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Second-order Stable Finite Difference Schemes for the Time-fractional Diffusion-wave EquationJul 20 2014Nov 08 2014We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and the central ... More

On the analysis of mixed-index time fractional differential equation systemsSep 05 2017In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system ... More

A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equationsApr 26 2019In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using tensor product ... More

A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equationsApr 16 2019The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this work, a second-order ... More

Fractional differentiation matrices with applicationsApr 17 2014Nov 04 2015In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices are investigated ... More

Optimal order finite element approximations for variable-order time-fractional diffusion equationsMay 14 2019We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order accuracy in space) ... More

A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equationsAug 07 2018Aug 11 2018We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters. Subsequently, ... More

Implicit-Explicit difference schemes for nonlinear fractional differential equations with non-smooth solutionsAug 02 2016We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order $0<\beta<1$. From the known structure of the non-smooth solution and by introducing corresponding correction terms, ... More

Efficient multistep methods for tempered fractional calculus: Algorithms and SimulationsDec 03 2018Dec 08 2018In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative operator is interpreted ... More

A Novel Block-DCT and PCA Based Image Perceptual Hashing AlgorithmJun 18 2013Image perceptual hashing finds applications in content indexing, large-scale image database management, certification and authentication and digital watermarking. We propose a Block-DCT and PCA based image perceptual hash in this article and explore the ... More

About Stability of Irreducibility for Germs of Holomorphic FunctionsApr 11 2005This survey is about irreducibility for germs of a holomorphic functions $f$. I will show that when the dimension of the domain $U$ of this holomorphic function $f$ is greater than 2, the irreducibility of germs are not necessary to be stable. That means, ... More

Derived categories and Calabi-Yau algebrasNov 23 2017We show that for two derived equivalent algebras, if one is Calabi-Yau, so is the other.

A Topic Modeling Toolbox Using Belief PropagationJan 04 2012Apr 05 2012Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This ... More

Sample-based Population ObserversNov 29 2017In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is established. The results ... More

An IMU-Aided Carrier-Phase Differential GPS Positioning SystemJun 05 2012We consider the problem of carrier-phase differential GPS positioning for an land vehicle navigation system (LVNS), tightly coupled with an inertial measurement unit (IMU) and a speedometer. The primary focus is to apply Bayesian network to an IMU-aided ... More

Poincaré type inequalities for group measure spaces and related transportation cost inequalitiesJun 25 2013Nov 15 2013Let $G$ be a countable discrete group with an orthogonal representation $\alpha$ on a real Hilbert space $H$. We prove $L_p$ Poincar\'e inequalities for the group measure space $L_\infty(\Omega_H,\gamma)\rtimes G$, where both the group action and the ... More

How Vertex reinforced jump process arises naturallyNov 11 2013Nov 05 2015We prove that the only nearest neighbor jump process with local dependence on the occupation times satisfying the partial exchangeability property is the vertex reinforced jump process, under some technical conditions. This result gives a counterpart ... More

A Russo Seymour Welsh Theorem for critical site percolation on \(\mathbb{Z}^2\)Sep 09 2013The Russo-Seymour-Welsh Theorem for Z^2 bond or T (triangular lattice) site percolation states that at criticality, for all fixed real {\lambda}, the probability of the existence of a horizontal occupied crossing of each rectangle with size n*{\lambda}n ... More

A general approach to enhance slope limiters on non-uniform rectilinear gridsJan 06 2013May 20 2014Most slope limiter functions in high-resolution finite volume methods to solve hyperbolic conservation laws are designed assuming one-dimensional uniform grids, and they are also used to compute slope limiters in computations on non-uniform rectilinear ... More

Artificial Persuasion in Pedagogical GamesJan 23 2016A Persuasive Teachable Agent (PTA) is a special type of Teachable Agent which incorporates a persuasion theory in order to provide persuasive and more personalized feedback to the student. By employing the persuasion techniques, the PTA seeks to maintain ... More

Cylindrically Symmetric Ground State Solutions for Curl-Curl Equations with Critical ExponentSep 30 2016We study the following nonlinear critical curl-curl equation \begin{equation}\label{eq0.1}\nabla\times \nabla\times U +V(x)U=|U|^{p-2}U+ |U|^4U,\quad x\in \mathbb{R}^3,\end{equation} where $V(x)=V(r, x_3)$ with $r=\sqrt{x_1^2+x_2^2}$ is 1-periodic in ... More

