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A propagation matting method based on the Local Sampling and KNN Classification with adaptive feature spaceMay 03 2016Closed Form is a propagation based matting algorithm, functioning well on images with good propagation . The deficiency of the Closed Form method is that for complex areas with poor image propagation , such as hole areas or areas of long and narrow structures. ... More

Trust-aware Collaborative Denoising Auto-Encoder for Top-N RecommendationMar 06 2017May 08 2017Both feedback of ratings and trust relationships can be used to reveal users' tastes for improving recommendation performance, especially for cold users. However, both of them are facing data sparsity problem, which may severely degrade recommendation ... More

Observation of Majorana conductance plateau by scanning tunneling spectroscopyApr 12 2019Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits perfect ... More

Upper triangular matrices and Billiard ArraysAug 18 2015Jan 15 2016Fix a nonnegative integer $d$, a field $\mathbb{F}$, and a vector space $V$ over $\mathbb{F}$ with dimension $d+1$. Let $T$ denote an invertible upper triangular matrix in ${\rm Mat}_{d+1}(\mathbb{F})$. Using $T$ we construct three flags on $V$. We find ... More

Bound-preserving discontinuous Galerkin method for compressible miscible displacement in porous mediaJul 18 2017In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the $i$th component ... More

Existence and nondegeneracy of ground states in critical free boundary problemsMay 06 2014Mar 17 2015Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. The corresponding study of higher critical points was recently initiated in Jerison and Perera [30, 31]. In particular, the existence ... More

Decay of correlations for maximal measure of maps derived from AnosovOct 03 2016Oct 23 2017It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables, assuming the ... More

Transformations between nonlocal and local integrable equationsApr 30 2017Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable equations can ... More

Local Hardy Spaces of Musielak-Orlicz Type and Their ApplicationsAug 13 2011Jun 28 2012Let $\phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S. Rychkov). In this ... More

Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticityAug 04 2018Jan 04 2019We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor can be uniquely ... More

Geometric Measure of non-Commuting Simultaneous Measurement based on K-Means ClusteringDec 13 2018Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The rationality of our ... More

The Inverse Problem for the Dirichlet-to-Neumann map on Lorentzian manifoldsJul 29 2016Sep 27 2016We consider the Dirichlet-to-Neumann map $\Lambda$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric $g$, a magnetic field $A$ and a potential $q$. We show that we can recover the jet of $g,A,q$ on the boundary ... More

Smooth Adjustment for Correlated EffectsJan 16 2019This paper considers a high dimensional linear regression model with corrected variables. A variety of methods have been developed in recent years, yet it is still challenging to keep accurate estimation when there are complex correlation structures among ... More

On some properties of nonnegative weakly irreducible tensorsNov 03 2011Mar 13 2012In this paper, we mainly focus on how to generalize some conclusions from nonnegative irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and important lemma is proven using new tools. First, we give the definition of stochastic ... More

Botnets Drilling Away Privacy InfrastructureDec 20 2015In this paper, we explore various technologies and their roles in subverting the privacy infrastructure of the Internet. We also provide mitigation techniques on the attack vectors the technologies provide, and assess the overall severity of these threats. ... More

A note on the geometric simplicity of the spectral radius of nonnegative irreducible tensorsJan 13 2011Mar 13 2012We prove that the spectral radius of even order nonnegative irreducible tensors is real geometrically simple. In the case when the order of the tensor is odd, or in the complex field, some conditions are given to guarantee the geometric simplicity of ... More

Musielak-Orlicz Hardy Spaces Associated with Operators and Their ApplicationsJan 26 2012Jun 29 2012Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a nonnegative self-adjoint operator in $L^2(\mathcal{X})$ satisfying the Davies-Gaffney estimates. Let $\varphi:\,\mathcal{X}\times[0,\infty)\to[0,\infty)$ be a function such that $\varphi(x,\cdot)$ ... More

Boundedness of Linear Operators via Atoms on Hardy Spaces with Non-doubling MeasuresJun 07 2009Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear operator $T$ ... More

Thermo and photoacoustic Tomography with variable speed and planar detectorsMay 03 2016We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propose ... More

Multiwave tomography with reflectors: Landweber's iterationMar 23 2016Apr 19 2016We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the step size for ... More

Atomic and Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators on Spaces of Homogeneous TypeAug 30 2018Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ whose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth function $\varphi:\ \mathcal{X}\times[0,\infty) ... More

