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Pair density wave, charge density wave and vortex in high Tc cupratesFeb 08 2018Mar 02 2018A recent scanning tunneling microscopy (STM) experiment reports the observation of charge density wave (CDW) with period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately period 4a CDW that are ... More

Optical Conductivity From Pair Density WavesAug 03 2016We present a theory of optical conductivity in systems with finite-momentum Cooper pairs. In contrast to the BCS pairing where AC conductivity is purely imaginary in the clean limit, there is nonzero AC absorption across the superconducting gap for finite-momentum ... More

Pair density wave, charge density wave and vortex in high Tc cupratesFeb 08 2018A recent scanning tunneling microscopy (STM) experiment reports the observation of charge density wave (CDW) with period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately period 4a CDW that are ... More

High-performance K-means Implementation based on a Coarse-grained Map-Reduce ArchitectureOct 17 2016Nov 10 2016The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means algorithm necessary. ... More

High-performance K-means Implementation based on a Coarse-grained Map-Reduce ArchitectureOct 17 2016The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means algorithm necessary. ... More

Visualizing the Effect of an Electrostatic Gate with Angle-Resolved Photoemission SpectroscopyApr 20 2019Electrostatic gating is pervasive in materials science, yet its effects on the electronic band structure of materials has never been revealed directly by angle-resolved photoemission spectroscopy (ARPES), the technique of choice to non-invasively probe ... More

High-performance K-means Implementation based on a Simplified Map-Reduce ArchitectureOct 17 2016Nov 22 2016The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means algorithm necessary. ... More

An Alternative Method of Extracting $V_{bu}$ from Semi-leptonic B DecayMay 12 1994We propose a new method of extracting $V_{bu}$ from measurements of Semi-leptonic B decay which has much less theoretical uncertainties than conventional methods.

Grünwald version of van der Waerden's theorem for semi-modulesDec 29 2015Jun 17 2016Let $(G,\pmb{+})$ be any given semimodule over a discrete semiring $(R,+,\cdot)$ with a finite coloring, say $G=B_1\cup\dotsm\cup B_q$. By establishing a Regional Multiple Recurrence Theorem for semimodules, we prove that one of the colors $j$ has the ... More

Almost automorphy of invertible semiflows with compact Hausdorff phase spacesJun 15 2018Let $T\times X\rightarrow X, (t,x)\mapsto tx$ be a minimal semiflow on a compact Hausdorff space $X$ with phase semigroup $T$ such that each $t\in T$ is an invertible map of $X$. An $x\in X$ is called an \textit{a.a. point} of $(T,X)$ if $(t_nx, t_n^{-1}y)\to(y, ... More

Almost automorphy of surjective semiflows on compact Hausdorff spacesJun 15 2018Mar 15 2019Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be a semiflow on a compact $\textrm{T}_2$-space $X$ with phase semigroup $T$ such that $tX=X$ for each $t$ of $T$. An $x\in X$ is called an \textit{a.a. point} if $t_nx\to y, x_n^\prime\to x^\prime$ and ... More

An extension of Furstenberg's structure theorem for Noetherian modules and multiple recurrence theorems IMay 27 2016We extend Furstenberg's structure theorem to any standard Borel $G$-space, where $G$ is any locally compact second countable Noetherian module over a syndetic ring.

An extension of Furstenberg's structure theorem for Noetherian modules and multiple recurrence theorems IIIMay 27 2016Jun 09 2016Using a recent Furstenberg structure theorem, we obtain Multiple Recurrence Theorems relative to any locally compact second countable Noetherian module $G$ over a syndetic ring $R$, which generalizes Furstenberg's multiple recurrence theorem. In addition ... More

Optimal Rate Scheduling via Utility-Maximization for J-User MIMO Markov Fading Wireless Channels with CooperationJun 22 2011We design a dynamic rate scheduling policy of Markov type via the solution (a social optimal Nash equilibrium point) to a utility-maximization problem over a randomly evolving capacity set for a class of generalized processor-sharing queues living in ... More

Product-form solutions for integrated services packet networks and cloud computing systemsSep 03 2013We iteratively derive the product-form solutions of stationary distributions of priority multiclass queueing networks with multi-sever stations. The networks are Markovian with exponential interarrival and service time distributions. These solutions can ... More

