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Thermal radiation from optically driven Kerr ($χ^{(3)}$) photonic cavitiesMar 12 2015We study thermal radiation from nonlinear ($\chi^{(3)}$) photonic cavities coupled to external channels and subject to incident monochromatic light. Our work extends related work on nonlinear mechanical oscillators [Phys. Rev. Lett. 97, 110602 (2006)] ... More

Light Transport in Random Media with ${\cal PT}$-SymmetryMay 09 2012The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size, with an enhanced ... More

Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversionJan 19 2017We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear $\chi^{(2)}$ and $\chi^{(3)}$ frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ... More

Inverse designed photonic fibers and metasurfaces for nonlinear frequency conversionNov 21 2017Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and band gap engineering, and are based on simple shapes with high degrees of symmetry. We show that recently ... More

Inverse design of third-order Dirac exceptional points in photonic crystalsMay 19 2016We propose a novel inverse-design method that enables brute-force discovery of photonic crystal (PhC) structures with complex spectral degeneracies. As a proof of principle, we demonstrate PhCs exhibiting third-order Dirac points formed by the \emph{accidental} ... More

Topology optimization of freeform large-area metasurfacesFeb 08 2019We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, ... More

Experimental observation of the dual behavior of ${\cal PT}$-symmetric scatteringMay 10 2012We investigate experimentally parity-time (${\cal PT}$) symmetric scattering using $LRC$ circuits in an inductively coupled ${\cal PT}$- symmetric pair connected to transmission line leads. In the single-lead case, the ${\cal PT}$-symmetric circuit acts ... More

Huge quantum particle number fluctuations in a two-component Bose gas in a double-well potentialApr 09 2010May 24 2011Two component Bose gas in a double well potential with repulsive interactions may undergo a phase separation transition if the inter-species interactions outweigh the intra-species ones. We analyze the transition in the strong interaction limit within ... More

Enhanced nonlinear frequency conversion and Purcell enhancement at exceptional pointsMay 21 2017Jun 03 2017We derive analytical formulas quantifying radiative emission from subwavelength emitters embedded in triply resonant nonlinear $\chi^{(2)}$ cavities supporting exceptional points (EP) made of dark and leaky modes. We show that the up-converted radiation ... More

Design of diamond microcavities for single photon frequency down-conversionApr 07 2015Apr 10 2015We propose monolithic diamond cavities that can be used to convert color-center Fock-state single photons from emission wavelengths to telecommunication bands. We present a detailed theoretical description of the conversion process, analyzing important ... More

Material Scaling and Frequency-Selective Enhancement of Near-Field Radiative Heat Transfer for Lossy Metals in Two Dimensions via Inverse DesignFeb 15 2018Aug 24 2018The super-Planckian features of radiative heat transfer in the near-field are known to depend strongly on both material and geometric design properties. However, the relative importance and interplay of these two facets, and the degree to which they can ... More

Cavity-enhanced second harmonic generation via nonlinear-overlap optimizationMay 12 2015May 18 2015We describe an approach based on topology optimization that enables automatic discovery of wavelength-scale photonic structures for achieving high-efficiency second-harmonic generation (SHG). A key distinction from previous formulation and designs that ... More

Topology Optimized Multi-layered Meta-opticsJun 21 2017We propose a general topology optimization framework for metasurface inverse design that can automatically discover highly complex multi-layered meta-structures with increased functionalities. In particular, we present topology-optimized multi-layered ... More

On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their MonodromiesApr 23 2007We prove John Hubbard's conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex H\'enon map. Indeed, we show that there exist several non-trivial loops in the locus which generate infinitely many mutually different monodromies. ... More

High-efficiency degenerate four wave-mixing in triply resonant nanobeam cavitiesNov 16 2013We demonstrate high-efficiency, degenerate four-wave mixing in triply resonant Kerr $\chi^(3)$ photonic crystal (PhC) nanobeam cavities. Using a combination of temporal coupled mode theory and nonlinear finite-difference time-domain (FDTD) simulations, ... More

Unidirectional Invisibility induced by PT-Symmetric Periodic StructuresAug 11 2011We show that parity-time (PT) symmetric Bragg periodic structures, near the spontaneous PT - symmetry breaking point, can act as unidirectional invisible media. In this regime, the re flection from one end is diminished while it is enhanced from the other. ... More

