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State Transition AlgorithmMay 30 2012Dec 09 2013In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, ... More

A new transformation into State Transition Algorithm for finding the global minimumAug 01 2012To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization problems are used ... More

Initial Version of State Transition AlgorithmAug 01 2012Sep 12 2012In terms of the concepts of state and state transition, a new algorithm-State Transition Algorithm (STA) is proposed in order to probe into classical and intelligent optimization algorithms. On the basis of state and state transition, it becomes much ... More

Nonlinear system identification and control using state transition algorithmJun 04 2012Nov 17 2015By transforming identification and control for nonlinear system into optimization problems, a novel optimization method named state transition algorithm (STA) is introduced to solve the problems. In the proposed STA, a solution to a optimization problem ... More

On noncommutative distributional symmetries and de Finetti type theorems associated with themNov 18 2015We prove general de Finetti theorems for classical, free and boolean independence. Our general de Finetti theorems work for non-easy quantum groups, which generalizes a recent work of Banica, Curran and Speicher. For infinite sequences, we will determine ... More

Parallel Higher-order Boundary Integral Electrostatics Computation on Molecular Surfaces with Curved TriangulationJan 24 2013In this paper, we present a parallel higher-order boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace linear ... More

Fixed points of commutative Lüders operationsAug 18 2009Sep 14 2010This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming a resolution ... More

On Fixed Points of Lüders OperationJun 08 2009Sep 08 2009In this paper, we prove that if $\mathcal{A}=\{E_i\}_{i=1}^{n}$ is a finite commutative quantum measurement, then the fixed points set of L\"{u}ders operation $L_{{\cal A}}$ is the commutant ${\cal A}'$ of ${\cal A}$, the result answers an open problem ... More

On supremum of bounded quantum observableApr 25 2009Jun 05 2009In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our results have nice ... More

Delayed spin-up and persistent shift phenomena of Crab pulsar glitches: two sides of the same coin?Jun 28 2019Pulsar glitches are sudden increase in their spin frequency, in most cases followed by the long timescale recovery process. As of this writing, about 546 glitches have been reported in 188 pulsars, the Crab pulsar is a special one with unique manifestations. ... More

Distributed optimization with nonconvex velocity constraints, nonuniform position constraints and nonuniform stepsizesJun 14 2019This note is devoted to the distributed optimization problem of multi-agent systems with nonconvex velocity constraints, nonuniform position constraints and nonuniform stepsizes. Two distributed constrained algorithms with nonconvex velocity constraints ... More

Distributed Continuous-Time and Discrete-Time Optimization With Nonuniform Unbounded Convex Constraint Sets and Nonuniform StepsizesMar 27 2017Apr 12 2019This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are not required ... More

A Discrete State Transition Algorithm for Generalized Traveling Salesman ProblemApr 29 2013Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition algorithm (DSTA) for ... More

Distributed Continuous-Time and Discrete-Time Optimization With Nonuniform Unbounded Convex Constraint Sets and Nonuniform StepsizesMar 27 2017Jun 14 2019This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are not required ... More

Distributed Continuous-Time and Discrete-Time Optimization With Nonuniform Unbounded Convex Constraint Sets and Nonuniform StepsizesMar 27 2017Nov 21 2018This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are not required ... More

Categorization Problem on Controllability of Boolean Control NetworksApr 12 2019A Boolean control network (BCN) is a discrete-time dynamical system whose variables take values from a binary set $\{0,1\}$. At each time step, each variable of the BCN updates its value simultaneously according to a Boolean function which takes the state ... More

Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting timesSep 29 2016The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for a stochastic ... More

Numerical schemes of the time tempered fractional Feynman-Kac equationMay 13 2016This paper focuses on providing the computation methods for the backward time tempered fractional Feynman-Kac equation, being one of the models recently proposed in [Wu, Deng, and Barkai, Phys. Rev. E, 84 (2016) 032151]. The discretization for the tempered ... More

Multiresolution Galerkin method for solving the functional distribution of anomalous diffusion described by time-space fractional diffusion equationSep 09 2015The functional distributions of particle trajectories have wide applications, including the occupation time in half-space, the first passage time, and the maximal displacement, etc. The models discussed in this paper are for characterizing the distribution ... More

