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Dual morse index estimates and application to Hamiltonian systems with P-boundary conditionsJun 14 2016In this paper, we study the multiplicity of Hamiltonian systems with P-boundary conditions.

Minimal $P$-symmetric periodic solutions of nonlinear Hamiltonian systemsJun 14 2016In this paper some existence results for the minimal P-symmetric periodic solutions are proved for first order autonomous Hamiltonian systems when the Hamiltonian function is superquadratic, asymptotically linear and subquadratic. These are done by using ... More

Application of Bounded Total Variation Denoising in Urban Traffic AnalysisAug 04 2018Feb 25 2019While it is believed that denoising is not always necessary in many big data applications, we show in this paper that denoising is helpful in urban traffic analysis by applying the method of bounded total variation denoising to the urban road traffic ... More

Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power UnitsMar 14 2019Mar 28 2019Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to its universal representation power and successful applications. Some theoretical progresses on deep ReLU network approximation power for functions in Sobolev ... More

Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power UnitsMar 14 2019Apr 01 2019Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to its universal representation power and successful applications. Some theoretical progresses on deep ReLU network approximation power for functions in Sobolev ... More

Subharmonic solutions of first order Hamiltonian systems with subquadratic conditionDec 24 2016Using a homologically link theorem in variational theory and iteration inequalities of Maslov-type index, we prove the existences of a sequence of subharmonic solutions for one type of sub-quadratic non-autonomous Hamiltonian systems. Moreover, we also ... More

AMRec: An Intelligent System for Academic Method RecommendationApr 10 2019Finding new academic Methods for research problems is the key task in a researcher's research career. It is usually very difficult for new researchers to find good Methods for their research problems since they lack of research experiences. In order to ... More

Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power UnitsMar 14 2019Deep neural networks with rectified linear units (ReLU) get very popular recently due to its universal representation power and successful applications. In this paper, we show that deep networks with rectified power units (RePU) can give better approximations ... More

Representations and cohomologies of Hom-pre-Lie algebrasFeb 20 2019In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the cohomology theory of Hom-Lie algebras. As applications, we study linear ... More

Coherence measure: Logarithmic coherence numberNov 06 2018We introduce a measure of coherence, which is extended from the coherence rank via the standard convex roof construction, we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory, We study some ... More

Dynamic change-point detection using similarity networksDec 05 2016From a sequence of similarity networks, with edges representing certain similarity measures between nodes, we are interested in detecting a change-point which changes the statistical property of the networks. After the change, a subset of anomalous nodes ... More

Restricted Sumsets in Finite Nilpotent GroupsJun 27 2012Aug 21 2012Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A\not=B$, then the cardinality of the restricted sumset $$A\dotplus B={a+b: a\in A, b\in B, a\neq b} $$ is at least $$\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the ... More

A generalization of Frieman's 3k-3 theoremAug 18 2013Sep 12 2016We prove a generalization of Frieman's $3k-3$ theorem for the sumset $$ \Sigma^{l}(A_1,\ldots,A_k)=\{a_{j_{1}}+\cdots+a_{j_{l}}:\,1\leq j_{1}<\cdots<j_{l}\leq k,\ a_{j_{s}}\in A_{j_{s}}\text{ for all }s\}. $$

A Generalization of Fueter's Theorem in Dunkl-Clifford AnalysisFeb 10 2011In this paper we first offer an alternative approach to extend the original Fueter's Theorem in Dunkl-Clifford analysis to a version of the higher order case. Then this result is used to prove a generlized version of Fueter's Theorem with an extra homogeneous ... More

Local fluctuations of the signed traded volumes and the dependencies of demands: a copula analysisJun 28 2017Apr 03 2018We investigate how the local fluctuations of the signed traded volumes affect the dependence of demands between stocks. We analyze the empirical dependence of demands using copulas and show that they are well described by a bivariate $\mathcal{K}$ copula ... More

