total 6204took 0.12s

An Efficient Sufficient Dimension Reduction Method for Identifying Genetic Variants of Clinical SignificanceJan 15 2013Fast and cheaper next generation sequencing technologies will generate unprecedentedly massive and highly-dimensional genomic and epigenomic variation data. In the near future, a routine part of medical record will include the sequenced genomes. A fundamental ... More

Observation of nodal-line semimetal with ultracold fermions in an optical latticeAug 22 2018May 06 2019Observation of topological phases beyond two-dimension (2D) has been an open challenge for ultracold atoms. Here, we realize for the first time a 3D spin-orbit coupled nodal-line semimetal in an optical lattice and observe the bulk line nodes with ultracold ... More

The excitation functions of 187Re(n,2n)186m,gRe ReactionsAug 27 2015A new value for the emission probability of 137.144keV g-ray of 186gRe decay are re-recommended to be 9.47+-0.03 (%). From this new g-ray emission probability, the measured cross sections for 187Re(n,2n)186mRe and 187Re(n,2n)186gRe reactions around 14MeV ... More

Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein CondensatesNov 24 2015Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling for boson and fermion ... More

A trigonometric integrator for the constrained ring polymer Hamiltonian dynamicsNov 27 2014Jan 04 2016A class of trigonometric integrator is proposed for the constrained ring polymer Hamiltonian dynamics, arising from the path integral molecular dynamics. The integrator is formulated by the composition of flows, thereby integrating the Cartesian equations ... More

Anderson localization of electron states in graphene in different types of disorderDec 29 2007Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorder in the absence of magnetic field is investigated by using the standard finite-size scaling analysis. In the presence of diagonal disorder all states ... More

On cyclic codes of composite length and the minimal distanceMar 31 2017In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and dimension ... More

On best subset regressionDec 05 2011Dec 04 2012In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We prove that ... More

Extended Klein model and a bound on curves with negative self-intersectionOct 26 2016Let $S$ be an irreducible smooth projective surface and $\mathcal{F}$ a collection of curves with negative self-intersection on $S$ such that no positive combination $aC_1 + bC_2$ is ample. In this paper, we provide an alternate proof that $\mathcal{F}$ ... More

Better Solution Principle: A Facet of Concordance between Optimization and StatisticsFeb 16 2014May 23 2014Many statistical methods require solutions to optimization problems. When the global solution is hard to attain, statisticians always use the better if there are two solutions for chosen, where the word "better" is understood in the sense of optimization. ... More

The number of simultaneous core partitionsSep 24 2014Oct 12 2014Amdeberhan conjectured that the number of $(t,t+1, t+2)$-core partitions is $\sum_{0\leq k\leq [\frac{t}{2}]}\frac{1}{k+1}\binom{t}{2k}\binom{2k}{k}$. In this paper, we obtain the generating function of the numbers $f_t$ of $(t, t + 1, ..., t + p)$-core ... More

The critical semilinear elliptic equation with isolated boundary singularitiesApr 19 2017We establish quantitative asymptotic behaviors for nonnegative solutions of the critical semilinear equation $-\Delta u=u^{\frac{n+2}{n-2}}$ with isolated boundary singularities, where $n\ge 3$ is the dimension.

On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley propertyDec 03 2017Jul 02 2018Let $\mathds{k}$ be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over $\mathds{k}$ whose Hopf coradical is isomorphic to the unique $12$-dimensional Hopf algebra $\mathcal{C}$ without the dual ... More

On positive proportion of rank zero twists of elliptic curves over QNov 20 2013Extending the idea of \cite{dab2} and using the 2-descent method, we provide three general families of elliptic curves over Q such that a positive proportion of prime-twists of such elliptic curves have rank zero simultaneously.

The number of cubic partitions modulo powers of 5Apr 27 2010Jun 18 2010The notion of cubic partitions is introduced by Hei-Chi Chan and named by Byungchan Kim in connection with Ramanujan's cubic continued fractions. Chan proved that cubic partition function has Ramanujan Type congruences modulo powers of $3$. In a recent ... More

Ramanujan-Type congruences for cubic partition functionsMar 01 2010Jun 22 2010The cubic partitions of a natural number $n$, introduced by Chan and Kim, have generating function $\sum_{n=0}^{\infty}a(n)q^n= \frac{1}{(q; q)_{\infty}(q^2; q^2)_{\infty}}.$ In this paper, we generalize some results of Chen-Lin, which suggest that $a(n)$ ... More

Noncommutative harmonic analysis on semigroup and ultracontractivityMar 14 2016Mar 15 2016We extend some classical results of Cowling and Meda to the noncommutative setting. Let $(T_t)_{t>0}$ be a symmetric contraction semigroup on a noncommutative space $L_p(\mathcal{M}),$ and let the functions $\phi$ and $\psi$ be regularly related. We prove ... More

A character of Siegel modular group of level 2 from theta constantsJan 10 2017Mar 23 2017Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are also obtained. By using our theorems, some key theorems of Igusa [1] can be recovered.

Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identitiesJul 26 2016In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give $q$-difference equations for the related generating function ... More

The weight distributions of a class of cyclic codesNov 14 2011Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special case. We make ... More

The fundamental theorem of affine geometry in $(L^0)^n$Dec 20 2018Let $L^0$ be the algebra of equivalence classes of real valued random variables on a probability space. For each integer $n\geq 2$, we consider $(L^0)^n$--the $n$-ary Cartesian power of $L^0$--as a free $L^0$-module and establish the fundamental theorem ... More

A representation theorem of the dual of the Orlicz heart of a random normed moduleNov 03 2015In this paper, we introduce the notion of the Orlicz space and the Orlicz heart for a random normed module $E$, and give a representation theorem which identify the dual of the Orlicz heart of $E$ with the Orlicz space generated by the random conjugate ... More

Finite Groups Whose Character Graphs Associated with Codegrees Have No TrianglesAug 28 2015Motivated by the Problem $164$ proposed by Y. Berkovich and E. Zhmud' in their book "Characters of finite groups, Part $1$", we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind ... More

A stochastic log-Laplace equationOct 06 2004We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making ... More

Equivalent description of Hom-Lie algebroidsJul 04 2018Sep 05 2018In this paper, we study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be transformed into ... More

Realization of a Josephson SwitchAug 27 2013Oct 02 2013It has been proposed that intermittent weak links between spontaneously broken symmetry systems can give rise to a novel type of time crystal. Here a practical construction is analyzed in greater detail. For a film-geometry Josephson junction, an applied ... More

A derivation of the sharp Moser-Trudinger-Onofri inequalities from the fractional Sobolev inequalitiesApr 09 2018Sep 14 2018We derive the sharp Moser-Trudinger-Onofri inequalities on the standard $n$-sphere and CR $(2n+1)$- sphere as the limit of the sharp fractional Sobolev inequalities for all $n\ge 1$. On the $2$-sphere and $4$-sphere, this was established recently by S.-Y. ... More

Distribution of zeta zeroes for abelian covers of algebraic curves over a finite fieldJan 30 2013For a function field $k$ over a finite field with $\mathbb{F}_q$ as the field of constant, and a finite abelian group $G$ whose exponent is divisible by $q-1$, we study the distribution of zeta zeroes for a random $G$-extension of $k$, ordered by the ... More

Hom-Lie groups of a class of Hom-Lie algebraOct 18 2018In this paper, the definition of Hom-Lie groups is given and one conntected component of Lie group $GL(V)$, which is not a subgroup of $GL(V)$, is a Hom-Lie group. More, we proved that there is a one-to-one relationship between Hom-Lie groups and Hom-Lie ... More

A complement on representations of Hom-Lie algebrasMar 04 2017Sep 05 2018In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the relation between ... More

Small Values of Coefficients of a Half Lerch SumMay 31 2016Jun 03 2016Andrews, Dyson and Hickerson proved many interesting properties of coefficients for a Ramanujan's $q$-hypergeometric series by relating it to real quadratic field $\Q(\sqrt{6})$ and using the arithmetic of $\Q(\sqrt{6})$, hence solved a conjecture of ... More

Congruences modulo powers of 5 for three-colored Frobenius partitionsFeb 27 2010Apr 27 2010Motivated by a question of Lovejoy \cite{lovejoy}, we show that three-colored Frobenius partition function $\c3$ and related arithmetic fuction $\cc3$ vanish modulo some powers of 5 in certain arithmetic progressions.

