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A novel design to realize deterministic switching of perpendicularly magnetic layers by spin orbital torque through antiferromagnetic couplingApr 17 2017May 05 2017We proposed a novel and simple multilayer structure to realize the deterministic switching of perpendicularly magnetized layers (Co in our work) by spin orbital torque from the spin Hall Effect in this paper. A pinned layer is introduced, antiferromagnetically ... More

Massive MIMO versus Small-Cell Systems: Spectral and Energy Efficiency ComparisonSep 14 2015In this paper, we study the downlink performance of two important 5G network architectures, i.e. massive multiple-input multiple-output (M-MIMO) and small-cell densification. We propose a comparative modeling for the two systems, where the user and antenna/base ... More

Stochastic Geometry-Based Performance Bounds for Non-Fading and Rayleigh Fading Ad Hoc NetworksSep 14 2015In this paper, we study the performance of non-fading and Rayleigh fading ad hoc networks. We first characterize the distribution of the signal-to-interference-plus-noise ratio (SINR) through the Laplace transform of the inverted SINR for non-fading channels. ... More

Principal Component Analysis (PCA)-based Massive-MIMO Channel FeedbackDec 16 2015Channel-state-information (CSI) feedback methods are considered, especially for massive or very large-scale multiple-input multiple-output (MIMO) systems. To extract essential information from the CSI without redundancy that arises from the highly correlated ... More

Spectral Efficiency and Energy Efficiency of OFDM Systems: Impact of Power Amplifiers and CountermeasuresMay 17 2013In wireless communication systems, the nonlinear effect and inefficiency of power amplifier (PA) have posed practical challenges for system designs to achieve high spectral efficiency (SE) and energy efficiency (EE). In this paper, we analyze the impact ... More

Improper Signaling for Symbol Error Rate Minimization in K-User Interference ChannelMay 29 2014The rate maximization for the $K$-user interference channels (ICs) has been investigated extensively in the literature. However, the dual problem of minimizing the error probability with given signal modulations and/or data rates of the users is less ... More

Energy Cooperation in Cellular Networks with Renewable Powered Base StationsJan 21 2013May 27 2013In this paper, we propose a model for energy cooperation between cellular base stations (BSs) with individual hybrid power supplies (including both the conventional grid and renewable energy sources), limited energy storages, and connected by resistive ... More

Electromagnetically induced transparency and optical memories in an optomechanical system with $N$ membranesMar 06 2014We study the propagation of a weak probe field through an optomechanical system in which $N$ nearly degenerate mechanical membranes are inside a Febry-Perot cavity, and couple dispersively to an intracavity field. We derive a general analytical expression ... More

Comparative Study of SVD and QRS in Closed-Loop Beamforming SystemsJun 23 2008We compare two closed-loop beamforming algorithms, one based on singular value decomposition (SVD) and the other based on equal diagonal QR decomposition (QRS). SVD has the advantage of parallelizing the MIMO channel, but each of the sub-channels has ... More

Comparative Study of Open-loop Transmit Diversity Schemes for Four Transmit Antennas in Coded OFDM SystemsJun 23 2008We compare four open-loop transmit diversity schemes in a coded Orthogonal Frequency Division Multiplexing (OFDM) system with four transmit antennas, namely cyclic delay diversity (CDD), Space-Time Block Code (STBC, Alamouti code is used) with CDD, Quasi-Orthogonal ... More

Full-Duplex Wireless-Powered Communication Network with Energy CausalityApr 02 2014In this paper, we consider a wireless communication network with a full-duplex hybrid access point (HAP) and a set of wireless users with energy harvesting capabilities. The HAP implements the full-duplex through two antennas: one for broadcasting wireless ... More

Opportunistic Multicast Scheduling for Unicast Transmission in MIMO-OFDM SystemNov 11 2014We propose a multicast scheduling scheme to exploit content reuse when there is asynchronicity in user requests. A unicast transmission setup is used for content delivery, while multicast transmission is employed opportunistically to reduce wireless resource ... More

