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3-D Surface Segmentation Meets Conditional Random FieldsJun 11 2019Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based approach, e.g. ... More

Fractionalized Metals and Superconductors in Three DimensionsMay 05 2014May 15 2014We study three-dimensional metals with nontrivial correlation functions and fractionalized excitations. We formulate for such states a gauge theory, which also naturally describes the fractional quantization of chiral anomaly. We also study fractional ... More

Singularity formation to the Cauchy problem of the two-dimensional non-baratropic magnetohydrodynamic equations without heat conductivityJan 28 2018We study the breakdown of strong solutions to the two-dimensional (2D) Cauchy problem of the non-baratropic compressible magnetohydrodynamic equations without heat conductivity. It is proved that the strong solution exists globally if the gradient of ... More

Free Brownian motion and free convolution semigroups: multiplicative caseOct 23 2012Nov 24 2013We consider a pair of probability measures $\mu,\nu$ on the unit circle such that $\Sigma_{\lambda}(\eta_{\nu}(z))=z/\eta_{\mu}(z)$. We prove that the same type of equation holds for any $t\geq 0$ when we replace $\nu$ by $\nu\boxtimes\lambda_t$ and $\mu$ ... More

Strong solutions to the Cauchy problem of the two-dimensional non-baratropic non-resistive magnetohydrodynamic equations with zero heat conductionJan 21 2018This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy estimates, we ... More

A blow-up criterion for strong solutions to three-dimensional compressible magnetohydrodynamic equationsMar 28 2016Mar 31 2016We are concerned with an initial boundary value problem for the compressible magnetohydrodynamic equations with viscosity depending on the density. It is show that for the initial density away from vacuum, the strong solution to the problem exists globally ... More

Universal scaling in first-order phase transitions mixed with nucleation and growthOct 14 2017Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only qualitatively ... More

Eigenvector Under Random Perturbation: A Nonasymptotic Rayleigh-Schrödinger TheoryFeb 01 2017Rayleigh-Schr\"{o}dinger perturbation theory is a well-known theory in quantum mechanics and it offers useful characterization of eigenvectors of a perturbed matrix. Suppose $A$ and perturbation $E$ are both Hermitian matrices, $A^t = A + tE$, $\{\lambda_j\}_{j=1}^n$ ... More

Indirect information measure and dynamic learningSep 03 2018In this paper, I first showed that an indirect information measure is supported by expected learning cost minimization if and only if it satisfies: 1. monotonicity in Blackwell order, 2. sub-additivity in compound experiment and 3. linearity in mixing ... More

Bernstein Polynomial Model for Grouped Continuous DataJun 21 2015Jul 18 2015Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein polynomial, as ... More

Totally invariant divisors of amplified endomorphisms of normal projective varietiesMay 14 2019We consider an arbitrary int-amplified surjective endomorphism $f$ of a normal projective variety $X$ over $\mathbb{C}$ and its $f^{-1}$-stable prime divisors. We extend the early result for the case of polarized endomorphisms to the case of int-amplified ... More

Bijections between t-Core Partitions and t-TuplesMar 18 2019This note introduces some bijections relating core partitions and tuples of integers. We apply these bijections to count the number of cores with various types of restriction, including fixed number of parts, limited size of parts, parts divisible by ... More

Sets of minimal distances and characterizations of class groups of Krull monoidsJun 26 2016Oct 18 2016Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor. Then every non-unit $a \in H$ can be written as a finite product of atoms, say $a=u_1 \cdot \ldots \cdot u_k$. The set $\mathsf L (a)$ of all possible ... More

On elasticities of locally finitely generated monoidsJul 30 2018Let $H$ be a commutative and cancellative monoid. The elasticity $\rho(a)$ of a non-unit $a \in H$ is the supremum of $m/n$ over all $m, n$ for which there are factorizations of the form $a=u_1 \cdot \ldots \cdot u_m=v_1 \cdot \ldots \cdot v_{n}$, where ... More

Right-unitary transformation theory and applicationsApr 30 1996We develop a new transformation theory in quantum physics, where the transformation operators, defined in the infinite dimensional Hilbert space, have right-unitary inverses only. Through several theorems, we discuss the properties of state space of such ... More

On the free convolution with a free multiplicative analogue of the normal distributionNov 13 2012Apr 24 2014We obtain a formula for the density of the free convolution of an arbitrary probability measure on the unit circle of $\mathbb{C}$ with the free multiplicative analogues of the normal distribution on the unit circle. This description relies on a characterization ... More