Random Walks and Subfractional Brownian MotionMar 21 2013Jan 15 2014In this article, we show a result of approximation in law to subfractional Brownian motion, with $H>\frac{1}{2}$, in the Skorohod topology. The construction of these approximations is based on a sequence of I.I.D random variables

The Salvetti Complex and the Little CubesFeb 05 2006Sep 11 2008We study how the combinatorial structure of the Salvetti complexes of the braid arrangements are related to homotopy theoretic properties of iterated loop spaces. We prove the skeletal filtrations on the Salvetti complexes of the braid arrangements give ... More

Unilateral global bifurcation for fourth-order eigenvalue problems with sign-changing weightJul 31 2012In this paper, we shall establish the unilateral global bifurcation result for a class of fourth-order eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that $(\mu_k^\nu,0)$ is a bifurcation ... More

Unilateral global interval bifurcation theorem for $p$-Laplacian and its applicationsJul 28 2012In this paper, we establish a unilateral global bifurcation result from interval for a class of $p$-Laplacian problems. By applying the above result, we study the spectrum of a class of half-quasilinear problems. Moreover, we also investigate the existence ... More

Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distributionMay 13 2018May 03 2019A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire joint distribution ... More

Numerical Methods and Analysis via Random Field Based Malliavin Calculus for Backward Stochastic PDEsJun 28 2013We study the adapted solution, numerical methods, and related convergence analysis for a unified backward stochastic partial differential equation (B-SPDE). The equation is vector-valued, whose drift and diffusion coefficients may involve nonlinear and ... More

Subdifferential representation of convex functions on $X^*$Nov 28 2017In this paper, we obtain subdifferential representation of a proper $w^*$-lower semicontinous convex function on $X^*$ as follows: Let $g$ be a proper convex $w^*$-lower semicontinuous function on $X^*$. Assume that int dom $g$ $\neq\emptyset$ (resp. ... More

Some criteria for spectral finiteness of a finite subset of the real matrix space $\mathbb{R}^{d\times d}$Jun 11 2012In this paper, we present some checkable criteria for the spectral finiteness of a finite subset of the real $d\times d$ matrix space $\mathbb{R}^{d\times d}$, where $2\le d<\infty$.

Grünwald version of van der Waerden's theorem for semi-modulesDec 29 2015Sep 14 2018Let $(G,\pmb{+})$ be any given semimodule over a discrete semiring $(R,+,\cdot)$ with a finite coloring, say $G=B_1\cup\dotsm\cup B_q$. By establishing a Regional Multiple Recurrence Theorem for semimodules, we prove that one of the colors $j$ has the ... More

Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zerosNov 20 2015In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem from infinity ... More

Regularity criterion for the 3D Hall-magneto-hydrodynamicsJul 21 2015Sep 06 2017This paper studies the regularity problem for the 3D incompress- ible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence predicts that there exists a critical wavenumber above which the ... More

Rotation of the cosmic microwave background polarization from weak gravitational lensingNov 14 2013Jan 30 2014When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs ... More

Stability of Solutions to the Quasi-Geostrophic Equations in $\mathbb R^2$Mar 16 2015We consider the stationary Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a force $f$. Under certain assumptions of $f$, we establish the existence of solutions with finite $L^2$ norm. This solution is unique among all solutions ... More

Congruences for the number of partitions and bipartitions with distinct even partsApr 22 2014Let $ped(n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $ped(n)$ modulo $8$. We also examine the behavior of $ped_{-2}(n)$ modulo $8$ in detail ... More

The Exit Distribution for Smart Kinetic Walk with Symmetric Transition ProbabilityNov 29 2016It has been proved that the distribution of the point where the Smart Kinetic Walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there ... More

Regularity criterion for the 3D Hall-magneto-hydrodynamicsJul 21 2015May 02 2016This paper studies the regularity problem for the 3D incompress- ible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence predicts that there exists a critical wavenumber above which the ... More

An Improved Feedback Coding Scheme for the Wire-tap ChannelDec 13 2017Apr 25 2018The model of wiretap channel (WTC) is important as it constitutes the essence of physical layer security (PLS). Wiretap channel with noiseless feedback (WTC-NF) is especially interesting as it shows what can be done when a private feedback is available. ... More

Equations For Parseval's Frame Wavelets In $L^2(\R^d)$ With Compact SupportsJul 31 2016Let $d\geq 1$ be a natural number and $A_0$ be a $d\times d$ expansive integral matrix with determinant $\pm 2.$ Then $A_0$ is integrally similar to an integral matrix $A$ with certain additional properties. A finite solution to the system of equations ... More

