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Reliable Electrical Switching of Tri-State Antiferromagnetic Néel Order in $α$-Fe$_2$O$_3$ Epitaxial FilmsJun 11 2019The ability to manipulate antiferromagnetic (AF) moments is a key requirement for the emerging field of antiferromagnetic spintronics. Electrical switching of bi-state AF moments has been demonstrated in metallic AFs, CuMnAs and Mn$_2$Au. Recently, current-induced ... More

Anisotropic Magnetoresistance and Nontrivial Spin Magnetoresistance in Pt/$α$-Fe$_2$O$_3$ Bilayers: Evidence for Antiferromagnetic Proximity EffectJun 11 2019To date, magnetic proximity effect (MPE) has only been conclusively observed in ferromagnet (FM) based systems. We report the observation of anomalous Hall effect and anisotropic magnetoresistance in angular dependent magnetoresistance (ADMR) measurements ... More

Anisotropic Magnetoresistance and Nontrivial Spin Magnetoresistance in Pt/$α$-Fe$_2$O$_3$ Bilayers: Evidence for Antiferromagnetic Proximity EffectJun 11 2019Jul 19 2019To date, magnetic proximity effect (MPE) has only been conclusively observed in ferromagnet (FM) based systems. We report the observation of anomalous Hall effect and anisotropic magnetoresistance in angular dependent magnetoresistance (ADMR) measurements ... More

A Multi-variable Stacked Long-Short Term Memory Network for Wind Speed ForecastingNov 24 2018Precisely forecasting wind speed is essential for wind power producers and grid operators. However, this task is challenging due to the stochasticity of wind speed. To accurately predict short-term wind speed under uncertainties, this paper proposed a ... More

Decorated marked surfaces II: Intersection numbers and dimensions of HomsNov 14 2014Jun 02 2017We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface $\mathbf{S}_\bigtriangleup$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection ... More

Cluster categories for marked surfaces: punctured caseOct 31 2013May 24 2015We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting ... More

Weil asymptotic formula for the Laplacian on domains with rough boundariesOct 07 2003We study asymptotic distribution of eigenvalues of the Laplacian on a bounded domain in $ \R^n$. Our main results include an explicit remainder estimate in the Weyl formula for the Dirichlet Laplacian on an arbitrary bounded domain, sufficient conditions ... More

Asymptotic properties of one-step weighted $M$-estimators and applications to some regression problemsMay 11 2015Jul 04 2015We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted $M$-estimators. ... More

On the existence of natural self-oscillation of a free electronJan 11 2012Jan 27 2013The possibility of the existence of natural self-oscillation of a free electron is suggested. This oscillation depends on the interaction of the electron with its own electromagnetic fields. Suitable standing wave solutions of the electromagnetic fields ... More

Decorated marked surfaces II: Intersection numbers and dimensions of HomsNov 14 2014May 28 2015We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface $\mathbf{S}_\bigtriangleup$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection ... More

Finite presentations for spherical/braid twist groups from decorated marked surfacesMar 29 2017Oct 29 2018We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3-Calabi-Yau ... More

MIDAS: A Dialog Act Annotation Scheme for Open Domain Human Machine Spoken ConversationsAug 27 2019Dialog act prediction is an essential language comprehension task for both dialog system building and discourse analysis. Previous dialog act schemes, such as SWBD-DAMSL, are designed for human-human conversations, in which conversation partners have ... More

Displacement induced electric force and natural self-oscillation of a free electronApr 13 2013Jun 13 2013We show that a kind of displacement induced temporary electric force of a single point charge can be derived by using Maxwell stress analysis. This force comes from the variation of the charge's electric intensities that follow Coulomb's inverse square ... More

Asymptotic properties of one-step $M$-estimators based on nonidentically distributed observations with applications to nonlinear regression problemsMar 11 2015Apr 11 2016We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These estimators ... More

Cluster categories for marked surfaces: punctured caseOct 31 2013Jan 08 2017We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting ... More

Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flowsJul 20 2010Aug 03 2010G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, ... More

A Numerical Study of Turbulent Flame Speeds of Curvature and Strain G-equations in Cellular FlowsFeb 28 2012We study front speeds of curvature and strain G-equations arising in turbulent combustion. These G-equations are Hamilton-Jacobi type level set partial differential equations (PDEs) with non-coercive Hamiltonians and degenerate nonlinear second order ... More