Compelling evidence for the theory of dynamic scaling in first-order phase transitionsApr 11 2017Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only qualitatively ... More

Periodic Anderson model meets Sachdev-Ye-Kitaev interaction: A solvable playground for heavy fermion physicsMar 26 2018Nov 27 2018The periodic Anderson model is a classic theoretical model for understanding novel physics in heavy fermion systems. Here, we modify it with the Sachdev-Ye-Kitaev interaction, (random all-to-all interaction) thus the resultant model admits an exact solution ... More

Efficient Similarity Indexing and Searching in High DimensionsMay 12 2015Efficient indexing and searching of high dimensional data has been an area of active research due to the growing exploitation of high dimensional data and the vulnerability of traditional search methods to the curse of dimensionality. This paper presents ... More

Selling InformationSep 18 2018Oct 17 2018I consider the monopolistic pricing of informational good. A buyer's willingness to pay for information is from inferring the unknown payoffs of actions in decision making. A monopolistic seller and the buyer each observes a private signal about the payoffs. ... More

Time preference and information acquisitionSep 13 2018Oct 20 2018I consider the sequential implementation of a target information structure. I characterize the set of decision time distributions induced by all signal processes that satisfy a per-period learning capacity constraint. I find that all decision time distributions ... More

Information Design Possibility SetApr 16 2018Sep 04 2018Let $\mathcal{V}$ be the set of all combinations of expected value of finite objective functions from designing information. I showed that $\mathcal{V}$ is a compact and convex set implemented by signal structures with finite support when unknown states ... More

Global Strong Solution for 3D Viscous Incompressible Heat Conducting Navier-Stokes Flows with Non-negative DensityMay 17 2016Aug 07 2017We are concerned with an initial boundary value problem for the nonhomogeneous heat conducting Navier-Stokes flows with non-negative density. First of all, we show that for the initial density allowing vacuum, the strong solution exists globally if the ... More

Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein PolynomialJan 24 2016Jan 26 2018A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial model, a finite ... More

Iterated Bernstein polynomial approximationsSep 03 2009Oct 16 2009Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i=0,1,...,n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is significantly improved ... More

Renormalization-group theory of dynamics of first-order phase transitions in a field-driven scalar modelMay 07 2012We show by a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a $\varphi^{3}$ theory that its instability fixed points with their associated ... More

Theory of Coupled Phase Transitions: Phase Separation and Variation of Order ParameterJul 13 1998A simplified Ginzburg-Landau theory is presented to study generally a coupling of a first-order phase transition (FOPT) to a second-order phase transition (SOPT). We show analytically that, due to the coupling between the two phase transitions, the SOPT ... More

Efficient Scheme for Active Particle Selection in N-body SimulationsSep 02 2014Sep 13 2014We propose an efficient method for active particle selection, working with Hermite Individual Time Steps (HITS) scheme in direct N-body simulation code $\varphi$GRAPE. For a simulation with $N$ particles, this method can reduce the computation complexity ... More

Singularity formation to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domainSep 29 2018We consider the singularity formation of strong solutions to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain. It is shown that for the initial density allowing vacuum, the strong solution exists ... More

Singularity formation to the 2D Cauchy problem of the full compressible Navier-Stokes equations with zero heat conductionMay 15 2017Jun 07 2017The formation of singularity and breakdown of strong solutions to the two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction are considered. It is shown that for the initial density allowing vacuum, ... More

Singularity formation to the Cauchy problem of the two-dimensional non-baratropic magnetohydrodynamic equations without heat conductivityJan 28 2018Sep 02 2018We study the singularity formation of strong solutions to the two-dimensional (2D) Cauchy problem of the non-baratropic compressible magnetohydrodynamic equations without heat conductivity. It is proved that the strong solution exists globally if the ... More

Watermark Embedding and DetectionJun 02 2007The embedder and the detector (or decoder) are the two most important components of the digital watermarking systems. Thus in this work, we discuss how to design a better embedder and detector (or decoder). I first give a summary of the prospective applications ... More

Global Strong Solutions for 3D Viscous Incompressible Heat Conducting Navier-Stokes Flows with Non-negative DensityMay 17 2016We are concerned with an initial boundary value problem for the nonhomogeneous heat conducting fluids with non-negative density. First of all, we show that for the initial density allowing vacuum, the strong solution to the problem exists globally if ... More