Berry-Phase Induced Dynamical Instability and Minimum Conductivity in GrapheneFeb 02 2007Single-layer carbon, or graphene, demonstrates amazing transport properties, such as the minimum conductivity near $\frac{4e^2}{h}$ independent of shapes and mobility of samples. This indicates there exist some unusual effects due to specific Dirac dispersion ... More

Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in GrapheneDec 29 2007We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation using Floquet scheme. In a period of vibration the fermions acquire different geometric phases ... More

Magnetic extraction of energy from accretion disc around a rotating black holeMay 05 2004May 07 2004An analytical expression for the disc power is derived based on an equivalent circuit in black hole (BH) magnetosphere with a mapping relation between the radial coordinate of the disc and that of unknown astrophysical load. It turns out that this disc ... More

Observing topological charges and dynamical bulk-surface correspondence with ultracold atomsMay 16 2019In quenching a topological phase across phase transition, the dynamical bulk-surface correspondence emerges that the bulk topology of $d$-dimensional ($d$D) phase relates to the nontrivial pattern of quench dynamics emerging on $(d-1)$D subspace, called ... More

Probing the Electron States and Metal-Insulator Transition Mechanisms in Atomically Thin MoS2 Based on Vertical HeterostructuresJul 21 2014The metal-insulator transition (MIT) is one of the remarkable electrical transport properties of atomically thin molybdenum disulphide (MoS2). Although the theory of electron-electron interactions has been used in modeling the MIT phenomena in MoS2, the ... More

A Low-latency Pipeline for GRB Light Curve and Spectrum using Fermi/GBM Near Real-time DataFeb 26 2018Rapid response and short time latency are very important for Time Domain Astronomy, such as the observations of Gamma-ray Bursts (GRBs) and electromagnetic (EM) counterparts of gravitational waves (GWs). Based on the near real-time Fermi/GBM data, we ... More

Two-dimensional superconductivity at (110) LaAlO3/SrTiO3 interfacesSep 20 2014Sep 24 2014Novel low dimensional quantum phenomena are expected at (110) LaAlO3/SrTiO3 (LAO/STO) interfaces after the quasi two dimensional electron gas similar to that of (001) LAO/STO interfaces was found [G. Herranz et al., Sci. Rep. 2, 758 (2012) and A. Annadi ... More

A note on the Brown-Erdős-Sós conjecture in finite groupsFeb 20 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... More

A note on the Brown-Erdős-Sós conjecture in finite groupsFeb 20 2019Mar 01 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... More

Semiclassical Cauchy Estimates and ApplicationsFeb 21 2013In this note, we study solutions to semiclassical Schrodinger equations on a real analytic manifold with a real analytic potential and prove the semiclassical version of Cauchy estimates on derivatives. As an application, we use Donnelly and Fefferman's ... More

Phylogenetic trees and homomorphismsJan 02 2018In Chapter 1 we fully characterise pairs of finite graphs which form a gap in the full homomorphism order. This leads to a simple proof of the existence of generalised duality pairs. We also discuss how such results can be carried to relational structures ... More

Large unavoidable subtournamentsFeb 18 2015Mar 11 2016Let $D_k$ denote the tournament on $3k$ vertices consisting of three disjoint vertex classes $V_1, V_2$ and $V_3$ of size $k$, each of which is oriented as a transitive subtournament, and with edges directed from $V_1$ to $V_2$, from $V_2$ to $V_3$ and ... More

Three-body system of $ππΣ_c$Sep 27 2016The existence of near-threshold charmed baryon $\Lambda_c^+(2595)$ implies the pion and the lightest, isospin-$1$ charmed baryon $\Sigma_c$ interact very strongly at extremely low energies. Using the two-flavor version of heavy hadron chiral perturbation ... More

On the uniqueness of conical Kähler-Einstein metricsFeb 17 2014The purpose of this paper is to prove the uniqueness of conical K\"ahler-Einstein metrics, under the condition that the twisted $Ding$-functional is proper. This is a generalization of the author's previous work, and we shall first investigate the uniqueness ... More

The effective dynamics of loop quantum $R^2$ cosmologyNov 20 2018The effective dynamics of loop quantum $f (R)$ cosmology in Jordan frame is considered by using the dynamical system method and numerical method. To make the analyze in detail, we focus on $R^2$ model since it is simple and favored from observations. ... More

On Atkin and Swinnerton-Dyer congruence relations (3)Jan 10 2007In the previous two papers with the same title ([LLY05] by W.C. Li, L. Long, Z. Yang and [ALL05] by A.O.L. Atkin, W.C. Li, L. Long), the authors have studied special families of cuspforms for noncongruence arithmetic subgroups. It was found that the Fourier ... More

Robust Strictly Positive Real Synthesis for Polynomial Families of Arbitrary OrderNov 01 2002For any two $n$-$th$ order polynomials $a(s)$ and $b(s),$ the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real.