Incentive Mechanisms for Motivating Mobile Data Offloading in Heterogeneous Networks: A Salary-Plus-Bonus ApproachFeb 08 2018In this paper, a salary-plus-bonus incentive mechanism is proposed to motivate WiFi Access Points (APs) to provide data offloading service for mobile network operators (MNOs). Under the proposed salary-plus-bonus scheme, WiFi APs are rewarded not only ... More

Energy-Efficient, Large-scale Distributed-Antenna System (L-DAS) for Multiple UsersDec 06 2013Jan 20 2014Large-scale distributed-antenna system (L-DAS) with very large number of distributed antennas, possibly up to a few hundred antennas, is considered. A few major issues of the L-DAS, such as high latency, energy consumption, computational complexity, and ... More

Data Offloading in Load Coupled Networks: A Utility Maximization FrameworkDec 25 2013We provide a general framework for the problem of data offloading in a heterogeneous wireless network, where some demand of cellular users is served by a complementary network. The complementary network is either a small-cell network that shares the same ... More

On Tractability Aspects of Optimal Resource Allocation in OFDMA SystemsDec 11 2011Joint channel and rate allocation with power minimization in orthogonal frequency-division multiple access (OFDMA) has attracted extensive attention. Most of the research has dealt with the development of sub-optimal but low-complexity algorithms. In ... More

Modulated Unit-Norm Tight Frames for Compressed SensingNov 27 2014In this paper, we propose a compressed sensing (CS) framework that consists of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a column-wise orthonormal matrix. We prove that this structure satisfies the restricted isometry property ... More

Energy-Efficient Relaying over Multiple Slots with Causal CSIMay 22 2012Nov 29 2012In many communication scenarios, such as in cellular systems, the energy cost is substantial and should be conserved, yet there is a growing need to support many real-time applications that require timely data delivery. To model such a scenario, in this ... More

Deterministic Sequences for Compressive MIMO Channel EstimationNov 02 2013This paper considers the problem of pilot design for compressive multiple-input multiple-output (MIMO) channel estimation. In particular, we are interested in estimating the channels for multiple transmitters simultaneously when the pilot sequences are ... More

Gaussian Two-way Relay Channel with Private Information for the RelaySep 19 2011We introduce a generalized two-way relay channel where two sources exchange information (not necessarily of the same rate) with help from a relay, and each source additionally sends private information to the relay. We consider the Gaussian setting where ... More

On Power and Load Coupling in Cellular Networks for Energy OptimizationFeb 24 2014Aug 26 2014We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio (SINR) coupling ... More

Iterative Channel Estimation Using LSE and Sparse Message Passing for MmWave MIMO SystemsNov 17 2016We propose an iterative channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are approximately modeled ... More

Beamforming Matrix Quantization with Variable Feedback RateJun 20 2008We propose an improved beamforming matrix compression by Givens Rotation with the use of variable feedback rate. The variable feedback rate means that the number of bits used to represent the quantized beamforming matrix is based on the value of the matrix. ... More

Fountain Codes with Varying Probability DistributionsJan 12 2010Apr 07 2010Fountain codes are rateless erasure-correcting codes, i.e., an essentially infinite stream of encoded packets can be generated from a finite set of data packets. Several fountain codes have been proposed recently to minimize overhead, many of which involve ... More

Iterative Channel Estimation Using LSE and Sparse Message Passing for MmWave MIMO SystemsNov 17 2016Oct 28 2018We propose an iterative channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are approximately modeled ... More

Power and Channel Allocation for Non-orthogonal Multiple Access in 5G Systems: Tractability and ComputationMar 24 2016Network capacity calls for significant increase for 5G cellular systems. A promising multi-user access scheme, non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC), is currently under consideration. In NOMA, spectrum efficiency ... More

Cost minimization for fading channels with energy harvesting and conventional energyApr 04 2014In this paper, we investigate resource allocation strategies for a point-to-point wireless communications system with hybrid energy sources consisting of an energy harvester and a conventional energy source. In particular, as an incentive to promote the ... More

