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Polaron Properties of an Impurity in Bose-Einstein-CondensationNov 24 2008In this paper we study an impurity in Bose-Einstein-Condensate system at $T=0K$ and suppose the contact forms for boson-boson and boson-impurity interactions. Using Bogoliubov theory and a further approximation corresponding to only think over the forward ... More

Excitation Spectrum and Momentum Distribution of Bose-Hubbard Model with On-site Two- and Three-body InteractionDec 16 2012An effective action for Bose-Hubbard model with two- and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis. From this effective action, superfluid-Mott insulator ... More

Finite Temperature Phase Diagram in Rotating Bosonic Optical LatticeNov 24 2008Finite temperature phase boundary between superfluid phase and normal state is analytically derived by studying the stability of normal state in rotating bosonic optical lattice. We also prove that the oscillation behavior of critical hopping matrix directly ... More

Metal-Mott Insulator Transition and Spin Exchange of Two-Component Fermi Gas with Spin-Orbit Coupling in Two-Dimension Square Optical LatticesJul 21 2011Oct 12 2011Effects of spin-orbit coupling (SOC) on metal-Mott insulator transition (MMIT) and spin exchange physics (SEP) of two-component Fermi gases in two-dimension half-filling square optical lattices are investigated. In the frame of Kotliar and Ruckenstein ... More

BCS-BEC Crossover in Mix-dimensional Fermi GasesApr 13 2011We investigate a mix-dimensional Fermi-Fermi mixture in which one species is confined in two-dimensional(2D) space while the other is free in three-dimensional space(3D). We determine the superfluid transition temperature $T_{c}$ for the entire BCS-BEC ... More

A New Non-Abelian Topological Phase of Cold Fermi Gases in Anisotropic and Spin-Dependent Optical LatticesJun 25 2012Jun 26 2012To realize non-Abelian s-wave topological superfluid (TS) of cold Fermi gases, generally a Zeeman magnetic field larger than superfluid pairing gap is necessary. In this paper we find that using an anisotropic and spin-dependent optical lattice (ASDOL) ... More

Topological superfluid of spinless Fermi gases in p-band honeycomb optical lattices with on-site rotationJun 18 2012In this paper, we put forward to another route realizing topological superfluid (TS). In contrast to conventional method, spin-orbit coupling and external magnetic field are not requisite. Introducing an experimentally feasible technique called on-site ... More

Type-I and type-II topological nodal superconductors with $s$-wave interactionJun 06 2017Topological nodal superconductors are generally realized based on unconventional pairings. In this work, we propose a minimal model to realize these topological nodal phases with only $s$-wave interaction. In our model the linear and quadratic spin-orbit ... More

Dynamical instability towards finite-momentum pairing in quenched BCS superconducting phasesOct 22 2018In this work we numerically investigate the fate of the Bardeen-Cooper-Schrieffer (BCS) pairing in the presence of quenched phase under Peierls substitution using time-dependent real space and momentum space Bogoliubov-de Gennes equation methods and Anderson ... More

Oscillation of Pauli Paramagnetism in Rotating Two-Component Fermionic Atom GasesNov 24 2008By rotating two-component fermionic atom gases in uniform magnetic field, a similar physical situation with de Haas-van Alphen effect is constructed. We calculate magnetic moment of the system and find that owing to an existence of effective magnetic ... More

Condensate Fraction and Pair Coherence Lengths of Two-Dimension Fermi Gases with Spin-Orbit CouplingSep 19 2011The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at $T=0K$ indicate that (1) when the strength of SOC ... More

Topological indexes in symmetry preserving dynamicsFeb 08 2018The quench dynamics of topological phases have received intensive investigations in recent years. In this work, we prove exactly that the topological invariants for both $\mathbb{Z}$ and $\mathbb{Z}_2$ indexes are independent of time in symmetry preserving ... More

Phase Diagram of a Spin-Orbit Coupled Fermi Gases in a Bilayer Optical LatticeJan 29 2013We investigate the stability of helical superfluid phase in a spin-orbit coupled Fermi gas loaded in a bilayer optical lattice. The phase diagram of the system is constructed in the mean field framework. We investigate the topological properties of the ... More

Large Chern Number Topological Superfluids in Coupled Layer SystemAug 13 2014Aug 30 2014We investigate the topological phase transition with large Chern number in a coupled layer system. The topological transitions between different topological superfluids can be realized by controlling the binding energy, interlay tunneling and layer asymmetry ... More