On regularity for measures in multiplicative free convolution semigroupsDec 13 2011Oct 22 2012Given a probability measure $\mu$ on the real line, there exists a semigroup $\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $\mu_n$ obtained by iterating its free convolution. It was shown in \cite{[BB2004]} that ... More

Universal scaling in first-order phase transitions mixed with nucleation and growthApr 23 2018Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only qualitatively ... More

Is an imaginary fixed point physical or unphysical?May 08 2012It has been proposed that a first-order phase transition driven to happen in the metastable region exhibits scaling and universality near an instability point controlled by an instability fixed point of a $\varphi^3$ theory. However, this fixed point ... More

Smoothed Analysis of Edge Elimination for Euclidean TSPSep 27 2018Nov 21 2018One way to speed up the calculation of optimal TSP tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so several edge elimination approaches have been proposed in the past. In this ... More

Distributed Demand Response and User Adaptation in Smart GridsJul 30 2010This paper proposes a distributed framework for demand response and user adaptation in smart grid networks. In particular, we borrow the concept of congestion pricing in Internet traffic control and show that pricing information is very useful to regulate ... More

Efficient and Robust Density Estimation Using Bernstein Type PolynomialsApr 28 2014Jun 21 2015Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed model. The approximating ... More

Regularity for variational problems in the Heisenberg groupNov 09 2017Mar 07 2018We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group.

On the γ-filtration of oriented cohomology of complete spin-flagsSep 08 2012Jul 31 2013We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihilator of the torsion part of the $\gamma$-filtration. Moreover, if the ... More

Smoothed Analysis of Edge Elimination for Euclidean TSPSep 27 2018Apr 26 2019One way to speed up the calculation of optimal TSP tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so several edge elimination approaches have been proposed in the past. In this ... More

A characterization of finite abelian groups via sets of lengths in transfer Krull monoidsNov 15 2017Jan 11 2018Let $H$ be a transfer Krull monoid over a finite ablian group $G$ (for example, rings of integers, holomorphy rings in algebraic function fields, and regular congruence monoids in these domains). Then each nonunit $a \in H$ can be written as a product ... More

Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein PolynomialJan 24 2016A new method for deconvoluting density in measurement error models using the Bernstein type polynomial model which is actually a finite mixture of specific beta distributions is proposed and studied. The change-point detection method is used to choose ... More

On the Interaction of Electrons, Magnetic Monopoles, and PhotonsSep 18 2014Feb 18 2015We study quantum systems of interacting electrons, magnetic monopoles, and electromagnetic field. We formulate a convenient field theory, in which the electron-photon, monopole-photon, and electron-monopole interactions take simple forms.

Time Relaxation with Iterative Modified Lavrentiev RegularizationSep 25 2018A new time relaxation model with iterative modified Lavrentiev regularization method is studied. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially faster by an appropriate and often ... More

Understanding one-dimensional topological Kondo insulator: Poor man's non-uniform antiferromagnetic mean-field theory versus quantum Monte Carlo simulationMar 13 2019The topological Kondo insulator (TKI) is an important example of interacting topological insulator, where electron correlation effect plays a key role. However, most of our understanding on this hot topic comes from numerical simulations, (particularly ... More

On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conductionMay 17 2017Sep 14 2017We are concerned with the formation of singularity and breakdown of strong solutions to the Cauchy problem of the three-dimensional full compressible magnetohydrodynamic equations with zero heat conduction. It is proved that for the initial density allowing ... More

On the formal affine Hecke algebraJan 31 2013May 05 2014We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept called the ... More

Comparison of Dualizing ComplexesNov 12 2010Sep 23 2011We prove that there is a map from Bloch's cycle complex to Kato's complex of Milnor K-theory, which induces a quasi-isomorphism from \'{e}tale sheafified cycle complex to the Gersten complex of logarithmic de Rham--Witt sheaves. Next we show that the ... More

Energy of zeros of random sections on Riemann SurfaceMay 14 2007The purpose of this paper is to determine the asymptotic of the average energy of a configuration of N zeros of system of random polynomials of degree N as N tends to infinity and more generally the zeros of random holomorphic sections of a line bundle ... More

On the arithmetic of Mori monoids and domainsNov 02 2018Let $R$ be a Mori domain with complete integral closure $\widehat R$, nonzero conductor $\mathfrak f = (R \ :\ \widehat R)$, and suppose that both $v$-class groups $\mathcal C_v (R)$ and $\mathcal C_v (\widehat R)$ are finite. If $R/\mathfrak f$ is finite, ... More