Surgery on links with unknotted components and three-manifoldsJan 22 2008It is shown that any closed three-manifold M obtained by integral surgery on a knot in the three-sphere can always be constructed from integral surgeries on a 3-component link L with each component being an unknot in the three-sphere. It is also interesting ... More

Turbulent Flame Speeds of G-equation Models in Unsteady Cellular FlowsOct 05 2012We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The curvature-strain ... More

The augmentation category map induced by exact Lagrangian cobordismsJun 19 2016To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and ... More

Nonlinear variable selection with continuous outcome: a nonparametric incremental forward stagewise approachJan 20 2016Nov 07 2016We present a method of variable selection for the situation where some predictors are nonlinearly associated with a continuous outcome variable. The method doesn't assume any specific functional form, and can select from a large number of candidates. ... More

Lyapunov graphs of nonsingular Smale flows on $S^{1}\times S^{2}$Mar 11 2011In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on $S^1 \times S^2$. More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov ... More

The equivalence between Feynman transform and Verdier dualityOct 29 2016Nov 01 2016The equivalence between dg duality and verdier duality has been established for cyclic operad. We generalize this correspondence from cyclic operad and dg duality to twisted modular operad and Feynman transform. Specifically, to each twisted modular operad ... More

Exact Non-identity check is NQP-completeMar 04 2009We define a problem "exact non-identity check": Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a sense of the ... More

$K_L-K_S$ mass difference from Lattice QCDDec 02 2013We will report on the first full calculation of the $K_L-K_S$ mass difference in lattice QCD. The calculation is performed on a 2+1 flavor, domain wall fermion, $24^3\times 64$ ensemble with a 329 MeV pion mass and a 575 MeV kaon mass. Both double penguin ... More

Cell-probe Lower Bounds for Dynamic Problems via a New Communication ModelDec 04 2015In this paper, we develop a new communication model to prove a data structure lower bound for the dynamic interval union problem. The problem is to maintain a multiset of intervals $\mathcal{I}$ over $[0, n]$ with integer coordinates, supporting the following ... More

A note on Kaehler-Ricci flowOct 03 2008Let $g(t)$ with $t\in [0,T)$ be a complete solution to the Kaehler-Ricci flow: $\frac{d}{dt}g_{i\bar j}=-R_{i\bar j}$ where $T$ may be $\infty$. In this article, we show that the curvatures of $g(t)$ is uniformly bounded if the solution $g(t)$ is uniformly ... More

Curvature of almost Hermitian manifolds and applicationsSep 23 2012In this paper, by introducing a notion of local quasi holomorphic frame, we obtain a curvature formula for almost Hermitian manifolds which is similar to that of Hermitian manifolds. Moreover, as applications of the curvature formula, we extend a result ... More

Energy conservation for the weak solutions of the compressible Navier-Stokes equationsMay 02 2016Nov 01 2016In this paper, we prove the energy conservation for the weak solutions of the compressible Navier-Stokes equations for any time $t>0$, under certain conditions. The results hold for the renormalized solutions of the equations with constant viscosities, ... More

Phase vortices of the quenched Haldane ModelNov 27 2016Using the recently developed Bloch-state tomography technique, the quasimomentum $\bf k$-dependent Bloch states ${\left( {\sin \left( {{\theta _{\mathbf{k}}}/2} \right),\; - \cos \left( {{\theta _{\mathbf{k}}}/2} \right){e^{i{\phi _{\mathbf{k}}}}}} \right)^T}$ ... More

Spatial double choreographies of the Newtonian $2n$-body problemAug 29 2016In this paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial double choreographies, ... More

A Systematic Improvement for Calculation to Conductivity in Anomalous Propagation of Surface Acoustic Wave at $ν={1/2}$Jan 14 1998We report a systematic improvement to calculate the conductivity which associates to the anomaly of the propagation of surface acoustic waves at $\nu={1/2}$ above a two-dimensional electron gas. We try to resolve the discrepancy between theoretical and ... More

On the realization of impossible anomaliesApr 09 2018The Wess-Zumino consistency condition allows more exotic forms of anomalies than those we usually encounter. For example in two-dimensional conformal field theories in the curved background with space-time dependent coupling constant $\lambda^i(x)$, a ... More

Topologically twisted renormalization group flow and its holographic dualJun 07 2016Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and if the subsequent ... More

