arXiv subjects

Yan Li

Publications and source records attributed to Yan Li.

At least 613 records · Page 34Linked to original sources

arXiv2016

Symmetry and nonexistence of positive solutions for fractional systems

This paper is devoted to study the nonexistence results of positive solutions for the following fractional H$\acute{e}$non system \begin{eqnarray*}\left\{ \begin{array}{lll} &(-\triangle)^{α/2}u=|x|^av^p,~~~&x\in R^n, &(-\triangle)^{α/2}v=|x|^bu^q,~~~ &x\in R^n, &u\geq0, v\geq 0, \end{array} \right. \end{eqnarray*} where $0<α<2$, $0<p,q<\infty$, $a$, $b$ $\geq0$, $n\geq2$. Using a direct method of moving planes, we prove non-existence of positive solution in the subcritical case.

math.AP↗

arXiv2016

A Liouville Theorem for the Higher Order Fractional Laplacian

We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differential equation. The latter works directly on the differential equations. We first derive nonexistence of positive solutions, often known as the Liouville type theorem, for the integral and differential equations. Then through an delicate iteration, we show symmetry for positive solutions.

math.AP↗

arXiv2016

Multiple resonances of a moving, oscillating surface disturbance on a shear current

We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $τ=|\boldsymbol{V}|ω_0/g$ equals the critical value $1/4$ ($\boldsymbol{V}$: velocity of disturbance, $ω_0$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of the sub-surface shear current can change this picture radically. Not only does the resonant value of $τ$ depend strongly on the angle between $\boldsymbol{V}$ and the current's direction and the "shear-Froude number" $\mathrm{Frs}=|\boldsymbol{V}|S/g$; when $\mathrm{Frs}>1/3$, multiple resonant values --- as many as $4$ --- can occur for some directions of motion. At sufficiently large values of $\mathrm{Frs}$, the smallest resonance frequency tends to zero, representing the phenomenon of critical velocity for ship waves. We provide a detailed analysis of the dispersion relation for the moving, oscillating disturbance, in both finite and infinite water depth, including for the latter case an overview of the different far-field waves which exist in different sectors of wave vector space under different conditions. Owing to the large number of parameters, a detailed discussion of the structure of resonances is provided for infinite depth only, where analytical results are available.

physics.flu-dyn↗

arXiv2016

Skipping Word: A Character-Sequential Representation based Framework for Question Answering

Recent works using artificial neural networks based on word distributed representation greatly boost the performance of various natural language learning tasks, especially question answering. Though, they also carry along with some attendant problems, such as corpus selection for embedding learning, dictionary transformation for different learning tasks, etc. In this paper, we propose to straightforwardly model sentences by means of character sequences, and then utilize convolutional neural networks to integrate character embedding learning together with point-wise answer selection training. Compared with deep models pre-trained on word embedding (WE) strategy, our character-sequential representation (CSR) based method shows a much simpler procedure and more stable performance across different benchmarks. Extensive experiments on two benchmark answer selection datasets exhibit the competitive performance compared with the state-of-the-art methods.

cs.CL↗

arXiv2016

Transcoder for the spatial and temporal modes of a photon

Encoding information in light with orbital angular momentum (OAM) enables networks to increase channel capacity significantly. However, light in only the fundamental Gaussian mode is suitable for fibre transmission, and not higher order Laguerre Gaussian modes, which carry OAM. Therefore, building a bridge to interface light with OAM and Gaussian mode time-binning is crucially important. Here, we report the realization of a photonic space-time transcoder, by which light with an arbitrary OAM superposition is experimentally converted into a time-bin Gaussian pulse, and vice versa. Furthermore, we clearly demonstrate that coherence is well conserved and there is no cross-talk between orthogonal modes. This photonic device is simple and can be built with scalable architecture. Our experimental demonstration paves the way towards a mixed optical communication in free-space and optical fibre.

quant-ph↗

arXiv2016

Symmetry of Solutions for a Fractional System

We consider the following equations: \begin{equation*} \left\{\begin{array}{ll} (-\triangle)^{α/2}u(x)=f(v(x)), \\ (-\triangle)^{β/2}v(x)=g(u(x)), &x \in R^{n},\\ u,v\geq 0, &x \in R^{n}, \end{array} \right. \end{equation*} for continuous $f, g$ and $α, β\in (0,2)$. Under some natural assumptions on $f$ and $g$, by applying the \emph{method of moving planes} directly to the system, we obtain symmetry on non-negative solutions without any decay assumption on the solutions at infinity.

