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Practical Issues of Action-conditioned Next Image PredictionFeb 08 2018The problem of action-conditioned image prediction is to predict the expected next frame given the current camera frame the robot observes and an action selected by the robot. We provide the first comparison of two recent popular models, especially for ... More

On Unparticles and B\to X_s Missing EnergyApr 11 2008Sep 25 2008We analyze the inclusive decay mode $B\to X_s+{\rm Missing Energy}$ in the unparticle model, where an unparticle can also serve as the missing energy. We use the Heavy Quark Effective Theory in the calculation. The analytical result of the decay width ... More

Proton Decay and Fermion Masses in Supersymmetric SO(10) Model with Unified Higgs SectorSep 07 2009We make a detailed analysis on the proton decay in a supersymmetric SO(10) model proposed by K.Babu, I.Gogoladze, P.Nath, and R. Syed. We introduce quark mixing, and find that this model can generate fermion mass without breaking the experimental bound ... More

Study of non-minimal SUSY SU(5) model with realistic fermion sectorsJan 18 2011We study a supersymmetric SU(5) model with the extra Higgs multiplets of 45+\bar 45. The unification of the gauge couplings, the fermion masses and the proton lifetime are discussed in details. The dimension-five operators mediated by different colored ... More

On Unparticles and K+ to pi+ Missing EnergyDec 23 2007We analyze the branching ratio and spectrum for the decay mode $K^+ \to\pi^++{\not}E$(missing energy) in the unparticle model, where an unparticle can also serve as the missing energy. A vector unparticle can even mediate the $K^+ \to \pi^+ +\nu \bar{\nu}$, ... More

Quantum state transfer in frequency down-conversion via nondegenerate optical parametric amplifierFeb 23 2011By utilizing the nondegenerate optical parametric amplifier, the quantum state transfer from a pump state with high frequency to a signal state of lower frequency is studied theoretically. The noiseless state transfer is characterized by frequency conversion ... More

Invariance Preserving Discretization Methods of Dynamical SystemsJul 05 2016In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of local and uniform ... More

A Novel Unified Approach to Invariance for a Dynamical SystemMay 20 2014Jul 05 2016In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear continuous ... More

Conversational Recommendation System with Unsupervised LearningSep 22 2016We will demonstrate a conversational products recommendation agent. This system shows how we combine research in personalized recommendation systems with research in dialogue systems to build a virtual sales agent. Based on new deep learning technologies ... More

p-i-n Tunnel FETs vs. n-i-n MOSFETs: Performance Comparison from Devices to CircuitsJan 28 2010The band-to-band tunneling transistors have some performance advantages over the conventional MOSFETs due to the <60mV/dec sub-threshold slope. In this paper, carbon nanotubes are used as a model channel material to address issues that we believe will ... More

Oversampling smoothness (OSS): an effective algorithm for phase retrieval of noisy diffraction intensitiesNov 19 2012Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free electron lasers, high harmonic generation, soft X-ray laser and electrons. Despite ... More

On the relationship between G-band bright point dynamics and their magnetic field strengthsApr 01 2016G-band bright points (GBPs) are regarded as good manifestations of magnetic flux concentrations. We aim to investigate the relationship between the dynamic properties of GBPs and their longitudinal magnetic field strengths. High spatial and temporal resolution ... More

Differential Neutrino Condensation onto Cosmic StructureSep 28 2016Astrophysical techniques have pioneered the discovery of neutrino mass properties. Current cosmological observations give an upper bound on neutrino masses by attempting to disentangle the small neutrino contribution from the sum of all matter using precise ... More

Outage Probability of Dual-Hop Selective AF With Randomly Distributed and Fixed InterferersOct 04 2014The outage probability performance of a dual-hop amplify-and-forward selective relaying system with global relay selection is analyzed for Nakagami-$m$ fading channels in the presence of multiple interferers at both the relays and the destination. Two ... More

Invariance Conditions for Nonlinear Dynamical SystemsJul 05 2016Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions, sufficient ... More

Steplength Thresholds for Invariance Preserving of Discretization Methods of Dynamical Systems on a PolyhedronJun 26 2014Oct 29 2014Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first ... More

Analysis of Spectrum Occupancy Using Machine Learning AlgorithmsMar 24 2015In this paper, we analyze the spectrum occupancy using different machine learning techniques. Both supervised techniques (naive Bayesian classifier (NBC), decision trees (DT), support vector machine (SVM), linear regression (LR)) and unsupervised algorithm ... More