IAU WG, Data-driven Astronomy Education and Public Outreach,current status and working plansJan 16 2018IAU Inter-Commission B2-C1-C2 WG Data-driven Astronomy Education and Public Outreach (DAEPO) was launched officially in April 2017. With the development of many mega-science astronomical projects, for example CTA, DESI, EUCLID, FAST, GAIA, JWST, LAMOST, ... More

Evaluation of Spectral Zeta-Functions with the Renormalization GroupJul 18 2016Feb 24 2017We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi networks and those hierarchical networks obtained by the Migdal-Kadanoff bond ... More

On the Near Horizon Canonical Quantum Microstates from $AdS_2/CFT_1$ and Conformal Weyl GravityJul 18 2017We compute the full asymptotic symmetry group of black holes belonging to the same equivalence class of solutions within the Conformal Weyl Gravity formalism. We do this within an $AdS_2/CFT_1$ correspondence and by performing a Robinson-Wilczek two dimensional ... More

Real-Space Renormalization Group for Spectral Properties of Hierarchical NetworksMay 24 2015Oct 07 2015We derive the determinant of the Laplacian for the Hanoi networks and use it to determine their number of spanning trees (or graph complexity) asymptotically. While spanning trees generally proliferate with increasing average degree, the results show ... More

Epsilon-smooth measure of coherenceOct 09 2018Jan 14 2019In this paper, by minimizing the coherence quantifiers over all states in an $\epsilon$ ball around a given state, we define a generalized smooth quantifier, called the $\epsilon$-smooth measure of coherence. We use it to estimate the difference between ... More

Thermalization of charm quarks in infinite and finite QGP matterAug 25 2011Dec 04 2011We study the thermalization process of charm quarks in hot and dense matter. The diffusion of heavy quarks is calculated via a Langevin equation, both for a static medium as well as a QGP medium generated by a (3+1)D hydrodynamic model. We define two ... More

Arithmetic properties of the $\ell$-regular partitionsFeb 15 2013For a given prime $p$, we study the properties of the $p$-dissection identities of Ramanujan's theta functions $\psi(q)$ and $f(-q)$, respectively. Then as applications, we find many infinite family of congruences modulo 2 for some $\ell$-regular partition ... More

Physical properties of KMgBi single crystalOct 09 2016KMgBi single crystals are successfully grown using Bi flux. Transport measurements show that KMgBi exhibits semiconducting behavior with resistivity plateau at low temperature, suggesting KMgBi could be a topological insulator with a very small band gap. ... More

Global stability of epidemic models with imperfect vaccination and quarantine on scale-free networksJun 07 2018Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic models have a long ... More

Grasping asymmetric information in market impactsOct 22 2017Apr 22 2019The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market. We quantify ... More

Critical current density and vortex pinning mechanism of Lix(NH3)yFe2Te1.2Se0.8 single crystalsJun 07 2017Sep 19 2017We grew Lix(NH3)yFe2Te1.2Se0.8 single crystals successfully using the low-temperature ammonothermal method and the onset superconducting transition temperature Tc,onset is increased to 21 K when compared to 14 K in the parent compound FeTe0.6Se0.4. The ... More

Does Quantum Interference exist in Twitter?Jul 04 2011It becomes more difficult to explain the social information transfer phenomena using the classic models based merely on Shannon Information Theory (SIT) and Classic Probability Theory (CPT), because the transfer process in the social world is rich of ... More

Feature Affinity based Pseudo Labeling for Semi-supervised Person Re-identificationMay 16 2018Person re-identification aims to match a person's identity across multiple camera streams. Deep neural networks have been successfully applied to the challenging person re-identification task. One remarkable bottleneck is that the existing deep models ... More

Linearized Boltzmann transport model for jet propagation in the quark-gluon plasma: Heavy quark evolutionMay 20 2016Jul 26 2016A Linearized Boltzmann Transport (LBT) model coupled with hydrodynamical background is established to describe the evolution of jet shower partons and medium excitations in high energy heavy-ion collisions. We extend the LBT model to include both elastic ... More