math.AP↗

arXiv2016

Orbital angular momentum-entanglement frequency transducer

Entanglement is a vital resource for realizing many tasks such as teleportation, secure key distribution, metrology and quantum computations. To effectively build entanglement between different quantum systems and share information between them, a frequency transducer to convert between quantum states of different wavelengths while retaining its quantum features is indispensable. Information encoded in the photons orbital angular momentum OAM degrees of freedom is preferred in harnessing the information carrying capacity of a single photon because of its unlimited dimensions. A quantum transducer, which operates at wavelengths from 1558.3 nm to 525 nm for OAM qubits, OAMpolarization hybrid entangled states, and OAM entangled states, is reported for the first time. Nonclassical properties and entanglements are demonstrated following the conversion process by performing quantum tomography, interference, and Bell inequality measurements. Our results demonstrate the capability to create an entanglement link between different quantum systems operating in photons OAM degrees of freedoms, which will be of great importance in building a high capacity OAM quantum network.

quant-ph↗

arXiv2016

A Pohozaev Identity for the Fractional H$\acute{e}$non System

In this paper, we study the Pohozaev identity associated with a H$\acute{e}$non-Lane-Emden system involving the fractional Laplacian: \begin{equation} \left\{\begin{array}{ll} (-\triangle)^su=|x|^av^p,&x\inΩ, (-\triangle)^sv=|x|^bu^q,&x\inΩ, u=v=0,&x\in R^n\backslashΩ, \end{array} \right. \end{equation} in a star-shaped and bounded domain $Ω$ for $s\in(0,1)$. As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases.

math.AP↗

arXiv2016

Audio Recording Device Identification Based on Deep Learning

In this paper we present a research on identification of audio recording devices from background noise, thus providing a method for forensics. The audio signal is the sum of speech signal and noise signal. Usually, people pay more attention to speech signal, because it carries the information to deliver. So a great amount of researches have been dedicated to getting higher Signal-Noise-Ratio (SNR). There are many speech enhancement algorithms to improve the quality of the speech, which can be seen as reducing the noise. However, noises can be regarded as the intrinsic fingerprint traces of an audio recording device. These digital traces can be characterized and identified by new machine learning techniques. Therefore, in our research, we use the noise as the intrinsic features. As for the identification, multiple classifiers of deep learning methods are used and compared. The identification result shows that the method of getting feature vector from the noise of each device and identifying them with deep learning techniques is viable, and well-preformed.

cs.SD↗

arXiv2016

High-dimensional entanglement between distant atomic ensemble memories

Entangled quantum states in high-dimensional space show many advantages compared with entangled states in two-dimensional space. The former enable quantum communication with higher channel capacity, enable more efficient quantum-information processing, and are more feasible for closing the detection loophole in Bell test experiments. Establishing high-dimensional entangled memories is essential for long-distance communication, but its experimental realization is lacking. We experimentally established high-dimensional entanglement in orbital angular momentum space between two atomic ensembles separated by 1 m. We reconstructed the density matrix for a three-dimensional entanglement and obtained an entanglement fidelity of 83.9+/-2.9%. More importantly, we confirmed the successful preparation of a state entangled in more than three-dimensional space (up to seven-dimensional) using entanglement witnesses. Achieving high-dimensional entanglement represents a significant step towards a high-capacity quantum network.

quant-ph↗

arXiv2016

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current [Ellingsen, J.~Fluid Mech.\ {\bf 742} R2 (2014)]. We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth, and the angle between the shear current and the ship's motion. Formulae for both the normal and lateral wave resistance force are derived, and we analyse its dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to $10$-$20\%$ of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. (Continues...)

physics.flu-dyn↗

arXiv2016

A direct method of moving planes for the fractional Laplacian

In this paper, we develop a direct method of moving planes for the fractional Laplacian. Instead of conventional extension method introduced by Caffarelli and Silvestre, we work directly on the non-local operator. Using the integral defining the fractional Laplacian, by an elementary approach, we first obtain the key ingredients needed in the method of moving planes either in a bounded domain or in the whole space, such as strong maximum principles for anti-symmetric functions, narrow region principles, and decay at infinity. Then, using a simple example, a semi-linear equation involving the fractional Laplacian, we illustrate how this new method of moving planes can be employed to obtain symmetry and non-existence of positive solutions. We firmly believe that the ideas and methods introduced here can be conveniently applied to study a variety of nonlocal problems with more general operators and more general nonlinearities.

math.AP↗

arXiv2016

Direct Method of Moving Spheres on Fractional Order Equations

In this paper, we introduce a direct method of moving spheres for the nonlocal fractional Laplacian $(-\triangle)^{α/2}$ for $0<α<2$, in which a key ingredient is the narrow region maximum principle. As immediate applications, we classify the non-negative solutions for a semilinear equation involving the fractional Laplacian in $\mathbb{R}^n$; we prove a non-existence result for prescribing $Q_α$ curvature equation on $\mathbb{S}^n$; then by combining the direct method of moving planes and moving spheres, we establish a Liouville type theorem on the half Euclidean space. We expect to see more applications of this method to many other equations involving non-local operators.