Topological superfluids with time-reversal symmetry from $s$-wave interaction in a bilayer systemNov 05 2015Topological superconducting phases with time-reversal (TR) symmetry have been widely explored in recent years. However the involved unconventional pairings are generally implausible in realistic materials. Here we demonstrate via detailed self-consistent ... More

Dark Matter, Mass Scales Sequence, and Superstructure in the Universe (with extension)Sep 18 1999Oct 26 2015There is a category of stable non-baryonic dark matter particles in the universe at the present time: fermions or bosons with mass ~10^(-1) eV. The existence of these do not contradict the dip phenomena of the ultra-high energy primary cosmic ray spectrum ... More

Dark Matter, Quasars, and Superstructures in the UniverseAug 10 2009Feb 02 2016From the observed results of the space distribution of quasars we deduced that neutrino mass is about 10^(-1) eV. The fourth stable elementary paticle (delta particle) with mass about 10^(0) eV can help explain the energy resource mechanism in quasars, ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

Automorphism group of the complete alternating group graphMay 21 2016Jun 02 2016Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

Dark energy and normalization of cosmological wave function in modified gravitationsMay 05 2017Based on Wheeler-DeWitt equation derived from general relativity, it had been found that only dark energy can lead to a normalizable cosmological wave function. It is shown in the present work that, for dRGT gravity, Eddington-inspired-Born-Infeld gravity ... More

Gorenstein Syzygy ModulesMar 26 2009Oct 15 2010For any ring $R$ and any positive integer $n$, we prove that a left $R$-module is a Gorenstein $n$-syzygy if and only if it is an $n$-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016Mar 27 2017In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

On regular graphs with four distinct eigenvaluesMay 18 2016Sep 17 2016Let $\mathcal{G}(4,2)$ be the set of connected regular graphs with four distinct eigenvalues in which exactly two eigenvalues are simple, $\mathcal{G}(4,2,-1)$ (resp. $\mathcal{G}(4,2,0)$) the set of graphs belonging to $\mathcal{G}(4,2)$ with $-1$ (resp. ... More

Hierarchical low rank approximation of likelihoods for large spatial datasetsMay 28 2016Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive computational burden. ... More

An $hp$-version error analysis of the discontinuous Galerkin method for linear elasticityAug 14 2016Dec 24 2017An $hp$-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the $hp$-version error estimates of two $L^2$ projection operators. Then incorporated with the techniques ... More

Enumerating Cayley (di-)graphs on dihedral groupsDec 12 2016Let $p$ be an odd prime, and $D_{2p}=\langle \tau,\sigma\mid \tau^p=\sigma^2=e,\sigma\tau\sigma=\tau^{-1}\rangle$ the dihedral group of order $2p$. In this paper, we provide the number of (connected) Cayley (di-)graphs on $D_{2p}$ up to isomorphism by ... More

Total Variation Depth for Functional DataNov 15 2016There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation ... More

The $hp$-version Error Analysis of A Mixed DG Method for Linear ElasticityAug 14 2016This paper focuses on the $hp$-version error analysis of a mixed discontinuous Galerkin (DG) method for the linear elasticity problem. We first derive some error estimates for two $L^2$ projection operators in terms of the results in [7,13,23]. Using ... More

Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-DisturbanceJan 01 2017This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent ... More

Large Number, Dark Matter, Dark Energy, and the Superstructures in the Universe (with Extension)Apr 16 2008Sep 12 2016Since there are dark matter particles (neutrino) with mass about 10^(-1)eV in the universe, the superstructures with a scale of 10^(19) solar mass [large number A is about 10^(19)] appeared around the era of the hydrogen recombination. The redshift z ... More

Note on the spectra of a class of graphs derived from set inclusion relationsSep 04 2018Sep 08 2018For any given integers $n$, $k$ and $l$ with $n\geq 1$ and $0\leq k<l\leq n$, we denote by $G(n,k,l)$ the graph whose vertex set consists of all $k$- and $l$-subsets of $[n]=\{1,2,\ldots,n\}$, where two distinct vertices are adjacent if one of them is ... More