Time-evolution stability of order parameters and phase diagrams of bosons on optical latticeMar 01 2004Stemming from the Heisenberg equations of motion, we study the time-evolution stability of the order parameters for the cold atoms on optical lattices. The requirement of this stability of the order parameters endows the phase diagram with a fruitful ... More

Vector Beta functionOct 02 2013Oct 10 2013We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like ... More

(0,2) Chiral Liouville Field TheoryMay 16 2013As an existence proof of the (0,2) heterotic supercurrent supermultiplets in (1+1) dimensional quantum field theories which are consistent with the warped superconformal algebra, we construct the (0,2) chiral Liouville field theories. The two distinct ... More

Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge TheoryFeb 28 2006Mar 22 2006We compute the index for the conifold gauge theory from type IIB supergravity (superstring) on AdS_5 \times T^{1,1}. We discuss its implication from the gauge theory viewpoint.

Effective Gauge Degrees of Freedom and the (Non)existence of the Glueball SuperpotentialJun 02 2003Dec 17 2003We propose an efficient way to obtain a correct Veneziano-Yankielowicz type integration constant of the effective glueball superpotential $W_{eff}(S,g,\Lambda)$, even for massless theories. Applying our method, we show some $\mathcal{N} = 1$ theories ... More

Bootstrapping critical Ising model on three-dimensional real projective spaceJan 25 2016Apr 19 2016Given a conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three-dimensional real projective space. We check the rapid convergence of ... More

Perturbative search for dead-end CFTsJan 09 2015May 07 2015To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three ... More

4D and 2D superconformal index with surface operatorMay 24 2011Jul 23 2011We study the superconformal index of the N=4 super-Yang-Milles theory on S^3 X S^1 with the half BPS superconformal surface operator (defect) inserted at the great circle of S^3. The half BPS superconformal surface operators preserve the same supersymmetry ... More

Emerging AdS from Extremally Rotating NS5-branesDec 11 2008Feb 17 2009We investigate the near-horizon limit of extremally rotating NS5-branes. The resulting geometry has SL(2,R) \times U(1)^2 isometry. The asymptotic symmetry group contains a chiral Virasoro algebra, and we obtain two different realizations depending on ... More

An Index for Non-relativistic Superconformal Field TheoriesJul 21 2008Mar 05 2009We study the highest-weight representation of N=2 supersymmetric Schrodinger algebra which appears in non-relativistic superconformal field theories in (1+2) dimension. We define the index for the non-relativistic superconformal field theories and study ... More

Conformal invariance and universal critical exponents in the two-dimensional percolation modelJun 05 2009Jun 14 2009This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

A Novel Meron-induced Pseudospin Wave in Bilayer Quantum Hall Coherent State and the Residual Zero-bias Peak in Tunneling ConductanceJun 14 2002In the bilayer quantum Hall coherent state for $\nu_T$ deviating slightly from one, we show that, instead of the global order parameter, the spontaneous breaking of the pseudospin U(1) rotational symmetry is reflected by the periodic domain structure ... More

A note on cutting spin networks and the area spectrum in loop quantum gravityJun 11 2015Oct 28 2015In this paper, I show that if a spin network is cut by a surface separating space-time into two regions, the sum of spins of edges crossing the surface must be an integer. This gives a restriction on the area spectrum of such surfaces, including black ... More

A quantum homomorphic encryption scheme for polynomial-sized circuitsOct 02 2018Jun 03 2019Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program ... More

Incompressible excitonic superfluid of ultracold Bose atoms in an optical lattice: a new superfluid phase in the one-component Bose-Hubbard modelJan 04 2005We predict that a new superfluid phase, the incompressible excitonic superfluid (IESF), in the phase diagram of ultracold Bose atoms in $d>1$ dimensional optical lattices, which is caused by the spontaneous breaking of the symmetry of translation of the ... More

Short-range coherence of a lattice Bose atom gas in the Mott insulating phaseMay 09 2005Nov 24 2005We study the short-range coherence of ultracold lattice Bose gases in the Mott insulating phase. We calculate the visibility of the interference pattern and the results agree quantitatively with the recent experimental measurement [Phys. Rev. Lett. 95, ... More

Many Boson Realizations of Universal Nonlinear $W_{\infty}$-AlgebrasJan 14 1993An infinite number of free field realizations of the universal nonlinear $\hat{W}_{\infty}^{(N)}$ ($\hat{W}_{1+\infty}^{(N)}$) algebras, which are identical to the KP Hamiltonian structures, are obtained in terms of $p$ plus $q$ scalars of different signatures ... More