Inverse design of large-area metasurfacesAug 13 2018Dec 14 2018We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and demultiplexers. To optimize ... More

Outlook for inverse design in nanophotonicsJan 20 2018Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields: moving from ... More

Topology-optimized Dual-Polarization Dirac ConesMay 10 2017Sep 21 2017We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which ... More

Inverse Design of Compact Multimode Cavity CouplersMar 16 2018Sep 03 2018Efficient coupling between on-chip sources and cavities plays a key role in silicon photonics. However, despite the importance of this basic functionality, there are few systematic design tools to simultaneously control coupling between multiple modes ... More

Integrated high quality factor lithium niobate microdisk resonatorsOct 09 2014Lithium Niobate (LN) is an important nonlinear optical material. Here we demonstrate LN microdisk resonators that feature optical quality factor ~ 100,000, realized using robust and scalable fabrication techniques, that operate over a wide wavelength ... More

Non-monotonic field-dependence of the ZFC magnetization peak in some systems of magnetic nanoparticlesMay 23 1997Sep 30 1997We have performed magnetic measurements on a diluted system of gamma-Fe2O3 nanoparticles (~7nm), and on a ferritin sample. In both cases, the ZFC-peak presents a non-monotonic field dependence, as has already been reported in some experiments,and discussed ... More

Interference of Fock states in a single measurementMar 29 2007We study analytically the structure of an arbitrary order correlation function for a pair of Fock states and prove without any approximations that in a single measurement of particle positions interference effects must occur as experimentally observed ... More

A Knowledge-based Automated Debugger in Learning SystemJan 12 2001Currently, programming instructors continually face the problem of helping to debug students' programs. Although there currently exist a number of debuggers and debugging tools in various platforms, most of these projects or products are crafted through ... More

On parameter loci of the Hénon familyJan 07 2015Feb 29 2016We characterize the hyperbolic horseshoe locus and the maximal entropy locus of the H\'enon family defined on $\mathbb{R}^2$. More specifically, we show that (i) the two parameter loci are both connected and simply connected (by adding their corresponding ... More

Properties of atomic pairs produced in the collision of Bose-Einstein condensatesMar 16 2017Collisions of Bose-Einstein condensates can be used as a mean to generate correlated pairs of atoms. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of ... More

Anomalies in the Relaxation of Small Magnetic Particles at Very Low TemperaturesSep 03 1996The magnetization relaxation rate of small gamma-Fe2O3 particles dispersed in a silica matrix has been measured from 60 mK to 5 K. It shows a minimum around 150 mK, that can be discussed in terms of either thermal or quantum relaxation regime.

The influence of the interaction between quasiparticles on parametric resonance in Bose-Einstein quasicondensatesApr 23 2018We perform a simulation of the experiment [1] where the temporal modification of the effective one dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate huge impact of interaction ... More

Adaptively Compressed Exchange OperatorJan 26 2016Jan 27 2016The Fock exchange operator plays a central role in modern quantum chemistry. The large computational cost associated with the Fock exchange operator hinders Hartree-Fock calculations and Kohn-Sham density functional theory calculations with hybrid exchange-correlation ... More

400%/W second harmonic conversion efficiency in $\mathrm{14 μ m}$-diameter gallium phosphide-on-oxide resonatorsOct 10 2018Second harmonic conversion from 1550~nm to 775~nm with an efficiency of 400% W$^{-1}$ is demonstrated in a gallium phosphide (GaP) on oxide integrated photonic platform. The platform consists of doubly-resonant, phase-matched ring resonators with quality ... More

Localized spectrum slicingNov 22 2014Nov 23 2015Given a sparse Hermitian matrix $A$ and a real number $\mu$, we construct a set of sparse vectors, each approximately spanned only by eigenvectors of $A$ corresponding to eigenvalues near $\mu$. This set of vectors spans the column space of a localized ... More

Randomized estimation of spectral densities of large matrices made accurateApr 29 2015Nov 23 2015For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or density of states) ... More