Mobile Data Offloading through A Third-Party WiFi Access Point: An Operator's PerspectiveAug 22 2014WiFi offloading is regarded as one of the most promising techniques to deal with the explosive data increase in cellular networks due to its high data transmission rate and low requirement on devices. In this paper, we investigate the mobile data offloading ... More

Ergodic Sum-Rate Maximization for Fading Cognitive Multiple Access Channels without Successive Interference CancellationMar 03 2014In this paper, the ergodic sum-rate of a fading cognitive multiple access channel (C-MAC) is studied, where a secondary network (SN) with multiple secondary users (SUs) transmitting to a secondary base station (SBS) shares the spectrum band with a primary ... More

Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless NetworksFeb 15 2015Mar 25 2015Optimizing activation and deactivation of base station transmissions provides an instrument for improving energy efficiency in cellular networks. In this paper, we study optimal cell clustering and scheduling of activation duration for each cluster, with ... More

Carrier Frequency Offset Estimation for Two-Way Relaying: Optimal Preamble and Estimator DesignAug 16 2012We consider the problem of carrier frequency offset (CFO) estimation for a two-way relaying system based on the amplify-and-forward (AF) protocol. Our contributions are in designing an optimal preamble, and the corresponding estimator, to closely achieve ... More

A LSE and Sparse Message Passing-Based Channel Estimation for mmWave MIMO SystemsSep 11 2016In this paper, we propose a novel channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing algorithm (SMP), which is of special interest for Millimeter Wave (mmWave) systems, since this algorithm can leverage ... More

Secrecy Throughput Maximization for Full-Duplex Wireless Powered IoT Networks under Fairness ConstraintsJan 28 2019In this paper, we study the secrecy throughput of a full-duplex wireless powered communication network (WPCN) for internet of things (IoT). The WPCN consists of a full-duplex multi-antenna base station (BS) and a number of sensor nodes. The BS transmits ... More

Enhancement of Cavity Cooling of a Micromechanical Mirror Using Parametric InteractionsOct 15 2008Feb 04 2009It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature 300 K to sub-Kelvin temperatures, ... More

Nanomechanical Inverse Electromagnetically Induced Transparency and Confinement of Light in Normal modesApr 27 2013Mar 27 2014We demonstrate the existence of the phenomenon of the inverse electromagnetically induced transparency (IEIT) in an opto mechanical system consisting of a nanomechanical mirror placed in an optical cavity. We show that two weak counter-propagating identical ... More

The Electromagnetically Induced Transparency in Mechanical Effects of LightNov 21 2009Apr 24 2010We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field ... More

Weak value amplification of atomic cat statesJan 10 2015Sep 09 2015We show the utility of the weak value amplification to observe the quantum interference between two close lying atomic coherent states in a post-selected atomic cat state, produced in a system of $N$ identical two-level atoms weakly interacting with a ... More

Coherent perfect absorption of path entangled single photonsFeb 28 2014Aug 22 2014We examine the question of coherent perfect absorption (CPA) of single photons, and more generally, of the quantum fields by a {\it macroscopic} medium. We show the CPA of path entangled single photons in a Fabry-Perot interferometer containing an absorptive ... More

Can reactive coupling beat motional quantum limit of nano waveguides coupled to microdisk resonatorJul 09 2010Oct 05 2010Dissipation is generally thought to affect the quantum nature of the system in an adverse manner, however we show that dissipatively coupled nano systems can be prepared in states which beat the standard quantum limit of the mechanical motion. We show ... More

Squeezing of a nanomechanical oscillatorMay 26 2009We show that squeezing of a nanomechanical mirror can be generated by injecting broad band squeezed vacuum light and laser light into the cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum momentum squeezing of ... More

Reactive-Coupling-Induced Normal Mode Splittings in Microdisk Resonators Coupled to WaveguidesFeb 15 2010May 09 2010We study the optomechanical design introduced by M. Li et al. [Phys. Rev. Lett. {\bf 103}, 223901 (2009)], which is very effective for investigation of the effects of reactive coupling. We show the normal mode splitting which is due solely to reactive ... More