Model and parameter dependence of heavy quark energy loss in a hot and dense mediumMay 10 2012Jun 27 2013Within the framework of the Langevin equation, we study the energy loss of heavy quark due to quasi-elastic multiple scatterings in a quark-gluon plasma created by relativistic heavy-ion collisions. We investigate how the initial configuration of the ... More

ReS2-based field-effect transistors and photodetectorsMar 06 2015Atomically-thin two-dimensional (2D) layered transition metal dichalcogenides (TMDs) have been extensively studied in recent years because of their appealing electrical and optical properties. Here, we report on the fabrication of ReS2 field-effect transistors ... More

The Griffiths Phase on Hierarchical Modular Networks with Small-world EdgesAug 25 2016Sep 04 2016The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self-organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, such as the hierarchical ... More

Smallest Irreducible of the Form $x^2-dy^2$Mar 01 2016It is a classical result that prime numbers of the form $x^2+ny^2$ can be characterized via class field theory for an infinite set of $n$. In this paper we derive the function field analogue of the classical result. Then we apply an effective version ... More

Electric-triple-layer model based AC electroosmosis flowJun 21 2010Feb 02 2012The paper presents an novel electric triple layer(ETL) model as an improved model of electrical double layer(EDL) to predict electroosmosis flow rate on the electrode surface at low frequency. The predicted slip velocity based on classical EDL theory ... More

Transport Theory of Heavy Flavor in Relativistic Nuclear CollisionsNov 13 2015A short overview is presented for the recent progress in the theory of heavy flavor transport in ultra-relativistic nuclear collisions, including a summary of different transport models, their phenomenological results of heavy meson quenching and flow ... More

Tensor Powers of the Defining Representation of $S_n$Aug 21 2015Feb 05 2016We give a decomposition formula for tensor powers of the defining representation of $S_n$ and apply it to bound the mixing time of a Markov chain on $S_n$.

Trading strategies for stock pairs regarding to the cross-impact costJan 11 2017Jul 06 2017We extend the framework of trading strategies of Gatheral [2010] from single stocks to a pair of stocks. Our trading strategy with the executions of two round-trip trades can be described by the trading rates of the paired stocks and the ratio of their ... More

Two Propositions Involving the Standard Representation of $S_n$Feb 10 2013We present here two standalone results from a forthcoming work on the analysis of Markov chains using the representation theory of $S_n$. First, we give explicit formulas for the decompositions of tensor powers of the defining and standard representations ... More

Enhanced superconductivity and anisotropy of FeTe0.6Se0.4 single crystals with Li-NH3 intercalationAug 17 2017Dec 09 2017We report a systematic study of anisotropy resistivity, magnetoresistance and Hall effect of Li0.32(NH3)yFe2Te1.2Se0.8 single crystals. When compared to the parent compound FeTe0.6Se0.4, the Li-NH3 intercalation not only increases the superconducting ... More

On Spectrum and Infrastructure Sharing in Multi-Operator Cellular NetworksAug 22 2016In this paper, we introduce a mathematical framework for analyzing and optimizing multi-operator cellular networks that are allowed to share spectrum licenses and infrastructure elements. The proposed approach exploits stochastic geometry for modeling ... More

Simulating Quantum Spin Hall Effect in Topological Lieb Lattice of Linear CircuitOct 19 2017Apr 03 2018Inspired by the topological insulator circuit proposed and experimentally verified by Jia., et al. \cite{1}, we theoretically realized the topological Lieb lattice, a line centered square lattice with rich topological properties, in a radio-frequency ... More

SEAL: Spatio-Textual Similarity SearchMay 30 2012Location-based services (LBS) have become more and more ubiquitous recently. Existing methods focus on finding relevant points-of-interest (POIs) based on users' locations and query keywords. Nowadays, modern LBS applications generate a new kind of spatio-textual ... More

Single Pass PCA of Matrix ProductsOct 21 2016Oct 26 2016In this paper we present a new algorithm for computing a low rank approximation of the product $A^TB$ by taking only a single pass of the two matrices $A$ and $B$. The straightforward way to do this is to (a) first sketch $A$ and $B$ individually, and ... More