Power Allocation Strategies for Fixed-Gain Half-Duplex Amplify-and-Forward Relaying in Nakagami-m FadingNov 26 2012Dec 16 2012In this paper, we study power allocation strategies for a fixed-gain amplify-and-forward relay network employing multiple relays. We consider two optimization problems for the relay network: 1) optimal power allocation to maximize the end-to-end signal-to-noise ... More

Wideband Spectrum Sensing for Cognitive Radio Networks: A SurveyFeb 07 2013Mar 04 2013Cognitive radio has emerged as one of the most promising candidate solutions to improve spectrum utilization in next generation cellular networks. A crucial requirement for future cognitive radio networks is wideband spectrum sensing: secondary users ... More

Simulation of the Spin Field Effect Transistors: Effects of Tunneling and Spin Relaxation on its PerformanceFeb 26 2010A numerical simulation of spin-dependent quantum transport for a spin field effect transistor (spinFET) is implemented in a widely used simulator nanoMOS. This method includes the effect of both spin relaxation in the channel and the tunneling barrier ... More

Critical Current Distribution in Spin Transfer Switched Magnetic Tunnel JunctionsApr 15 2005The spin transfer switching current distribution within a cell was studied in magnetic tunnel junction based structures having alumina barriers with resistance-area product (RA) of 10 to 30 Ohm-um2 and tunneling magneto-resistance (TMR) of ~20%. These ... More

A FETI-DP preconditioner of discontinuous Galerkin method for multiscale problems in high constrast mediaMay 14 2014In this paper we consider second order elliptic partial differential equations with highly varying (heterogeneous) coefficients on a two-dimensional region. The problems are discretized by a composite finite element (FE) and discontinuous Galerkin (DG) ... More

Domain Decomposition Preconditioners for a Discontinuous Galerkin Formulation of a Multiscale Elliptic ProblemMar 19 2012In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a nonoverlapping ... More

Performance Analysis of Spectrum Sensing With Multiple Status Changes in Primary User TrafficApr 11 2012In this letter, the impact of primary user traffic with multiple status changes on the spectrum sensing performance is analyzed. Closed-form expressions for the probabilities of false alarm and detection are derived. Numerical results show that the multiple ... More

Aging associated domain evolution in the orthorhombic phase of <001> textured (K0.5Na0.5)Nb0.97Sb0.03O3 ceramicsDec 15 2011An aging effect due to a domain evolution in (K0.5,Na0.5)Nb0.97Sb0.03O3 <001> textured ceramics was investigated by piezoresponse force microscopy. We find that such an aging effect is pronounced in the orthorhombic single phase field. A more uniform ... More

Simultaneous Information and Energy Flow for IoT Relay Systems with Crowd HarvestingSep 02 2016It is expected that the number of wireless devices will grow rapidly over the next few years due to the growing proliferation of Internet-of-Things (IoT). In order to improve the energy efficiency of information transfer between small devices, we review ... More

Investigation of Umbral Dots with the New Vacuum Solar TelescopeSep 01 2015Dec 22 2015Umbral dots (UDs) are small isolated brightenings observed in sunspot umbrae. They are convective phenomena existing inside umbrae. UDs are usually divided into central UDs (CUDs) and peripheral UDs (PUDs) according to their positions inside an umbra. ... More

Ion and water transport in charge-modified graphene nanoporesJul 30 2016Porous graphene has high mechanical strength and atomic layer thickness, which make it a promising material for material separation and biomolecule sensing. Electrostatic interactions between charges in aqueous solution are a kind of strong long-range ... More

Some Results on Ethnic Conflicts Based on Evolutionary Game SimulationDec 29 2013The force of the ethnic separatism, essentially origining from negative effect of ethnic identity, is damaging the stability and harmony of multiethnic countries. In order to eliminate the foundation of the ethnic separatism and set up a harmonious ethnic ... More

Dispersal of G-band bright points at different longitudinal magnetic field strengthsSep 04 2015G-band bright points (GBPs) are thought to be the foot-points of magnetic flux tubes. The aim of this paper is to investigate the relation between the diffusion regimes of GBPs and the associated longitudinal magnetic field strengths. Two high resolution ... More

A note on the Hitchin-Thorpe inequality and Ricci flow on 4-manifoldsMar 14 2009Mar 06 2011In this short paper, we prove a Hitchin-Thorpe type inequality for closed 4-manifolds with non-positive Yamabe invariant, and admitting long time solutions of the normalized Ricci flow equation with bounded scalar curvature.