Strong Mechanical Squeezing and its DetectionFeb 06 2016Mar 17 2016We report an efficient mechanism to generate a squeezed state of a mechanical mirror in an optomechanical system. We use especially tuned parametric amplifier (PA) inside the cavity and the parametric photon phonon processes to transfer quantum squeezing ... More

Normal mode splitting in a coupled system of nanomechanical oscillator and parametric amplifier cavityApr 21 2009Jun 24 2009We study how an optical parametric amplifier inside the cavity can affect the normal mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the ... More

Optomechanical Systems as Single Photon RoutersSep 20 2011Feb 03 2012We demonstrate theoretically the possibility of using nano mechanical systems as single photon routers. We show how EIT in cavity optomechanical systems can be used to produce a switch for a probe field in a single photon Fock state using very low pumping ... More

Robust force sensing for a free particle in a dissipative optomechanical system with a parametric amplifierOct 10 2016We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity ... More

Electromagnetically Induced Transparency with Quantized Fields in Optocavity MechanicsFeb 01 2011Feb 10 2011We report electromagnetically induced transparency using quantized fields in optomechanical systems. The weak probe field is a narrow band squeezed field. We present a homodyne detection of EIT in the output quantum field. We find that the EIT dip exists ... More

Electromagnetically Induced Transparency from Two Phonon Processes in Quadratically Coupled MembranesOct 05 2010We describe how electromagnetically induced transparency can arise in quadratically coupled optomechanical systems. Due to quadratic coupling the underlying optical process involves a two phonon process in optomechanical system and this two phonon process ... More

Normal Mode Splitting and Antibunching in Stokes and Anti-Stokes Processes in Cavity Optomechanics: Radiation Pressure Induced Four-Wave Mixing Cavity OptomechanicsSep 10 2009Mar 30 2010We study Stokes and anti-Stokes processes in cavity optomechanics in the regime of strong coupling. The Stokes and anti-Stokes signals exhibit prominently the normal-mode splitting. We report gain for the Stokes signal. We also report lifetime splitting ... More

Entangling nanomechanical oscillators in a ring cavity by feeding squeezed lightAug 11 2009Oct 28 2009A scheme is presented for entangling two separated nanomechanical oscillators by injecting broad band squeezed vacuum light and laser light into the ring cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum entanglement ... More

Robust force sensing for a free particle in a dissipative optomechanical system with a parametric amplifierOct 10 2016Mar 02 2017We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Aug 16 2016Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Sep 25 2017Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

SPLZ: An Efficient Algorithm for Single Source Shortest Path Problem Using Compression MethodAug 11 2014Jan 11 2015Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing ... More

Sphere theorems for submanifolds in Kähler ManifoldOct 17 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.

Sphere theorems for Lagrangian and Legendrian submanifoldsOct 22 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for Lagrangian submanifolds in K\"ahler manifold and Legendrian submanifolds in Sasaki space form.

Deterministic switching of perpendicularly magnetic layers by spin orbital torque through stray field engineeringOct 20 2017We proposed a novel multilayer structure to realize the deterministic switching of perpendicularly magnetized layers by spin orbital torque from the spin Hall effect through stray field engineering. In our design, a pinned magnetic layer is introduced ... More

Superluminal and Ultraslow Light Propagation in Optomechanical SystemsOct 25 2012Feb 04 2013We consider an optomechanical double-ended cavity under the action of a coupling laser and a probe laser in electromagnetically induced transparency configuration. It is shown how the group delay and advance of the probe field can be controlled by the ... More

Different Particle Sizes Obtained from Static and Dynamic Laser Light ScatteringMay 31 2004Dec 08 2004Detailed investigation of static and dynamic laser light scattering has been attempted in this work both theoretically and experimentally based on dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) ... More

The Star of David RuleMay 09 2008In this note, a new concept called {\em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are ... More

Measures of Intermediate Entropies for Skew Product DiffeomorphismsJun 10 2009Jan 18 2010In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate entropies. ... More

W-Operators and Permutation GroupsOct 20 2016W-operators are differential operators on the polynomial ring. A special example of W-operators is the cut-and-join operator. We study the relation between W-operators and permutation groups. We find the W-operator $W([d])$ can be written as the sum of ... More

Stability of sheaves of locally closed and exact formsMay 13 2009For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of exact 1-forms ... More

Suspicion on Engrafting HBT From Astronomy to Heavy Ion CollisionDec 13 2004Aug 19 2005HBT method in astronomy and heavy ion collision is contrasted in present article.Some differences are found and validity of using HBT in heavy ion collision is suspected.