Applications of Wavelet Bases to The Numerical Solutions of Fractional PDEsMay 05 2015Oct 09 2016For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first order moment ... More

WSLD operators II: the new fourth order difference approximations for space Riemann-Liouville derivativeJun 25 2013High order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but for fractional ... More

Synchronization of Limit SetsOct 10 2005In this Letter, we derive a sufficient condition of synchronizing limit sets (attractors and repellers) by using the linear feedback control technique proposed here. There examples are included. The numerical simulations and computer graphics show that ... More

A Modified Version of Free Orbit-Dimension of von Neumann AlgebrasJan 05 2008Based on the notion of free orbit-dimension introduced by D. Hadwin and J. Shen [4], we introduce a new invariant on finite von Neumann algebras that do not necessarily act on separable Hilbert space. We show that this invariant is independent on the ... More

Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential EquationsJan 28 2012Feb 25 2012We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight ... More

The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\varepsilon (H)$Dec 03 2008Apr 22 2009A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$. We denote the set of all quantum effects by ${\cal E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\cal E}(H)$ which shows, ... More

Crossed Products and MF algebrasJan 19 2013We prove that the crossed product AxG of a unital finitely generated MF algebra A by a discrete finitely generated amenable residually finite group G is an MF algebra, provided that the action is almost periodic. This generalizes a result of Hadwin and ... More

Second order WSGD operators II: A new family of difference schemes for space fractional advection diffusion equationOct 29 2013The second order weighted and shifted Gr\"{u}nwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of second order ... More

Discretized fractional substantial calculusOct 11 2013This paper discusses the properties and the numerical discretizations of the fractional substantial integral $$I_s^\nu f(x)=\frac{1}{\Gamma(\nu)} \int_{a}^x{\left(x-\tau\right)^{\nu-1}}e^{-\sigma(x-\tau)}{f(\tau)}d\tau,\nu>0, $$ and the fractional substantial ... More

High order algorithms for the fractional substantial diffusion equation with truncated Lévy flightsJun 07 2014Aug 11 2014The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time random walk in ... More

Unitarity of the modular tensor categories associated to unitary vertex operator algebras, IIDec 13 2017Aug 27 2018This is the second half of a two-part series studying tensor categories of unitary vertex operator algebras from a unitary point of view.

Unitarity of the modular tensor categories associated to unitary vertex operator algebras, INov 08 2017Aug 27 2018This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).

Tracking Performance Limitations of MIMO Networked Control Systems with Multiple Communication ConstraintsApr 25 2019In this paper, the tracking performance limitation of networked control systems (NCSs) is studied. The NCSs is considered as continuous-time linear multi-input multi-output (MIMO) systems with random reference noises. The controlled plants include unstable ... More

Categorical extensions of conformal netsDec 11 2018Apr 07 2019An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct new structures ... More

Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebrasSep 19 2018Nov 25 2018The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$ affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by V.Toledano-Laredo for type $D$ ... More

Effect of in-medium mass-shift on transverse-momentum spectrum and elliptic anisotropy of $φ$ mesonMar 07 2019We study the effect of in-medium mass-shift on transverse-momentum spectrum and elliptic anisotropy of $\phi$ meson. It is found that the mass-shift improves the $\phi$ yields and suppresses the elliptic flow v2 in large momentum region, and the effect ... More

Robust supervised learning under uncertainty in dataset shiftNov 07 2016When machine learning is deployed in the real world, its performance can be significantly undermined because test data may follow a different distribution from training data. To build a reliable machine learning system in such a scenario, we propose a ... More

Coordination-based Medium Access Control with Space-reservation for Wireless Ad Hoc NetworksOct 19 2015Efficient radio spectrum utilization and low energy consumption in mobile devices are essential in developing next generation wireless networks. This paper presents a new medium access control (MAC) mechanism to enhance spectrum efficiency and reduce ... More

Second order finite difference approximations for the two-dimensional time-space Caputo-Riesz fractional diffusion equationJul 09 2012In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit ... More

Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshesOct 03 2014This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial discretization ... More