Gamma-Ray Burst Prompt Emission Light Curves and Power Density Spectra in the ICMART ModelDec 30 2013Feb 27 2014In this paper, we simulate the prompt emission light curves of gamma-ray bursts (GRBs) within the framework of the Internal-Collision-induced MAgnetic Reconnection and Turbulence (ICMART) model. This model applies to GRBs with a moderately-high magnetization ... More

Observability of Boolean control networks: A unified approach based on the theories of finite automataMay 27 2014Dec 09 2015The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this paper, we propose a unified approach to determine all the four types of observability of BCNs in the literature. We define ... More

Quantum teleportation and Birman-Murakami-Wenzl algebraJul 06 2016In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman-Murakami-Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, ... More

Quantum optomechanical straight-twin engineOct 06 2016We propose a scheme to realize a quantum polariton heat engine in a hybrid microwave-opto-mechanical system. The engine transfers the heat obtained from the effective temperature difference between the microwave and optical cavity fields to the work extracted ... More

Imaging of locally rough surfaces from intensity-only far-field or near-field dataOct 19 2016This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration algorithm in frequencies ... More

A novel integral equation for scattering by locally rough surfaces and application to the inverse problemFeb 01 2013This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation ... More

Pointwise second-order necessary conditions for stochastic optimal controls, Part I: The case of convex control constraintSep 09 2014This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region is assumed to ... More

Symmetry analysis for time-fractional convection-diffusion equationDec 04 2015Dec 08 2015The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and similarity reductions ... More

The Discovery of Mutated Driver Pathways in Cancer: Models and AlgorithmsApr 05 2016The pathogenesis of cancer in human is still poorly understood. With the rapid development of high-throughput sequencing technologies, huge volumes of cancer genomics data have been generated. Deciphering those data poses great opportunities and challenges ... More

Subalgebras and finitistic dimensions of Artin algebrasJul 21 2011Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.

SVM and ELM: Who Wins? Object Recognition with Deep Convolutional Features from ImageNetJun 08 2015Deep learning with a convolutional neural network (CNN) has been proved to be very effective in feature extraction and representation of images. For image classification problems, this work aim at finding which classifier is more competitive based on ... More

Confinement-induced Resonances in Quasi-one-dimensional Traps with Transverse AnisotropyDec 23 2010We study atom-atom scattering in quasi-one-dimensional geometries with transverse anisotropy. By assuming an s-wave pseudo-potential of contact interaction, we show that the system would exhibit a single confinement-induced resonance, where the scattering ... More

Approaching the Cramer-Rao Bound in Weak Lensing with PDF SymmetrizationJun 30 2016Weak lensing statistics is typically measured as weighted sum of shear estimators or their products (shear-shear correlation). The weighting schemes are designed in the hope of minimizing the statistical error without introducing systematic errors. It ... More

Recovering scattering obstacles by multi-frequency phaseless far-field dataOct 19 2016It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location of the obstacle ... More

The continuity method on Fano bundlesDec 05 2016We prove that the continuity method on a Fano bundle starting from a suitable K\"ahler metric converges to a K\"ahler metric on the base in Gromov-Hausdorff topology.

Disjunctive Logic Programs versus Normal Logic ProgramsApr 02 2013This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is proposed and ... More

Hierarchical Bayesian Models with Factorization for Content-Based RecommendationDec 28 2014Most existing content-based filtering approaches learn user profiles independently without capturing the similarity among users. Bayesian hierarchical models \cite{Zhang:Efficient} learn user profiles jointly and have the advantage of being able to borrow ... More

Repetitive cluster-tilted algebrasFeb 18 2009Jan 29 2013Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field $k$ and $\mathscr{C}_{F^m}$ be the repetitive cluster category of $H$ with $m\geq 1$. We investigate the properties of cluster tilting objects in $\mathscr{C}_{F^m}$ ... More

Expressiveness of Logic Programs under General Stable Model SemanticsDec 02 2014The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of normal and disjunctive ... More

An Ordinal Bargaining Solution with Fixed-Point PropertyJan 15 2014Shapleys impossibility result indicates that the two-person bargaining problem has no non-trivial ordinal solution with the traditional game-theoretic bargaining model. Although the result is no longer true for bargaining problems with more than two agents, ... More