Real-variable Characterizations of Orlicz-Hardy Spaces on Strongly Lipschitz Domains of $\mathbb{R}^n$Jul 17 2011Let $\Omega$ be a strongly Lipschitz domain of $\mathbb{R}^n$, whose complement in $\mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (\Omega)$ with the Dirichlet boundary condition, and the heat semigroup ... More

Research on Information Security Enhancement Approaches and the Applications on HCI SystemsFeb 02 2016With rapid development of computer techniques, the human computer interaction scenarios are becoming more and more frequent. The development history of the human-computer interaction is from a person to adapt to the computer to the computer and continually ... More

$L^2$ Forms and Ricci flow with bounded curvature on Complete Non-compact manifoldsSep 11 2005In this paper, we study the evolution of $L^2$ one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the $L^2$ norm of a smooth one form with compact support is non-increasing along the ... More

Decay of correlations for maximal measure of maps derived from Anosov: I: mostly contracting centerOct 03 2016It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables, assuming the ... More

Full quantum theory of control-not gate in ion-trap quantum computationNov 26 2015We investigate the exact effect on ion trap quantum computation after field quantization. First an exact expression of failure probability from field quantization after many CNOT operations in Cirac-Zoller scheme is given. It is proportional to operation ... More

Further Results for Perron-Frobenius Theorem for Nonnegative Tensors IIApr 02 2011Nov 20 2012In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.

Adaptive elastic net and Separate Selection from Least Squares for ultra-high dimensional regression modelsOct 14 2014This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy. Besides, we ... More

Bott-Chern blow-up formula and bimeromorphic invariance of the $\partial\bar{\partial}$-Lemma for threefoldsDec 24 2017Sep 22 2018The purpose of this paper is to study the bimeromorphic invariants of compact complex manifolds in terms of Bott-Chern cohomology. We prove a blow-up formula for Bott-Chern cohomology. As an application, we show that for compact complex threefolds the ... More

The Heart-shaped Supernova Remnant 3C391 viewed in Multi-bandsMar 29 2007Using Chandra X-ray, Spitzer mid-IR, and 1.5 GHz radio data, we examine the spatial structure of SNR 3C391. The X-ray surface brightness is generally anti-correlative with the IR and radio brightness. The multiband data clearly exhibit a heart-shaped ... More

Narrow Band Chandra X-ray Analysis of Supernova Remnant 3C391May 02 2005We present the narrow-band and the equivalent width (EW) images of the thermal composite supernova remnant (SNR) 3C391 for the X-ray emission lines of elements Mg, Si, & S using the Chandra ACIS Observational data. These EW images reveal the spatial distribution ... More

On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equationMar 14 2019This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue waves are derived ... More

General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equationNov 16 2017Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves ... More

On supercritical nonlinear Schrödinger equations with ellipse-shaped potentialsMay 23 2019In this paper, we study the existence and concentration of normalized solutions to the supercritical nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} -\Delta u + V(x) u = \mu_q u + a|u|^q u \quad {\rm in}\quad \mathbb{R}^2,\\ ... More

Real-Variable Characterizations Of Hardy Spaces Associated With Bessel OperatorsFeb 07 2011Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0, \infty), dm_\lambda)$ ... More

A Hierarchical Butterfly LU Preconditioner for Two-Dimensional Electromagnetic Scattering Problems Involving Open SurfacesJan 31 2019This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect electrically ... More

Singularites in the Bousseneq equation and in the generalized KdV equationAug 16 2001In this paper, two kinds of the exact singular solutions are obtained by the improved homogeneous balance (HB) method and a nonlinear transformation. The two exact solutions show that special singular wave patterns exists in the classical model of some ... More

Normalized solutions and mass concentration for supercritical nonlinear Schrödinger equationsMay 23 2019In this paper, we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} -\Delta u + V(x) u = \mu_q u + a|u|^q u \quad {\rm in}\quad \mathbb{R}^2,\\ ... More

Existence and mass concentration of pseudo-relativistic Hartree equationApr 12 2017In this paper, we investigate the constrained minimization problem \begin{equation}\label{eq:0.1} e(a):=\inf_{\{u\in \mathcal{H},\|u\|_2^2=1\}}E_a(u), \end{equation} where the energy functional \begin{equation} \label{eq:0.2} E_a(u)=\int_{\mathbb{R}^3}(u\sqrt{-\Delta+m^2}\,u+Vu^2)\,dx ... More

