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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

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

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

A kind of conditional connectivity of transposition networks generated by $k$-treesAug 09 2017For a graph $G = (V, E)$, a subset $F\subset V(G)$ is called an $R_k$-vertex-cut of $G$ if $G -F$ is disconnected and each vertex $u \in V(G)- F$ has at least $k$ neighbors in $G -F$. The $R_k$-vertex-connectivity of $G$, denoted by $\kappa^k(G)$, is ... 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

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

A GPU-accelerated Direct-sum Boundary Integral Poisson-Boltzmann SolverJan 24 2013In this paper, we present a GPU-accelerated direct-sum 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 based ... More

Reliability evaluation of folded hypercubes in terms of component connectivityMar 04 2018The component connectivity is the generalization of connectivity which is an parameter for the reliability evaluation of interconnection networks. The $g$-component connectivity $c\kappa_{g}(G)$ of a non-complete connected graph $G$ is the minimum number ... More

On the existence of specified cycles in bipartite tournamentsJun 20 2017For two integers $n\geq 3$ and $2\leq p\leq n$, we denote $D(n,p)$ the digraph obtained from a directed $n$-cycle by changing the orientations of $p-1$ consecutive arcs. In this paper, we show that a family of $k$-regular $(k\geq 3)$ bipartite tournament ... More

The Turán problem for a family of tight linear forestsDec 05 2018Dec 10 2018Let $\mathcal{F}$ be a family of $r$-graphs. The Tur\'an number $ex_r(n;\mathcal{F})$ is defined to be the maximum number of edges in an $r$-graph of order $n$ that is $\mathcal{F}$-free. The famous Erd\H{o}s Matching Conjecture shows that \[ ex_r(n,M_{k+1}^{(r)})= ... 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

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 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

Turing-Hopf bifurcation and spatiotemporal patterns in a ratio-dependent diffusive Holling-Tanner system with time delayFeb 28 2018The Turing-Hopf type spatiotemporal patterns in a diffusive Holling-Tanner model with discrete time delay is considered. A global Turing bifurcation theorem for $\tau=0$ and a local Turing bifurcation theorem for $\tau>0$ are given by the method of eigenvalue ... 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

Vertex-disjoint cycles in tournamentsJun 02 2017May 03 2018The Bermond-Thomassen conjecture states that, for any positive integer $r$, a digraph of minimum out-degree at least $2r-1$ contains at least $r$ vertex-disjoint directed cycles. Bessy, Sereni and Lichiardopol proved that a regular tournament $T$ of minimum ... More

Ergodic Properties of Fractional Brownian-Langevin MotionSep 15 2008We investigate the time average mean square displacement $\overline{\delta^2}(x(t))=\int_0^{t-\Delta}[x(t^\prime+\Delta)-x(t^\prime)]^2 dt^\prime/(t-\Delta)$ for fractional Brownian and Langevin motion. Unlike the previously investigated continuous time ... More

Nonresonant Hopf-Hopf bifurcation and a chaotic attractor in neutral functional differential equationsFeb 03 2014Nonresonant Hopf-Hopf singularity in neutral functional differential equation (NFDE) is considered. An algorithm for calculating the third-order normal form is established by using the formal adjoint theory, center manifold theorem and the traditional ... More

Levy walk with multiple internal statesDec 19 2017Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for dealing with the ... 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

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

The State Space of Perturbative Quantum Field Theory in Curved SpacetimesAug 09 2001The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains the Wick-polynomials ... More

A Note on Approximately Divisible C$^*$-algebrasApr 03 2008Apr 21 2008Let $\mathcal A$ be a separable, unital, approximately divisible C$^*$-algebra. We show that $\mathcal A$ is generated by two self-adjoint elements and the topological free entropy dimension of any finite generating set of $\mathcal A$ is less than or ... More

High order schemes for the tempered fractional diffusion equationsFeb 01 2014Sep 25 2014L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes which combine ... 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

A Note on Approximate LiftingsApr 09 2008In this paper, we prove approximate lifting results in the C$^{\ast}$-algebra and von Neumann algebra settings. In the C$^{\ast}$-algebra setting, we show that two (weakly) semiprojective unital C*-algebras, each generated by $n$ projections, can be glued ... More

Spontaneous polygonization of multi-walled carbon nanotubes: perturbation analysisAug 08 2011Spontaneous polygonization for a multi-walled carbon nanotubes (MWCNTs) have been observed for about two decades. In present manuscript, this phenomenon is understood by the competition between cohesion energy (with lattice mismatching effect) and curvature ... More

Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in $\Er^2$Feb 19 2011In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed.

Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two DimensionsFeb 19 2011In this paper, we prove even symmetry and monotonicity of certain solutions of Allen-Cahn equation in a half plane. We also show that entire solutions with {\it finite Morse index} and {\it four ends} must be evenly symmetric with respect to two orthogonal ... More

Electronic Conduction in Short DNA WiresDec 11 2002Dec 29 2005A strict method is used to calculate the current-voltage characteristics of a double-stranded DNA. A more reliable model considering the electrostatic potential drop along an individual DNA molecular wire between the contacts is considered and the corresponding ... More

Empirical Bayes methods for controlling the false discovery rate with dependent dataAug 07 2007False discovery rate (FDR) has been widely used as an error measure in large scale multiple testing problems, but most research in the area has been focused on procedures for controlling the FDR based on independent test statistics or the properties of ... 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

