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Suggestion of the DLV dimensionless number system to represent the scaled behavior of structures under impact loadsMar 21 2019A group of dimensionless numbers, termed DLV (Density-Length-Velocity) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham Pi theorem with an alternative basis. The distinct ... More

Suggestion of the DLV dimensionless number system to represent the scaled behavior of structures under impact loadsMar 21 2019Apr 04 2019A group of dimensionless numbers, termed DLV (Density-Length-Velocity) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham Pi theorem with an alternative basis. The distinct ... More

Larger mutual inclinations for the shortest-period planetsAug 25 2018Sep 20 2018The {\it Kepler} mission revealed a population of compact multiple-planet systems with orbital periods shorter than a year, and occasionally even shorter than a day. By analyzing a sample of 102 {\it Kepler} and {\it K2} multi-planet systems, we measure ... More

Ultrabroadband Super-Planckian Radiative Heat Transfer with Profile-Patterned Hyperbolic MetamaterialSep 14 2016We demonstrate the possibility of ultrabroadband super-Planckian radiative heat transfer be- tween two metal plates patterned with tapered hyperbolic metamaterial arrays. It is shown that, by employing profile-patterned hyperbolic media, one can design ... More

A constant extension ensembles model of double-stranded chain moleculesDec 16 2002Because the constant extension ensemble of single chain molecule is not always equivalent with constant force ensemble, a model of double-stranded conformations, as in RNA molecules and $\beta$-sheets in proteins, with fixed extension constraint is built ... More

A model for the force stretching double-stranded chain moleculesDec 12 2002We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by including the ... More

Maximum-entropy calculation of end-to-end distance distribution of force stretching chainsDec 12 2002Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one ... More

The stellar obliquity, planet mass, and very low albedo of Qatar-2 from K2 PhotometrySep 05 2016Nov 15 2016The Qatar-2 transiting exoplanet system was recently observed by the {\it Kepler} telescope as part of {\it K2} Campaign 6. The photometric time series has one-minute time sampling and a precision of about 690~ppm, after filtering out artifacts and spurious ... More

Can WiFi Estimate Person Pose?Mar 30 2019Apr 02 2019WiFi human sensing has achieved great progress in indoor localization, activity classification, etc. Retracing the development of these work, we have a natural question: can WiFi devices work like cameras for vision applications? In this paper We try ... More

ADMM-IDNN: Iteratively Double-reweighted Nuclear Norm Algorithm for Group-prior based Nonconvex Compressed Sensing via ADMMMar 23 2019Group-prior based regularization method has led to great successes in various image processing tasks, which can usually be considered as a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex ... More

Dusty outflows in planetary atmospheres: Understanding "super-puffs" and transmission spectra of sub-NeptunesFeb 11 2019`Super-puffs' are planets with anomalously low mean densities ($\lesssim 10^{-1}~{\rm g\ cm}^{-3}$). With a low surface gravity, the extended atmosphere is susceptible to extreme hydrodynamic mass loss (`boil off') on a timescale much shorter than the ... More

Hybrid Weyl SemimetalJul 28 2016We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed "hybrid Weyl ... More

Discovery of Six Optical Phase Curves with K2Dec 21 2018Mar 07 2019We have systematically searched for the phase curves among the planets discovered by \textit{K2}. Using the reported planetary parameters, we screen out the best potential candidates, and examine their light curves in detail. For our work, we consider ... More

Primary damage production in the presence of extended defects and growth of vacancy-type dislocation loops in hcp zirconiumMar 27 2019Production rates in long-term predictive radiation damage accumulation models are generally considered independent of the material's microstructure for reactor components. In this study, the effect of pre-existing microstructural elements on primary damage ... More

DeepTrend: A Deep Hierarchical Neural Network for Traffic Flow PredictionJul 11 2017In this paper, we consider the temporal pattern in traffic flow time series, and implement a deep learning model for traffic flow prediction. Detrending based methods decompose original flow series into trend and residual series, in which trend describes ... More

DTNC: A New Server-side Data Cleansing Framework for Cellular Trajectory ServicesMar 01 2017Mar 03 2017It is essential for the cellular network operators to provide cellular location services to meet the needs of their users and mobile applications. However, cellular locations, estimated by network-based methods at the server-side, bear with {\it high ... More