Estimates at or beyond endpoint in harmonic analysis: Bochner-Riesz means and spherical meansMar 03 2011We introduce some new functions spaces to investigate some problems at or beyond endpoint. First, we prove that Bochner-Riesz means $B_R^\lambda$ are bounded from some subspaces of $L^p_{|x|^\alpha}$ to $L^p_{|x|^\alpha}$ for $ \frac{n-1}{2(n+1)}<\lambda ... More

Correlation function of modular HamiltoniansJul 01 2019We investigate varies correlation functions of modular Hamiltonians defined with respect to spatial regions in quantum field theories. These correlation functions are divergent in general. We extract finite correlators by removing divergent terms for ... More

Convexity, translation invariance and subadditivity for $g$-expectations and related risk measuresJan 22 2008Under the continuous assumption on the generator $g$, Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] showed some connections between $g$ and the conditional $g$-expectation $({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$ and Rosazza ... More

Extremes of multifractional Brownian motionNov 15 2017Mar 30 2019Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\} \end{eqnarray*} ... More

Parisian ruin of Brownian motion risk model over an infinite-time horizonFeb 20 2017Let $B(t), t\in \mathbb{R}$ be a standard Brownian motion. In this paper, we derive the exact asymptotics of the probability of Parisian ruin on infinite time horizon for the following risk process \begin{align}\label{Rudef} R_u^{\delta}(t)=e^{\delta ... More

Extremes of $α(t)$-Locally stationary Gaussian processes with non-constant variancesJun 22 2016Aug 21 2016With motivation from K. D\c{e}bicki and P. Kisowski (2007), in this paper we derive the exact tail asymptotics of $\alpha(t)$-locally stationary Gaussian processes with non-constant variance functions. We show that some certain variance functions lead ... More

Estimation of Change-point ModelsMay 01 2018May 08 2018We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields with trend ... More

Simultaneous approximation for scheduling problemsApr 15 2013Motivated by the problem to approximate all feasible schedules by one schedule in a given scheduling environment, we introduce in this paper the concepts of strong simultaneous approximation ratio (SAR) and weak simultaneous approximation ratio (WAR). ... More

Differentiation of IntegralsJul 08 2014No functions class for general measurable sets classes are known whose functions have the property of differentiability of integrals associated to such sets classes. In this paper,we give some subspaces of $L^s$ with $1<s<\infty$, whose functions are ... More

On the Spectrum of weighted Laplacian operator and its application to uniqueness of Kähler Einstein metricsOct 31 2013Nov 08 2013The purpose of this paper is to provide a new proof of Bando-Mabuchi's uniqueness theorem of K\"ahler Einstein metrics on Fano manifolds, based on Chen's weak C^{1,1} geodesic without using any further regularities. Unlike the smooth case, the lack of ... More

The 90/10 phenomenon in directed signed social networksApr 14 2016We empirical study the signs' property in the directed signed social networks of Slashdot and Epinions by using an reshuffled approach. Through calculating the entropy $S_{out}$ and the giant component $G$, we find an interesting 90/10 phenomenon: each ... More

Polarized 3He(e,e'n) Asymmetries in Three Orthogonal MeasurementsSep 12 2012Asymmetry measurements were conducted in Jefferson Lab's experimental Hall A through electron scattering from a polarized $^3$He target in the quasi-elastic $^3\mathrm{He}(e,e'n)$ reaction. Measurements were made with the target polarized in the longitudinal ... More

Regularity of many-body Schrödinger evolution equation and its application to numerical analysisMar 06 2018May 10 2019A decade ago, the mixed regularity of stationary many-body Schr\"o\-dinger equation has been studied by Harry Yserentant through the Pauli Principle and the Hardy inequality (Uncertainty Principle). In this article, we prove that the many-body evolution ... More

Some Numeric Hypergeometric SupercongruencesDec 18 2018Apr 18 2019In this article, we list a few hypergeometric supercongruence conjectures based on two evaluation formulas of Whipple and numeric data computed using Magma and Sagemath.