Spectra of Cantor measuresJan 19 2014Feb 09 2015Let $\mu_{q, b}$ be the Cantor measure associated with the iterated function system $f_i(x)=x/b+i/q, 0\le i\le q-1$, where $2\le q, b/q\in \Z$. In this paper, we consider spectra and maximal orthogonal sets of the Cantor measure $\mu_{q, b}$ and their ... More

Heterogeneity and aggregation in evolutionary dynamics: a general framework without aggregabilityMay 13 2018We consider general evolutionary dynamics under persistent payoff heterogeneity and study the dynamic relation between the strategy composition over different types and the aggregate strategy distribution of the entire population. It is rigorously proven ... More

Characterizations of function spaces on the sphere using framesOct 04 2005In this paper we introduce a polynomial frame on the unit sphere $\sph$ of $\mathbb{R}^d$, for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere $\sph$, such as $L^p$, $H^p$ and ... More

On the E^1-term of the gravity spectral sequenceMar 26 2009The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, ... More

Pointwise convergence of ergodic averages of bounded measurable functions for amenable groupsApr 03 2016Jun 16 2016Given any amenable group $G$ (with a left Haar measure $|\cdot|$ or $dg$), we can select out a \textit{F{\o}lner subnet} $\{F_\theta,\theta\in\Theta\}$ from any left F{\o}lner net in $G$, which is \textit{$L^\infty$-admissible}, namely, for any Borel ... More

A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed FlowNov 28 2013Mar 21 2015Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.

Stability of Solutions to the Quasi-Geostrophic Equations in $\mathbb R^2$Mar 16 2015Feb 16 2017We consider the stationary Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a force $f$. Under certain smallness assumptions of $f$, we establish the existence of solutions with finite $L^2$ norm. This solution is unique among all ... More

Criteria of stabilizability for switching-control systems with solvable linear approximationsJan 10 2012We study the stability and stabilizability of a continuous-time switched control system that consists of the time-invariant $n$-dimensional subsystems \dot{x}=A_ix+B_i(x)u\quad (x\in\mathbb{R}^n, t\in\mathbb{R}_+ \textrm{and} u\in\mathbb{R}^{m_i}),\qquad ... More

Uniform positive recursion frequency of any minimal dynamical system on a compact spaceJun 25 2018Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage $\varepsilon$ of $X$, ... More

An Application of Ubiquitous Video Services and Management Systems in Civil DefenseMar 27 2018This paper proposes a model of ubiquitous video services and management systems for solving current issues of video surveillance services and management in the smart city. The author presents the Enterprise Service Bus (ESB) based methods of integrating ... More

Eta Invariant and Conformal CobordismJun 20 2001Jun 21 2001In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an abelian group, the conformal cobordism group, which classifies ... More

Spectrum of Navier $p$-biharmonic problem with sign-changing weightJul 31 2012Aug 27 2016In this paper, we consider the following eigenvalue problem {{l} (|u"|^{p-2}u")"=\lambda m(x)|u|^{p-2}u, x\in (0,1), u(0)=u(1)=u"(0)=u"(1)=0, where $1<p<+\infty$, $\lambda$ is a real parameter and $m$ is sign-changing weight. We prove there exists a unique ... More

Connected Heegaard Floer homology of sums of Seifert fibrationsApr 17 2018Nov 03 2018We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3-manifolds, including all linear combinations of Seifert fibered homology spheres. We show that for such manifolds, the connected Floer homology ... More

The Exit Distribution for Smart Kinetic Walk with Symmetric and Asymmetric Transition ProbabilityNov 29 2016Feb 03 2017It has been proved that the distribution of the point where the Smart Kinetic Walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there ... More

Some Results on the Scattering Theory for Nonlinear Schrödinger Equations in Weighted $L^{2}$ SpaceAug 16 2011We investigate the scattering theory for the nonlinear Schr\"{o}dinger equation $i \partial_{t}u+ \Delta u+\lambda|u|^\alpha u=0$ in $\Sigma=H^{1}(\mathbb{R}^{d})\cap L^{2}(|x|^{2};dx)$. We show that scattering states $u^{\pm}$ exist in $\Sigma$ when ... More