Integrated four-channel all-fiber up-conversion single-photon-detector with adjustable efficiency and dark countSep 30 2016Oct 03 2016Up-conversion single photon detector (UCSPD) has been widely used in many research fields including quantum key distribution (QKD), lidar, optical time domain reflectrometry (OTDR) and deep space communication. For the first time in laboratory, we have ... More

FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture SearchDec 09 2018Dec 14 2018Designing accurate and efficient ConvNets for mobile devices is challenging because the design space is combinatorially large. Due to this, previous neural architecture search (NAS) methods are computationally expensive. ConvNet architecture optimality ... More

Kepler-730b is probably a hot Jupiter with a small companionAug 31 2018Here we draw attention to a candidate system with one hot Jupiter and one small, nearby companion, revealed by the recent Kepler data release (DR25). The hot Jupiter, Kepler-730b, has radius $R_{\rm p}=11.36^{+1.14}_{-0.98}~R_\oplus$ and orbital period ... More

LightLDA: Big Topic Models on Modest Compute ClustersDec 04 2014When building large-scale machine learning (ML) programs, such as big topic models or deep neural nets, one usually assumes such tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners ... More

Experimental protection of the coherence of a molecular qubit exceeding a millisecondJun 28 2017There are several important solid-state systems, such as defects in solids, superconducting circuits and molecular qubits, for attractive candidates of quantum computations. Molecular qubits, which benefit from the power of chemistry for the tailored ... More

A Ni-Fe Layered Double Hydroxide-Carbon Nanotube Complex for Water OxidationMar 13 2013May 24 2013Highly active, durable and cost-effective electrocatalysts for water oxidation to evolve oxygen gas hold a key to a range of renewable energy solutions including water splitting and rechargeable metal-air batteries. Here, we report the synthesis of ultrathin ... More

ChamNet: Towards Efficient Network Design through Platform-Aware Model AdaptationDec 21 2018This paper proposes an efficient neural network (NN) architecture design methodology called Chameleon that honors given resource constraints. Instead of developing new building blocks or using computationally-intensive reinforcement learning algorithms, ... More

Doping effects of Cr on the physical properties of BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$Jul 04 2018We present a systematic study on the heavily Cr doped iron pnictides BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$ by using elastic neutron scattering, high-resolution synchrotron X-ray diffraction (XRD), resistivity and Hall transport measurements. When the ... More

Magellan/PFS Radial Velocities of GJ 9827, a late K dwarf at 30 pc with Three Transiting Super-EarthsNov 03 2017Feb 28 2018The Kepler mission showed us that planets with sizes between that of Earth and Neptune appear to be the most common type in our Galaxy. These "super-Earths" continue to be of great interest for exoplanet formation, evolution, and composition studies. ... More

A low stellar obliquity for WASP-47, a compact multiplanet system with a hot Jupiter and an ultra-short period planetSep 17 2015We have detected the Rossiter-Mclaughlin effect during a transit of WASP-47b, the only known hot Jupiter with close planetary companions. By combining our spectroscopic observations with Kepler photometry, we show that the projected stellar obliquity ... More

Consistency of least squares estimation to the parameter for stochastic differential equations under distribution uncertaintyApr 29 2019Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by $G$-Brownian motion. ... More

Optimal control of uncertain stochastic systems with Markovian switching and its applications to portfolio decisionsJan 11 2014This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman ... More

A class of cyclotomic linear codes and their generalized Hamming weightsAug 15 2017Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas ... More

Monte Carlo Study of a 137Cs calibration field of the China institute of atomic energyFeb 10 2015The MCNP code was used to study the characteristics of gamma radiation field with collimated beam geometry. A close-to-reality simulation model of the facility was used for calculation air-kerma along the whole range of source-detector-distance (SDD) ... More

Counting using Hall Algebras III. Quivers with PotentialsJul 10 2013Sep 15 2018For a quiver with potential, we can associate a vanishing cycle to each representation space. If there is a nice torus action on the potential, the vanishing cycles can be expressed in terms of truncated Jacobian algebras. We study how these vanishing ... More