Criterion for rays landing togetherMar 19 2015Let $f$ be a polynomial with degree $\geq 2$ and the Julia set $J_f$ locally connected. We give a partition of complex plane $\mathbb{C}$ and show that, if $z$, $z'$ in $J_f$ have the same itineriary respect to the partition, then either $z=z'$ or both ... More

Unitary representations of the extended affine Lie algebra $\widetilde{\frak{gl}_{3}(\bc_q)}$Jan 18 2006We present modules for the extended affine Lie algebra $\widetilde{\frak{gl}_{3}(\bc_q)}$ by using the idea of free fields. A necessary and sufficient condition for the modules being unitary is given.

Notes On Hilbert's 12th ProblemMay 03 2006In this note we will study the Hilbert 12th problem for a primitive CM field, and the corresponding Stark conjectures. Using the idea of Mirror Symmetry, we will show how to generate all the class fields of a given primitive CM field, thus complete the ... More

An expansion formula for the inversions and excedances in the symmetric groupJun 15 2012We prove a recent conjecture of Blanco and Petersen (arXiv:1206.0803v2) about an expansion formula for inversions and excedances in the symmetric group.

Cylindrically Symmetric Ground State Solutions for Curl-Curl Equations with Critical ExponentSep 30 2016Dec 14 2017We study the following nonlinear critical curl-curl equation \begin{equation}\label{eq0.1}\nabla\times \nabla\times U +V(x)U=|U|^{p-2}U+ |U|^4U,\quad x\in \mathbb{R}^3,\end{equation} where $V(x)=V(r, x_3)$ with $r=\sqrt{x_1^2+x_2^2}$ is 1-periodic in ... More

A hybrid FD-FV method for first-order hyperbolic conservation laws on Cartesian grids: The smooth problem caseDec 21 2012Nov 28 2016We present a class of hybrid FD-FV (finite difference and finite volume) methods for solving general hyperbolic conservation laws written in first-order form. The presentation focuses on one- and two-dimensional Cartesian grids; however, the generalization ... More

A simple eavesdropping strategy of BB84 protocolDec 22 1998A simplified eavesdropping-strategy for BB84 protocol in quantum cryptography (refer to quant-ph/9812022) is proposed. This scheme implements by the `indirect copying' technology. Under this scheme, eavesdropper can exactly obtain the exchanged information ... More

A hybrid finite difference--finite volume approach to solve first-order hyperbolic conservation laws with superior accuracyDec 21 2012A hybrid finite difference--finite volume (FD-FV) approach for discretization in space is proposed to solve first-order hyperbolic conservation laws. Unlike any conventional finite difference method (FDM) or finite volume method (FVM), this approach uses ... More

Drell-Yan process with jet vetoes: breaking of generalized factorizationJul 07 2015Oct 29 2015Resummation of hadron collision cross sections, when the measurement imposes a hierarchy of scales, relies on factorization. Cancellation of Glauber / Coulomb gluons is a necessary condition for factorization. For Drell-Yan-like processes, the known proofs ... More

Inferring network topology via the propagation processNov 20 2013Inferring the network topology from the dynamics is a fundamental problem with wide applications in geology, biology and even counter-terrorism. Based on the propagation process, we present a simple method to uncover the network topology. The numerical ... More

Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical VacuumOct 30 2014For the physical vacuum free boundary problem with the sound speed being $C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous near vacuum boundaries of the three-dimensional compressible Euler equations with damping, the global existence of spherically symmetric ... More

Resource Sharing for Multi-Tenant NoSQL Data Store in CloudJan 05 2016Multi-tenancy hosting of users in cloud NoSQL data stores is favored by cloud providers because it enables resource sharing at low operating cost. Multi-tenancy takes several forms depending on whether the back-end file system is a local file system (LFS) ... More

Fast Optimal Joint Tracking-Registration for Multi-Sensor SystemsMay 09 2012Sensor fusion of multiple sources plays an important role in vehicular systems to achieve refined target position and velocity estimates. In this article, we address the general registration problem, which is a key module for a fusion system to accurately ... More