A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential EquationsSep 02 2018Mar 21 2019In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression ... More

Long paths and cycles in subgraphs of the cubeJun 15 2010Mar 20 2015Let $Q_n$ denote the graph of the $n$-dimensional cube with vertex set $\{0,1\}^n$ in which two vertices are adjacent if they differ in exactly one coordinate. Suppose $G$ is a subgraph of $Q_n$ with average degree at least $d$. How long a path can we ... More

Search for Lorentz Violation using Short-Range Tests of GravityJul 24 2016Experimental tests of the newtonian inverse square law at short range, one at Indiana University and the other at the Huazhong University of Science and Technology, have been used to set limits on Lorentz violation in the pure gravity sector of the nonminimal ... More

Higher Spin Entanglement EntropyAug 06 2014Dec 04 2014In this paper, we develop a perturbation formulation to calculate the single interval higher spin R$\acute{e}$nyi and entanglement entropy for two dimensional conformal field theory with $\mathcal{W}_{\infty}(\lambda)$ symmetry. The system is at finite ... More

The Lelong number, the Monge-Ampère mass and the Schwarz symmetrization of plurisubharmonic functionsMay 25 2019The aim of this paper is to study the Lelong number, the integrability index and the Monge-Amp\`ere mass at the origin of an $S^1$-invariant plurisubharmonic function on a balanced domain in $\mathbb{C}^n$ under the Schwarz symmetrization. We prove that ... More

Robust Performance of A Class of Control SystemsFeb 23 2002Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications ... More

A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential EquationsSep 02 2018Jun 25 2019In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression ... More

Extremes of $L^p$-norm of Vector-valued Gaussian processes with TrendJun 26 2017Jun 01 2018Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\left\|\boldsymbol{X}(t)\right\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been ... More

Exponential decay and symmetry of solitary waves to the Degasperis-Procesi equationJan 20 2019Jan 24 2019We prove that solitary waves to the steady Degasperis-Procesi equation, if they exist, decay as $e^{-|x|}$ for large $|x|$ and are symmetric with respect to the unique symmetry axis located at the only crest (although only peaked solitary waves are allowed). ... More

A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential EquationsSep 02 2018In this work, we study solving (decoupled) forward-backward stochastic differential equations FBSDEs numerically using the regression trees. For the one-step scheme, we apply firstly the the general theta-discretization for the time-integrands and show ... More

A note on the Brown--Erdős--Sós conjecture in groupsFeb 20 2019Apr 09 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... More

Vortical Motions of Baryonic Gas in the Cosmic Web: Growth History and Scaling RelationAug 27 2015The vortical motions of the baryonic gas residing in large scale structures are investigated by cosmological hydrodynamic simulations. Proceeding in the formation of the cosmic web, the vortical motions of baryonic matter are pumped up by baroclinity ... More

Attention-Based Deep Distance Metric Learning for Aspect-Phrase GroupingApr 29 2016Aspect phrase grouping is an important task for aspect finding in aspect-level sentiment analysis and it is a challenging problem due to polysemy and its context dependency. In this paper we propose an Attention-based Deep Distance Metric Learning (ADDML) ... More

Gluon multiplication in high energy heavy ion collisionsSep 29 1993Hot gluons are the dominant components of the QCD plasma to be formed in future high energy heavy ion experiments. In this paper we study the elementary processes in the plasma medium for gluon multiplication based on all orders of the tree-diagrams in ... More

Orlicz-Legendre EllipsoidsAug 24 2014The Orlicz-Legendre ellipsoids, which are in the framework of emerging dual Orlicz Brunn-Minkowski theory, are introduced for the first time. They are in some sense dual to the recently found Orlicz-John ellipsoids, and have largely generalized the classical ... More

Branching random walk solutions to the Wigner equationJul 03 2019The stochastic solutions to the Wigner equation, which explain the nonlocal oscillatory integral operator $\Theta_V$ with an anti-symmetric kernel as {the generator of two branches of jump processes}, are analyzed. All existing branching random walk solutions ... More

Universal characterizing topological insulator and topological semi-metal with Wannier functionsApr 22 2015The nontrivial evolution of Wannier functions (WF) for the occupied bands is a good starting point to understand topological insulator. By modifying the definition of WFs from the eigenstates of the projected position operator to those of the projected ... More

Defining Data ScienceJan 21 2015Data science is gaining more and more and widespread attention, but no consensus viewpoint on what data science is has emerged. As a new science, its objects of study and scientific issues should not be covered by established sciences. Data in cyberspace ... More

Jackiw-Rebbi-type bound state carrying fractional fermion parityJul 14 2014Nov 24 2014We find the coexistence of two kinds of non-abelian anyons, Majorana fermion at the geometric ends and Jackiw-Rebbi-type bound state (JRBS)at a domain-wall, in a topological superconducting phase in one-dimensional (1D) systems. Each localized JRBS carries ... More

Stochastic maximum principle under probability distortionOct 31 2017Aug 23 2018Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite ... More