Orlicz-Hardy Spaces Associated with Divergence Operators on Unbounded Strongly Lipschitz Domains of $\mathbb{R}^n$Jul 15 2011Jun 29 2012Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and $\Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,\infty)$ of upper type 1 and of strictly critical lower type $p_{\Phi}\in(n/(n+1),1]$. ... More

Weighted Local Orlicz-Hardy Spaces with Applications to Pseudo-differential OperatorsJul 17 2011Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orlicz-Hardy space $h^{\Phi}_{\omega}(\mathbb{R}^n)$ via the local ... More

Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators Satisfying Gaussian EstimatesMar 16 2016Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\,\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that $\varphi(x,\cdot)$ ... More

On the geodesic hypothesis in general relativitySep 18 2012Aug 19 2015In this paper, we give a rigorous derivation of Einstein's geodesic hypothesis in general relativity. We use scaling stable solitons for nonlinear wave equations to approximate the test particle. Given a vacuum spacetime $([0, T]\times\mathbb{R}^3, h)$, ... More

K-theoretic Chow groups of derived categories of schemes-on a question by Green-GriffithsNov 01 2013Feb 19 2016Based on Balmer's tensor triangular Chow group, we propose K-theoretic Chow groups of derived categories of noetherian schemes and their Milnor variants for regular schemes and their thickenings. We discuss functoriality and show that our Chow groups ... More

K-theory, local cohomology and tangent spaces to Hilbert schemesApr 10 2016By using K-theory, we construct a map from tangent spaces to Hilbert schemes to local cohomology groups. We use this map to discuss a question by Mark Green and Phillip Griffiths, see Question 1.2. For q = dim(X), our map agrees with the one constructed ... More

Sharp value for the Hausdorff dimension of the range and the graph of stable-like processesSep 29 2015We determine the Hausdorff dimension of the range of a class of Markov processes taking value in $\mathbb{R}^d$. This dimension turns out to be random and depends on the time interval where we observe the range. The techniques developed here also allow ... More

Numerical Reconstruction of the Linac Beam De-bunching in the DC-operated BoosterJan 06 2005It is difficult for us to measure the Booster ring impedance up to the GHz range due to the instrumentation limit. Since the de-bunching process in the Linac to Booster transfer is determined by the complex impedance of the Booster ring, one can obtain ... More

Multifractality of jump diffusion processesFeb 13 2015We study the local regularity and multifractal nature of the sample paths of a class of jump diffusion processes, which are solutions to the stochastic differential equation $$ M_t = \int_0^t \sigma(M_{s-}) dB_s + \int_0^t b(M_s) ds + \int_0^t \int_{[-1,1]\backslash\{0\}} ... More

Structure Learning of Probabilistic Graphical Models: A Comprehensive SurveyNov 29 2011Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical ... More

D4 brane probes in gauge/gravity dualitySep 08 2008Feb 26 2009We propose a DBI vertex brane + $N_c$ fundamental strings configuration for a probe baryon in the finite-temperature thermal gauge field via AdS/CFT correspondence. In particular, we investigate properties of this configuration in QCD_4 and warped AdS_6\times ... More

A probability based approach on ananlyzing dynamics of oscillators on a bidirectional ring with propagation delayJul 01 2005In this paper, we presented a model of pulse-coupled oscillators distributed on a bidirectional ring with propagation delay. In numerical simulations based on this model, we observed phenomena of asynchrony in a certain range of delay factor $\alpha$. ... More

Associated production of Z boson and a pair of new quarks at the LHCMay 13 2010The associated production of $Z$ boson and a pair of new quarks at the Large Hadron Collider (LHC) is studied. The cross sections for both sequential fermions and vector-like fermions are presented. It is found that for sequential fermions the cross sections ... More

Existence and space-time regularity for damped stochastic wave equations on p.c.f. fractalsNov 15 2016It is well-known that a p.c.f. fractal with a regular harmonic structure admits an associated Dirichlet form, which is itself associated with a Laplacian. We use this fact to pose an analogue of the damped stochastic wave equation on the fractal. We show ... More

The Frenet-Serret formulas of a discrete centroaffine curveJan 25 2016In this paper, we build the fundamental theory of a discrete centroaffine curve. For a discrete plane curve, we define its first and second centroaffine curvatures which are invariant under the affine transformation. Using the centroaffine curvatures, ... More