Existence and applications of Ricci flows via pseudolocalityOct 06 2016We prove the short-time existence of Ricci flows on complete manifolds with scalar curvature bounded below uniformly, Ricci curvature bounded below by a negative quadratic function, and with almost Euclidean isoperimetric inequality holds locally. In ... More

Spectra of tensor triangulated categories over category algebrasSep 13 2013Let C be a finite EI category and k be a field. We consider the category algebra kC. Suppose K(C)=D^b(kC-mod) is the bounded derived category of finitely generated left modules. This is a tensor triangulated category and we compute its spectrum in the ... More

Riemann hypothesis is not correctJul 17 2014This paper use Nevanlinna's Second Main Theorem of the value distribution theory, we got an important conclusion by Riemann hypothesis. this conclusion contradicts the Theorem 8.12 in Titchmarsh's book "Theory of the Riemann Zeta-functions", therefore ... More

A Corollary of Riemann HypothesisJun 26 2011This paper use the results of the value distribution theory, got a significant conclusion by Riemann hypothesis

Cluster Algebras, Invariant Theory, and Kronecker Coefficients IINov 01 2017We prove that the semi-invariant ring of the standard representation space of the $l$-flagged $m$-arrow Kronecker quiver is an upper cluster algebra for any $l,m\in \mathbb{N}$. The quiver and cluster are explicitly given. We prove that the quiver with ... More

Cluster Algebras and Semi-invariant Rings II. ProjectionsAug 23 2015Aug 30 2015Let ${\rm SI}_\beta(Q)$ be the semi-invariant ring of $\beta$-dimensional representations of a quiver $Q$. Suppose that $(Q,\beta)$ projects to another quiver with dimension vector $(Q',\beta')$ through an exceptional representation $E$. We show that ... More

Cluster Algebras, Invariant Theory, and Kronecker Coefficients IApr 12 2015Aug 25 2015We relate the $m$-truncated Kronecker products of symmetric functions to the semi-invariant rings of a family of quiver representations. We find cluster algebra structures for these semi-invariant rings when $m=2$. Each {\sf g}-vector cone ${\sf G}_{\Diamond_l}$ ... More

Cluster Algebras and Semi-invariant Rings I. Triple FlagsNov 17 2014Mar 03 2015We prove that each semi-invariant ring of the complete triple flag of length $n$ is an upper cluster algebra associated to an ice hive quiver. We find a rational polyhedral cone ${\sf G}_n$ such that the generic cluster character maps its lattice points ... More

Counting Using Hall Algebras I. QuiversNov 28 2011Sep 24 2012We survey some results on counting the rational points of moduli spaces of quiver representations. We then make generalizations to Grassmannians and flags of quiver representations. These results have nice applications to the cluster algebra. Along the ... More

Some Torsional Local Models of Heterotic StringsAug 23 2015Oct 06 2015We construct solutions to the Strominger system on a class of noncompact Calabi-Yau 3-folds. These spaces include $\mathbb{C}^3$ and resolved conifold $\mathcal{O}(-1,-1)$ as special examples.

A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger SystemJul 01 2015Oct 08 2015We propose a new construction of compact non-K\"ahler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on $\Sigma_g\times T^4$, where ... More

On the Banach-Mazur Distance between the Cube and the CrosspolytopeMay 03 2017In this note we study the Banach-Mazur distance between the $n$-dimensional cube and the crosspolytope. Previous work shows that the distance has order $\sqrt{n}$, and here we will prove some explicit bounds improving on former results. Even in dimension ... More

Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifoldsNov 18 2013Sep 12 2016Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, ... More

Supersymmetric QFT, Super Loop Spaces and Bismut-Chern CharacterNov 24 2007Jul 24 2008In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in ... More

Parabolic and near-parabolic renormalization for local degree threeSep 30 2015Oct 25 2016The invariant class under parabolic and near-parabolic renormalization constructed by Inou and Shishikura has proved extremely useful in recent years. It leads to several important progresses on the dynamics of certain holomorphic maps with a local degree ... More