Bi-Hamiltonian Sturcture of Super KP HierarchySep 06 1991We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i} \theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected ... More

Maxima of the signless Laplacian spectral radius for planar graphsJul 19 2014The signless Laplacian spectral radius of a graph is the largest eigenvalue of its signless Laplacian. In this paper, we prove that the graph $K_{2}\nabla P_{n-2}$ has the maximal signless Laplacian spectral radius among all planar graphs of order $n\geq ... More

Covering 2-connected 3-regular graphs with disjoint pathsJun 19 2018A path cover of a graph is a set of disjoint paths so that every vertex in the graph is contained in one of the paths. The path cover number $p(G)$ of graph $G$ is the cardinality of a path cover with the minimum number of paths. Reed in 1996 conjectured ... More

CM Values of Green Functions Associated to Special Cycles on Shimura Varieties with Applications to Siegel 3-Fold $X_2(2)$Oct 10 2017May 27 2019We generalize the definition of CM cycles beyond the small and big CM ones studied by various authors and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts. ... More

Design of a multichannel 127 degree cylindrical spectrometer for sputtered ionsNov 12 2008Jun 12 2017Design details of a 127 degree electrostatic cylindrical spectrometer equipped with a position-sensitive micro-channel plate detector for measuring the sputtered ions in collisions of highly charged ions with solid surface is described. The nonlinear ... More

Envy-free Matchings with Lower QuotasApr 17 2017Sep 20 2017While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-free matching, which is a relaxation ... More

The last (lost) charge of a black holeApr 01 2018The topological charge of a maximally symmetric black hole naturally arise in holography, which can be viewed as the last (lost) charge of the black hole in the sense that it together with all other known charges satisfies the Gibbs-Duhem-like relation ... More

Some Peculiarities of Newton-Hooke Space-TimesSep 18 2011Sep 28 2011Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke ... More

A new eddy-viscosity model for large eddy simulation in helical turbulenceNov 26 2012Dec 12 2012In isotropic helical turbulence, a new single helical model is suggested for large eddy simulation. Based on the Kolmogrov's hypotheses, the helical model is proposed according to the balance of helicity dissipation and the average of helicity flux across ... More

Quantum Fisher Information as the Convex Roof of VarianceFeb 21 2013Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given observable has the minimal ... More

Central limit theorem and almost sure central limit theorem for the product of some partial sumsJul 31 2007In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

How shall we determine detection sensitivity in radio pulsar search?Nov 17 2018Determination of detection sensitivity in a number of previous pulsar search programmes was done via the straightfoward use of the radiometer equation. In the same surveys, the Fourier domain method was used to search for pulsars. As detection sensitivity ... More

Have we seen all glitches?Mar 26 2018Neutron star glitches are observed via artificially scheduled pulsar pulse arrival-time observations. Detection probability density of glitch events for a given data set is essentially required knowledge for realizing glitch detectability with specified ... More

A note on closed subgroups of compact Lie groupsDec 22 2009Mar 27 2012We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly controlling fusions" ... More

Cube packings in Euclidean spacesNov 17 2017Jan 06 2018In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension ... More

Measure-theoretic mean equicontinuity and bounded complexityJul 13 2018Let $(X,\mathcal{B},\mu,T)$ be a measure preserving system. We say that a function $f\in L^2(X,\mu)$ is $\mu$-mean equicontinuous if for any $\epsilon>0$ there is $k\in \mathbb{N}$ and measurable sets ${A_1,A_2,\cdots,A_k}$ with $\mu\left(\bigcup\limits_{i=1}^k ... More

Decoherence and Localization in Quantum Two-Level SystemsMay 31 1996We study and compare the decoherent histories approach, the environment-induced decoherence and the localization properties of thesolutions to the stochastic Schr\"{o}dinger equation in quantum jump simulationand quantum state diffusion approaches, for ... More

Extreme rays of the $\ell^\infty$-nearest ultrametric tropical polytopeJul 24 2019The set of ultrametrics on $[n]$ nodes that are $\ell^\infty$-nearest to a given dissimilarity map forms a $(\max,+)$ tropical polytope. Previous work of Bernstein has given a superset of the set containing all the phylogenetic trees that are extreme ... More

Uniform Approximation from Symbol Calculus on a Spherical Phase SpaceMay 21 2011Nov 25 2011We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely, the uniform approximation ... More