Hidden $sl(2)$-algebraic structure in Rabi model and its 2-photon and two-mode generalizationsAug 19 2016It is shown that the (driven) quantum Rabi model and its 2-photon and 2-mode generalizations possess a hidden $sl(2)$-algebraic structure which explains the origin of the quasi-exact solvability of these models. It manifests the first appearance of a ... More

Hidden $sl(2)$-algebraic structure in Rabi model and its 2-photon and two-mode generalizationsAug 19 2016Oct 17 2016It is shown that the (driven) quantum Rabi model and its 2-photon and 2-mode generalizations possess a hidden $sl(2)$-algebraic structure which explains the origin of the quasi-exact solvability of these models. It manifests the first appearance of a ... More

Open and Closed Creations of Black HolesOct 25 1998Nov 12 1998We study pair creation of Kerr-Newman-anti-de Sitter and Kerr-Newman-de Sitter black holes.

Pair Creation of Black Hole in Anti-de Sitter Space BackgroundOct 05 1998Jan 28 1999In the absence of a general no-boundary proposal for open creation, the complex constrained instanton is used as the seed for the open pair creations of black holes in the Kerr-Newman-anti-de Sitter family. The relative probability of the chargeless and ... More

Pair Creation of Black Holes in Anti-de Sitter Space Background (I)Oct 04 1998Oct 25 1998For a spherically symmetric vacuum model with a negative cosmological constant, a complex constrained instanton is considered as the seed for the quantum pair creation of Schwarzschild-anti-de Sitter black holes. The relative creation probability is found ... More

Quantum Fields in Schwarzschild-de Sitter SpaceDec 15 1997In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized ... More

Strict upper and lower bounds for quantities of interest in static response sensitivity analysisNov 16 2016In this paper, a goal-oriented error estimation technique for static response sensitivity analysis is proposed based on the constitutive relation error (CRE) estimation for finite element analysis (FEA). Strict upper and lower bounds of various quantities ... More

Pinned interface dipole-induced tunneling electroresistance in ferroelectric tunnel junctionsSep 28 2014Based on the structure predicted in a ferroelectric tunnel junction in the resent density functional theory study, we investigate the electron transport through the FTJ with asymmetric interfaces, i.e., one interface dipole is pinned and the other interface ... More

Relativistically Covariant Symmetry in QEDDec 15 1994We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether ... More

Topological Hamiltonian as an Exact Tool for Topological InvariantsJul 31 2012Mar 26 2013We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show that topological ... More

Fluctuation Effect in Superconductivity in an Electron Model with d-Wave AttractionJul 05 2001Oct 17 2001On the basis of $t$-matrix approximation, we study the superconductivity in the tight-binding model with d-wave attraction. The low-lying collective modes are considered as the predominant long-range fluctuations in the system. The Green's function is ... More

Joint Channel Estimation and Training Signal Design for Two-way MIMO Relay SystemsJun 13 2016In this paper, a two-stage channel estimation scheme for two-way MIMO relay systems with a single relay antenna is proposed. The backward channel is estimated by using linear minimum mean square estimator (LMMSE) at the first stage, where the optimal ... More

A magnetic reconnection origin for the soft X-ray excess in AGNMay 31 2013We present a new scenario to explain the soft X-ray excess in Active Galactic Nucleus. The magnetic reconnection could happen in a thin layer on the surface of accretion disk. Electrons are accelerated by shock wave and turbulence triggered by magnetic ... More

Strong decays of the newly observed $D(2550)$, $D(2600)$, $D(2750)$, and $D(2760)$Sep 02 2010Dec 21 2010The strong decay properties of the newly observed $D(2550)$, $D(2600)$, $D(2750)$ and $D(2760)$ are studied in a constituent quark model. It is predicted that the $D(2760)$ and $D(2750)$ seem to be two overlapping resonances. The $D(2760)$ could be identified ... More

Exact solution to the Schrödinger equation for the quantum rigid bodyNov 26 1999The exact solution to the Schr\"{o}dinger equation for the rigid body with the given angular momentum and parity is obtained. Since the quantum rigid body can be thought of as the simplest quantum three-body problem where the internal motion is frozen, ... More

On the Stronger Statement of Levinson's Theorem for the Dirac EquationDec 26 1994Recently a stronger statement of Levinson's theorem for the Dirac equation was presented, where the limits of the phase shifts at $E=\pm M$ are related to the numbers of nodes of radial functions at the same energies, respectively. However, in this letter ... More