DCLab: A Web-based System for Digital Logic Experiment TeachingOct 23 2018This Research-to-Practice Work in Progress paper presents DCLab, a web-based system for conducting digital logic experiments online, to improve both the effectiveness and the efficiency of digital logic experiment teaching. DCLab covers all experimental ... More

Novel Features of Gamma Ray from Dark MatterDec 10 2015In this study, we present some general and novel features of gamma ray from dark matter. We find that gamma-ray spectra with sharp features exist in a wide class of dark matter models and mimic the gamma line signals. The generated gamma rays would generally ... More

Cycles in the de Rham cohomology of abelian varieties over number fieldsOct 05 2015Jan 03 2016In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of $\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the ... More

No Time to Observe: Adaptive Influence Maximization with Partial FeedbackSep 01 2016In this paper, we investigate the adaptive influence maximization problem in social networks with partial feedback. Although the influence maximization problem problem has been extensively studies over the past ten years, majority of existing work fall ... More

Algebra endomorphisms and Derivations of Some Localized Down-Up AlgebrasMar 26 2014We study algebra endomorphisms and derivations of some localized down-up algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$ is an algebra automorphism ... More

Two-Parameter Quantum Groups and Ringel-Hall algebras of $A_{\infty}-$typeJun 09 2011Jul 04 2011In this paper, we study the two-parameter quantum group $U_{r,s}(\mathfrak sl_{\infty})$ associated to the Lie algebra $\mathfrak sl_{\infty}$ of infinite rank. We shall prove that the two-parameter quantum group $U_{r,s}(\mathfrak sl_{\infty})$ admits ... More

Fractal Dimension of Julia Set for Non-analytic MapsFeb 27 1998Apr 17 1998The Hausdorff dimensions of the Julia sets for non-analytic maps: f(z) = z^2 + epsilon z^* and f(z) = {z^*}^2 + epsilon are calculated perturbatively for small epsilon. It is shown that Ruelle's formula for Hausdorff dimensions of analytic maps can not ... More

J/psi production at high pT at STARDec 01 2010We report results on J/psi-hadron azimuthal angular correlations in 200 GeV p+p collision in the STAR experiment at RHIC. The extracted B-hadron feed-down contribution to inclusive J/psi yield is found to be 10-25% in 4<p_T<12 GeV/c and has no significant ... More

On Certain Monomial SequencesDec 02 2004We give equivalent conditions for a monomial sequence to be a d-sequence or a proper sequence, and a sufficient condition for a monomial sequence to be an s-sequence in order to compute invariants of the symmetric algebra of the ideal generated by it. ... More

Weighted norm inequalities for Schrödinger type operatorsSep 01 2011Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while nonnegative potential $V$ belongs to the reverse H\"{o}lder class. In this paper, we establish the weighted norm inequalities for some Schr\"odinger ... More

Directed and Elliptic Flow at RHICSep 28 2004Nov 15 2004We present the directed flow measurement ($v_1$) from Au+Au collisions at $\sqrtsNN = 62$ GeV. Over the pseudorapidity range we have studied, which covers $\eta$ from -1.2 to 1.2 and $2.4 < |\eta| < 4$, the magnitude of $v_1$ for charged particles is ... More

Equivariant mirror symmetry for the weighted projective lineDec 13 2017Aug 09 2018In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017]. More precisely, ... More

Exponentially convergent stochastic k-PCA without variance reductionApr 03 2019We present Matrix Krasulina, an algorithm for online k-PCA, by generalizing the classic Krasulina's method (Krasulina, 1969) from vector to matrix case. We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness ... More

Biderivations of finite dimensional complex simple Lie algebrasOct 12 2016Dec 19 2016In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find ... More

A monotone data augmentation algorithm for multivariate nonnormal data: with applications to controlled imputations for longitudinal trialsNov 20 2018An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models including the ... More

A noniterative sample size procedure for tests based on t distributionsApr 12 2018A noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending Guenther's (1981) approach for the one sample and two sample t tests. The generalized procedure is employed to determine ... More