Ramification estimates for the hyperbolic Gauss mapApr 03 2008Dec 04 2008We give the best possible upper bound on the number of exceptional values and the totally ramified value number of the hyperbolic Gauss map for pseudo-algebraic constant mean curvature one surfaces in the hyperbolic three-space and some partial results ... More

Ising antiferromagnet on the Archimedean latticesJun 27 2016Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte-Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis ... More

Whitney's Theorem for oscillatiing on $R$ functionsDec 15 2006We find the order of Whitney's constants for oscillating functions

Bernoulli decomposition and arithmetical independence between sequencesNov 28 2018In this paper we study the following set\[A=\{p(n)+2^nd \mod 1: n\geq 1\}\subset [0.1],\] where $p$ is a polynomial with at least one irrational coefficient on non constant terms, $d$ is any real number and for $a\in [0,\infty)$, $a \mod 1$ is the fractional ... More

Existence results for superlinear elliptic equations with nonlinear boundary value conditionsOct 10 2014In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition $$ \left\{ \begin{array}{ll} -\Delta u+u=|u|^{r-2}u &\text{in} \; \Omega,\\ \\ \frac{\partial u}{\partial \nu}=|u|^{q-2}u ... More

On Convergence of some Gradient-based Temporal-Differences Algorithms for Off-Policy LearningDec 27 2017Mar 28 2018We consider off-policy temporal-difference (TD) learning methods for policy evaluation in Markov decision processes with finite spaces and discounted reward criteria, and we present a collection of convergence results for several gradient-based TD algorithms ... More

Weak Convergence Properties of Constrained Emphatic Temporal-difference Learning with Constant and Slowly Diminishing StepsizeNov 23 2015Jan 20 2017We consider the emphatic temporal-difference (TD) algorithm, ETD($\lambda$), for learning the value functions of stationary policies in a discounted, finite state and action Markov decision process. The ETD($\lambda$) algorithm was recently proposed by ... More

A novel scheme for simple and precise measurement of the complex refractive index and thickness of thin filmsDec 02 2013We demonstrate applications of a novel scheme which is used for measuring refractive index and thickness of thin film by analyzing the relative phase difference and reflected ratio at reflection point of a monolithic folded Fabry-Perot cavity (MFC). The ... More

Do most polynomials generate a prime ideal?Sep 07 2015Jan 11 2016For which monomial supports do most polynomials generate a prime ideal? We give necessary and sufficient conditions for the radical of the ideal to be prime over an algebraically closed field. In characteristic zero, the same conditions give primeness. ... More

On GILP's group theoretic approach to Falconer's distance problemOct 01 2018In this paper, we follow and extend a group-theoretic method introduced by Greenleaf-Iosevich-Liu-Palsson (GILP) to study finite points configurations spanned by Borel sets in $\mathbb{R}^n,n\geq 2,n\in\mathbb{N}.$ We remove a technical continuity condition ... More

Kakeya books and projections of Kakeya setsApr 14 2017Here we show some results related with Kakeya conjecture which says that for any integer $n\geq 2$, a set containing line segments in every dimension in $\mathbb{R}^n$ has full Hausdorff dimension as well as box dimension. We proved here that the Kakeya ... More

Efficient Time-Evolving Stream Processing at ScaleJun 03 2018Time-evolving stream datasets exist ubiquitously in many real-world applications where their inherent hot keys often evolve over times. Nevertheless, few existing solutions can provide efficient load balance on these time-evolving datasets while preserving ... More

Dynamical Environment in the Vicinity of Asteroids with an Application to 41 DaphneMay 28 2018We studied the dynamical environment in the vicinity of the primary of the binary asteroid. The gravitational field of the primary is calculated by the polyhedron model with observational data of the irregular shape. The equilibrium points, zero velocity ... More

Two Dimensional NLS Equation With Random Radial DataAug 16 2010Nov 15 2010In this paper we study radial solutions of certain two-dimensional nonlinear Schr\"odinger equation with harmonic potential, which is supercritical with respect to the initial data. By combining the nonlinear smoothing effect of Schr \"odinger equation ... More

Superalgebraic interpretation of quantization maps of Weil algebrasFeb 08 2005Jun 07 2005In 1998, A.Alekseev and E.Meinrenken construct an explicit $G$-differential space homomorphism $\mathcal{Q}$, called the quantization map, between the Weil algebra $\Weil{\g}= \sym{\co{\g}} \otimes \ext{\co{\g}}$ and $\NWeil{\g}=\U{\g} \otimes \Cl{\g}$ ... More