Almost automorphy of surjective semiflows on compact Hausdorff spacesJun 15 2018Mar 29 2019Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be a semiflow on a compact $\textrm{T}_2$-space $X$ with phase semigroup $T$ such that $tX=X$ for each $t$ of $T$. An $x\in X$ is called an \textit{a.a. point} if $t_nx\to y, x_n^\prime\to x^\prime$ and ... More

Non-uniqueness of Leray-Hopf weak solutions of the 3D Hall-MHD systemDec 29 2018Jan 11 2019Non-uniqueness of Leray-Hopf type of solutions is obtained for the three dimensional magneto-hydrodynamics with Hall effect. It seems to be the first result in the literature on non-uniqueness of Leray-Hopf weak solutions for dissipative equations. As ... More

Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$Sep 07 2017We establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2$. The previously known local well-posedness space was $\left(H^s(\mathbb{R}^n)\right)^2$ with ... More

Cellular Stratified Spaces I: Face Categories and Classifying SpacesJun 19 2011Sep 16 2016The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz\'alez, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that ... More

Collisionless Magnetic Reconnection via Alfven EigenmodesJul 04 2009We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical ... More

Convergence Rates of Finite Difference Stochastic Approximation AlgorithmsJun 30 2015Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes ... More

Equations For Frame Wavelets In $L^2(\R^2)$Sep 17 2015We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.

Live Video Comment Generation Based on Surrounding Frames and Live CommentsAug 13 2018In this paper, we propose the task of live comment generation. Live comments are a new form of comments on videos, which can be regarded as a mixture of comments and chats. A high-quality live comment should be not only relevant to the video, but also ... More

An extension of Furstenberg's structure theorem for Noetherian modules and multiple recurrence theorems IIMay 27 2016Jun 09 2016Using a recent Furstenberg structure theorem, we obtain a quantitative multiple recurrence theorem relative to any locally compact second countable Noetherian module over a syndetic ring.

Finer filtration for matrix-valued cocycle based on Oseledec's multiplicative ergodic theoremAug 28 2013Apr 08 2014In this paper, we improve the classical multiplicative ergodic theorem.

Cellular Stratified Spaces II: Basic ConstructionsNov 21 2011Sep 16 2016This is a sequel to [1106.3772], in which a systematic study of cellular stratified spaces and related concepts was initiated. In this paper, we study important operations on cellular and stellar stratified spaces, including taking subspaces, subdivisions, ... More

Gains in evolutionary dynamics: A unifying approach to dynamic stability of contractive games and ESSMay 13 2018Nov 26 2018In this paper, we investigate gains from strategy revisions in deterministic evolutionary dynamics. To clarify the gain from revision, we propose a framework to reconstruct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) ... More

Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamicsMay 13 2018In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces to a homogenized ... More

Two Whyburn type topological theorems and its applications to Monge-Ampère equationsJun 25 2014In this paper we correct a gap of Whyburn type topological lemma and establish two superior limit theorems. As the applications of our Whyburn type topological theorems, we study the following Monge-Amp\`{e}re equation \begin{eqnarray} \left\{ \begin{array}{lll} ... More

Asymptotic Joint Distribution of Extreme Eigenvalues of the Sample Covariance Matrix in the Spiked Population ModelJul 18 2012In this paper, we consider a data matrix $X\in\mathbb{C}^{N\times M}$ where all the columns are i.i.d. samples being $N$ dimensional complex Gaussian of mean zero and covariance $\Sigma\in\mathbb{C}^{N\times N}$. Here the population matrix $\Sigma$ is ... More

Cellular stratified spacesSep 15 2016The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz{\'a}lez, and Rudyak with the aim of constructing a cellular model of the configuration space of a sphere. Although the original aim was not achieved ... More

On the Pin(2)-Equivariant Monopole Floer Homology of Plumbed 3-ManifoldsJul 11 2016Sep 23 2016We compute the Pin(2)-equivariant monopole Floer homology for the class of plumbed 3-manifolds with at most one "bad" vertex (in the sense of Oszv\'ath and Szab\'o). We show that for these manifolds, the Pin(2)-equivariant monopole Floer homology can ... More

Stability and Evolution of Color Skyrmions in the Quark-Gluon PlasmaDec 20 2006Feb 01 2007We show the existence of unstable color skyrmions in a class of nonabelian fluid models. Oscillating and expanding solutions are found in the time-dependent case.