Detecting Potential Instabilities of Numerical AlgorithmsSep 07 2015It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught absolute time. We will prove it is not true in general. It depends on algorithms. We will prove that forward ... More

A practical attack to Bouftass's cryptosystemMay 03 2016Recently, a new fast public key exchange protocol was presented by S. Bouftass. The protocol is based on the difficulty of inverting the function $F(x)=\lfloor (zx \mod 2^p)/ 2^q \rfloor$. In this paper, we describe a practical attack against this protocol ... More

Riemannian Median and Its EstimationNov 18 2009In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also propose a subgradient ... More

Quantum no-key protocol for direct and secure transmission of quantum and classical messagesSep 28 2003We present a quantum no-key protocol for direct and secure transmission of quantum and classical messages based on simple Boolean function computation with several quantum gates and Shamir's interactive idea of classical message encryption. This protocol ... More

Quantum Theory Cannot Forbid Superluminal SignalingMar 28 2001Apr 08 2001This note analyzed the angle-distribution of the probabilities of two-photon states come out of a single-photon's stimulated emission amplification, show that one can exploit EPR photon pairs combined with stimulated emission to realize superluminal signaling. ... More

Twisted representations for vertex operator algebras associated to affine Lie algebrasMay 23 2016In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted generalization of Zhu's ... More

Uniform Definability in Propositional Dependence LogicDec 31 2014Mar 12 2015In this paper, we study the uniform definability problem of connectives of propositional dependence logic (PD). Every propositional formula with intuitionistic disjunction and intuitionistic implication of team semantics can be translated equivalently ... More

Eliminate obstructions: curves on a 3-foldNov 22 2016By using higher K-theory, we reinterpret and generalize an idea on eliminating obstructions of deformation of cycles, which is known to Mark Green, Phillip Griffiths and TingFai Ng. As an application, we show how to eliminate obstructions of deformation ... More

On the Hamiltonian and Geometric structure of the Craik-Leibovich equationDec 01 2016In this paper we show that the Craik-Leibovich (CL) equation in hydrodynamics is the Euler equation on the dual of a certain central extension of the Lie algebra of divergence-free vector fields. From this geometric viewpoint, one can give a generalization ... More

Quantum oblivious transfer and bit commitment protocols based on two non-orthogonal states codingJun 25 2013Mar 12 2015Oblivious transfer (OT) protocol is presented based on non-orthogonal states transmission. Then, the bit commitment protocols on the top of it are constructed. Contrast to classical cryptography, the bit commitment protocols may insecure even if the OT ... More

On Conformal Vector Fields of a Class of Finsler Spaces IApr 13 2014Aug 27 2016An $(\alpha,\beta)$-metric is defined by a Riemannian metric $\alpha$ and $1$-form $\beta$. In this paper, we characterize conformal vector fields of $(\alpha,\beta)$-spaces by some PDEs. Further, we determine the local solutions of conformal vector fields ... More

Background Study on Supernova Relic Neutrinos Search in SuperK-GdOct 29 2016Nov 02 2016The detection of supernova relic neutrinos could provide precious information on the evolution of the universe, the formation of stars, the mechanism of supernova bursts and the related neutrino physics. Many experiments, such as Kamland, Borexino, Sudbury ... More

A Further Step Towards an Understanding of the Tournament Equilibrium SetNov 12 2016We study some problems pertaining to the tournament equilibrium set (TEQ for short). A tournament $H$ is a TEQ-retentive tournament if there is a tournament $T$ which has a minimal TEQ-retentive set $R$ such that $T[R]$ is isomorphic to $H$. We study ... More

Transversely Stable Soliton Trains in Photonic LatticesSep 21 2011We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from X-symmetry points with saddle-shaped diffraction inside the first Bloch ... More

Chemical sensing by cell-surface chemoreceptor arrays: the roles of receptor cooperativity and adaptationJun 25 2012Feb 20 2013Most sensory cells use cross-membrane chemoreceptors to detect chemical signals in the environment. The biochemical properties and spatial organization of chemoreceptors play important roles in achieving and maintaining sensitivity and accuracy of chemical ... More

A numerical method for computing time-periodic solutions in dissipative wave systemsAug 27 2014A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation constant, are ... More

Holomorphy of Adjoint L-functions for $GL(n):$ $n\leq 4$Mar 23 2019We show entireness of complete adjoint L-functions associated to \textbf{any} cuspidal representations of $GL(3)$ or $GL(4)$ over an arbitrary global field. We also get a conditional result for general $GL(n)$ case.