Symmetry breaking in the collisions of double channel BEC solitonsJul 07 2013We investigate an attractive Bose-Einstein condensate in two coupled one dimensional channels. In this system a stable double channel soliton can be formed. It is symmetric for small interaction parameters and asymmetric for large ones. We study this ... More

Rapidity correlations test stochastic hydrodynamicsNov 02 2016We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time $\tau_{\pi}$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity ... More

Information MechanicsMay 03 2016Jul 30 2016Despite the wide usage of the concept of information, we have yet to develop a unified scientific definition. Inspired by Shannon's and Boltzmann's work, by investigating information's role in various working processes, we recognised that information's ... More

Globally Constructed Adaptive Local Basis Set for Spectral Projectors of Second Order Differential OperatorsJul 23 2017Jun 01 2018Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number of degrees ... More

Decay estimates of discretized Green's functions for Schrödinger type operatorsNov 25 2015Jun 15 2016For a sparse non-singular matrix $A$, generally $A^{-1}$ is a dense matrix. However, for a class of matrices, $A^{-1}$ can be a matrix with off-diagonal decay properties, i.e. $\lvert A^{-1}_{ij}\rvert$ decays fast to $0$ with respect to the increase ... More

Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part II: Non-perturbative analysisSep 09 2018Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the combinatorially growing number ... More

Variational structure of Luttinger-Ward formalism and bold diagrammatic expansion for Euclidean lattice field theoryNov 20 2017The Luttinger-Ward functional was proposed more than five decades ago to provide a link between static and dynamic quantities in a quantum many-body system. Despite its widespread usage, the derivation of the Luttinger-Ward functional remains valid only ... More

A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump NoiseDec 26 2017This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of ... More

Sparsity pattern of the self-energy for classical and quantum impurity problemsFeb 13 2019We prove that for various impurity models, in both classical and quantum settings, the self-energy matrix is a sparse matrix with a sparsity pattern determined by the impurity sites. In the quantum setting, such a sparsity pattern has been known since ... More

A posteriori error estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part I: Second order linear PDEFeb 05 2015Jun 17 2015We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving second order linear PDEs. Our residual type upper and ... More

Sequence-covering maps on generalized metric spacesJun 20 2011Let $f:X\rightarrow Y$ be a map. $f$ is a {\it sequence-covering map}\cite{Si1} if whenever $\{y_{n}\}$ is a convergent sequence in $Y$ there is a convergent sequence $\{x_{n}\}$ in $X$ with each $x_{n}\in f^{-1}(y_{n})$; $f$ is an {\it 1-sequence-covering ... More

Strong-Field QED and the Inverse Mellin TransformFeb 10 2002We introduce the technique of inverse Mellin transform in a problem of strong-field QED. We show that the {\it moments} of pair production width in a uniform background magnetic field are proportional to the derivatives of photon polarization function ... More

Elastic scattering losses from colliding BEC'sDec 05 2005Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently ... More

Rapidity Correlation Structure in Nuclear CollisionsJun 08 2016Aug 17 2016We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time $\tau_\pi$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity $\nu ... More

Rapidity Correlation Structures from Causal HydrodynamicsAug 18 2016Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of unanticipated structure ... More

Hidden Markov Models on Variable Blocks with a Modal Clustering Algorithm and ApplicationsJun 28 2016Motivated by high-throughput single-cell cytometry data with applications to vaccine development and immunological research, we consider statistical clustering in large-scale data that contain multiple rare clusters. We propose a new hierarchical mixture ... More

Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part I: Perturbative approachSep 09 2018Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the combinatorially growing number ... More

Robust Determination of the Chemical Potential in the Pole Expansion and Selected Inversion Method for Solving Kohn-Sham density functional theoryAug 14 2017Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi ... More

A New Currency of the Future: The Novel Commodity Money with Attenuation Coefficient Based on the Logistics Cost of AnchorJun 22 2016In this paper, we reveal the attenuation mechanism of anchor of the commodity money from the perspective of logistics warehousing costs, and propose a novel Decayed Commodity Money (DCM) for the store of value across time and space. Considering the logistics ... More

A posteriori error estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part II: Eigenvalue problemsMar 14 2016We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second order linear ... More

Information MechanicsMay 03 2016Nov 10 2016Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside its intimate ... More