Inequalities for Casorati curvatures of submanifolds in real space formsAug 21 2014Jun 15 2015By using T. Oprea's optimization methods on submanifolds, we give another proof of the inequalities relating the normalized $\delta-$Casorati curvature $\hat{\delta}_c(n-1)$ for submanifolds in real space forms. Also, inequalities relating the normalized ... More

Spatial-Spectral Boosting Analysis for Stroke Patients' Motor Imagery EEG in Rehabilitation TrainingOct 23 2013Current studies about motor imagery based rehabilitation training systems for stroke subjects lack an appropriate analytic method, which can achieve a considerable classification accuracy, at the same time detects gradual changes of imagery patterns during ... More

Some results on pointwise second-order necessary conditions for stochastic optimal controlsMay 28 2014The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control region is convex, ... More

Molecular dynamics studies on the NMR and X-ray structures of rabbit prion protein wild-type and mutantsApr 29 2013Aug 26 2013Prion diseases are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of mammalian species such as sheep, goats, mice, humans, chimpanzees, hamsters, cattle, elks, deer, minks, cats, chicken, pigs, turtles, etc. ... More

Quantum Limited DPSK Receivers with Optical Mach-Zehnder Interferometer DemodulationOct 12 2004We present an analysis of quantum-limited DPSK receivers with optical Mach-Zehnder interferometer (MZI) demodulation. It is shown for the first time that the quantum limits for DPSK/MZI receivers with single-port and balanced detections exactly differ ... More

Quantum coin flipping secure against channel noisesMay 27 2015So far, most of existed single-shot quantum coin flipping(QCF) protocols failed in a noisy quantum channel. Here, we present a nested-structured framework that makes it possible to achieve partially noise-tolerant QCF, due to that there is a trade-off ... More

Pointwise second-order necessary conditions for stochastic optimal controls, Part II: The general caseSep 26 2015Oct 19 2015This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex, and the control ... More

Minimality of a Kind of Pseudo-Umbilical Totally Real Submanifolds in Non-Flat Complex Space FormsDec 27 2015In this paper, by studying the position of umbilical normal vectors in the normal bundle, we prove that pseudo-umbilical totally real submanifolds with flat normal connection in non-flat complex space forms must be minimal.

Global well-posedness of 3-D inhomogeneous Navier-Stokes equations with ill-prepared initial dataSep 05 2014In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier-Stokes equations with ill-prepared large initial data which are slowly varying in one space variable, that is, initial data of the form $\bigl(1+\e^{\be}a_0(x_{\rm ... More

Long time well-posdness of Prandtl system with small and analytic initial dataSep 05 2014In this paper, we investigate the long time existence and uniqueness of small solution to $d,$ for $d=2,3,$ dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that $d$ dimensional ... More

Cusp-shaped structure of a jet observed by IRIS and SDONov 15 2016On 29 August 2014, the trigger and evolution of a cusp-shaped jet were captured in detail at 1330 {\AA} by the Interface Region Imaging Spectrograph.At first, two neighboring mini-prominences arose in turn from low solar atmosphere and collided with a ... More

Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin-orbit couplingMar 03 2012Oct 28 2012We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the ... More

On Tree Based Phylogenetic NetworksSep 05 2015Sep 08 2015A large class of phylogenetic networks can be obtained from trees by the addition of horizontal edges between the tree edges. These networks are called tree based networks. Reticulation-visible networks and child-sibling networks are all tree based. In ... More

A note on the growth of regularity with respect to FrobeniusNov 30 2015Let $R=k[x_1,\dots,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\dots,x_n)$ by $\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) ... More

Shock of three-state model for intracellular transport of kinesin KIF1AMay 16 2011Recently, a three-state model is presented to describe the intracellular traffic of unconventional (single-headed) kinesin KIF1A [Phys. Rev. Lett. {\bf 95}, 118101 (2005)], in which each motor can bind strongly or weakly to its microtubule track, and ... More

New approach to Monte Carlo calculation of buckling of supercoiled DNA loopsSep 11 2000The short supercoiled circular DNA molecules are shown to be glassy systems and canonical Metropolis Monte Carlo simulations of the systems tend to get stuck in local metastable energy basins. A novel Monte Carlo algorithm is developed to alleviate the ... More