A Novel Statistical Method Based on Dynamic Models for ClassificationOct 26 2014Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have infinite dimensions ... More

Persistence of invariant tori in integrable Hamiltonian systems under almost periodic perturbationsJun 18 2017In this paper we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems \begin{equation*} H=h(y)+f(x,y,t), \end{equation*} where $y\in D\subseteq\mathbb{R}^n$ with $D$ being a closed bounded domain, $x\in \mathbb{T}^n$, ... More

Protecting Locations with Differential Privacy under Temporal CorrelationsOct 22 2014Nov 04 2015Concerns on location privacy frequently arise with the rapid development of GPS enabled devices and location-based applications. While spatial transformation techniques such as location perturbation or generalization have been studied extensively, most ... More

Periodic solutions of semilinear Duffing equations with impulsive effectsMay 24 2017In this paper we are concerned with the existence of periodic solutions for semilinear Duffing equations with impulsive effects. Firstly for the autonomous one, basing on Poincar\'{e}-Birkhoff twist theorem, we prove the existence of infinitely many periodic ... More

Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphereAug 26 2013In this paper, firstly, inspired by Nat\'{a}rio's recent work \cite{Na}, we use the isoperimetric inequality to derive some Alexandrov-Fenchel type inequalities for closed convex hypersurfaces in the hyperbolic space $\H^{n+1}$ and in the sphere $\SS^{n+1}$. ... More

Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularitiesJan 07 2019Jan 14 2019We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension of the celebrated ... More

Solutions of some Monge-Ampère equations with isolated and line singularitiesDec 18 2012Jun 03 2013In this paper, we study existence, regularity, classification, and asymptotical behaviors of solutions of some Monge-Amp\`ere equations with isolated and line singularities. We classify all solutions of $\det \nabla^2 u=1$ in $\R^n$ with one puncture ... More

The Schrödinger equation for general non-hermitian quantum systemFeb 23 2017We derive a new time-dependent Schr\"odinger equation(TDSE) for quantum models with non-hermitian Hamiltonian. Within our theory, the TDSE is symmetric in the two Hilbert spaces spanned by the left and the right eigenstates, respectively. The physical ... More

A Method for Calculating Collision Probability Between Space ObjectsNov 28 2013A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter events in near ... More

Nonnegatively curved hypersurfaces with free boundary on a sphereJul 11 2017Mar 31 2019We prove that in Euclidean space $R^{n+1}$ any compact immersed nonnegatively curved hypersurface $M$ with free boundary on the sphere $S^n$ is an embedded convex topological disk. In particular, when the $m^{th}$ mean curvature of $M$ is constant, for ... More

An Algorithm for Computing $m$-Tight Error Linear Complexity of Sequences over $GF(p^{m})$ with Period $p^{m}$Sep 21 2011The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity profile, the ... More

A Note on the Non-Commutative Wess-Zumino ModelSep 11 2000Oct 16 2000We show that the noncommutative Wess-Zumino (NCWZ) Lagrangian with permutation terms in the interaction parts is renormalizable at one-loop level by only a wave function renormalization. When the non-commutativity vanishes, the logarithmic divergence ... More

Congruences for an arithmetic function from 3-colored Frobenius partitionsMar 02 2010Apr 27 2010Let $a(n)$ defined by $\sum_{n=1}^{\infty}a(n)q^n := \prod_{n=1}^{\infty}\frac{1}{(1-q^{3n})(1-q^n)^3}.$ In this note, we prove that for every non-negative integer $n$, a(15n+6) \equiv 0\pmod{5}, a(15n+12) \equiv 0\pmod{5}. As a corollary, we obtained ... More

Mapping properties of operator-valued pseudo-differential operatorsApr 10 2018In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces $F_1^{\alpha,c}(\mathbb{R}^d,\mathcal{M})$ obtained ... More

Leaking Information Through Cache LRU StatesMay 20 2019The widely deployed Least-Recently Used (LRU) cache replacement policy and its variants are an essential component of modern processors. However, we show for the first time in detail that the LRU states of caches can be used to leak information. The LRU ... More

Kinetic studies on using photocatalytic coatings for removal of indoor volatile organic compoundsDec 16 2018Titanium dioxide (TiO2) is a known photocatalyst with a capability of decomposing organic substance. However, the photocatalysis of the pure TiO2 is not effective for the indoor environment due to a lack of the ultraviolet irradiation inside the building. ... More

Cookie Monster Plays GamesJul 06 2014We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and Nim. We discuss ... More