The second largest eigenvalues of some Cayley graphs on alternating groupsNov 24 2017Dec 12 2018Let $A_n$ denote the alternating group of degree $n$ with $n\geq 3$. The alternating group graph $AG_n$, extended alternating group graph $EAG_n$ and complete alternating group graph $CAG_n$ are the Cayley graphs $\mathrm{Cay}(A_n,T_1)$, $\mathrm{Cay}(A_n,T_2)$ ... More

Torsionfree Dimension of Modules and Self-Injective Dimension of RingsJun 06 2009Jan 14 2011Let $R$ be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated $R$-modules. For any $n\geq 0$, we prove that $R$ is a Gorenstein ring with self-injective dimension at most $n$ if and only if every ... More

The Auslander-Type Condition of Triangular Matrix RingsMar 26 2009Let $R$ be a left and right Noetherian ring and $n,k$ any non-negative integers. $R$ is said to satisfy the Auslander-type condition $G_n(k)$ if the right flat dimension of the $(i+1)$-st term in a minimal injective resolution of $R_R$ is at most $i+k$ ... More

A Fast HOG Descriptor Using Lookup Table and Integral ImageMar 18 2017The histogram of oriented gradients (HOG) is a widely used feature descriptor in computer vision for the purpose of object detection. In the paper, a modified HOG descriptor is described, it uses a lookup table and the method of integral image to speed ... More

Dark Matter Particles with Low Mass (and FTL)Mar 26 2010Apr 17 2012From the observed results of the space distribution of quasars and the mass scale sequence table, we deduced the existence of superstructure (feeble dark structure) with mass scale of 10^(19) solar mass, as well as the lightest stable fermion with mass ... More

Parameter Optimization of Multi-Agent Formations based on LQR DesignJan 24 2011In this paper we study the optimal formation control of multiple agents whose interaction parameters are adjusted upon a cost function consisting of both the control energy and the geometrical performance. By optimizing the interaction parameters and ... More

Automorphism group of the complete alternating group graphMay 21 2016Aug 26 2017Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

A heuristic view about the evolution and speciesApr 16 2010The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern theory of evolution ... More

On Legendrian foliations in contact manifolds II: Deformation theoryNov 23 2014Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find an interesting ... More

A polynomial-time algorithm for the ground state of one-dimensional gapped HamiltoniansJun 24 2014Oct 26 2015A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon,n,\eta$ be the energy gap, the system size, and the desired precision, respectively. Neglecting ... More

Approximation capability of the convolution methods for fuzzy numbersAug 06 2014This paper shows that how to approximate general fuzzy number by using convolution method.

Convergence of the calabi flow on toric varieties and related Kaehler manifoldsJul 25 2012Let $X$ be a toric variety and $u$ be a normalized symplectic potential of the corresponding polytope $P$. Suppose that the Riemannian curvature is bounded by 1 and $ \int_{\partial P} u ~ d \sigma < C_1, $ then there exists a constant $C_2$ depending ... More

A note on the Ricci flow on noncompact manifoldsJul 01 2008Jul 07 2008Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with initial data $(M^3,g_0)$ ... More

Backwards uniqueness of the mean curvature flowJul 06 2009In this note we prove the backwards uniqueness of the mean curvature flow in codimension one case. More precisely,let $F_t, \widetilde{F}_t:M^n \to \overline{M}^{n+1}$ be two complete solutions of the mean curvature flow on $M^n \times [0,T]$ with bounded ... More

Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifoldsSep 20 2016We determine the greatest lower bounds on the transverse Ricci curvature of compact toric Sasaki manifolds with positive basic first Chern class and with the first Chern class of the contact bundle being trivial. This is based on Wang-Zhu's and Futaki-Ono-Wang's ... More

Entanglement dynamics in critical random quantum Ising chain with perturbationsNov 15 2016We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Oct 06 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More

On Structure and History of Space-time with Variable Speed of LightOct 15 2004We apply the variable speed of light into general relativity in order to solve the problems we met in the standard cosmology. We're surprised to find that, the results from the general relativity in cosmology are exactly the same as those we got from ... More

An Eye Tracking Study into the Effects of Graph LayoutOct 24 2008Graphs are typically visualized as node-link diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an essential part of the ... More

An Aggregation-Based Overall Quality Measurement for VisualizationJun 11 2013Aesthetics are often used to evaluate the quality of graph drawings. However, the existing aesthetic criteria are useful in judging the extents to which a drawing conforms to particular drawing rules. They have limitations in evaluating overall quality. ... More