Some weak versions of the $M_{1}$-spacesFeb 18 2013We mainly introduce some weak versions of the $M_{1}$-spaces, and study some properties about these spaces. The mainly results are that: (1) If $X$ is a compact scattered space and $i(X)\leq 3$, then $X$ is an $s$-$m_{1}$-space; (2) If $X$ is a strongly ... More

Uniform bases at non-isolated points and mapsJun 21 2011In this paper, the authors mainly discuss the images of spaces with an uniform base at non-isolated points, and obtain the following main results: (1)\ Perfect maps preserve spaces with an uniform base at non-isolated points; (2)\ Open and closed maps ... More

The technique of inverse Mellin transform for processes occurring in a background magnetic fieldOct 25 2002We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to the Mellin ... More

The inclusive B->eta' X_s decay and b-> sg* form factorsOct 25 1999We compute the branching ratio of inclusive $B \to \eta' X_s$ decay based upon the QCD anomaly mechanism: $b\to s+g^*\to s+g+\eta'$. To obtain a reliable $B \to \eta' X_s$ branching ratio, we calculate the $b\to s+g^*$ form factors up to the next-to-leading-logarithmic(NLL) ... More

Classification of degree three polynomial solutions to the Polubarinova-Galin equationSep 19 2013The Polubarinova-Galin equation is derived from zero-surface-tension Hele-Shaw flow driven by injection. In this paper, we classify degree three polynomial solutions to the Polubarinova-Galin equation into three categories: global solutions, solutions ... More

Large-time rescaling behaviors of Stokes and Hele-Shaw flows driven by injectionJun 04 2009In this paper, we give a precise description of the rescaling behaviors of global strong polynomial solutions to the reformulation of zero surface tension Hele-Shaw problem driven by injection, the Polubarinova-Galin equation, in terms of Richardson complex ... More

Minimum tree-stretch of Hamming graphs and higher-dimensional gridsJul 22 2018The minimum stretch spaning tree problem for a grah G is to find a spaning tree T of G such as that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a grpah invariant {\sigma} ... More

$π$-metrizable spaces and strongly $π$-metrizable spacesFeb 18 2013A space $X$ is said to be $\pi$-metrizable if it has a $\sigma$-discrete $\pi$-base. In this paper, we mainly give affirmative answers for two questions about $\pi$-metrizable spaces. The main results are that: (1) A space $X$ is $\pi$-metrizable if and ... More

Like Sign Top Pair Production at LHCMay 26 1997Having a mass comparable to the weak scale, the top quark may have a sizable flavor changing couplings to Higgs bosons. We show that such couplings can be probed at the LHC through the parton subprocess $c(\bar c)g \to t (\bar t)A^0$, where the pseudoscalar ... More

The Dispersive Approach to Electroweak Processes in the Background Magnetic FieldNov 07 2000We propose a new method to compute amplitudes of electroweak processes in the strong background magnetic field, using $\gamma\to e^+e^-$ as an example. We show that the {\it moments} of $\gamma\to e^+e^-$ width are proportional to the derivatives of photon ... More

Quantum Dynamics with the Parallel Transport GaugeApr 06 2018The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of freedom irrelevant to physical observables) of the Schrodinger equation can ... More

An Approach to the High-level Maintenance Planning for EMU Trains Based on Simulated AnnealingApr 10 2017A high-speed train needs high-level maintenance when its accumulated running mileage or time reaches predefined threshold. The date of delivering an Electric Multiple Unit (EMU) train to maintenance ranges within a time window rather than be a fixed date. ... More

Elliptic preconditioner for accelerating the self consistent field iteration in Kohn-Sham density functional theoryJun 11 2012May 09 2013We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied ... More

About remainders in compactifications of paratopological groupsJun 20 2011In this paper, we prove a dichotomy theorem for remainders in compactifications of paratopological groups: every remainder of a paratopological group $G$ is either Lindel\"{o}f and meager or Baire. Moreover, we give a negative answer for a question posed ... More

Open uniform (G) at non-isolated points and mapsJun 21 2011In this paper, we mainly introduce the notion of an open uniform (G) at non-isolated points, and show that a space $X$ has an open uniform (G) at non-isolated points if and only if $X$ is the open boundary-compact image of metric spaces. Moreover, we ... More