On dually flat $(α,β)$-metricsMay 16 2013In this paper, I will show how to use $\beta$-deformations to deal with dual flatness of $(\alpha,\beta)$-metrics. It is a natural continuation of the research on dually flat Randers metrics(see arxiv:1209.1150). $\beta$-deformations is a new method in ... More

On Riemann curvature of singular square metricsJul 22 2018Square metrics is an important class of Finsler metrics. Recently, we introduced a special class of non-regular Finsler metrics called singular square metrics. The main purpose of this paper is to provide a necessary and sufficient condition for singular ... More

Stochastic Ordering of Exponential Family Distributions and Their MixturesSep 24 2009We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general theorem based ... More

Efficient Simulation of a Bivariate Exponential Conditionals DistributionSep 23 2009The bivariate distribution with exponential conditionals (BEC) is introduced by Arnold and Strauss [Bivariate distributions with exponential conditionals, J. Amer. Statist. Assoc. 83 (1988) 522--527]. This work presents a simple and fast algorithm for ... More

Dynamics of edge Majorana fermions in $ν=\frac{5}2$ fractional quantum Hall effectsAug 24 2006Oct 25 2007Commencing with the composite fermion description of the $\nu=5/2$ fractional quantum Hall effect, we study the dynamics of the edge neutral Majorana fermions. We confirm that these neutral modes are chiral and show that a conventional p-wave pairing ... More

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifoldsApr 29 2007Jan 22 2008We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, ... More

Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$May 08 2018In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schr\"odinger equation in $\mathbb{R}^2$ with general data in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$. We show that if a solution remains ... More

Elliptic fibrations on K3 surfaces and Salem numbers of maximal degreeMay 30 2016Aug 24 2016We study the maximal Salem degree of automorphisms of K3 surfaces via elliptic fibrations. By generalizing \cite{EOY14}, we establish a characterization of such maximum in terms of elliptic fibrations with infinite automorphism groups. As an application, ... More

Emotional Interaction between Artificial Companion Agents and the ElderlyJan 21 2016Jan 22 2016Artificial companion agents are defined as hardware or software entities designed to provide companionship to a person. The senior population are facing a special demand for companionship. Artificial companion agents have been demonstrated to be useful ... More

On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefoldsFeb 21 2013We give some necessary conditions for a smooth irreducible curve $C\subset \mathbb{P}^4$ to be isolated in a smooth quintic threefold, and also find a lower bound for $h^1(\mathcal{N}_{C/{\mathbb{P}^4}})$. Combining these with beautiful results in Castelnuovo ... More

Geometric Phases of Two Ising-interacting Spins in a Rotating Magnetic FieldFeb 20 2009Nov 04 2009We consider how to obtain a nontrivial two-qubit unitary transformation purely based on geometric phases of two spin-1/2's with Ising-like interaction in a magnetic field with a static z-component and a rotating xy-component. This is an interesting problem ... More

Superfluidity or supersolidity as a Consequence of Off-diagonal Long-range OrderJan 19 2005Aug 13 2006We present a general derivation of Hess-Fairbank effect or non-classical rotational inertial (NCRI), i.e. the refusal to rotate with its container, as well as the quantization of angular momentum, as consequences of off-diagonal long-range order (ODLRO) ... More

Entanglement in Relativistic Quantum Field TheoryAug 09 2004Nov 11 2004I present some general ideas about quantum entanglement in relativistic quantum field theory, especially entanglement in the physical vacuum. Here, entanglement is defined between different single particle states (or modes), parameterized either by energy-momentum ... More

Comment on "Off-diagonal Long-range Order in Bose Liquids: Irrotational Flow and Quantization of Circulation"Jun 13 2003In the context of an application to superfluidity, it is elaborated how to do quantum mechanics of a system with a rotational velocity. Especially, in both the laboratory frame and the non-inertial co-rotating frame, the canonical momentum, which corresponds ... More

Quantum Disentanglement in Long-range Orders and Spontaneous Symmetry BreakingMay 13 2002Jan 31 2003We investigate the nature of quantum entanglement in long-range orders and spontaneous symmetry breaking. It is shown that diminishing of entanglement between the condensate mode and the rest of the system underlies off-diagonal long-range order, which ... More