Estimating Rigid Transformation Between Two Range Maps Using Expectation Maximization AlgorithmMar 31 2012We address the problem of estimating a rigid transformation between two point sets, which is a key module for target tracking system using Light Detection And Ranging (LiDAR). A fast implementation of Expectation-maximization (EM) algorithm is presented ... More

Decomposition of Cartan Matrix and conjectures on Brauer character degreesJul 24 2007Oct 20 2008Let $G$ be a finite group and $N$ be a normal subgroup of $G$. Let $J=J(F[N])$ denote the Jacboson radical of $F[N]$ and $I={\rm Ann}(J)=\{\alpha \in F[G]|J\alpha =0\}$. We have another algebra $F[G]/I$. We study the decomposition of Cartan matrix of ... More

Analytic Center Cutting Plane Methods for Variational Inequalities over Convex BodiesJun 12 2017Oct 31 2017An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational inequalities whose ... More

$μ$- Integrable Functions and Weak Convergence of Finite MeasuresSep 14 2017Nov 16 2018This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.

Models of Quantum Algorithms in Sets and RelationsMar 19 2015Jul 19 2015We construct abstract models of blackbox quantum algorithms using a model of quantum computation in sets and relations, a setting that is usually considered for nondeterministic classical computation. This alternative model of quantum computation (QCRel), ... More

Chern-Simons Theory of Fractional Quantum Hall Effect in (Pseudo) Massless Dirac ElectronsSep 01 2011We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be $\sigma_{xy}=\frac{e^2}{h}(2k-1)$ ... More

Kolmogorov's law of the iterated logarithm for noncommutative martingalesDec 06 2012Jan 20 2014We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout. The key ingredient is an exponential inequality proved recently by Junge and the author.

Linear characters and block algebraMar 01 2011This paper will prove that: 1. $G$ has a block only having linear ordinary characters if and only if $G$ is a $p$-nilpotent group with an abelian Sylow $p$-subgroup; 2. $G$ has a block only having linear Brauer characters if and only if $O_{p'}(G)\leq ... More

The Abstract Structure of Quantum AlgorithmsDec 26 2015Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances foundations ... More

Computing points on modular curves over finite fieldsMay 20 2013In this paper, we present a probabilistic algorithm to compute the number of $\mathbb{F}_p$-points of modular curve $X_1(n)$. Under the Generalized Riemann Hypothesis(GRH), the algorithm takes $\textrm{O}(n^{56+\delta+\epsilon}\log^{9+\epsilon} p)$ bit ... More

The Gaps of Consecutive Eigenvalues of Laplacian on Riemannian ManifoldsJun 08 2016In this paper, we investigate the Dirichlet problem of Laplacian on complete Riemannian manifolds. By constructing new trial functions, we obtain a sharp upper bound of the gap of the consecutive eigenvalues in the sense of the order, which affirmatively ... More

Warasian Economic Equilibrium Problems in Convex RegionsJun 16 2017Nov 23 2017We define Walrasian economic equilibrium in convex regions. We introduce the definition of strict-proper quasimonotone functions, and derive some necessary and sufficient conditions for the existence and uniqueness of Walrasian equilibrium vectors in ... More

Infinite solutions having a prescribed number of nodes for a p-Laplacian problemNov 28 2014In this paper, we are concern with the multiplicity of solutions for a p-Laplacian problem. A weaker super-quadratic assumptions is required on the nonlinearity. Under the weaker condition we give a new proof for the infinite solutions having a prescribed ... More

On some $q$-identities related to divisor functionsJun 16 2004We give generalizations and simple proofs of some $q$-identities of Dilcher, Fu and Lascoux related to divisor functions.

Upper Bound Estimates for Eigenvalues of the Poly-LaplacianJul 19 2013May 12 2016In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of Differential Equations, ... More

Likelihood approach for marginal proportional hazards regression in the presence of dependent censoringMay 27 2005In many public health problems, an important goal is to identify the effect of some treatment/intervention on the risk of failure for the whole population. A marginal proportional hazards regression model is often used to analyze such an effect. When ... More

Estimating marginal survival function by adjusting for dependent censoring using many covariatesSep 10 2004Oct 05 2004One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric ... More

A Class of Irreducible Modules for the Extended Affine Lie Algebra $\widetilde{\frak{gl}_l({\mathbb{C}_q})}$Apr 07 2009We construct a class of modules for extended affine Lie algebra $\widetilde{\frak{gl}_l({\bc_q})}$ by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.