Remarks on the Sequential ProductsSep 14 2010In this paper, we show that those sequential products which were proposed by Liu and Shen and Wu in [J. Phys. A: Math. Theor. {\bf 42}, 185206 (2009), J. Phys. A: Math. Theor. {\bf 42}, 345203 (2009)] are just unitary equivalent to the sequential product ... More

An Elementary Proof of the Free-additivity of Voiculescu's Free EntropyFeb 03 2008D. Voiculescu [2] proved that a standard family of independent random unitary k by k matrices and a constant k by k unitary matrix is asymtotically free as k goes to infinity. This result was a key ingredient in Voiculescu's proof [3] that his free entropy ... More

Numerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal statesNov 12 2018Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distributions for different internal states, which describe the distribution ... More

Central local discontinuous Galerkin method for the space fractional diffusion equationOct 26 2018This paper provides the semi-discrete scheme by the central local discontinuous Galerkin method for space fractional diffusion equation on two sets of overlapping cells, and then we give the stability analysis and error estimates for the scheme. Lastly, ... More

Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivativeJan 16 2019Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723], which use convolution quadrature to approximate the Riemann-Liouville ... More

Worst-case Redundancy of Optimal Binary AIFV Codes and their Extended CodesJul 25 2016Jul 26 2016Binary AIFV codes are lossless codes that generalize the class of instantaneous FV codes. The code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain better compression ... More

DeepMetabolism: A Deep Learning System to Predict Phenotype from Genome SequencingMay 08 2017Life science is entering a new era of petabyte-level sequencing data. Converting such big data to biological insights represents a huge challenge for computational analysis. To this end, we developed DeepMetabolism, a biology-guided deep learning system ... More

Fourth order quasi-compact difference schemes for (tempered) space fractional diffusion equationsAug 27 2014The continuous time random walk (CTRW) underlies many fundamental processes in non-equilibrium statistical physics. When the jump length of CTRW obeys a power-law distribution, its corresponding Fokker-Planck equation has space fractional derivative, ... More

Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting timesSep 29 2016Dec 12 2016The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for a stochastic ... More

Langevin dynamics for Lévy walk with memoryOct 27 2018Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the stochastic process with ... More

A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion EquationsJan 28 2012Mar 07 2012A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations ... More

Positivity and boundedness preserving schemes for the fractional reaction-diffusion equationJan 14 2013In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes, and numerically ... More

Theory of relaxation dynamics for anomalous diffusion processes in harmonic potentialJul 04 2019Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and time-averaged mean ... More

Affine Combination of Two Adaptive Sparse Filters for Estimating Large Scale MIMO ChannelsJul 23 2014Large scale multiple-input multiple-output (MIMO) system is considered one of promising technologies for realizing next-generation wireless communication system (5G) to increasing the degrees of freedom in space and enhancing the link reliability while ... More

Parametrization of Tachyon FieldMar 22 2007We assume that universe is dominated by non-relativistic matter and tachyon field and reconstruct the potential of tachyon field directly from the effective equation of state (EOS) of dark energy. We apply the method to four known parametrization of equation ... More

Regularization Parameter Selection Method for Sign LMS with Reweighted L1-Norm Constriant AlgorithmMar 12 2015Apr 28 2015Broadband frequency-selective fading channels usually have the inherent sparse nature. By exploiting the sparsity, adaptive sparse channel estimation (ASCE) algorithms, e.g., least mean square with reweighted L1-norm constraint (LMS-RL1) algorithm, could ... More

Construction of Nth-order rogue wave solutions for Hirota equation by means of bilinear methodSep 23 2014In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of rogue waves are ... More

TFH Mixing Patterns, Large $θ_{13}$ and $Δ(96)$ Flavor SymmetryJan 16 2012Apr 25 2012We perform a comprehensive analysis of the Toorop-Feruglio-Hagedorn (TFH) mixing patterns within the family symmetry $\Delta(96)$. The general neutrino mass matrix for the TFH mixing and its symmetry properties are investigated. The possible realizations ... More

