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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

$k$-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

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

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

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

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

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

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

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

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

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

$f(T)$ theories from holographic dark energy modelsMar 25 2013We reconstruct $f(T)$ theories from three different holographic dark energy models in different time durations. For the HDE model, the dark energy dominated era with new setting up is chosen for reconstruction, and the radiation dominated era is chosen ... More

Some gradient estimates for a diffusion equation on Riemannian manifoldsJul 27 2007Apr 24 2008In this note we present some gradient estimates for the diffusion equation $\partial_t u=\Delta u-\nabla \phi \cdot \nabla u $ on Riemannian manifolds, where $\phi $ is a C^2 function, which generalize estimates of R. Hamilton's and Qi S. Zhang's on the ... More

An ultimate storage ring lattice with vertical emittance generated by damping wigglersSep 26 2014Oct 07 2014We discuss the approach of generating round beams for ultimate storage rings using vertical damping wigglers (with horizontal magnetic field). The vertical damping wigglers provide damping and excite vertical emittance. This eliminates the need to generate ... More

A simple efficient algorithm in frustration-free one-dimensional gapped systemsOct 05 2015Nov 05 2015We propose an efficient algorithm for the ground state of frustration-free one-dimensional gapped Hamiltonians. This algorithm is much simpler than the original one by Landau et al., and thus may be easily accessible to a general audience in the community. ... More

Learning Efficient Representations for Reinforcement LearningAug 28 2015Markov decision processes (MDPs) are a well studied framework for solving sequential decision making problems under uncertainty. Exact methods for solving MDPs based on dynamic programming such as policy iteration and value iteration are effective on ... More

Computing energy density in one dimensionMay 04 2015We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired precision if the ... More

The powers of smooth words over arbitrary 2-letter alphabetsApr 03 2009Aug 09 2011Carpi (1993) and Lepisto (1994) proved independently that smooth words are cube-free for the alphabet {1, 2}, but nothing is known on whether for the other 2-letter alphabets, smooth words are k-power-free for some suitable positive integer k. In this ... More

Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codesJul 03 2014Sep 18 2014The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function ... More

Sparse Hopfield network reconstruction with $\ell_{1}$ regularizationDec 26 2012Nov 14 2013We propose an efficient strategy to infer sparse Hopfield network based on magnetizations and pairwise correlations measured through Glauber samplings. This strategy incorporates the $\ell_{1}$ regularization into the Bethe approximation by a quadratic ... More

Some Extensions of Witt's TheoremMay 25 2007We extend Witt's theorem to several kinds of simultaneous isometries of subspaces. We determine sufficient and necessary conditions for the extension of an isometry of subspaces $\phi:E\to E'$ to an isometry $\phi_V:V\to V'$ that also sends a given subspace ... More

Characterizations of precompact sets in fuzzy star-shaped numbers space with Lp-metricJul 23 2015In this paper, we consider the characterizations of precompact sets in fuzzy star-shaped number space with Lp-metric.

Continuous $\times p,\times q$-invariant measures on the unit circleJul 09 2016We express continuous $\times p,\times q$-invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p,\times q$-invariant measure is the weak-$*$ limit of average of Dirac measures along an irrational orbit. On the ... More

Calabi flow on toric varieties with bounded Sobolev constant, IJun 25 2014Let $(X, P)$ be a toric variety. In this note, we show that the $C^0$-norm of the Calabi flow $\varphi(t)$ on $X$ is uniformly bounded in $[0, T)$ if the Sobolev constant of $\varphi(t)$ is uniformly bounded in $[0, T)$. We also show that if $(X, P)$ ... More

A remark on odd dimensional normalized Ricci flowOct 24 2007Dec 17 2007Let $(M^n,g_0)$ ($n$ odd) be a compact Riemannian manifold with $\lambda(g_0)>0$, where $\lambda(g_0)$ is the first eigenvalue of the operator $-4\Delta_{g_0}+R(g_0)$, and $R(g_0)$ is the scalar curvature of $(M^n,g_0)$. Assume the maximal solution $g(t)$ ... More

Calabi flow on projective bundles, INov 19 2015In this paper, we obtain several a-priori estimates for the Calabi flow on projective bundles admitting the generalized Calabi constructions.

Certainty Equivalence, Separation Principle, and Cooperative Output Regulation of Multi-Agent Systems by Distributed Observer ApproachAug 18 2015The cooperative output regulation problem of linear multi-agent systems was formulated and studied by the distributed observer approach in [20, 21]. Since then, several variants and extensions have been proposed, and the technique of the distributed observer ... More

A gluing construction for polynomial invariantsMay 17 2010Sep 15 2010We give a polynomial gluing construction of two groups $G_X\subseteq GL(\ell,\mathbb F)$ and $G_Y\subseteq GL(m,\mathbb F)$ which results in a group $G\subseteq GL(\ell+m,\mathbb F)$ whose ring of invariants is isomorphic to the tensor product of the ... More

Simplifying Local BRST Cohomology Calculation via Spectral SequenceAug 30 2010We simplify some crucial calculations in \cite{1} by using the technique of spectral sequence of a double complex.