Saddle-point theorems for the generalized cone-convex optimizations of set-valued functionsSep 14 2017This paper works with preconvexlike set-valued vector optimization problems in topological linear spaces. A Fakas-Minkowski alternative theorem, a scalarization theorem, some vector saddle-point theorems and some scalar saddle point theorem are proved. ... More

Lagrangian Multipliers for Presubconvexlike Optimization Problems of Set Valued FunctionsJun 12 2017In this paper, we discuss scalar Lagrangian multipliers and vector Lagrangian multipliers for constrained set-valued optimization problems. We obtain some necessary conditions, sufficient conditions, as well as necessary and sufficient conditions for ... More

Improvement of quantum key distribution protocolsOct 07 1998The security of the previous quantum key distribution protocols, which is guaranteed by the nature of physics law, is based on the legitimate users. However, the impersonation of Alice or Bob by eavesdropper, in practice. will be existed in a large probability. ... More

Quantum key distribution based on Greenberger-Horne-Zeilinger stateJan 13 2000An unsymmetrical quantum key distribution scheme is proposed, its security is guaranteed by the correlation of the Greenberger-Horne-Zeilinger triplet state. In the proposed protocol, the distribution of quantum states are unsymmetrical. This unsymmetrical ... More

Finite W-superalgebras for basic classical Lie superalgebrasApr 04 2014May 11 2014We consider the finite W-superalgebras for a basic classical Lie superalgebra g associated with an even nilpotent element in g both over the field of complex numbers field and and over a filed of positive characteristic. We present the PBW theorem for ... More

ExtraPush for Convex Smooth Decentralized Optimization over Directed NetworksNov 10 2015Sep 13 2016In this note, we extend the algorithms Extra and subgradient-push to a new algorithm ExtraPush for consensus optimization with convex differentiable objective functions over a directed network. When the stationary distribution of the network can be computed ... More

Object Manipulation Learning by ImitationMar 03 2016Nov 19 2017We aim to enable robot to learn object manipulation by imitation. Given external observations of demonstrations on object manipulations, we believe that two underlying problems to address in learning by imitation is 1) segment a given demonstration into ... More

An Exact Hairy Black Hole Solution for AdS/CFT SuperconductorsMar 15 2009Aug 30 2009We provide an exact hairy black hole solution to an $n+1$ dimensional complex scalar field model coupled with gravity. The model is characterized by a potential with one parameter. Depending on the magnitude of this parameter, the effective mass square ... More

Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 modelApr 30 2015Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able to capture ... More

Distribution of crossings, nestings and alignments of two edges in matchings and partitionsJan 04 2006We construct an involution on set partitions which keeps track of the numbers of crossings, nestings and alignments of two edges. We derive then the symmetric distribution of the numbers of crossings and nestings in partitions, which generalizes Klazar's ... More

Combinatorics of $(q,y)$-Laguerre polynomialsJan 03 2019We consider a $(q,y)$-analogue of Laguerre polynomials $L^{(\alpha)}_n(x)$ with integral $\alpha\geq -1$, which turns out to be a rescaled version Al-Salam-Chihara polynomials. A combinatorial interpretation for the $(q,y)$-Laguerre polynomials $L^{(\alpha)}_n(x;y;q)$ ... More

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear latticesJun 08 2017The nonlinear lattice---a new and nonlinear class of periodic potentials---was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse ... More

On Nonconvex Decentralized Gradient DescentAug 20 2016Jan 26 2018Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for {convex} consensus optimization. However, to the behaviors or consensus \emph{nonconvex} optimization, our understanding ... More

Non-recurrent parameter rays of the Mandelbrot setDec 26 2015In this paper, we prove that any parameter ray at a non-recurrent angle $\theta$ lands at a non-recurrent parameter $c$ with $\theta$ a characteristic angle of $f_c$; and conversely, every non-recurrent parameter $c$ is the landing point of one or two ... More

Some new identities for Schur functionsOct 26 2000Some new identities for Schur functions are proved. In particular, we settle in the affirmative a recent conjecture of Ishikawa-Wakayama and solve a problem raised by Bressoud.