Factorization of generalized theta functions at reducible caseApr 17 2000We proved the factorization of generalized theta functions when the curve has two irreducible components meeting at one node.

Topological Phases of Fermionic Ladders with Periodic Magnetic FieldsDec 14 2015In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting ... More

On uniform estimate of complex elliptic equations on closed Hermitian manifoldsDec 16 2014Feb 10 2015In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed K\"ahler manifolds. ... More

On a class of fully nonlinear elliptic equations on closed Hermitian manifoldsOct 01 2013We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive $C^\infty$ {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed to launch ... More

Compactness of Constant Mean Curvature Surfaces in Three Manifold with Positive Ricci CurvatureApr 25 2018Dec 06 2018In this paper we prove a compactness theorem for constant mean curvature surfaces with area and genus bound in three manifold with positive Ricci curvature. As an application, we give a lower bound of first eigenvalue of constant mean curvature surfaces ... More

Exact Controllability of linear KP-I equationFeb 28 2018We prove the exact controllability of linear KP-I equation if the control input is added on a vertical domain. More generally, we have obtained the least dispersion needed to insure observability for fractional linear KP I equation.

The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Oct 17 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... More

Topics in Quantum NetworkingMar 07 2019It is an era full of imaginations and lack of impossibilities. The knowledge boundaries have been being pushed back on and on. The quantum age is on the edge of transforming quantum theories into quantum technologies. We present a sketch of the advances ... More

Frobenius morphism and semi-stable bundlesApr 09 2009This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008, Seoul. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct ... More

Universal central extensions of twisted forms of split simple Lie algebras over ringsNov 17 2010Nov 19 2010We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are obtained by ... More

Direct images of bundles under Frobenius morphismsNov 13 2006Mar 31 2008Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded ... More

A probabilistic approach to enumeration of Gessel walksMar 02 2009We consider Gessel walks in the plane starting at the origin $(0, 0)$ remaining in the first quadrant $i, j \geq 0$ and made of West, North-East, East and South-West steps. Let $F(m; n_1, n_2)$ denote the number of these walks with exact $m$ steps ending ... More

Two laws of large numbers for sublinear expectationsNov 18 2015In this paper, we consider the sublinear expectation on bounded random vari- ables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the no- tion of independence for ... More

W-Operator and Differential Equation for 3-Hurwitz NumberDec 09 2016We consider a new type of Hurwitz number, the number of ordered transitive factorizations of an arbitrary permutation into d-cycles. In this paper, we focus on the special case d = 3. The minimal number of transitive factorizations of any permutation ... More

Dark Matter Searches in Jet plus Missing Energy in $\rm γp$ collision at CERN LHCJul 21 2014Aug 01 2014In this paper, we investigate the $\rm \gamma p$ photoproduction of jet plus missing energy signal to set limits on the couplings of the fermionic dark matter to the quarks at the LHC via the main reaction $\rm pp\rightarrow p\gamma p\rightarrow p \chi\chi ... More

Counting Hypergraphs in Data StreamsApr 28 2013We present the first streaming algorithm for counting an arbitrary hypergraph $H$ of constant size in a massive hypergraph $G$. Our algorithm can handle both edge-insertions and edge-deletions, and is applicable for the distributed setting. Moreover, ... More

Pluricanonical maps of varieties of Albanese fiber dimension twoNov 28 2012Feb 23 2014In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the 6-canonical map is birational. And we also show that the 5-canonical map is birational for any such variety with some geometric restrictions. ... More

A Transcendental Invariant of Pseudo-Anosov MapsSep 12 2012May 09 2013For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will ... More

