimate ... More

Geometirc Arveson-Douglas Conjecture - Decomposition of VarietiesApr 12 2017In this paper, we prove the Geometric Arveson-Douglas Conjecture for a special case which allow some singularity on $\partial{\mathbb{B}_n}$. More precisely, we show that if a variety can be decomposed into two varieties, each having nice properties and ... More

Membrane paradigm of black holes in Chern-Simons modified gravityDec 07 2015Jun 05 2016The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress ... More

E-string spectrum and typical F-theory geometryNov 07 2018Feb 22 2019In recent scans of 4D F-theory geometric models, it was shown that a dominant majority of the base geometries only support SU(2), $G_2$, $F_4$ and $E_8$ gauge groups. Moreover, most of these gauge groups are shown to couple to strongly coupled "conformal ... More

Polynomials with real zeros and Polya frequency sequencesNov 27 2006Let $f(x)$ and $g(x)$ be two real polynomials whose leading coefficients have the same sign. Suppose that $f(x)$ and $g(x)$ have only real zeros and that $g$ interlaces $f$ or $g$ alternates left of $f$. We show that if $ad\ge bc$ then the polynomial ... More

Bounds for the positive or negative inertia index of a graphSep 18 2014Let $G$ be a graph and let $A(G)$ be adjacency matrix of $G$.The positive inertia index (respectively, the negative inertia index) of $G$, denoted by $p(G)$ (respectively, $n(G)$), is defined to be the number of positive eigenvalues (respectively, negative ... More

Log-convex and Stieltjes moment sequencesDec 13 2016We show that Stieltjes moment sequences are infinitely log-convex, which parallels a famous result that (finite) P\'olya frequency sequences are infinitely log-concave. We introduce the concept of $q$-Stieltjes moment sequences of polynomials and show ... More

Half-arc-transitive graphs of prime-cube order of small valenciesMay 26 2016A graph is called {\em half-arc-transitive} if its full automorphism group acts transitively on vertices and edges, but not on arcs. It is well known that for any prime $p$ there is no tetravalent half-arc-transitive graph of order $p$ or $p^2$. Xu~[Half-transitive ... More

Dissipation Effects in Hybrid SystemsOct 25 2006The dissipation effect in a hybrid system is studied in this Letter. The hybrid system is a compound of a classical magnetic particle and a quantum single spin. Two cases are considered. In the first case, we investigate the effect of the dissipative ... More

On the unimodality of independence polynomials of some graphsAug 16 2010In this paper we study unimodality problems for the independence polynomial of a graph, including unimodality, log-concavity and reality of zeros. We establish recurrence relations and give factorizations of independence polynomials for certain classes ... More

Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field TheoryJan 07 2015Jan 30 2015We construct exceptional field theory for the duality group SL(3)$\times$SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the $(3,2)$ fundamental representation, leading to a 14-dimensional generalized ... More

A fully nonlinear Sobolev trace inequalityMay 31 2016The $k$-Hessian operator $\sigma_k$ is the $k$-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the $k$-Hessian equation $\sigma_k(D^2u)=f$ with Dirichlet boundary condition $u=0$ is variational; indeed, this problem ... More

$q$-Eulerian polynomials and polynomials with only real zerosNov 27 2006Jul 01 2007Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the location and multiplicity of the real zeros of $f$ and $F$, which generalizes and unifies many known results, including the results of Brenti ... More

Fractional-order Backpropagation Neural Networks: Modified Fractional-order Steepest Descent Method for Family of Backpropagation Neural NetworksJun 23 2019This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A promising mathematical ... More

The spectral radius of the square of graphsApr 29 2014The square of a connected graph $G$ is obtained from $G$ by adding an edge between every pair of vertices at distance $2$. In this paper we give some upper or lower bounds for the spectral radius of the square of connected graphs, trees and unicyclic ... More

Fractional-order Backpropagation Neural Networks: Modified Fractional-order Steepest Descent Method for Family of Backpropagation Neural NetworksJun 23 2019Jul 10 2019This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A promising mathematical ... More

On unimodality problems in Pascal's triangleSep 09 2008Many sequences of binomial coefficients share various unimodality properties. In this paper we consider the unimodality problem of a sequence of binomial coefficients located in a ray or a transversal of the Pascal triangle. Our results give in particular ... More

PerformanceNet: Score-to-Audio Music Generation with Multi-Band Convolutional Residual NetworkNov 11 2018Music creation is typically composed of two parts: composing the musical score, and then performing the score with instruments to make sounds. While recent work has made much progress in automatic music generation in the symbolic domain, few attempts ... More

Dark Energy Model with Spinor Matter and Its Quintom ScenarioJun 24 2008Jul 01 2008A class of dynamical dark energy models, dubbed Spinor Quintom, can be constructed by a spinor field $\psi$ with a nontraditional potential. We find that, if choosing suitable potential, this model is able to allow the equation-of-state to cross the cosmological ... More