An efficient multiple imputation algorithm for control-based and delta-adjusted pattern mixture models using SASOct 12 2016In clinical trials, mixed effects models for repeated measures (MMRM) and pattern mixture models (PMM) are often used to analyze longitudinal continuous outcomes. We describe a simple missing data imputation algorithm for the MMRM that can be easily implemented ... More

More Is Different: Reconciling eV Sterile Neutrinos with Cosmological Mass BoundsDec 31 2014Sep 24 2015It is generally expected that adding light sterile species would increase the effective number of neutrinos, $N_{eff}$. In this paper we discuss a scenario that $N_{eff}$ can actually decrease due to the neutrino oscillation effect if sterile neutrinos ... More

Implications of LHC Searches for Massive GravitonJun 29 2012Jul 31 2012With the latest LHC available results, we consider the generic constraints on massive graviton. Both dijet and dilepton resonance searches are used. The limits on parameter space can be applied to many models. As an illustration, we show the constraints ... More

Comment on "Could the Excess Seen at 124-126 GeV Be due to the Randall-Sundrum Radion?"Apr 27 2012In recent Letter by Cheung et al.[PRL {\bf 108},141602(2012)], one very interesting suggestion for the excess around 125 GeV seen at the LHC is a RS radion with $\Lambda_\phi=680$GeV. In this note, we show that taking constraints on the RS graviton into ... More

Topological QCD with a TwistSep 22 2003Oct 02 2003Non-supersymmetric Yang-Mill gauge theory in 4-dimension is shown to be dual to 4-dimensional non-supersymmetric string theory in a twisted AdS2(n)xT2 spacetime background. The partition function of a generic hadron is calculated to illustrate the mathematical ... More

MKN Theory of Bound StatesMar 02 2001Mar 19 2001This paper derives most of the formulas in the MKN (Maung-Kahana-Norbury) Theory of bound states which incorporates the Lande Subtraction method to remove the singularities of the Cornell potential.

System Identification in Dynamical SamplingFeb 10 2015Aug 31 2015We consider the problem of spatiotemporal sampling in a discrete infinite dimensional spatially invariant evolutionary process $x^{(n)}=A^nx$ to recover an unknown convolution operator $A$ given by a filter $a \in \ell^1(\mathbb{Z})$ and an unknown initial ... More

An arithmetic Lefschetz-Riemann-Roch theorem. With an appendix by Xiaonan MaMar 26 2015May 14 2019In this article, we consider regular arithmetic schemes in the context of Arakelov geometry, endowed with an action of the diagonalisable group scheme associated to a finite cyclic group. For any equivariant and proper morphism between such arithmetic ... More

Localization theorem for higher arithmetic K-theoryNov 23 2014May 14 2019Quillen's localization theorem is well known as a fundamental theorem in the study of algebraic K-theory. In this paper, we present its arithmetic analogue for the equivariant K-theory of arithmetic schemes, which are endowed with an action of certain ... More

Uniqueness of equivariant singular Bott-Chern classesMay 27 2010Feb 22 2011In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic ... More

Simple Models of the Protein Folding ProblemDec 26 1999The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I will give an ... More

Derivations of the two-parameter quantized enveloping algebra $\U$Jun 09 2011Let $r,s$ be two parameters chosen from $\C^{\ast}$ such that $r^{m}s^{n}=1$ implies $m=n=0$. We compute the derivations of the two-parameter quantized enveloping algebra $\U$ and calculate its first degree Hochschild cohomology group. We further determine ... More

A Counter Example of Invariant Deformation QuantizationNov 29 2004In this note, we will show one example of hamiltonian Lie algebra action which has no invariant star product.