Symmetry of solutions of a mean field equation on flat toriMay 23 2016We study symmetry of solutions of the mean field equation \[ \Delta u +\rho(\frac{Ke^u}{\int_{T_\epsilon} Ke^u} -\frac{1}{|T_\epsilon|} )=0\] on the flat torus $T_\epsilon=[-\frac{1}{2\epsilon}, \frac{1}{2\epsilon}] \times [-\frac{1}{2}, \frac{1}{2}]$ ... More

On nonlocal systems with jump processes of finite range and with decaysJul 17 2018We study the following system of equations $$ L_i(u_i) = H_i(u_1,\cdots,u_m) \quad \text{in} \ \ \RR^n , $$ when $m\ge 1$, $u_i: \RR^n\to \RR$ and $H=(H_i)_{i=1}^m$ is a sequence of general nonlinearities. The nonlocal operator $L_i$ is given by $$L_i(f ... More

The ground state energy of the frustrated ferromagnetic spin chain near the transition pointApr 15 2011The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then is treated by ... More

The General Quantum Interference Principle and the Duality ComputerDec 15 2005May 10 2006In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. ... More

Uniqueness of solutions of mean field equations in $\R^2$Dec 26 2016May 11 2017In this paper, we prove uniqueness of solutions of mean field equations with general boundary conditions for the critical and subcritical total mass regime, extending the earlier results for null Dirichlet boundary condition. The proof is based on new ... More

Reconstructing the Equation of State for Dark Energy In the Double Complex Symmetric Gravitational TheoryMar 22 2007We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory (DCSGT). The universe we live in is taken as the real part of the whole spacetime ${\cal M}^4_C(J)$ which is double complex. By introducing ... More

Statefinder Parameters for Tachyon Dark Energy ModelMar 22 2007In this paper we study the statefinder parameters for the tachyon dark energy model. There are two kinds of stable attractor solutions in this model. The statefinder diagrams characterize the properties of the tachyon dark energy model. Our results show ... More

An Assumption About The Free Energy Near The Critical PointNov 29 2003Dec 04 2003We divide the free energy near the critical point into two parts. One is the regular part, the other is the singular part. The singular part is assumed to be a concrete possible form. The singular part in this form is different from Widom scaling hypothesis ... More

The origin of the unusual anisotropic electrical conductivity of Ba3Al2As4Feb 24 2014Mar 04 2015Ba3Al2As4 exhibits an unusual anisotropic electrical conductivity, that is, the electrical conductivity along the chain is smaller than those along other two directions which conflicts previous conclusion. Earlier studies on Ca5M2Pn6 showed a high electrical ... More

New explicit exact solutions for the Liénard equation and its applicationsMar 15 2010In this letter, new exact explicit solutions are obtained for the Li\'enard equation, and the applications of the results to the generalized Pochhammer-Chree equation, the Kundu equation and the generalized long-short wave resonance equations are presented. ... More

Meson Spectra from an Effective Light Cone QCD-Inspired ModelOct 31 2003I present some recent applications of a light cone QCD-inspired model with the mass squared operator consisting of a harmonic oscillator potential as confinement in the meson spectra. The model gives an universal and satisfactory description of both singlet ... More

Multidimensionally-constrained covariant density functional theories --- nuclear shapes and potential energy surfacesMay 03 2016May 23 2016The intrinsic nuclear shapes deviating from a sphere not only manifest themselves in nuclear collective states but also play important roles in determining nuclear potential energy surfaces (PES's) and fission barriers. In order to describe microscopically ... More

Gas-Liquid Phase Transition in Statistical MechanicsApr 28 2004Apr 30 2004A new theory on gas-liquid phase transition is given. The new idea is that the total intermolecular potential energy for a classical system in equilibrium is relative with the average distance of molecules. A new space homogeneity assumption is postulated, ... More

Comment on quant-ph/0506105: The modified Grover algorithm cannot speedup unsorted database searchJun 15 2005In a recent paper (quant-ph/0506105), A S Gupta, M. Gupta and A. Pathak proposed a modified Grover algorithm that would exponentially accelerate the unsorted database search problem if the number of marked items is known. If this were true, it would represent ... More

The single-ion anisotropy in LaFeAsOJan 04 2010We use Green's function method to study the Heisenberg model of LaFeAsO with the striped antiferromagnetic collinear spin structure. In addition to the intra-layer spin couplings $J_{1a},J_{1b},J_2$ and the inter-layer coupling $J_c$, we further consider ... More