Badly approximable points on curves and unipotent orbits in homogeneous spacesMar 09 2017In this paper, we study the weighted $n$-dimensional badly approximable points on curves. Given an analytic non-degenerate curve $\varphi: I= [a,b] \to \mathbb{R}^n$, we will show that any countable intersection of the sets of the weighted badly approximable ... More

On the Hamiltonian and Geometric structure of the Craik-Leibovich equationDec 01 2016Dec 24 2016In this paper we show that the Craik-Leibovich (CL) equation in hydrodynamics is the Euler equation on the dual of a certain central extension of the Lie algebra of divergence-free vector fields. From this geometric viewpoint, one can give a generalization ... More

Continuity of the complex Monge-Ampere operatorJun 30 1994The complex Monge-Amp\`ere operator $(dd^c)^n$ is an important tool in complex analysis. It would be interesting to find the right notion of convergence $u_j\to u$ such that $(dd^cu_j)^n\to (dd^cu)^n$ in the weak topology. In this paper, using the $C_{n-1}$-capacity, ... More

Blow-up solutions for $L^2$-supercritical gKdV equations with exactly $k$ blow-up pointsFeb 27 2016Jun 02 2017In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . In the previous work of the author we know that there exists an stable ... More

Online Combinatorial Optimization for Interconnected Refrigeration Systems: Linear Approximation and SubmodularityApr 23 2016Apr 01 2017Commercial refrigeration systems consume 7% of the total commercial energy consumption in the United States. Improving their energy efficiency contributes to the sustainability of global energy systems and the supermarket business sector. This paper proposes ... More

Generalizations of Joints ProblemJun 28 2016We generalize the joints problem to sets of varieties and prove almost sharp bound on the number of joints. As a special case, given a set of $N$ $2$-planes in $\mathbb{R}^6$, the number of points at which three $2$-planes intersect and span $\mathbb{R}^6$ ... More

Semiclassical Green Function in Mixed SpacesDec 03 1997Feb 11 1998A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations of Green functions ... More

Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel DerivationFeb 13 2019Mar 01 2019Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to study wide random ... More

Scattering amplitudes at strong coupling for 4K gluonsApr 22 2010Nov 21 2010In this paper we study the scattering amplitudes at strong coupling for the case where the number of gluons is a multiple of four. This is an important missing piece in arXiv:1002.2459. The tricky point for n=4K is that there is some accidental degeneracy ... More

A Large Convective-Core Overshoot in \textit{Kepler} Target KIC 11081729Aug 05 2015Apr 14 2016The frequency ratios $r_{01}$ and $r_{10}$ of KIC 11081729 decrease firstly and then increase with the increase in frequency. For different spectroscopic constraints, all models with overshooting parameter $\delta_{\mathrm{ov}}$ less than 1.7 can not ... More

Ramanujan-type identities for Shimura curvesJan 15 2013Mar 25 2013In 1914, Ramanujan gave a list of 17 identities expressing $1/\pi$ as linear combinations of values of hypergeometric functions at certain rational numbers. Since then, identities of similar nature have been discovered by many authors. Nowadays, one of ... More

Computing modular equations for Shimura curvesMay 23 2012Jun 04 2012In the classical setting, the modular equation of level $N$ for the modular curve $X_0(1)$ is the polynomial relation satisfied by $j(\tau)$ and $j(N\tau)$, where $j(\tau)$ is the standard elliptic $j$-function. In this paper, we will describe a method ... More

Horseshoes for $\mathcal{C}^{1+α}$ mappings with hyperbolic measuresNov 25 2014We present here a construction of horseshoes for any $\mathcal{C}^{1+\alpha}$ mapping $f$ preserving an ergodic hyperbolic measure $\mu$ with $h_{\mu}(f)>0$ and then deduce that the exponential growth rate of the number of periodic points for any $\mathcal{C}^{1+\alpha}$ ... More

Computabilities of Validity and Satisfiability in Probability Logics over Finite and Countable ModelsOct 12 2014Dec 12 2014The $\epsilon$-logic (which is called $\epsilon$E-logic in this paper) of Kuyper and Terwijn is a variant of first order logic with the same syntax, in which the models are equipped with probability measures and in which the $\forall x$ quantifier is ... More