Disentanglement via entanglement: A unified method for Wannier localizationMar 20 2017Jun 05 2018The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials ... More

Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulationSep 25 2018Feb 04 2019We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is the application ... More

Element orbitals for Kohn-Sham density functional theoryJan 27 2012May 01 2012We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, ... More

Convergence of adaptive compression methods for Hartree-Fock-like equationsMar 16 2017Nov 20 2017The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator that is possibly ... More

Perturbation theorems for Hele-Shaw flows and their applicationsMay 21 2010In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions ... More

Uniform covers at non-isolated pointsJun 21 2011In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base properties.\ The main ... More

The minimum stretch spanning tree problem for typical graphsDec 10 2017With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The problem has been ... More

Probing the coupling of heavy dark matter to nucleons by detecting neutrino signature from the Earth coreApr 02 2014We argue that the detection of neutrino signature from the Earth core is an ideal approach for probing the coupling of heavy dark matter ($m_{\chi}>10^{4}$ GeV) to nucleons. We first note that direct searches for dark matter (DM) in such a mass range ... More

The Supergravity Dual of the BMN Matrix ModelJul 29 2004Oct 11 2004We propose type IIA supergravity solutions dual to the 1/2 BPS vacua of the BMN matrix model. These dual solutions are analyzed using the Polchinski-Strassler method and have brane configurations of concentric shells of D2 branes (or NS5 branes) with ... More

Unitary equivalences for essential extensions of $C^*$-algebrasMar 15 2004Let $A$ be a unital separable \CA and $B=C\otimes {\cal K},$ where $C$ is a unital \CA. Let $\tau: A\to M(B)/B$ be a weakly unital full essential extensions of $A$ by $B.$ We show that there is a bijection between a quotient group of $K_0(B)$ onto the ... More

A Proposed Absolute Entropy of Near Extremal Kerr-Newman Black HoleApr 29 2001May 06 2001Some problems have been found as to the definition of entropy of black hole being applied to the extremal Kerr-Newman case, which has conflicts with the third law of thermodynamics. We have proposed a new modification for the near extremal one, which ... More

A Statistical Treatment to the Evolution Equation for Quark DistributionsJun 11 2001The evolution of polarized quark distribution functions is taken into account the gluon emission and absorption, quark pair production and annihilation processes and treated by a statistical method which provides quark distribution functions at small ... More

Index computations on FJRW theoryOct 23 2012Nov 29 2012We compute the index of the real Cauchy-Riemann operator defined in FJRW theory in case of the smooth metric. For the cylindrical metric, we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev ... More

On the Regularity of the Solutions for Cauchy Problem of Incompressible 3D Navier-Stokes EquationOct 14 2013Jan 26 2016In this paper we will prove that the vorticity belongs to $L^{\infty}(0, T; L^2(R^3))$ for the Cauchy problem of 3D incompressible Navier-Stokes equation, then the existence of a global smooth solution is obtained. Our approach is to construct a set of ... More

Type-IV Two-Higgs-Doublet Models And Their CP-ViolationAug 28 2013Several new two-Higgs-doublet models which are naturally free of FCNC will be presented in this manuscript. These models solved the FCNC problem in a way quite different to the previous three types of 2HDMs. In these models, the mass matrices corresponding ... More

Regularity Normalization: Constraining Implicit Space with Minimum Description LengthFeb 27 2019Inspired by the adaptation phenomenon of biological neuronal firing rate, we propose regularity normalization: a reparametrization of the activation in the neural network that take into account the statistical regularity in the implicit space. The implicit ... More

Finite dimensional approximation on manifold with codimension-$4$ foliationMar 06 2019For closed manifolds endowed with a Riemannian foliation of codimension $4$, one can define a transversal Seiberg-Witten map. We show that there is a finite dimensional approximation for such a map. By such a method and under the condition that $H^1_b(M)\cap ... More

Note on equivalence of cutpoint languages recognized by measure many quantum finite automataAug 15 2013Jun 17 2014This note revisits the equivalence of languages recognized by measure many one way quantum finite automata with non/strict cutpoint. The main contributions are as follows: \begin{enumerate}[(1)] \item {We provide an additional proof of the undecidability ... More