Disjointness of Möbius from asymptotically periodic functionsOct 17 2018Nov 08 2018In this paper, we introduce asymptotically periodic functions and study these functions from the point of view of operator algebras and dynamical systems. We show that the M\"{o}bius function is disjoint from any strongly asymptotically periodic functions. ... More

The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisorsNov 03 2016Jul 15 2017Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\mathrm{Aut}(X,D)$. We show that $G$ is a semi-abelian ... More

On Some Quiver Determinantal VarietiesMay 26 2014Apr 08 2015We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman's complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex ... More

The Upper Cluster Algebras of iARt Quivers I. DynkinMar 08 2016Mar 14 2016For each valued quiver $Q$ of Dynkin type, we construct a valued ice quiver $\Delta_Q^2$ called the iARt quiver of $C^2Q$. Let $G$ be a simple connected Lie group with Dynkin diagram the underlying valued graph of $Q$. The upper cluster algebra of $\Delta_Q^2$ ... More

An Improved Result on Rayleigh--Taylor Instability of Nonhomogeneous Incompressible Viscous FlowsJan 02 2015In [F. Jiang, S. Jiang, On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain, Adv. Math., 264 (2014) 831--863], Jiang et.al. investigated the instability of Rayleigh--Taylor steady-state of a three-dimensional ... More

Support varieties for transporter category algebrasMay 24 2011Aug 26 2011Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the G-space BP, while the k-category ... More

Tensor Product Multiplicities via Upper Cluster AlgebrasMar 08 2016Dec 20 2017For each valued quiver $Q$ of Dynkin type, we construct a valued ice quiver $\Delta_Q^2$. Let $G$ be a simple connected Lie group with Dynkin diagram the underlying valued graph of $Q$. The upper cluster algebra of $\Delta_Q^2$ is graded by the triple ... More

Constructing Coherently G-invariant ModulesFeb 25 2014Mar 15 2016Let $G$ be a reductive group acting on a path algebra $kQ$ as automorphisms. We assume that $G$ admits a graded polynomial representation theory, and the action is polynomial. We describe the quiver $Q_G$ of the smash product algebra $kQ\# k[M_G]^*$, ... More

Local Representation Theory of Transporter CategoriesMar 03 2017We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type of Gorenstein ... More

A Note on Large Time Behavior of Velocity in the Baratropic Compressible Navier-Stokes EquationsJun 20 2012Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible Navier{Stokes equations with no restrictions on the size of initial ... More

Deflected Anomaly Mediated SUSY Breaking Scenario With General Messenger-Matter InteractionsAug 06 2015Oct 27 2015We propose to introduce general messenger-matter interactions in the deflected anomaly mediated SUSY breaking scenario. The most general form for the resulting soft parameters are derived. New interference terms between the GMSB type and AMSB type contributions ... More

Revisiting the ExtraOrdinary Gauge Mediation Scenarios and EGM Extension of deflected AMSBNov 29 2018Extraordinary gauge mediation extension of deflected AMSB scenarios can be interesting because it can accommodate together the deflection in the Kahler potential and the superpotential. We revisit the EGM scenario and derive the analytical expressions ... More

Circulant Digraphs Integral over Number FieldsJan 04 2012A number field K is a finite extension of rational number field Q. A circulant digraph integral over K means that all its eigenvalues are algebraic integers of K. In this paper we give the sufficient and necessary condition for circulant digraphs which ... More

Remarks on the extension of the Ricci flowJun 04 2012Jul 14 2012We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.

Control refinement for DAE systems: A behavioral approach via simulation relationsMar 14 2017The controller design of the so-called "difference algebraic equation" (DAE) systems that are frequently shown in industrial processes, tend to be challenging because of the combination of algebraic equations and high state dimensions. In this paper, ... More

On existence and uniqueness of solutions to uncertain backward stochastic differential equationsJan 29 2014This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an $m$-dimensional Brownian motion and a $d$-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can ... More

On the Hessian of Shape Matching EnergyApr 08 2016Apr 13 2016In this technical report we derive the analytic form of the Hessian matrix for shape matching energy. Shape matching is a useful technique for meshless deformation, which can be easily combined with multiple techniques in real-time dynamics. Nevertheless, ... More