On the Clifford theorem for surfacesMar 04 2012We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

Orlicz-Besov imbedding and globally $n$-regular domainsOct 09 2018Denote by $ {\bf\dot B}^{\alpha,\phi}(\Omega)$ the Orlicz-Besov space, where $\alpha\in\mathbb{R}$, $\phi$ is a Young function and $\Omega\subset\mathbb{R}^n$ is a domain. For $\alpha\in(-n,0)$ and optimal $\phi$, in this paper we characterize domains ... More

Overview of top quark physics at the ep collidersOct 17 2017In this talk we present a short overview of top physics at the electron-proton (ep) colliders. Currently, the proposed ep collider is the Large Hadron Electron Collider (LHeC), which is a combination of 60 GeV electron beam and 7 TeV proton beam of the ... More

Chebyshev Interpolation for Function in 1DSep 24 2018This research is concerned with finding the roots of a function in an interval using Chebyshev Interpolation. Numerical results of Chebyshev Interpolation are presented to show that this is a powerful way to simultaneously calculate all the roots in an ... More

Shifted convolution sums of $GL_3$ cusp forms with $θ$-seriesSep 25 2015Sep 10 2016Let $A_f(1,n)$ be the normalized Fourier coefficients of a Hecke-Maass cusp form $f$ for $SL_3(\mathbb{Z})$ and $$ r_3(n)=\#\left\{(n_1,n_2,n_3)\in \mathbb{Z}^3:n_1^2+n_2^2+n_3^2=n\right\}. $$ Let $1\leq h\leq X$ and $\phi(x)$ be a smooth function compactly ... More

Shifted convolution sums involving theta seriesMay 02 2017Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $\lambda_f(n)$ its $n$-th Hecke eigenvalue. Let $$ r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}. $$ In this paper, we study the shifted ... More

Co-iterative augmented Hessian method for orbital optimizationOct 26 2016Jan 10 2017Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH) method. In ... More

An exact axisymmetric spiral solution of incompressible 3D Euler equationsJan 29 2011Jul 31 2011Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler equations. The solution, ... More

Strichartz-type Estimates for Wave Equation for Normally Hyperbolic Trapped DomainsJul 20 2015We establish a mixed-norm Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega,g)$, for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is ... More

Linear Quadratic Optimal Control Problems with Fixed Terminal States and Integral Quadratic ConstraintsMay 10 2017This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable and whose ... More

Virtual Domination of $3$-manifoldsJan 27 2014For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented $3$-manifold $N$, we will show that $M$ admits a finite cover $M'$, such that there exists a degree-$2$ map $f:M'\rightarrow N$, i.e. $M$ virtually $2$-dominates $N$.

Virtual Homological Torsion of Closed Hyperbolic 3-manifoldsSep 05 2013Jun 05 2014In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. ... More

A representation-theoretic proof of the branching rule for Macdonald polynomialsDec 01 2014We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal ... More

Zero-Entropy Dynamical Systems with Gluing Orbit PropertyOct 21 2018We show that a dynamical system with gluing orbit property and zero topological entropy is equicontinuous, hence it is topologically conjugate to a minimal rotation.

A New Bound on Hrushovski's Algorithm for Computing the Galois Group of a Linear Differential EquationMar 19 2018Feb 16 2019The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski's algorithm for computing the Galois group of a linear differential equation. This ... More

Rank $n$ swapping algebra for the $\operatorname{PSL}(n, \mathbb{R})$ Hitchin componentNov 11 2014Oct 24 2015F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce ... More

Virtual homological eigenvalue and mapping torus of pseudo-Anosov mapsAug 25 2016In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a finite cover which has a homological eigenvalue with modulus greater than $1$, then the monodromy of any fibered structure of any finite cover of $M_{\phi}$ has this property.

On Noether approach in the cosmological model with scalar and gauge fields: symmetries and the selection ruleApr 18 2015In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given ... More

Decomposition Theorem for Perverse sheaves on Artin stacks over finite fieldsSep 22 2010Mar 11 2012We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.