Moments and Cumulants of The Two-Stage Mann-Whitney StatisticSep 01 2017This paper illustrates how to calculate the moments and cumulants of the two-stage Mann-Whitney statistic. These results may be used to calculate the asymptotic critical values of the two-stage Mann-Whitney test. In this paper, a large amount of deductions ... More

Zero surface tension limit of viscous surface wavesDec 05 2012We consider the free boundary problem for a layer of viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom and below the atmosphere. For the "semi-small" initial data, we prove the zero surface tension limit of the ... More

Global well-posedness of the compressible bipolar Euler-Maxwell system in R^3Dec 25 2012We first construct the global unique solution by assuming that the initial data is small in the H^3 norm but its higher order derivatives could be large. If further the initial data belongs to \Dot{H}^{-s} (0\le s<3/2) or \dot{B}_{2,\infty}^{-s} (0< s\le3/2), ... More

A service system with packing constraints: Greedy randomized algorithm achieving sublinear in scale optimality gapNov 10 2015Mar 24 2018A service system with multiple types of arriving customers is considered. There is an infinite number of homogeneous servers. Multiple customers can be placed for simultaneous service into one server, subject to general packing constraints. Each new arriving ... More

The Origin of the Heavy Elements: Recent Progress in the Understanding of the r-ProcessJan 21 2003Feb 06 2003There has been significant progress in the understanding of the r-process over the last ten years. The conditions required for this process have been examined in terms of the parameters for adiabatic expansion from high temperature and density. There ... More

The set of minimal distances in Krull monoidsApr 10 2014Jun 17 2015Let $H$ be a Krull monoid with finite class group $G$. Then every non-unit $a \in H$ can be written as a finite product of atoms, say $a=u_1 \cdot \ldots \cdot u_k$. The set $\mathsf L (a)$ of all possible factorization lengths $k$ is called the set of ... More

The catenary degree of Krull monoids IIJul 02 2014Dec 03 2014Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree $\mathsf c (H)$ ... More

On the Limiting Stokes' Wave of Extreme Height in Arbitrary Water DepthSep 07 2017Feb 13 2018As mentioned by Schwartz (1974) and Cokelet (1977), it was failed to gain convergent results of limiting Stokes' waves in extremely shallow water by means of perturbation methods even with the aid of extrapolation techniques such as Pad\'{e} approximant. ... More

Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure --- Equations in Differential FormApr 21 2016Nov 30 2016The large deflection of a circular thin plate under uniform external pressure is a classic problem in solid mechanics, dated back to Von K{\'a}rm{\'a}n \cite{Karman}. {This problem is reconsidered in this paper using an analytic approximation method, ... More

An ALE-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundariesJun 05 2019In this paper, the original discrete unified gas kinetic scheme (DUGKS) is extended to arbitrary Lagrangian-Eulerian (ALE) framework for simulating the low-speed continuum and rarefied flows with moving boundaries. For ALE method, the mesh moving velocity ... More

Lattice equations and dielectric function for optical lattice vibrations in monolayer transition metal dichalcogenidesMay 31 2019Using a microscopic dipole lattice model including electronic polarization (EP) of ions and local field effects (LFEs) self-consistently, two sets of three equations are deduced for long wavelength in-plane and out-of-plane optical lattice vibrations ... More

Non-linear macro evolution of a dc driven micro atmospheric glow dischargeOct 15 2015We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge ... More

Discrete Hardy-type InequalitiesJun 08 2014Jun 23 2014This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates of the optimal ... More

Large Margin Low Rank Tensor AnalysisJun 11 2013Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent these tensor perceptions ... More

On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)Apr 12 2015Jul 07 2015This paper is the second part of a work devoted to the study of elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\begin{cases} -\Delta u-\lambda \frac{|u|^{2^*(s_1)-2}u}{|x|^{s_1}}=\kappa\alpha \frac{1}{|x|^{s_2}}|u|^{\alpha-2}u|v|^\beta\quad ... More

On Elliptic Systems involving critical Hardy-Sobolev exponentsApr 04 2015Jul 07 2015Let $\Omega\subset \R^N$ ($N\geq 3$) be an open domain which is not necessarily bounded. By using variational methods, we consider the following elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\begin{cases} -\Delta u-\lambda \frac{|u|^{2^*(s_1)-2}u}{|x|^{s_1}}=\kappa\alpha ... More