Generalisation de formules de type WaringApr 10 2000We evaluate the symmetric functions $e_k$, $h_k$ and $p_k$ on the alphabet $\{x_r/(1-tx_r)\}$ by elementary methods and give the related generating functions. Our formulas lead to a new and short proof of an ex-conjecture of Lassalle, which was proved ... More

Ground state, collective mode, phase soliton and vortex in multiband superconductorsAug 25 2014Nov 15 2014This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these ... More

An informationally-complete unification of quantum spacetime and matterDec 05 2014Jan 01 2019It was known long ago that quantum theory and general relativity, two pillars of modern physics, are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in ... More

The informationally-complete quantum theoryDec 02 2014Jan 01 2019Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum mechanics. What ... More

The $γ$-positivity of basic Eulerian polynomials via group actionsNov 12 2014Apr 30 2015We provide combinatorial interpretation for the $\gamma$-coefficients of the basic Eulerian polynomials that enumerate permutations by the excedance statistic and the major index as well as the corresponding $\gamma$-coefficients for derangements. Our ... More

Bäcklund transformations for the KP and mKP hierarchies with self-consistent sourcesOct 12 2005Using gauge transformations for the corresponding generating pseudo-differential operators $L^n$ in terms of eigenfunctions and adjoint eigenfunctions, we construct several types of auto-B\"{a}cklund transformations for the KP hierarchy with self-consistent ... More

Degree of entanglement for bipartite pure statesNov 20 2002May 02 2003This paper has been withdrawn.

Constant scalar curvature equation and the regularity of its weak solutionMay 03 2017In this paper we study constant scalar curvature equation (CSCK), a nonlinear fourth order elliptic equation, and its weak solutions on K\"ahler manifolds. We first define a notion of weak solution of CSCK for an $L^\infty$ K\"ahler metric. The main result ... More

Set theoretic complete intersection for curves in a smooth affine algebraAug 12 2005It is proved in this paper that a locally complete intersection curve in a smooth affine C-algebra with trival conormal bundle is a set theoretic complete intersection if its corresponding class in the Grothendieck Group is torsion.

Cognitive Radio with Random Number of Secondary Number of UsersOct 03 2013A single primary user cognitive radio system with multi-user diversity at the secondary users is considered where there is an interference constraint between secondary and primary users. The secondary user with the highest instantaneous SNR is selected ... More

On the dynamics of a family of renormalization transformationsDec 05 2013We study the family of renormalization transformations of the generalized $d$--dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where $d\geq 2$. In particular, ... More

Path Design for Cellular-Connected UAV with Reinforcement LearningMay 09 2019This paper studies the path design problem for cellular-connected unmanned aerial vehicle (UAV), which aims to minimize its mission completion time while maintaining good connectivity with the cellular network. We first argue that the conventional path ... More

On some analogues of Carlitz's identity for the hyperoctahedral groupSep 22 2009We give a new description of the flag major index, introduced by Adin and Roichman, by using a major index defined by Reiner. This allows us to establish a connection between an identity of Reiner and some more recent results due to Chow and Gessel. Furthermore ... More

Combinatorial interpretations of the Jacobi-Stirling numbersMay 18 2009May 20 2009The Jacobi-Stirling numbers of the first and second kinds were introduced in 2006 in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers. Andrews and Littlejohn have recently given a combinatorial interpretation for the ... More

Modeling of Electrons and Excitons Multiple-Exciton-Generation Dynamics in Silicon Clusters using Many-body Green Function TheoryJan 24 2019The electrons and excitons multiple exciton generation dynamics in two silicon clusters, or more specifically the inelastic scattering rates of electronic and excitonic states in the two silicon clusters, Si26 and Si46, are calculated using many-body ... More

Optimized Training Design for Wireless Energy TransferMar 31 2014Dec 18 2014Radio-frequency (RF) enabled wireless energy transfer (WET), as a promising solution to provide cost-effective and reliable power supplies for energy-constrained wireless networks, has drawn growing interests recently. To overcome the significant propagation ... More

Active Eavesdropping via Spoofing Relay AttackSep 29 2015This paper studies a new active eavesdropping technique via the so-called spoofing relay attack, which could be launched by the eavesdropper to significantly enhance the information leakage rate from the source over conventional passive eaves-dropping. ... More