math.AP↗

arXiv2016

Background-free coherent anti-stokes Raman spectroscopy and microscopy by dual-soliton pulse generation

We propose an all-fiber-generated dual-soliton pulses based scheme for the background-free detection of coherent anti-Stokes Raman spectroscopy under the spectral focusing mechanism. Due to the strong birefringence and high nonlinearity of a polarization-maintaining photonic crystal fiber (PM-PCF), two redshifted soliton pulses can be simultaneously generated relying on high-order dispersion and nonlinear effects along two eigenpolarization axes in the anomalous dispersion regime, while allowing feasible tunability of the frequency distance and temporal interval between them. This proposed scheme, termed as DS-CARS, exploits a unique combination of slight frequency-shift and advisable temporal walk-off of this two soliton pulses to achieve robust and efficient suppression of nonresonant background with compact all-fiber coherent excitation source. Capability of the DS-CARS is experimentally demonstrated by the background-free CARS spectroscopy and unambiguous CARS microscopy of polymer beads in the fingerprint region.

physics.optics↗

arXiv2016

Witnessing Multipartite Entanglement without Entanglement Witness Operators

Quantum mechanics predicts the existence of correlations between composite systems -- multipartite entanglement (ME) -- that, while puzzling our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect ME. Here we propose a novel paradigm based on the measurement of the statistical response of a quantum systems to a collective parametric evolution. As a major difference with respect to current approaches based on the implementation of entanglement witness operators, we witness ME without relying on measurement efficiencies or tomographic reconstructions of the quantum state. The protocol requires only two settings for any number of parties. To illustrate its user-friendliness we demonstrate ME in different experiments with ions and photons by analyzing published data on fidelity visibilities and averaged observables.

quant-ph↗

arXiv2016

Storing a single photon as a spin wave entangled with a flying photon in telecomband

Quantum memory is an essential building block for quantum communication and scalable linear quantum computation. Storing two color entangled photons, with one photon being at telecom-wavelength while the other photon being compatible of quantum memory, has great advantages toward the realization of the fiber based long-distance quantum communication with the aid of quantum repeaters. Here, we report an experimental realization of storing a photon entangled with a telecom photon in polarization as an atomic spin wave in a cold atomic ensemble, thus establishing the entanglement between the telecom-band photon and the atomic ensemble memory in polarization degree of freedom. The reconstructed density matrix and the violation of Clauser Horne Shimony Holt inequality clearly show the preservation of quantum entanglement during storage. Our result is very promising for establishing a long-distance quantum network based on cold atomic ensembles.

quant-ph↗

arXiv2016

Strongly-coupled nanotube electromechanical resonators

Coupling an electromechanical resonator with carbon-nanotube quantum dots is a significant method to control both the electronic charge and the spin quantum states. By exploiting a novel micro-transfer technique, we fabricate two strongly-coupled and electrically-tunable mechanical resonators on a single carbon nanotube for the first time. The frequency of the two resonators can be individually tuned by the bottom gates, and strong coupling is observed between the electron charge and phonon modes of each resonator. Furthermore, the conductance of either resonator can be nonlocally modulated by the phonon modes in the other resonator. Strong coupling is observed between the phonon modes of the two resonators, which provides an effective long distance electron-electron interaction. The generation of phonon-mediated-spin entanglement is also theoretically analyzed for the two resonators. This strongly-coupled nanotube electromechanical resonator array provides an experimental platform for future studies of the coherent electron-phonon interaction, the phonon mediated long-distance electron interaction, and entanglement state generation.

cond-mat.mes-hall↗

arXiv2016

New Insights for High-precision Asteroseismology: Acoustic Radius of KIC 6225718

Asteroseismology is a powerful tool for probing stellar interiors and determining stellar fundamental parameters. In previous works, $χ^2$-minimization method is usually used to find the best matching model to characterize observations. In this letter, we adopt the $χ^2$-minimization method but only using the observed high-precision oscillation to constrain theoretical models for solar-like oscillating star KIC 6225718, which is observed by \kepler\ satellite. We also take into account the influence of model precision. Finally, we find that the time resolution of stellar evolution can not be ignored in high-precision asteroseismic analysis. Based on this, we find the acoustic radius $τ_{0}$ is the only global parameter that can be accurately measured by $χ^2_ν$ matching method between observed frequencies and theoretical model calculations. We obtain $τ_{0}=4601.5^{+4.4}_{-8.3}$ seconds. In addition, we analyze the distribution of $χ^2_ν$-minimization models (CMMs), and find that the distribution range of CMMs is slightly enlarged by some extreme cases, which possess both of larger mass and higher (or lower) heavy element abundance, at lower acoustic radius end.

astro-ph.SR↗