An explicit family of unitaries with exponentially minimal length Pauli geodesicsJan 28 2007Recently, Nielsen et al have proposed a geometric approach to quantum computation. They've shown that the size of the minimum quantum circuits implementing a unitary U, up to polynomial factors, equals to the length of minimal geodesic from identity I ... More

Synthesis of Sugar and fixation of CO2 through Artificial Photosynthesis driving by Hydrogen or ElectricitySep 02 2010The overall process of photosynthesis consists of two main phases, the so-called light and dark eactions: light energy is absorbed by chlorophyll molecules and transferred to regenerate NADH and ATP, then drive Calvin-Benson cycle to synthesize sugar. ... More

$L^{2}$ harmonic forms on complete special holonomy manifoldsJan 13 2018Apr 01 2018In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a non-zero parallel form $\omega$. The main result is that if $(X,\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- ... More

Extension the Noether's theorem to Lagrangian formulation with nonlocalityMar 06 2012A Lagrangian formulation with nonlocality is investigated in this paper. The nonlocality of the Lagrangian is introduced by a new nonlocal argument that is defined as a nonlocal residual satisfying the zero mean condition. The nonlocal Euler-Lagrangian ... More

Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuliNov 19 2009In this paper, we investigate convergence dynamics of $2^N$ almost periodic encoded patterns of general neural networks (GNNs) subjected to external almost periodic stimuli, including almost periodic delays. Invariant regions are established for the existence ... More

Do W_L and H form a p-wave bound state?Mar 03 1995We examine the possibility of bound state formation in the W_L H --> W_L H channel. The dynamical calculation using the N/D method indicates that when the interactions among the Goldstone and Higgs bosons become sufficiently strong, a p-wave state [I^G(J^P)=1^-(1^+)] ... More

Lagrangian formulism of elasticity with relevance to surface energyNov 05 2012By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary constitutive ... More

Approximation presentations of modules and homological conjecturesSep 10 2004Mar 24 2007In this paper we give a sufficient condition of the existence of ${\rm \mathbb{W}}^{t}$-approximation presentations. We also introduce property (W$^{k}$). As an application of the existence of ${\rm \mathbb{W}}^{t}$-approximation presentations we give ... More

Understanding magnetic instability in gapless superconductorsSep 18 2005Magnetic instability in gapless superconductors still remains as a puzzle. In this article, we point out that the instability might be caused by using BCS theory in mean-field approximation, where the phase fluctuation has been neglected. The mean-field ... More

On the grade of modules over Noetherian ringsSep 09 2004Sep 02 2007Let $\Lambda$ be a left and right noetherian ring and $\mod \Lambda$ the category of finitely generated left $\Lambda$-modules. In this paper we show the following results: (1) For a positive integer $k$, the condition that the subcategory of $\mod \Lambda$ ... More

$k$-Gorenstein ModulesSep 10 2004Sep 07 2005Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then characterize ... More

Invariant subsets under compact quantum group actionsOct 21 2012Nov 13 2014We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable ... More

The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivityMar 06 2014Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal ... More

Noncommutative multiplicative norm identities for the quaternions and the octonionsFeb 14 2011We present Capelli type identities associated with the quaternions and the octonions, which are noncommutative versions of multiplicative norm identities for the quaternions and the octonions.

An Averaging Theorem for Perturbed KdV EquationJan 08 2013We consider a perturbed KdV equation: [\dot{u}+u_{xxx} - 6uu_x = \epsilon f(x,u(\cdot)), \quad x\in \mathbb{T}, \quad\int_\mathbb{T} u dx=0.] For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\in\mathbb{R}_+^{\infty}$ be the vector, formed ... More

Hecke algebras with independent parametersMay 07 2014Dec 03 2014We study the Hecke algebra $\H(\bq)$ over an arbitrary field $\FF$ of a Coxeter system $(W,S)$ with independent parameters $\bq=(q_s\in\FF:s\in S)$ for all generators. This algebra is always linearly spanned by elements indexed by the Coxeter group $W$. ... More

Asymptotic Expansion of Spherical IntegralSep 08 2013Dec 15 2014We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic expansions of these spherical integrals and derive the first and the second term in the asymptotic ... More