Interactive Retrieval Based on Wikipedia ConceptsDec 29 2014This paper presents a new user feedback mechanism based on Wikipedia concepts for interactive retrieval. In this mechanism, the system presents to the user a group of Wikipedia concepts, and the user can choose those relevant to refine his/her query. ... More

Simple transitive $2$-representations and Drinfeld center for some finitary $2$-categoriesJun 08 2015Aug 24 2015We classify all simple transitive $2$-representations for two classes of finitary $2$-categories associated with tree path algebras and also for one class of fiat $2$-categories associated with truncated polynomial rings. Additionally, we compute the ... More

Duflo involutions for 2-categories associated to tree quiversJan 13 2015Motivated by the definition of Duflo involution for fiat $2$-categories, we define certain analogues of Duflo involution for arbitrary finitary $2$-categories and show that such Duflo involutions exist for two classes of finitary $2$-categories associated ... More

Remarks on symplectic mean curvature flows in Kähler surfaces with positive holomorphic sectional curvaturesJul 24 2015Aug 18 2015In this paper, we mainly study the mean curvature flow in K\"ahler surfaces with positive holomorphic sectional curvatures. First, we prove that if the ratio $\lambda$ of the maximum and the minimum of the holomorphic sectional curvatures $< 2$, then ... More

Mixed spectral types for the one frequency discrete quasi-periodic Schrödinger operatorAug 12 2015Aug 13 2015We consider a family of one frequency discrete analytic quasi-periodic Schr\"odinger operators which appear in [Bjer]. We show that this family provides an example of coexistence of absolutely continuous and point spectrum for some parameters as well ... More

Inverse iterative simulation: An efficient approach for contaminant source identificationJun 02 2015Jun 16 2015In groundwater contaminant remediation and risk assessment, it is important to identify parameters of the contaminant source and hydraulic conductivity field by solving an inverse problem. However, if the dimensionality of the inverse problem is high, ... More

Conformal invariance and universal critical exponents in the two-dimensional percolation modelJun 05 2009Jun 14 2009This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

Representation of solutions to BSDEs associated with a degenerate FSDEAug 24 2005In this paper we investigate a class of decoupled forward-backward SDEs, where the volatility of the FSDE is degenerate and the terminal value of the BSDE is a discontinuous function of the FSDE. Such an FBSDE is associated with a degenerate parabolic ... More

The inverse of a real generalized Cartan matrixDec 16 2002The purpose of this note is to give explicit criteria to determine whether a real generalized Cartan matrix is of finite type, affine type or of hyperbolic type by considering the principal minors and the inverse of the matrix. In particular, it will ... More

Contraction of Ore Ideals with ApplicationsNov 25 2015Jan 29 2016Ore operators form a common algebraic abstraction of linear ordinary differential and recurrence equations. Given an Ore operator $L$ with polynomial coefficients in $x$, it generates a left ideal $I$ in the Ore algebra over the field $\mathbf{k}(x)$ ... More

Influence of Magnetic Field Decay on Electron Capture in MagnetarsSep 15 2013The de-excited energy of electron capture (EC) induced by magnetic field decay may be a new source for heating magnetar crust, so we do a quantitative calculation on the EC process near the outer crust and analyze their influence on persistent X-ray radiation ... More

Ricci Lower Bound for Kähler-Ricci FlowOct 27 2011In this note, we provide some general discussion on the Ricci lower bound along K\"ahler-Ricci flow with singularity over closed manifold.

The Singular Value Decomposition, Applications and BeyondOct 29 2015The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and then show the ... More

Nonconvex Penalization in Sparse Estimation: An Approach Based on the Bernstein FunctionOct 29 2015In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We ... More

Stochastic Partial Differential Equations with Unbounded and Degenerate CoefficientsAug 19 2009Aug 24 2009In this article, using DiPerna-Lions theory \cite{Di-Li}, we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, ... More

Global strong solution to a nonlinear Dirac type equation in one dimensionMay 21 2012This paper studies a class of nonlinear massless Dirac equations in one dimension, which include the equations for massless Thirring model and massless Gross-Neveu model. Under the assumptions that the initial data has small charge and is bounded, the ... More

Estimates and nonexistence of solutions of the scalar curvature equation on noncompact manifoldsAug 25 2005This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence ... More