On The Metal-poor non-Sagittarius Globular Cluster NGC 5053: Orbit, Mg, Al, and SiAug 10 2017Metal-poor globular clusters (GCs) show intriguing Al-Mg and Si-Al correlations, which are important clues to decipher the multiple population phenomenon. NGC 5053 is one of the most metal-poor GCs, and has been suggested to be associated with the Sagittarius ... More

Localization theorem for higher arithmetic K-theoryNov 23 2014Jul 02 2015Quillen's localization theorem is well known as a fundamental theorem in the study of algebraic K-theory. In this paper, we present its arithmetic analogue for the equivariant K-theory of arithmetic schemes, which are endowed with an action of certain ... More

Biderivations and commutative post-Lie algebra structure on the Schrödinger-Virasoro Lie algebraNov 13 2016Dec 19 2016In this paper, we characterize the biderivations of Schr\"odinger-Virasoro Lie algebra. We get a classes of non-inner and non-skewsymmetric biderivations. As application, we characterize the commutative post-Lie algebra structures on Schr\"odinger-Virasoro ... More

Two types of variational integrators and their equivalenceSep 18 2018In this paper, we introduce two types of variational integrators, one originating from the discrete Hamilton's principle while the other from Galerkin variational approach. It turns out that these variational integrators are equivalent to each other when ... More

Energy-preserving continuous-stage partitioned Runge-Kutta methodsAug 07 2018In this paper, we present continuous-stage partitioned Runge-Kutta (csPRK) methods for energy-preserving integration of Hamiltonian systems. A sufficient condition for the energy preservation of the csPRK methods is derived. It is shown that the presented ... More

An extended framework of continuous-stage Runge-Kutta methodsJun 13 2018Jul 26 2018We propose an extended framework for continuous-stage Runge-Kutta methods which enables us to treat more complicated cases especially for the case weighting on infinite intervals. By doing this, various types of weighted orthogonal polynomials (e.g., ... More

A note on continuous-stage Runge-Kutta methodsApr 23 2018May 25 2018We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK) methods, can give ... More

New super-quadratic conditions for asymptotically periodic Schrödinger equationJul 10 2015This paper is dedicated to studying the semilinear Schr\"odinger equation $\left\{\begin{array}{ll}-\Nabla u+V(x)u=f(x, u), \ \ \ \ x\in {\R}^{N},u\in H^{1}({\R}^{N}),\end{array}\right.$ where $f$ is a superlinear, subcritical nonlinearity. It focuses ... More

The curve complex and covers via hyperbolic 3-manifoldsApr 18 2011Rafi and Schleimer recently proved that the natural relation between curve complexes induced by a covering map between two surfaces is a quasi-isometric embedding. We offer another proof of this result using a distance estimate via hyperbolic 3-manifolds. ... More

Capillary Rise in Tubes with Sharp GroovesJan 17 1994Liquid in grooved capillaries, made by e.g. inserting a plate in a cylindrical tube, exhibits unusual spreading and flow properties. One example is capillary rise, where a long, upward tongue on top of the usual meniscus has been observed along the groove. ... More

Biderivations of finite dimensional complex simple Lie algebrasOct 12 2016Oct 13 2016In this paper, we prove that the biderivation of finite dimensional complex simple Lie algebra without the restriction of skew-symmetric is inner. As applications, we characterize the biderivation of general linear Lie algebra, it is a non-inner and non-skew-symmetric ... More

Biderivations of finite dimensional complex simple Lie algebrasOct 12 2016Oct 15 2016In this paper, we prove that the biderivation of finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As applications, we characterize the biderivation of general linear Lie algebra, it is a non-inner and non-skewsymmetric ... More

Closed-form REML estimators and sample size determination for mixed effects models for repeated measures under monotone missingnessNov 01 2016We derive the closed-form restricted maximum likelihood (REML) estimator and Kenward-Roger's variance estimator for fixed effects in the mixed effects model for repeated measures (MMRM) when the missing data pattern is monotone. As an important application ... More

Automorphisms for Some "symmetric" Multiparameter Quantized Weyl Algebras and Their LocalizationsOct 06 2016In this paper, we study the algebra automorphisms and isomorphisms for a family of "symmetric" multiparameter quantized Weyl algebras $\A$ and some related algebras in the generic case. First, we compute the Nakayama automorphism for $\A$ and give a necessary ... More