Weight hierarchy of a class of linear codes relating to non-degenerate quadratic formsAug 18 2017Sep 03 2017In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting results about ... More

Strong approximation for certain quadric fibrations with compact fibersJul 14 2014In this paper, we will show that strong approximation with Brauer-Manin obstruction holds for certain quadratic fibration such that none of fibers satisfies strong approximation with Brauer-Manin obstruction. Moreover, we develop the representation theory ... More

Cash sub-additive risk statistics with scenario analysisApr 16 2019Since the money is of time value, we will study a new class of risk statistics, named cash sub-additive risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, ... More

Toric surfaces over an arbitrary fieldOct 20 2016Sep 13 2018We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple algebras, ... More

On homology with coefficients and generalized inductionsFeb 15 2017Oct 22 2018In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of $G$-posets with $G$-equivariant coefficients. For this purpose, we need various local categories of a finite group $G$, which ... More

A tidal encounter caught in the act: modelling a star-disc fly-by in the young RW Aurigae systemFeb 23 2015Apr 04 2015RW Aurigae (RW Aur) is a binary star system with a long molecular arm trailing the primary star. Cabrit et al. (2006) noted the resemblance between this extended structure and the tidal arm stripped from the primary star in the simulations of star-disc ... More

Constraints on the Obliquities of Kepler Planet-Hosting StarsOct 12 2017Nov 24 2017Stars with hot Jupiters have obliquities ranging from 0-180 degrees, but relatively little is known about the obliquities of stars with smaller planets. Using data from the California-Kepler Survey, we investigate the obliquities of stars with planets ... More

Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic materialFeb 13 2015Apr 26 2015Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials light propagation is unusual, leading to novel and often non-intuitive optical phenomena. Here we report ... More

Raman evidence for dimerization and Mott collapse in $α$-RuCl$_3$ under pressuresJul 21 2018We perform Raman spectroscopy studies on $\alpha$-RuCl$_3$ at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about $p_1=1.1$~GPa and $p_2=1.7$~GPa, ... More

The stellar obliquity, planet mass, and very low albedo of Qatar-2 from K2 PhotometrySep 05 2016The Qatar-2 transiting exoplanet system was recently observed by the {\it Kepler} telescope as part of {\it K2} Campaign 6. The photometric time series has one-minute time sampling and a precision of about 690~ppm, after filtering out artifacts and spurious ... More

Electronic structure of BaNi$_2$As$_2$Oct 10 2010Jan 26 2011BaNi$_2$As$_2$, with a first order phase transition around 131 K, is studied by the angle-resolved photoemission spectroscopy. The measured electronic structure is compared to the local density approximation calculations, revealing similar large electronlike ... More

WiPIN: Operation-free Person Identification using WiFi SignalsOct 06 2018Person identification is critical for sensitive applications such as system login/unlock, access control and payment. In this paper, we present an operation-free person identification system, namely WiPIN, that identifies biometric features of users using ... More

An Efficient Deep Reinforcement Learning Model for Urban Traffic ControlAug 06 2018Aug 24 2018Urban Traffic Control (UTC) plays an essential role in Intelligent Transportation System (ITS) but remains difficult. Since model-based UTC methods may not accurately describe the complex nature of traffic dynamics in all situations, model-free data-driven ... More

Ultra-Broadband Super-Planckian Radiative Heat Transfer with Artificial Continuum Cavity States in Patterned Hyperbolic MetamaterialSep 14 2016Mar 31 2017Localized cavity resonances due to nanostructures at material surfaces can greatly enhance radiative heat transfer (RHT) between two closely placed bodies owing to stretching of cavity states in momentum space beyond light line. Based on such understanding, ... More

Edge and surface plasmons in graphene nanoribbonsDec 21 2015We report on nano-infrared (IR) imaging studies of confined plasmon modes inside patterned graphene nanoribbons (GNRs) fabricated with high-quality chemical-vapor-deposited (CVD) graphene on Al2O3 substrates. The confined geometry of these ribbons leads ... 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.

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

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

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

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

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

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

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

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.

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 $2\le d<\infty$.

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

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

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

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

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

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

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

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

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.