A Cosmology Forecast Toolkit -- CosmoLibJan 28 2012Jun 11 2012The package CosmoLib is a combination of a cosmological Boltzmann code and a simulation toolkit to forecast the constraints on cosmological parameters from future observations. In this paper we describe the released linear-order part of the package. We ... More

Stabilizing near-nonhyperbolic chaotic systems and its potential applications in neuroscienceMay 08 2004May 11 2004Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly any chaotic systems without any prior analytical knowledge of the systems. ... More

$β$-Nonintersecting Poisson Random Walks: Law of Large Numbers and Central Limit TheoremsAug 23 2017Sep 01 2017We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the Nekrasov's equation ... More

Mesoscopic Perturbations of Large Random MatricesDec 13 2014May 15 2015We consider the eigenvalues and eigenvectors of small rank perturbations of random $N\times N$ matrices. We allow the rank of perturbation $M$ increases with $N$, and the only assumption is $M=o(N)$. In both additive and multiplicative perturbation models, ... More

A compactness theorem of flat $SL(2,\mathbb{C})$ connections on $3$-foldsJun 12 2017In this article, we obtain a compactness theorem of flat $SL(2,\mathbb{C})$-connections by using a compactness theorem of Vafa-Witten equations proved by Tanaka (arXiv:1308.0862). We also using the compactness theorem to study the topology property of ... More

Non-existence of Higgs fields on Calabi-Yau ManifoldsMay 03 2017May 15 2017In this article, we study the Higgs $G$-bundles $(E,\theta)$ on a compact Calabi-Yau manifolds $X$. Our main result is that there is non-existence Higgs fields $\theta$ on a semistable Higgs $G$-bundle over a compact connected Calabi-Yau surface. The ... More

On a topology property for moduli space of Kapustin-Witten equationsMar 20 2017Apr 17 2018In this article, we study the Kapustin-Witten equations on a closed, simply-connected, four-manifold. We using a compactness theorem due to Taubes to prove that if $(A,\phi)$ is a solution of Kapustin-Witten equations and the connection $A$ is closed ... More

A lower bound on the solutions of Kapustin-Witten equationsJan 29 2016Sep 23 2016In this article, we consider the Kapustin-Witten equations on a closed $4$-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an $L^{2}$-lower bound on the extra fields ... More

Some Energy Properties of Yang-Mills ConnectionsFeb 11 2015Jun 14 2016We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density $|F_{A}|^{\frac{n}{2}}$.This ... More

Instantons on Cylindrical ManifoldsJan 19 2015Mar 07 2016We consider an instanton,$\textbf{A}$,with $L^{2}$-curvature $F_{\textbf{A}}$ on the cylindrical manifold $Z=\mathbf{R}\times M$,where $M$ is a closed Riemannian $n$-manifold, $n\geq 4$.We assume $M$ admits a $3$-form $P$ and a $4$-form $Q$ satisfy $dP=4Q$ ... More

Probing Anomalous Top Quark Couplings at the Future Linear CollidersSep 05 2000Sep 20 2000In terms of an effective Lagrangian we investigate the possibilities of probing anomalous top quark couplings, $t \bar{t} H$, $\gamma t \bar{t}$, $Z t \bar{t}$ and $tWb$ at the future linear colliders. It is found that probing anomalous top quark couplings, ... More

$L^{2}$ vanishing theorem on some Kähler manifoldsNov 27 2018Let $E$ be a Hermitian vector bundle over a complete K\"{a}hler manifold $(X^{2n},\omega)$ with a $d$(bounded) fundamental form $\omega$, $A$ be a Hermitian connection on $E$. The goal of this article is to study the $L^{2}$-Hodge theory on the vector ... More

A Lane-Change Path Planner and its application with a monocular cameraMar 06 2019Mar 10 2019Human drivers utilize the visual cues from the road to performance some fundamental driving tasks, e.g. lane keeping and lane change, for the complex driving maneuvers. Lane keeping and lane change can be generalized as one task, because both of them ... More

Bose Condensate in External Potential: A Thomas-Fermi ApproachSep 03 1996The Bose condensate in an external potential is treated in the Thomas-Fermi approximation.