A Novel Mathematical Model for the Unique Shortest Path Routing ProblemJun 30 2008Mar 04 2010Link weights are the principal parameters of shortest path routing protocols, the most commonly used protocols for IP networks. The problem of optimally setting link weights for unique shortest path routing is addressed. Due to the complexity of the constraints ... More

Collapsing of Calabi-Yau manifolds and special lagrangian submanifoldsNov 05 2009Dec 01 2009In this paper, the relationship between the existence of special lagrangian submanifolds and the collapsing of Calabi-Yau manifolds is studied. First, special lagrangian fibrations are constructed on some regions of bounded curvature and sufficiently ... More

Representing Primes as x^2 + 5y^2: An Inductive Proof that Euler MissedJun 22 2006Feb 11 2007We present an elementary inductive proof which Euler could have obtained, for the corresponding result as the title indicates, had he refined a bit his proof for Fermat's assertion on representing primes as two squares.

On Fixed Points of Order K of RSAJul 23 2009In this paper, we gave a preliminary dynamical analysis on the RSA cryptosystem and obtained a computational formulae of the number of the fixed points of $k$ order of the RSA. Thus, the problem in [8, 9] has been solved.

Notes on Dickson's ConjectureJun 21 2009Nov 11 2009In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson's conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson's conjecture to the higher order integral polynomial case. However, they did not generalize Dickson's ... More

On Lawson's Area-minimizing HyperconesJan 20 2015Nov 13 2015We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor \cite{Law}) following Lawson's original idea \cite{BL}. Moreover, each of them enjoys calibrations singular only at the origin. ... More

Generalizations of a theorem about the binomial coefficientJan 23 2009Sep 15 2009The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

Integers representable as the product of the sum of four integers with the sum of their reciprocalsAug 11 2016By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition for the integers with a positive representation.

Braided Hopf AlgebrasNov 10 2005Nov 06 2007In braided tensor categories we show the Maschke's theorem and give the necessary and sufficient conditions for double cross biproducts and crossbiproducts and biproducts to be bialgebras. We obtain the factorization theorem for braided Hopf algebras; ... More

On Wright's generalized Bessel kernelAug 09 2016Sep 20 2016In this paper, we consider the Wright's generalized Bessel kernel $K^{(\alpha,\theta)}(x,y)$ defined by $$\theta x^{\alpha}\int_0^1J_{\frac{\alpha+1}{\theta},\frac{1}{\theta}}(ux)J_{\alpha+1,\theta}((uy)^{\theta})u^\alpha\,\mathrm{d} u, \qquad \alpha>-1, ... More

A Complex Version of G-Expectation and its Application to Conformal MartingaleFeb 10 2015This paper is concerned with the connection between G-Brownian Motion and analytic functions. We introduce the complex version of sublinear expectation, and then do the stochastic analysis in this framework. Furthermore, the conformal G-Brownian Motion ... More

Value of Information Aware Opportunistic Duty Cycling in Solar Harvesting Sensor NetworksNov 26 2015The energy-harvested Wireless Sensor Networks (WSNs) may operate perpetually with the extra energy supply from ambient natural energy, such as solar energy. Nevertheless, the harvested energy is still limited so it's not able to support the perpetual ... More

Neutrino Mass Ordering in Future Neutrinoless Double Beta Decay ExperimentsMay 25 2016Motivated by recent intensive experimental efforts on searching for neutrinoless double beta decays, we present a detailed quantitative analysis on the prospect of resolving neutrino mass ordering in the next generation $^{76}$Ge-type experiments.

An elementary proof of uniqueness of Markoff numbers which are prime powersJun 12 2006Feb 01 2007We present a very elementary proof of the uniqueness of Markoff numbers which are prime powers or twice prime powers, in the sense that it uses neither algebraic number theory nor hyperbolic geometry.

An $S_4$ model inspired from self-complementary neutrino mixingDec 16 2015Jun 28 2016We build an $S_4$ model for neutrino masses and mixings based on the self-complementary (SC) neutrino mixing pattern. The SC mixing is constructed from the self-complementarity relation plus $\delta_{\rm CP}=-\frac{\pi}{2}$. We elaborately construct the ... More

Helicity Observation of Weak and Strong FieldsJun 09 2006We report in this letter our analysis of a large sample of photospheric vector magnetic field measurements. Our sample consists of 17200 vector magnetograms obtained from January 1997 to August 2004 by Huairou Solar Observing Station of the Chinese National ... More