On nodal solutions of a nonlocal Choquard equation in a bounded domainOct 13 2017In this paper, we are interested in the least energy nodal solutions to the following nonlocal Choquard equation with a local term \begin{equation*}\left\{\begin{array}{rll} -\Delta u&=\lambda|u|^{p-2}u+\mu \phi(x)|u|^{q-2}u\\ -\Delta \phi&=|u|^q\\ u&=\phi=0 ... More

Spectral Radii of Truncated Circular Unitary MatricesSep 16 2017Consider a truncated circular unitary matrix which is a $p_n$ by $p_n$ submatrix of an $n$ by $n$ circular unitary matrix by deleting the last $n-p_n$ columns and rows. Jiang and Qi (2017) proved that the maximum absolute value of the eigenvalues (known ... More

Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillatorFeb 21 2004The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and geometric phases. ... More

Dirac particles in a rotating magnetic fieldMar 04 2001We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a time-independent ... More

On the partial wave amplitude of Coulomb scattering in three dimensionsOct 22 2000The partial wave series for the Coulomb scattering amplitude in three dimensions is evaluated in a very simple way to give the closed result.

Levinson theorem for Dirac particles in two dimensionsJun 23 1998The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2, \pm 3/2, ... ... More

The Tricomi EquationNov 13 2013Jul 25 2015The Tricomi equation is a second-order partial differential equation of mixed elliptic-hyperbolic type. It was first analyzed in the work by Francesco Giacomo Tricomi (1923) on the well-posedness of a boundary value problem. The Tricomi equation can be ... More

Improved Channel Estimation with Partial Sparse Constraint for AF Cooperative Communication SystemsJul 30 2012Accurate channel state information (CSI) is necessary for coherent detection in amplify and forward (AF) broadband cooperative communication systems. Based on the assumption of ordinary sparse channel, efficient sparse channel estimation methods have ... More

Further study on periodic solutions of elliptic equations with a fractional LaplacianOct 13 2017Oct 19 2018We obtain some existence theorems for periodic solutions to several linear equations involving fractional Laplacian. We also prove that the lower bound of all periods for semilinear elliptic equations involving fractional Laplacian is not larger than ... More

Bound States of the Heavy Flavor Vector Mesons and Y(4008) and $Z^{+}_1(4050)$May 08 2009Sep 12 2009The $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. ... More

Are Y(4260) and {\rm Z$_2^{+}$(4250)} ${\rm D_1D}$ or ${\rm D_0D^{*}}$ Hadronic Molecules?Sep 28 2008Nov 28 2008In this work, we have investigated whether Y(4260) and ${\rm Z^{+}_2(4250)}$ could be ${\rm D_1D}$ or ${\rm D_0D^{*}}$ molecules in the framework of meson exchange model. The off-diagonal interaction induced by $\pi$ exchange plays a dominant role. The ... More

Understanding the Charged Meson Z(4430)Nov 09 2007Nov 26 2007The difference between Z(4430) as a $D^{*}D_1$ molecule and a tetraquark state and how to distinguish between them are discussed. We construct an effective Lagrangian with $D^{*}D_1$ contact interactions constrained by the heavy quark symmetry and chiral ... More

Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor SymmetryJun 24 2010Jan 19 2011We construct a supersymmetric (SUSY) $SU(5)$ model with the flavor symmetry $S_4\times Z_3\times Z_4$. Three generations of adjoint matter fields are introduced to generate the neutrino masses via the combined type I and type III see-saw mechanism. The ... More

Fermion Masses and Flavor Mixings in a Model with $S_4$ Flavor SymmetrySep 11 2009Nov 27 2009We present a supersymmetric model of quark and lepton based on $S_4\times Z_3\times Z_4$ flavor symmetry. The $S_4$ symmetry is broken down to Klein four and $Z_3$ subgroups in the neutrino and the charged lepton sectors respectively. Tri-Bimaximal mixing ... More

Possible Molecular States of $D^{*}_s\bar{D}^{*}_s$ System and Y(4140)Apr 11 2009Sep 12 2009The interpretation of Y(4140) as a $D^{*}_s\bar{D}^{*}_s$ molecule is studied dynamically in the one boson exchange approach, where $\sigma$, $\eta$ and $\phi$ exchange are included. Ten allowed $D^{*}_s\bar{D}^{*}_s$ states with low spin parity are considered, ... More

Mathematical Theory of the Duality Computer in the Density Matrix FormalismMay 09 2006Feb 28 2007We give the mathematical theory of duality computer in the density matrix formalism. This result complements the mathematical theory of duality computer of Gudder in the pure state formalism.