Down-up algebras defined over a polynomial base ring $\K[t_{1}, \cdots, t_{n}]$Mar 26 2014In this paper, we study a class of down-up algebras $\A$ defined over a polynomial base ring $\K[t_{1}, \cdots, t_{n}]$ and establish several analogous results. We first construct a $\K-$basis for the algebra $\A$. As a result, we prove that the Gelfand-Kirillov ... More

Are Chlorine Isotopologues of Polychlorinated Organic Compounds Exactly Binomially Distributed? A Theoretical Study and Implications to ExperimentsJun 14 2017Jun 15 2017Chlorine isotopologues of polychlorinated organic compounds are usually recognized to follow binomial distribution. Is this recognition exactly true? This study presents a solid theoretical derivation to prove whether the isotopologue distributions of ... More

Effect of histamine on the electric activities of cerebellar Purkinje cellJan 31 1999The effect of histamine (HA) on the electric activities of Purkinje cell (PC) is studied on the cerebellum slice. We find that: (1) HA's main effect on PC is excitative (72.9%); there are also a small amount of PC showing inhibitive (10.2%) or no (16.9%) ... More

The Non-uniform Fast Fourier Transform in Computed TomographyMay 17 2016This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the potential computational ... More

Continuous-stage Runge-Kutta-NystrÖm methodsJul 09 2018Jul 25 2018We develop continuous-stage Runge-Kutta-Nystr\"Om (csRKN) methods in this paper. By leading weight function into the formalism of csRKN methods and modifying the original pattern of continuous-stage methods, we establish a new and larger framework for ... More

Biderivations and commutative post-Lie algebra structures on the Lie algebra W(a,b)Dec 26 2017Jan 02 2018For $a,b\in \mathbb{C}$, the Lie algebra $\mathcal{W}(a,b)$ is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of $\mathcal{W}(a,b)$ are determined. Surprisingly, these Lie algebras ... More

Removing a ray from a noncompact symplectic manifoldDec 02 2018Mar 10 2019We prove that any noncompact symplectic manifold which admits a properly embedded ray with a wide neighborhood is symplectomorphic to the complement of the ray by constructing an explicit symplectomorphism in the case of the standard Euclidean space. ... More

A Lefschetz fixed point formula for singular arithmetic schemes with smooth generic fibresFeb 10 2010Feb 22 2011In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an analog, in the arithmetic ... More

Dual Representation as Stochastic Differential Games of Backward Stochastic Differential Equations and Dynamic EvaluationsFeb 15 2006In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a domination ... More

Submodular Maximization under Fading Model: Building Online Quizzes for Better Customer SegmentationJan 23 2019Feb 11 2019E-Commerce personalization aims to provide individualized offers, product recommendations, and other content to customers based on their interests. The foundation of any personalization effort is customer segmentation. The idea of customer segmentation ... More

Toward Optimal Coupon Allocation in Social Networks: An Approximate Submodular Optimization ApproachFeb 02 2018Feb 22 2018CMO Council reports that 71\% of internet users in the U.S. were influenced by coupons and discounts when making their purchase decisions. It has also been shown that offering coupons to a small fraction of users (called seed users) may affect the purchase ... More

Post-Lie algebra structures on the Witt algebraJan 01 2017Aug 19 2017In this paper, we characterize the graded post-Lie algebra structures and a class of shifting post-Lie algebra structures on the Witt algebra. We obtain some new Lie algebras and give a class of their modules. As an application, the homogeneous Rota-Baxter ... More

Automorphisms of the two-parameter Hopf algebra $\V$Jun 09 2011We determine the group of algebra automorphisms for the two-parameter quantized enveloping algebra $\V$. As an application, we prove that the group of Hopf algebra automorphisms for $\V$ is isomorphic to a torus of rank two.

Biderivations and commutative post-Lie algebra structure on the Schrödinger-Virasoro Lie algebraNov 13 2016In this paper, we characterize the biderivations of Schr\"{o}dinger-Virasoro Lie algebra. We get a classes of non-inner and non-skewsymmetric biderivations. As application, we characterize the commutative post-Lie algebra structures on Schr\"{o}dinger-Virasoro ... More