Landau's criterion for an anisotropic Bose-Einstein condensateJan 30 2017Mar 17 2017In this work, we discuss the Landau's criterion for anisotropic superfluidity. To this end, we consider a point-like impurity moving in a uniform Bose-Einstein condensate with either interparticle dipole-dipole interaction or Raman induced spin-orbit ... More

Euler-Mahonian Statistics On Ordered Set Partitions (II)Dec 11 2007We study statistics on ordered set partitions whose generating functions are related to $p,q$-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of \stein (Arxiv:math.CO/0605670). ... More

NMR Quantum Computation with a hyperpolarized nuclear spin bulkNov 18 1998Nov 19 1998We consider two new quantum gate mechanisms based on nuclear spins in hyperpolarized solid $^{129}Xe$ and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance ... More

Existence and asymptotic behavior for the ground state of quasilinear elliptic equationMar 01 2017In this paper, we are concerned with the existence and asymptotic behavior of minimizers for a minimization problem related to some quasilinear elliptic equations. Firstly, we proved that there exist minimizers when the exponent $q$ equals to the critical ... More

A unifying combinatorial approach to refined little Göllnitz and Capparelli's companion identitiesMar 23 2016Jun 25 2017Berkovich-Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage-Sills' new little G\"ollnitz identities. Noticing the connection between their results and Boulet's earlier four-parameter partition ... More

Normally Elliptic Singular Perturbations and Persistence of Homoclinic OrbitsDec 01 2010We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow variables. Assuming ... More

A priori estimates for fluid Interface problemsSep 20 2006Oct 12 2006We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in $H^{\frac32k +1}$ and the velocity fields in $H^{\frac32k}$. These ... More

Quantum Neural Network and Soft Quantum ComputingOct 10 2018A new paradigm of quantum computing, namely, soft quantum computing, is proposed for nonclassical computation using real world quantum systems with naturally occurring environment-induced decoherence and dissipation. As a specific example of soft quantum ... More

On $(n,k)$-quasi-*-paranormal operatorsSep 23 2012For nonnegative integers $n$ and $k$, we introduce in this paper a new class of $(n,k)$-quasi-*-paranormal operators satisfying $$||T^{1+n}(T^{k}x)||^{1/(1+n)}||T^{k}x||^{n/(1+n)} \geq ||T^*(T^{k}x)|| \makebox{\ for all} x \in H.$$ This class includes ... More

Common properties of bounded linear operators $AC$ and $BA$: Spectral theoryMar 23 2013Let $X,Y$ be Banach spaces, $A:X \longrightarrow Y$ and $B,C:Y \longrightarrow X$ be bounded linear operators satisfying operator equation $ABA=ACA$. Recently, as extensions of Jacobson's lemma, Corach, Duggal and Harte studied common properties of $AC-I$ ... More

3DContextNet: K-d Tree Guided Hierarchical Learning of Point Clouds Using Local and Global Contextual CuesNov 30 2017Dec 04 2018Classification and segmentation of 3D point clouds are important tasks in computer vision. Because of the irregular nature of point clouds, most of the existing methods convert point clouds into regular 3D voxel grids before they are used as input for ... More

Synopsis of a Unified Theory for All Forces and MatterOct 30 2016Dec 19 2018Assuming the Kaluza-Klein gravity interacting with elementary matter fermions in a (9+1)-dimensional spacetime ($\mathcal{M}_{9+1}$), we propose an information-complete unified theory for all forces and matter. Due to entanglement-driven symmetry breaking, ... More

Holistic Decomposition Convolution for Effective Semantic Segmentation of 3D MR ImagesDec 24 2018Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in many different 2D medical image analysis tasks. In clinical practice, however, a large part of the medical imaging data available is in 3D. This has motivated the development ... More

Quantum authentication protocolJan 13 2000In this letter, we proposed a quantum authentication protocol. The authentication process is implemented by the symmetric cryptographic scheme with quantum effects.

Stochastic differential equations with noise perturbations and Wong-Zakai approximation of fractional Brownian motionMay 20 2019In this article we study effects that small perturbations in the noise have to the solution of differential equations driven by H\"older continuous functions of order $H>\frac12$. As an application, we consider stochastic differential equations driven ... More

Homotopy Algebras in Higher Spin TheoryJul 16 2018Aug 01 2018Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation in terms of ... More