Stable Yang-Mills connections on Special Holonomy ManifoldsNov 16 2015Jul 19 2016We prove that energy minimizing Yang-Mills connections with certain condition on compact $G_{2}$-manifolds with holonomy equal to $G_{2}$ are $G_{2}$-instantons. We prove related results for compact Calabi-Yau $3$-folds with holonomy equal to $SU(3)$. ... More

Complex flat connections on compact manifoldsJun 13 2016Aug 28 2016We consider a complex flat connection on a principle bundle $P$ over a compact Riemannian manifold $M=M^{n}$,$n\geq5$.First,we prove that the complex part of complex flat connection must with $L^{2}$-bounded from below by some positive constant,if $M$ ... More

Bose-Einstein condensation of a Knudsen gasAug 16 2007We reconcile a long-standing controversy regarding the transition temperature of the Bose-Einstein condensation in a dilute interacting Bose gas, by showing that there is a crossover between ideal gas and interacting gas. The former corresponds to a Knudsen ... More

Cold Trapped Atoms: A Mesoscopic SystemDec 21 2000The Bose-Einstein condensates recently created in trapped atomic gases are mesoscopic systems, in two senses: (a) Their size fall between macroscopic and microscopic systems; (b) They have a quantum phase that can be manipulated in experiments. We review ... More

Quantum vorticity in natureAug 23 2015Quantum vorticity occurs in superfluidity, which arises from a spatial variation of the quantum phase. As such, it can occur in diverse systems over a wide range of scales, from the electroweak sector and QCD of the standard model of particle theory, ... More

Conditional statistical physical properties in two-joint complex systems having long-range interactionsJun 09 2013We propose the sum and the difference of the normalized velocity of two-joint systems to describe its long-range interaction. It is found that the conditional probability distribution function (CPDF) of the normalized velocity between two-joint systems ... More

Generalized tilting modules with finite injective dimensionFeb 25 2006Dec 31 2006Let $R$ be a left noetherian ring, $S$ a right noetherian ring and $_RU$ a generalized tilting module with $S={\rm End}(_RU)$. The injective dimensions of $_RU$ and $U_S$ are identical provided both of them are finite. Under the assumption that the injective ... More

Distribution locale des points rationnels de hauteur bornée sur une surface de del Pezzo de degré 6Oct 08 2016We establish a measure which describes precisely the local asymptotic distribution of rational points outside the locally accumulating subvarieties around a general rational point on a del Pezzo surface of degree 6 in the sense of diophantine approximation. ... More

Revisiting the cosmological bias due to local gravitational redshiftsApr 24 2015May 22 2015A recent article by Wojtak {\it et al} (arXiv:1504.00718) pointed out that the local gravitational redshift, despite its smallness ($\sim 10^{-5}$), can have a noticeable ($\sim 1\%$) systematic effect on our cosmological parameter measurements. The authors ... More

Reinterpretation of Thermal Dilepton Emission Rate by Spectral FunctionsJun 22 1995We reinterpret the dilepton emission rate from a hadronic gas expected to be produced in heavy ion collisions in terms of the spectral functions available from the $e^+e^-$ annihilation and the $\tau$ lepton decays experiments. We take into account all ... More

On the Anomalous Discrete SymmetrySep 14 1992We examine an interesting scenario to solve the domain wall problem recently suggested by Preskill, Trivedi, Wilczek and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such ... More

Spontaneous Nambu-Goldstone Currents Generation Driven by MismatchFeb 10 2006We review recent progress of understanding and resolving instabilities driven by mismatch between the Fermi surfaces of the pairing quarks in 2-flavor color superconductor. With the increase of mismatch, the 2SC phase exhibits chromomagnetic instability ... More

Spontaneous current generation in the gapless 2SC phaseApr 26 2005Jan 26 2006It is found that, except chromomagnetic instability, the gapless 2SC phase also exhibits a paramagnetic response to the perturbation of an external color neutral baryon current. The spontaneously generated baryon current driven by the mismatch is equivalent ... More

Unconditionally stable high-order time integration for moving mesh finite difference solution of linear convection-diffusion equationsOct 15 2013This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability of numerical ... More

Theoretical analysis of error transfer from surface slope to refractive ray and their application to the solar concentrated collectorDec 06 2011This paper presents the general equation to calculate the standard deviation of reflected ray error from optical error through geometry optics, applying the equation to calculate the standard deviation of reflected ray error for 8 kinds of solar concentrated ... More

Long-time dynamics of resonant weakly nonlinear CGL equationsJul 04 2014Consider a weakly nonlinear CGL equation on the torus~$\mathbb{T}^d$: \[u_t+i\Delta u=\epsilon [\mu(-1)^{m-1}\Delta^{m} u+b|u|^{2p}u+ ic|u|^{2q}u].\eqno{(*)}\] Here $u=u(t,x)$, $x\in\mathbb{T}^d$, $0<\epsilon<<1$, $\mu\geqslant0$, $b,c\in\mathbb{R}$ and ... More