Prediction of Electric Multiple Unit Fleet Size Based on Convolutional Neural NetworkSep 03 2018With the expansion of high-speed railway network and growth of passenger transportation demands, the fleet size of electric multiple unit (EMU) in China needs to be adjusted accordingly. Generally, an EMU train costs tens of millions of dollars which ... More

The design of courier transportation networks with a nonlinear zero-one programming modelMay 02 2018The courier industry is one of the most essential parts of the modern logistics. Meanwhile, the courier transportation network is one of the most important infrastructures of courier enterprises to take participate into operation. This paper presents ... More

Efficient Collection of Connected Vehicle Data based on Compressive SensingJun 06 2018Connected vehicles (CVs) can capture and transmit detailed data like vehicle position, speed and so on through vehicle-to-vehicle and vehicle-to-infrastructure communications. The wealth of CV data provides new opportunities to improve the safety, mobility, ... More

T-bulge single photon quantum router with three level systemFeb 26 2017This paper considers the transmission characteristics of incidenting from an infinte coupled-resonator waveguide (CRW) or a semi-infinite CRW, respectively. The Nth cavity of a semi-infinite CRW intersecting with an infinite CRW and a cascade three level ... More

Nondecoupling of Heavy Mirror-FermionMar 11 1994According to one-loop perturbation theory, fermions whose masses are totally generated from Yukawa couplings do not decouple in the heavy mass limit. We investigate this issue nonperturbatively in the strong coupling regime of the chiral $U(1)$ mirror-fermion ... More

Non-Abelian Class Field Theory for Riemann SurfacesNov 22 2001In this paper, using what we call a micro reciprocity law, we complete Weil's program for non-abelian class field theory of Riemann surfaces.

General Uniformity of Zeta FunctionsSep 20 2012Using analytic torsion associated to stable bundles, we introduce zeta functions for compact Riemann surfaces. To justify the well-definedness, we analyze the degenerations of analytic torsions at the boundaries of the moduli spaces, the singularities ... More

A Program For Geometric ArithmeticNov 22 2001Proposed is a program for what we call Geometric Arithmetic, based on our works on non-abelian zeta functions and non-abelian class field theory. Key words are stability and adelic intersection-cohomology theory.

Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic CurvesJan 23 2001New local and global non-abelian zeta functions for elliptic curves are studied using certain refined Brill-Noether loci in moduli spaces of semi-stable bundles. Examples of these zeta functions and a justification of using only semi-stable bundles are ... More

New Non-Abelian Zeta Functions for Curves over Finite FieldsJul 25 2000In this paper, we introduce and study two new types of non-abelian zeta functions for curves over finite fields, which are defined by using (moduli spaces of) semi-stable vector bundles and non-stable bundles. A Riemann-Weil type hypothesis is formulated ... More

Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank OneJan 18 2008May 11 2010Let $C$ be a unital AH-algebra and let $A$ be a unital separable simple C*-algebra with tracial rank no more than one. Suppose that $\phi, \psi: C\to A$ are two unital monomorphisms. With some restriction on $C,$ we show that $\phi$ and $\psi$ are approximately ... More

Full extensions and approximate unitary equivalencesJan 19 2004Let $A$ be a unital separable amenable \CA and $C$ be a unital \CA with certain infinite property. We show that two full monomorphisms $h_1, h_2: A\to C$ are approximately unitarily equivalent if and only if $[h_1]=[h_2]$ in $KL(A,C).$ Let $B$ be a non-unital ... More

Scattering of quasiparticle of spin-triplet pairs in diffusive superconductor-ferromagnetic nanowire-superconductor junctionMar 11 2011We analyze the proximity effect of superconductor/ferromagnet nanostructures and point out that the scattering of quasiparticle of spin-triplet pairs by local magnetic moments leads to large resistance peak slightly below the superconducting transition ... More

A short proof of the equivalence of any Reidemeister oriented move 3Nov 02 2012Nov 08 2012In this note we present a short proof that the 4 oriented Reidemeister moves of type 2 together with any one of the 8 oriented Reidemeister moves of type 3 are sufficient to imply the other 7.