The McMahon pseudo-metrics of minimal transformation semigroups with invariant measuresJun 25 2018Let $T\times X\rightarrow X$ be any minimal semiflow with phase semigroup $T$. When $(T,X)$ admits an invariant Borel probability measure, using McMahon pseudo-metrics we mainly show in this paper the following results: \begin{itemize} \item[(1)] $S_{\textit{eq}}(X)=Q(X)$, ... More

The McMahon pseudo-metrics of minimal semiflows with invariant measuresJun 25 2018Mar 29 2019Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be any minimal semiflow with phase semigroup $T$ and with compact $\textrm{T}_2$ phase space $X$. When $(T,X)$ admits an invariant Borel probability measure, using McMahon pseudo-metrics we consider the ... More

A Note on Positive Energy Theorem for Spaces with Asymptotic SUSY CompactificationJun 01 2004We extend the positive mass theorem proved previously by the author to the Lorentzian setting. This includes the original higher dimensional positive energy theorem whose spinor proof was given by Witten in dimension four and by Xiao Zhang in dimension ... More

Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processesOct 03 2014Aug 26 2015In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck ... More

Time-preserving structural stability of hyperbolic differential dynamics with noncompact phase spacesMay 17 2008In this paper, we study the structural stability of hyperbolic differential systems on Euclidean spaces using Liao theory.

Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equationsJul 16 2013Dec 17 2013In this paper we show that if a linear cocycle is robustly periodical stable then it is uniformly stable.

Eigenvalue, global bifurcation and positive solutions for a class of fully nonlinear problemsMar 23 2014In this paper, we shall study global bifurcation phenomenon for the following Kirchhoff type problem \begin{equation} \left\{ \begin{array}{l} -\left(a+b\int_\Omega \vert \nabla u\vert^2\,dx\right)\Delta u=\lambda u+h(x,u,\lambda)\,\,\text{in}\,\, \Omega,\\ ... More

The Grothendieck Construction and Gradings for Enriched CategoriesJul 01 2009The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small categories enriched over a symmetric monoidal category ... More

Cosmological magnetic fields: generation during inflation and evolutionSep 23 2003This paper concerns the generation and evolution of the cosmological (large-scale $\sim Mpc$) magnetic fields in an inflationary universe. The universe during inflation is represented by de Sitter space-time. We started with the Maxwell equations in spatially ... More

On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expandingJun 11 2012Using a sifting-shadowing combination, we prove in this paper that an arbitrary $\mathrm{C}^1$-class local diffeomorphism $f$ of a closed manifold $M^n$ is uniformly expanding on the closure $\mathrm{Cl}_{M^n}(\mathrm{Per}(f))$ of its periodic point set ... More

A positive solution to a conjecture of A. Katok for diffeomorphism caseJun 10 2008In this paper, using Pesin theory and Liao theory, we give a positive solution to a conjecture of A. Katok.

Chaotic dynamics of continuous-time topological semi-flows on Polish spacesJan 09 2015In this paper, we study the chaotic dynamics of a continuous-time topological semi-flow on a Polish space.

On chaotic minimal center of attraction of a Lagrange stable motion for topological semi flowsJul 02 2015Jul 09 2015In this paper, we study the chaotic dynamics of a minimal center of attraction of a Lagrange stable motion for semi flows.

The McMahon pseudo-metrics of minimal semiflows with invariant measuresJun 25 2018Apr 17 2019Using McMahon pseudo-metrics, for any minimal semiflow admitting an invariant measure, we study the relationships between its equicontinuous structure relation, regionally proximal relation and Veech's relations; and characterize its weak-mixing. We show ... More

Interpreting and Extending The Guided Filter Via Cyclic Coordinate DescentMay 30 2017In this paper, we will disclose that the Guided Filter (GF) can be interpreted as the Cyclic Coordinate Descent (CCD) solver of a Least Square (LS) objective function. This discovery implies a possible way to extend GF because we can alter the objective ... More

Propagation of regularity for the MHD system in optimal Sobolev spaceJul 24 2017Mar 14 2018We study the problem of propagation of regularity of solutions to the incompressible viscous non-resistive magneto-hydrodynamics system. According to scaling, the Sobolev space $H^{\frac n2-1}(\mathbb R^n)\times H^{\frac n2}(\mathbb R^n)$ is critical ... More