From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equationSep 19 2010The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful. However, what are the sufficient and necessary ... More

Quantum Observable Generalized OrthoalgebrasAug 29 2015Oct 12 2016Given a Hilbert space $\mathcal{H}$, we introduce a binary relation $\bot$ between two self-adjoint operators $A$ and $B$. We show that if $A\bot B$, then $A$ and $B$ are affiliated with some abelian von Neumann algebra. We prove that the relation $\bot$ ... 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

Models for characterizing the transition among anomalous diffusions with different diffusion exponentsFeb 05 2018Aug 16 2018Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take the waiting ... 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

Locating any two vertices on Hamiltonian cyclesAug 01 2017In this paper we give a proof of Enomoto's conjecture for graphs of sufficiently large order. Enomoto's conjecture states that, if $G$ is a graph of order $n$ with minimum degree $\delta(G)\geq \frac{n}{2}+1$, then for any pair of vertices $x$, $y$ in ... More

Squeezed back-to-back correlations of $K^+$$K^-$ in d+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Au+Au collisions at $\sqrt{s_{NN}}=62.4$ GeVSep 10 2018Feb 24 2019We investigate the squeezed back-to-back correlations (BBC) of $K^+$$K^-$, caused by the mass modification of the particle in the dense medium formed in d+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Au+Au collisions at $\sqrt{s_{NN}}=62.4$ GeV. Considering ... More

Localized plasmons in bilayer graphene nanodisksFeb 04 2016We study localized plasmonic excitations in bilayer graphene (BLG) nanodisks, comparing AA-stacked and AB-stacked BLG and contrasting the results to the case of two monolayers without electronic hybridization. The electrodynamic response of the BLG electron ... 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

On the number of proper paths between vertices in edge-colored hypercubesAug 09 2017Given an integer $1\leq j <n$, define the $(j)$-coloring of a $n$-dimensional hypercube $H_{n}$ to be the $2$-coloring of the edges of $H_{n}$ in which all edges in dimension $i$, $1\leq i \leq j$, have color $1$ and all other edges have color $2$. Cheng ... 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

Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^{s}$Sep 10 2010Feb 10 2012We consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation $i \partial_{t}u+ \Delta u=\lambda_{0}u+\lambda_{1}|u|^\alpha u$ in $\mathbb{R}^{N}$, where $\lambda_{0},\lambda_{1}\in\mathbb{C}$, in $H^s$ subcritical and critical case: $0<\alpha\leq\frac{4}{N-2s}$ ... More

A note on edge degree and spanning trail containing given edgesJun 22 2017Let $G$ be a simple graph with $n\geq4$ vertices and $d(x)+d(y)\geq n+k$ for each edge $xy\in E(G)$. In this work we prove that $G$ either contains a spanning closed trail containing any given edge set $X$ if $|X|\leq k$, or $G$ is a well characterized ... More

On the spanning connectivity of tournamentsJun 15 2017Let $D$ be a digraph. A $k$-container of $D$ between $u$ and $v$, $C(u,v)$, is a set of $k$ internally disjoint paths between $u$ and $v$. A $k$-container $C(u,v)$ of $D$ is a strong (resp. weak) $k^{*}$-container if there is a set of $k$ internally disjoint ... More

Numerical algorithms for the forward and backward fractional Feynman-Kac equationsJan 03 2014The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a Schr\"{o}dinger ... More

Formulation of the normal forms of Turing-Hopf bifurcation in reaction-diffusion systems with time delayFeb 28 2018The normal forms up to the third order for a Hopf-steady state bifurcation of a general system of partial functional differential equations (PFDEs) is derived based on the center manifold and normal form theory of PFDEs. This is a codimension-two degenerate ... 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

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

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

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

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

Wavelet Galerkin method for fractional elliptic differential equationsMay 27 2014Under the guidance of the general theory developed for classical partial differential equations (PDEs), we investigate the Riesz bases of wavelets in the spaces where fractional PDEs usually work, and their applications in numerically solving fractional ... 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

Weak Continuity and Compactness for Nonlinear Partial Differential EquationsAug 08 2014Jul 24 2015We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on the compactness ... 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

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

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

Bound states of neutral particles in external electric fieldsJan 11 2000Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be reduced to ... More

Geometric phases for wave packets in a uniform magnetic fieldJun 06 2002A wave packet of a charged particle always make cyclic circular motion in a uniform magnetic field, just like a classical particle. The nonadiabatic geometric phase for an arbitrary wave packet can be expressed in terms of the mean value of a number operator. ... More

Geometric phases for neutral and charged particles in a time-dependent magnetic fieldJan 08 2002It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, ... More

Scattering by a contact potential in three and lower dimensionsMar 04 2001We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives ... More

Vacuum polarization for neutral particles in 2+1 dimensionsFeb 22 2000In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric ... More

Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensionsMay 07 1999We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton solutions, ... 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

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

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

Non-axially symmetric solutions of a mean field equation on $\mathbb{S}^2$Sep 07 2017We prove the existence of a family of blow-up solutions of a mean field equation on sphere. The solutions blow up at four points where the minimum value of a potential energy function (involving the Green's function) is attained. The four blow-up points ... 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

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 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

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

Anisotropic harmonic oscillator in a static electromagnetic fieldDec 06 2002Dec 19 2002A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger equation is solved ... More

Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensionsJul 27 2000The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. The scattering problem for such two-body systems is ... 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

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.

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

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

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