Latest Progresses in Developing Wearable Monitoring and Therapy Systems for Managing Chronic DiseasesFeb 06 2018Chronic disease is a long-lasting condition that can be controlled but not cured. Owing to the portability and continuous action, wearable devices are regarded as promising ways for management and rehabilitation of patients with chronic diseases. Although ... More

Towards Faster Rates and Oracle Property for Low-Rank Matrix EstimationMay 18 2015Jul 06 2015We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we ... More

Schauder estimates on smooth and singular spacesMar 14 2018In this paper, we present a proof of Schauder estimate on Euclidean space and use it to generalize Donaldson's Schauder estimate on space with conical singularities in the following two directions. The first is that we allow the total cone angle to be ... More

Rediscussion on gas-liquid phase transitionApr 28 2004Apr 30 2004Liquid-gas phase transition in statistical mechanics is a long-standing dilemma not yet well explained. In this paper we propose a novel approach to this dilemma, by: 1). Putting forth a new space homogeneity assumption. 2). Giving a new formulation-- ... More

Global Finite-Time Attitude Tracking via Quaternion FeedbackFeb 21 2016Sep 23 2016This paper addresses the attitude tracking of a rigid body using a quaternion description. Global finite-time attitude controllers are designed with three types of measurements, namely, full states, attitude plus constant-biased angular velocity, and ... More

Global well-posedness of the 2-D incompressible Navier-Stokes-Cahn-Hilliard system with a singular free energy densityOct 30 2018Nov 16 2018This paper would focus on the subject of the 2-D incompressible Navier-Stokes-Cahn-Hilliard (NS-CH) system with a singular free energy density. Due to lack of the maximum principle for the convective Cahn-Hilliard equation (as a fourth-order parabolic ... More

The Sphere Covering Inequality and Its ApplicationsMay 20 2016Oct 27 2016In this paper, we show that the total area of two distinct surfaces with Gaussian curvature equal to 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least 4{\pi}. In other words, the areas ... More

Fermion Mass Hierarchies and Flavor Mixing from $T'$ SymmetryMar 15 2008Aug 11 2008We construct a supersymmetric model based on $T'\otimes Z_3\otimes Z_9$ flavor symmetry. At the leading order, the charged lepton mass matrix is not diagonal, $T'$ is broken completely, and the hierarchy in the charged lepton masses is generated naturally. ... More

Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn EquationsApr 16 2019In this paper we study stable solutions to the fractional equation \begin{align} (-\Delta)^s u =f(u), \quad |u| < 1 \quad \mbox{in $\mathbb{R}^d$}, \end{align}where $0<s<1$ and $f:[-1,1] \rightarrow \mathbb{R}$ is a $C^{1,\alpha}$ function for $\alpha>\max\{0, ... More

Modification to the Van der Waals Equation of StateFeb 08 2004In this paper, we modify the VDW equation of state by adding a temperature factor to it. As a result, we give out a good phase diagram and the correlation of the reduced pressure and the reduced temperature when a balanced liquid-gas coexistence canonical ... More

Achieving competitive advantage in academia through early career coauthorship with top scientistsJun 11 2019We quantify the long term impact that the coauthorship with established top-cited scientists has on the career of junior researchers in four different scientific disciplines. Through matched pair analysis, we find that junior researchers who coauthor ... More

Study of axial strain induced torsion of single wall carbon nanotubes by 2D continuum anharmonic anisotropic elastic modelJul 15 2009Recent molecular dynamic simulations have found chiral single wall carbon nanotubes (SWNTs) twist during stretching, which is similar to the motion of a screw. Obviously this phenomenon, as a type of curvature-chirality effect, can not be explained by ... More