Random conformal welding for finitely connected regionsOct 23 2014Given a finitely connected region $\Omega$ of the Riemann sphere whose complement consists of $m$ mutually disjoint closed disks $\bar{U}_j$, the random homeomorphism $h_j$ on the boundary component $\partial U_j$ is constructed using the exponential ... More

Improving the spatial resolution of NICA ECAL through new reconstruction methodFeb 10 2019May 12 2019A Shashlyk-type electromagnetic calorimeter (ECal) will be used in the Multi-purpose Detector at Nuclotron-based Ion Collider facility to study the properties of nuclear matter. In this experiment, the ECal detector is responsible for measuring the energy ... More

Comparison of variational and CSE methods to polaron ground-state energyDec 19 2004Taking the same trial wave function, the ground-state energy of Fr\"{o}hlich polaron is investigated by variational method and coherent-state expansion (CSE) one, respectively. Within the accuracy to $\alpha^{2}$(the electron-phonon coupling constant), ... More

Geometric phases induced in auxiliary qubits by many-body systems near its critical pointsMar 07 2007The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. ... More

Log-concavity and LC-positivityApr 08 2005Nov 27 2006A triangle $\{a(n,k)\}_{0\le k\le n}$ of nonnegative numbers is LC-positive if for each $r$, the sequence of polynomials $\sum_{k=r}^{n}a(n,k)q^k$ is $q$-log-concave. It is double LC-positive if both triangles $\{a(n,k)\}$ and $\{a(n,n-k)\}$ are LC-positive. ... More

Proof of a conjecture on unimodalitySep 09 2008Let $P(x)$ be a polynomial of degree $m$, with nonnegative and non-decreasing coefficients. We settle the conjecture that for any positive real number $d$, the coefficients of $P(x+d)$ form a unimodal sequence, of which the special case $d$ being a positive ... More

Geometric Arveson-Douglas Conjecture and Holomorphic ExtensionNov 03 2015Jan 28 2016In this paper we introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture for complex analytic subsets that is smooth on the boundary of the unit ball and intersects transversally with it. ... More

The signature of line graphs and power treesOct 03 2013Let $G$ be a graph and let $A(G)$ be the adjacency matrix of $G$. The signature $s(G)$ of $G$ is the difference between the positive inertia index and the negative inertia index of $A(G)$. Ma et al. [Positive and negative inertia index of a graph, Linear ... More

A subelliptic Bourgain-Brezis inequalityOct 06 2012Oct 22 2014We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space $\dot{NL}^{1,Q}$ by $L^{\infty}$ functions, generalizing a result of Bourgain-Brezis \cite{MR2293957}. We then ... More

Bipartite bi-Cayley graphs over metacyclic groups of odd prime-power orderJul 10 2017A graph $\Gamma$ is a bi-Cayley graph over a group $G$ if $G$ is a semiregular group of automorphisms of $\Gamma$ having two orbits. Let $G$ be a non-abelian metacyclic $p$-group for an odd prime $p$, and let $\Gamma$ be a connected bipartite bi-Cayley ... More

Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequencesMar 22 2013Mar 25 2013We develop techniques to deal with monotonicity of sequences z_{n+1}/z_n and \sqrt[n]{z_n}. A series of conjectures of Zhi-Wei Sun and of Amdeberhan et al. are verified in certain unified approaches.

Smoothing methods comparison for CMB E- and B-mode separationNov 04 2015The anisotropies of the B-mode polarization in the cosmic microwave background radiation play a crucial role for the study of the very early Universe. However, in the real observation, the mixture of the E-mode and B-mode can be caused by the partial ... More

Gauge field in ultra-cold bipartite atomsMar 25 2006The effects of entanglement and spin-spin collision on the gauge field in ultracold atoms are presented in this paper. Two gauge fields are calculated and discussed. One of the fields comes from space dependent spin-spin collisions in ultra-cold atoms, ... More

Diffusive Wave in the Low Mach Limit for Compressible Navier-Stokes EquationsMar 23 2016Oct 27 2016The low Mach limit for 1D non-isentropic compressible Navier-Stokes flow, whose density and temperature have different asymptotic states at infinity, is rigorously justified. The problems are considered on both well-prepared and ill-prepared data. For ... More

The limit to rarefaction wave with vacuum for 1D compressible fluids with temperature-dependent viscositiesJul 12 2013In this paper we study the zero dissipation limit of the one-dimensional full compressible Navier-Stokes(CNS) equations with temperature-dependent viscosity and heat-conduction coefficient. It is proved that given a rarefaction wave with one-side vacuum ... More