Phase Diagrams of Spinor Bose GasesJul 27 2009Using effective field theories dictated by the symmetry of the system, as well as microscopic considerations, we map out the magnetic coupling-temperature phase diagrams of spin-1 Bose gases in both two- and three-dimensions. We also determine the nature ... More

Inhomogeneous superconducting state in quasi-one-dimensional systemsDec 20 2000We report on results of theoretical study of non-uniform superconducting states in quasi-one-dimensional systems, with attractive interactions and Zeeman splitting between electron spins. Using bosonization to treat intrachain electron-electron interactions, ... More

Field Theoretical Description of Quantum Hall Edge ReconstructionFeb 17 2003We propose a generalization of the chiral Luttinger liquid theory to allow for a unified description of quantum Hall edges with or without edge reconstruction. Within this description edge reconstruction is found to be a quantum phase transition in the ... More

Rotating Solar Models with Low Metal Abundances as Good as Those with High Metal AbundancesJan 31 2019Standard solar models (SSM) constructed in accord with low metal abundances disagree with the seismically inferred results. We constructed rotating solar models with low metal abundances that included enhanced settling and convection overshoot. In one ... More

Hausdorff dimension of divergent diagonal geodesics on product of finite volume hyperbolic spacesMar 24 2013Nov 08 2015In this article, we consider the product space of several non-compact finite volume hyperbolic spaces, $V_1, V_2, \dots , V_k$ of dimension $n$. Let $\mathrm{T}^1(V_i)$ denote the unit tangent bundle of $V_i$ for each $i=1,\dots , k$, then for every $(v_1, ... More

Apery limits and special values of L-functionsSep 12 2007We describe a general method to determine the Apery limits of a differential equation that have a modular-function origin. As a by-product of our analysis, we discover a family of identities involving the special values of L-functions associated with ... More

Differential equations and logarithmic intertwining operators for strongly graded vertex algebrasMar 30 2013May 23 2016We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable assumptions. ... More

Equidistribution of expanding translates of curves and Diophantine approximation on matricesSep 23 2018Mar 02 2019We study the general problem of equidistribution of expanding translates of an analytic curve by an algebraic diagonal flow on the homogeneous space $G/\Gamma$ of a semisimple algebraic group $G$. We define two families of algebraic subvarieties of the ... More

Weak Hopf algebras corresponding to Cartan matricesApr 24 2005We replace the group of group-like elements of the quantized enveloping algebra $U_q({\frak{g}})$ of a finite dimensional semisimple Lie algebra ${\frak g}$ by some regular monoid and get the weak Hopf algebra ${\frak{w}}_q^{\sf d}({\frak g})$. It is ... More

A gradient flow for the prescribed Gaussian curvature problem on a closed Riemann surface with conical singularityJun 26 2017In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui \cite{BFR}is well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under certain assumptions. ... More

Derivation of the Chapman-Kolmogorov type equation from a stochastic hybrid systemOct 16 2017Apr 14 2018Both stochastic and PDE modeling approaches have been used and compared in various context in biology. Typically, stochastic models are easier to parameterize, can be used to integrate underlying biological phenomena, but hard to analyze mathematically ... More

Numerical Approximations for the Cahn-Hilliard phase field model of the binary fluid-surfactant systemJan 25 2017In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn-Hilliard equations. The main challenge in solving the system numerically is how to develop ... More

Discrete-Time Accelerated Block Successive Overrelaxation Methods for Time-Dependent Stokes EquationsNov 04 2015To further study the application of waveform relaxation methods in fluid dynamics in actual computation, this paper provides a general theoretical analysis of discrete-time waveform relaxation methods for solving linear DAEs. A class of discrete-time ... More

Capacity of Fading Channels without Channel Side InformationMar 29 2019There are currently a plurality of capacity theories of fading channels, including the ergodic capacity for fast fading channels and outage capacity for slow fading channels. However, analyses show that the outage capacity is a misconception. In this ... More

A multi-level soft frequency reuse technique for wireless communication systemsJun 11 2014A multi-level soft frequency reuse (ML-SFR) scheme and a resource allocation methodology are proposed for wireless communication systems in this letter. In the proposed ML-SFR scheme, there are 2N power density limit levels, achieving better interference ... More