The Likely Orbital Period of the Ultracompact Low-Mass X-Ray Binary 2S 0918-549Jun 21 2010Jan 02 2011We report the discovery of the likely orbital period of the ultracompact low-mass X-ray binary (LMXB) 2S 0918-549. Using time-resolved optical photometry carried out with the 8-m Gemini South Telescope, we obtained a 2.4-hr long, Sloan r' light curve ... More

Double Sided Watermark Embedding and Detection with Perceptual AnalysisMay 14 2007In our previous work, we introduced a double-sided technique that utilizes but not reject the host interference. Due to its nice property of utilizing but not rejecting the host interference, it has a big advantage over the host interference schemes in ... More

Kernelet: High-Throughput GPU Kernel Executions with Dynamic Slicing and SchedulingMar 21 2013Graphics processors, or GPUs, have recently been widely used as accelerators in the shared environments such as clusters and clouds. In such shared environments, many kernels are submitted to GPUs from different users, and throughput is an important metric ... More

The citation-based indicator and combined impact indicator - New options for measuring impactMay 11 2012Metrics based on percentile ranks (PRs) for measuring scholarly impact involves complex treatment because of various defects such as overvaluing or devaluing an object caused by percentile ranking schemes, ignoring precise citation variation among those ... More

New criteria of separability for tripartite and more high dimensional multipartite qubit density matrixesAug 26 2003In this Letter we find the new criteria of separability of multipartite qubit density matrixes. Especially, we discuss in detail the criteria of separability for tripartite qubit density matrixes. We find the sufficient and necessary conditions of separability ... More

Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its ApplicationsApr 13 2016This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed ... More

The Large Number Limit of Multifield InflationAug 21 2017Aug 28 2017We compute the tensor and scalar spectral index $n_t$, $n_s$, the tensor-to-scalar ratio $r$, the consistency relation $n_t/r$ in the general monomial multifield slow-roll inflation models with potentials $V \sim\sum_i\lambda_i \left|\phi_i\right|^{p_i}$. ... More

Instability of an inverse problem for the stationary radiative transport near the diffusion limitSep 06 2018In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll 1$. It is well-known that ... More

Bright-dark mixed $N$-soliton solutions of the multi-component Mel'nikov systemJun 17 2017By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed $N$-soliton solution to the multi-component Mel'nikov system comprised of multiple (say $M$) short-wave components and one long-wave component with all possible ... More

General mixed multi-soliton solution to the multi-component Maccari systemJun 17 2017Based on the KP hierarchy reduction method, the general bright-dark mixed multi-soliton solution of the multi-component Maccari system is constructed. The multi-component Maccari system considered comprised of multiple (say $M$) short-wave components ... More

Long sets of lengths with maximal elasticityJun 21 2017Sep 28 2017We introduce a new invariant describing the structure of sets of lengths in atomic monoids and domains. For an atomic monoid $H$, let $\Delta_{\rho} (H)$ be the set of all positive integers $d$ which occur as differences of arbitrarily long arithmetical ... More

Two-dimensional excitons in monolayer transition metal dichalcogenides from simple models and variational calculationsSep 04 2018Exciton spectra of monolayer transition metal dichalcogenides (TMDs) in various dielectric environments are studied. The screened hydrogen model (SHM) [Phys. Rev. Lett. 116, 056401 (2016)] is examined by comparing its exciton spectra with the radial equation ... More

Level-One Representations and Vertex Operators of Quantum Affine Superalgebra $U_q[\hat{gl(N|N)}]$Dec 15 1998Jul 02 1999Level-one representations of the quantum affine superalgebra $U_q[\hat{gl(N|N)}]$ associated to the appropriate non-standard system of simple roots and $q$-vertex operators (intertwining operators) associated with the level-one modules are constructed ... More

Asymptotic Behaviour of Truncated Stochastic Approximation procedures with Moving BoundsAug 08 2015Asymptotic behaviour of stochastic approximation procedures is studied with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. In particular, ... More

Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure (I): Equations in Differential FormApr 21 2016The large deflection of a circular plate under a uniform external pressure is a classic problem in mechanics, dated back to Von Karman. In this paper, we solve this famous problem by means of the homotopy analysis method (HAM), an analytic approximation ... More

Causality, Time Arrow and Half Cycling UniverseApr 13 1998If one introduces causality into quantum cosmology, then the prescription for the no-boundary universe should be revised. We show that the thermodymanic arrow of time associated with the perturbation modes should be reversed at the maximum expansion for ... More