Hahn echo and criticality in spin-chain systemsJan 15 2006Apr 20 2006We establish a relation between Hahn spin-echo of a spin-$\frac 1 2 $ particle and quantum phase transition in a spin-chain, which couples to the particle. The Hahn echo is calculated and discussed at zero as well as at finite temperatures. On the example ... More

Stability of the Superposition of a Viscous Contact Wave with two Rarefaction Waves to the bipolar Vlasov-Poisson-Boltzmann SystemOct 09 2017We investigate the nonlinear stability of the superposition of a viscous contact wave and two rarefaction waves for one-dimensional bipolar Vlasov-Poisson-Boltzmann (VPB) system, which can be used to describe the transportation of charged particles under ... More

Stability of planar rarefaction wave to 3D full compressible Navier-Stokes equationsJan 17 2018Jan 24 2019We prove the time-asymptotic stability toward planar rarefaction wave for the three-dimensional full compressible Navier-Stokes equations in an infinite long flat nozzle domain $\mathbb{R}\times\mathbb{T}^2$. Compared with one-dimensional case, the proof ... More

Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional compressible Navier-Stokes equationsFeb 28 2019The vanishing viscosity limit of the two-dimensional (2D) compressible isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that there exists ... More

Holographic Dark EnergyDec 01 2016Jun 21 2017We review the paradigm of holographic dark energy (HDE), which arises from a theoretical attempt of applying the holographic principle (HP) to the dark energy (DE) problem. Making use of the HP and the dimensional analysis, we derive the general formula ... More

Theoretical investigation on the ferromagnetic two-dimensional scandium monochloride sheet that has a high Curie temperature and could be exfoliated from a known materialJul 07 2018A two-dimensional scandium monochloride sheet was investigated by using density functional theory. It could be exfoliated from a known bulk material with a cleavage energy slightly lower than that of graphene. The sheet has a ferromagnetic ground state ... More

General Single Field Inflation with Large Positive Non-GaussianityDec 29 2007Mar 29 2008Recent analysis of the WMAP three year data suggests $f_{NL}^{local}\simeq86.8$ in the WMAP convention. It is necessary to make sure whether general single field inflation can produce a large positive $f_{NL}$ before turning to other scenarios. We give ... More

Weak and strong deflection gravitational lensings by a charged Horndeski black holeFeb 11 2019May 14 2019A charged black hole was predicted by the Einstein--Horndeski--Maxwell theory. In order to provide its observational signatures, we investigate its weak and strong deflection gravitational lensings. We find its weak deflection lensing observables, including ... More

The least H-eigenvalue of signless Laplacian of non-odd-bipartite hypergraphsFeb 12 2019Let $G$ be a connected non-odd-bipartite hypergraph with even uniformity. The least H-eigenvalue of the signless Laplacian tensor of $G$ is simply called the least eigenvalue of $G$ and the corresponding H-eigenvectors are called the first eigenvectors ... More

Random Bits Regression: a Strong General Predictor for Big DataJan 13 2015To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on the original ... More

On slope genera of knotted tori in 4-spaceOct 10 2011Feb 07 2013In this note, we investigate genera for the slopes of a knotted torus in the 4-sphere analogous to the genus of a classical knot. We compare various formulations of this notion, and use this notion to study the extendable subgroup of the mapping class ... More

A Combinatorial Method for Computing Characteristic Polynomials of Starlike HypergraphsJun 16 2018By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike hypergraphs ... More

Minimum Distance Spectral Radius of Graphs with Given Edge ConnectivityMar 14 2012In this paper we determine the unique graph with minimum distance spectral radius among all connected graphs of fixed order and given edge connectivity.

Possible particle-hole instabilities in interacting type-II Weyl semimetalsJul 30 2017Aug 01 2017Type II Weyl semimetal, a three dimensional gapless topological phase, has drawn enormous interest recently. These topological semimetals enjoy overtilted dispersion and Weyl nodes that separate the particle and hole pocket. Using perturbation renormalization ... More

Hybrid Quasi-Single Field InflationApr 20 2018The decay of massive particles during inflation generates characteristic signals in the squeezed limit of the primordial bispectrum. These signals are in particular distinctive in the regime of the quasi-single field inflation, where particles are oscillating ... More

Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphsJan 24 2019Unlike an irreducible $Z$-matrices, a weakly irreducible $Z$-tensor $\mathcal{A}$ can have more than one eigenvector associated with the least H-eigenvalue. We show that there are finitely many eigenvectors of $\mathcal{A}$ associated with the least H-eigenvalue. ... More

Global existence of weak solution to the heat and moisture transport system in fibrous porous mediaAug 09 2009This paper is concerned with theoretical analysis of a heat and moisture transfer model arising from textile industries, which is described by a degenerate and strongly coupled parabolic system. We prove the global (in time) existence of weak solution ... More