Connecting phase transition theory with unsupervised learningDec 15 2017Entropy and order parameter are two key concepts in phase transition theory. This paper proposes an unified method to both find order parameter and estimate entropy automatically with unsupervised learning. The contributions of this paper are threefold: ... More

Generalized Greatest Common Divisors for the Orbits under Rational FunctionsFeb 13 2017Aug 08 2018Assume Vojta's Conjecture. Suppose $a, b, \alpha,\beta \in \mathbb{Z}$, and $f(x),g(x) \in \mathbb{Z}[x]$ are polynomials of degree $d \ge 2$. Assume that the sequence $(f^{\circ n}(a), g^{\circ n}(b))_n$ is generic and $\alpha,\beta$ are not exceptional ... More

Impulse response of the Bayreuth FestspielhausMar 21 2017The Bayreuth Festspielhaus is well known for its architecture because its design is heavily influenced by composer Richard Wagner. Due to the special acoustic design, the reverberation time (i.e., time scale for the sound pressure level to decay $60$~dB) ... More

A Critical History of RenormalizationOct 21 2013The history of renormalization is reviewed with a critical eye, starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell-Mann & Low, and others, to Wilson's formulation and Polchinski's functional equation, and applications ... More

Protein Folding as a Physical Stochastic ProcessJul 17 2007We model protein folding as a physical stochastic process as follows. The unfolded protein chain is treated as a random coil described by SAW (self-avoiding walk). Folding is induced by hydrophobic forces and other interactions, such as hydrogen bonding, ... More

CSAW: a dynamical model of protein foldingJan 12 2006CSAW (conditioned self-avoiding walk) is a model of protein folding that combines SAW (self-avoiding walk) with Monte-Carlo. It simulates the Brownian motion of a chain molecule in the presence of interactions, both among chain residues, and with the ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Aug 03 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More

The properties of sendograph metric on fuzzy number spacesJul 24 2013This paper discusses the variation of sendograph distances under some algebra operations.

Equidistribution and measure rigidity under $\times p,\times q$Nov 17 2014Jun 08 2015We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.

The transverse Chern-Ricci flowJun 08 2015We introduce transverse Chern-Ricci flow for transversely Hermitian foliations, which is analogous to the Chern-Ricci flow. We show that when $\mathcal{F}$ is homologically orientable and the basic first Bott-Chern class is zero, starting at any transversely ... More

Sasaki manifolds with positive transverse orthogonal bisectional curvatureJan 07 2013Jan 09 2013In this short note we show the following result: Let $(M^{2n+1},g)$ ($n \geq 2$) be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then $\pi_1(M)$ is finite, and the universal cover of $(M^{2n+1},g)$ is isomorphic ... More

Three-orbifolds with positive scalar curvatureOct 27 2012We prove the following result: Let $(\mathcal{O},g_0)$ be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-suborbifolds. Then there is a finite collection $\mathcal{F}$ of spherical ... More

Ricci flow on open 4-manifolds with positive isotropic curvatureAug 15 2011Aug 30 2011In this note we prove the following result: Let $X$ be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry and with no essential incompressible space form. Then $X$ is diffeomorphic to $\mathbb{S}^4$, or ... More

State sampling dependence of the Hopfield network inferenceApr 26 2011Aug 31 2011The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the ... More

The $L^{3/2}$-norm of the scalar curvature under the Ricci flow on a 3-manifoldJan 04 2011Feb 28 2011Assume $M$ is a closed 3-manifold whose universal covering is not $S^3$. We show that the obstruction to extend the Ricci flow is the boundedness $L^{3/2}$-norm of the scalar curvature $R(t)$, i.e, the Ricci flow can be extended over time $T$ if and only ... More

Reconstructing the Hopfield network as an inverse Ising problemSep 10 2009Dec 14 2009We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing technique is adopted. ... More

A countable set derived by fuzzy setOct 19 2015In this paper, it shows that for each fuzzy set $u$ on $\mathbb{R}^m$, the set $D(u)$ is at most countable. Based on this, it modifies the proof of assertion (I) in step 2 of the sufficiency part of Theorem 4.1 in paper: Characterizations of compact sets ... More

A note on Morse's index theorem for Perelman's $\mathcal{L}$-lengthFeb 06 2006This is essentially a note on Section 7 of Perelman's first paper on Ricci flow. We list some basic properties of the index form for Perelman's $ \mathcal{L} $-length, which are analogous to the ones in Riemannian case (with fixed metric), and observe ... More