Regularity problem for the nematic LCD system with Q-tensor in $\mathbb R^3$Aug 26 2016We study the regularity problem of a nematic liquid crystal model with local configuration represented by Q-tensor in three dimensions. It was an open question whether the classical Prodi-Serrin condition implies regularity for this model. Applying a ... More

Regularity criterion and energy conservation for the supercritical Quasi-Geostrophic equationMay 09 2015Jul 12 2016This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a new regularity condition which is weaker than all the ... More

Existence of regular solutions to the full Liquid Crystal SystemSep 02 2013We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the solutions are ... More

Local well-posedness for the Hall-MHD system in optimal Sobolev SpacesMar 26 2018Jun 08 2018We show that the viscous resistive magneto-hydrodynamics system with Hall effect is locally well-posed in $H^s(\mathbb R^n)\times H^{s+1-\varepsilon}(\mathbb R^n)$ with $s>\frac{n}2-1$ and any small enough $\varepsilon>0$ such that $s+1-\varepsilon>\frac{n}2$. ... More

Gluon Radiation of an Expanding Color Skyrmion in the Quark-Gluon PlasmaApr 02 2007The density of states and energy spectrum of the gluon radiation are calculated for the color current of an expanding hydrodynamic skyrmion in the quark gluon plasma with a semiclassical method. Results are compared with those in literatures.

Quantified separably injective spacesFeb 10 2014Apr 28 2016Let $X$, $Y$ be two Banach spaces. Let $\varepsilon\geq 0$. A mapping $f: X\rightarrow Y$ is said to be a standard $\varepsilon-$ isometry if $f(0)=0$ and $|\|f(x)-f(y)\|-\|x-y\||\leq \varepsilon$. In this paper we first show that if $Y^*$ has the point ... More

Antiferromagnetic order and spin dynamics in iron-based superconductorsMar 08 2015Jun 18 2015High-transition temperature (high-$T_c$) superconductivity in the iron pnictides/chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxides superconductors. This raises a fundamental ... More

Intensity Distribution and Luminosity Function of the Swift Gamma-Ray BurstsDec 24 2008Apr 23 2009Using the sample of long Gamma-ray bursts (GRBs) detected by Swift-BAT before June 2007, we measure the cumulative distribution of the peak photon fluxes (log N - log P) of the Swift bursts. Compared with the BATSE sample, we find that the two distributions ... More

Eta Invariants for Even Dimensional ManifoldsOct 13 2011In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even dimensional manifolds, ... More

A Positive Mass Theorem for Spaces with Asymptotic SUSY CompactificationAug 26 2003We prove a positive mass theorem for spaces which asymptotically approach a flat Euclidean space times a Calabi-Yau manifold (or any special honolomy manifold except the quaternionic K\"ahler). This is motivated by the very recent work of Hertog-Horowitz-Maeda. ... More

On the Homology of Configuration Spaces Associated to Centers of MassApr 01 2010The aim of this paper is to make sample computations with the Salvetti complex of the "center of mass" arrangement introduced in [arXiv:math/0611732] by Cohen and Kamiyama. We compute the homology of the Salvetti complex of these arrangements with coefficients ... More

$L^p(Ω)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous DriftApr 09 2014We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the discontinuous ... More

Maximum principle and one-sign solutions for the elliptic $p$-LaplacianJul 28 2012In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.

Ill-posedness of the incompressible magneto-hydrodynamics system in $\dot{B}_{\infty,\infty}^{-1}$Nov 16 2012Jul 25 2014We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed in the largest scaling invariant space $\dot{B}_{\infty,\infty}^{-1}$. The construction method of initial data used in this paper is different from ... More

Approximation to multifractional Riemann-Liouville Brownian sheetDec 08 2012Dec 25 2012In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence ... More

Criterion for quasi-anosovian diffeomorphisms of closed manifoldsApr 08 2014Quasi-Anosov diffeomorphism is a kind of important dynamical system due to R. Mane 1970s. In this paper, we present a criterion for such dynamics using ergodic theory.

Lower order tensors in non-Kähler geometry and non-Kähler geometric flowMar 21 2015May 31 2016In recent years, Streets and Tian introduced a series of curvature flows to study non-K\"{a}hler geometry. In this paper, we study how to construct second order curvature flows in a uniform way, under some natural assumptions which holds in Streets and ... More

Asymptotics of orthogonal polynomials and the Painlevé transcendentsAug 16 2016Sep 14 2016In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev\'e transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of ... More