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Fractional Smoothness of Some Stochastic Integrals

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Acta Mathematica Sinica,English Series 2007年第6期23卷 1053-1058页

作者： Peng xiE xi cheng zhang Department of Mathematics Huazhong University of Science and Technology Wuhan 430074 P. R. China

We study the fractional smoothness in the sense of Malliavin calculus of stochastic integrals of the form ∫0^1Ф（Xs）dXs, where Xs is a semimartingale and Ф belongs to some fractional Sobolev space over R.

关键词： fractional Sobolev space stochastic integral interpolation

One Dimensional Stochastic Differential Equations with Distributional Drifts

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Acta Mathematicae Applicatae Sinica 2007年第3期23卷 501-512页

作者： Kai He xi-cheng zhang Institute of Applied Mathematics Academy of Mathematics and SystemSciences Chinese Academy of Sciences Beijing 100080 China Department of Mathematics Huazhong University of Science and Technology Wuhan 430074 China

In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion c... 详细信息

关键词： Strong solution Stochastic homeomorphism flows Dirichlet process Distributional drift

Terahertz wave generation from ring-Airy beam induced plasmas and remote detection by terahertz-radiation- enhanced-emission-of-fluorescence: a review

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Frontiers of Optoelectronics 2019年第2期12卷 117-147页

作者： Kang LIU Pingjie HUANG xi-cheng zhang The Institute of Optics University of Rochester Rochester NY14627USA State Key Laboratory of Industrial Control Technology College of Control Science and Engineering Zhejiang University Hangzhou 310027China The Beijing Advanced Innovation Centerfor Imaging Technology Capital Normal University Beijing 100037China

With the increasing demands for remote spectroscopy in many fields ranging from homeland security to environmental monitoring, terahertz (THz) spectroscopy has drawn a significant amount of attention because of its capability to acquire chemical spectral signatures non-invasively. However, advanced THz remote sensing techniques are obstructed by quite a few factors, such as THz waves being strongly absorbed by water vapor in the ambient air, difficulty to generate intense broadband coherent THz source remotely, and hard to transmit THz waveform information remotely without losing the signal to noise ratio, etc. In this review, after introducing different THz air-photonics techniques to overcome the difficulties of THz remote sensing, we focus mainly on theoretical and experimental methods to improve THz generation and detection performance for the purpose of remote sensing through tailoring the generation and detection media, air-plasma. For the THz generation part, auto-focusing ring-Airy beam was introduced to enhance the THz wave generation yield from two-color laser induced air plasma. By artificially modulated exotic wave packets, it is exhibited that abruptly auto-focusing beam induced air-plasma can give an up to 5.3-time-enhanced THz wave pulse energy compared to normal Gaussian beam induced plasma under the same conditions. At the same time, a red shift on the THz emission spectrum is also observed. A simulation using an interference model to qualitatively describe these behaviors has be developed. For the THz detection part, the results of THz remote sensing at 30 m using THz-radiation-enhanced-emission- of-fluorescence (THz-REEF) technique are demonstrated, which greatly improved from the 10 m demonstration last reported. The THz-REEF technique in the counter-propagation geometry was explored, which is proved to be more practical for stand-off detections than co-propagation geometry. We found that in the counter- propagating geometry the maximum amplitude

关键词： ultrafast terahertz (THz) techniques THz air- photonics ring-Airy beams THz-radiation-enhanced-emis- sion-of-fluorescence (THz-REEF) of air-plasma in co- propagation geometry THz-REEF of air-plasma in coun-ter-propagation geometry

Local measurement of terahertz field-induced second harmonic generation in plasma filaments

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Frontiers of Optoelectronics 2023年第4期16卷 135-178页

作者： Kareem J.Garriga Francis xi‑cheng zhang The Institute of Optics University of RochesterRochesterNY 14627USA

The concept of Terahertz Field-Induced Second Harmonic(TFISH)Generation is revisited to introduce a single-shot detection scheme based on third order *** specifcally on the further development of THz plasma-based sources,we begin our research by reimagining the TFISH system to serve as a direct plasma *** this work,an optical probe beam is used to mix directly with the strong ponderomotive current associated with laser-induced ionization.A four-wave mixing(FWM)process then generates a strong second-harmonic optical wave because of the mixing of the probe beam with the nonlinear current components oscillating at THz *** observed conversion efciency is high enough that for the frst time,the TFISH signal appears visible to the human *** perform spectral,spatial,and temporal analysis on the detected second-harmonic frequency and show its direct relationship to the nonlinear ***,a method to detect incoherent and coherent THz inside plasma flaments is devised using spatio-temporal *** single-shot detection confgurations are theoretically described using a combination of expanded FWM models with Kostenbauder and Gaussian *** show that the retrieved temporal traces for THz radiation from single-and twocolor laser-induced air-plasma sources match theoretical descriptions very *** temporal resolution is shown with a detection bandwidth limited only by the spatial extent of the probe laser *** detection bandwidth and temporal characterization is shown for THz radiation confned to under-dense plasma flaments induced by<100 fs lasers below the relativistic intensity limit.

关键词： Terahertz detection-Plasma characterization-Spectral characterization Single-shot detection

Optimization scheme with pre-processing for cooperative relay multicast networks in cellular system

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The Journal of China Universities of Posts and Telecommunications 2011年第3期18卷 16-21页

作者： WANG cheng-jin LI xi zhang Lin JI Hong Key Laboratory Of Universal Wireless Communication Ministry of Education Beijing University of Posts and Telecommunications Beijing 100876 China

For cooperative relay multicast networks, the general cross-layer optimization approaches converge to the global optimal value slowly because of the large quantity of relay terminals. However, the mobility of relay terminals requires quick converging optimization strategies to refresh the relay links frequently. Based on the capacity analysis of multiple relay channels, an improved cross-layer optimization scheme is proposed to resolve this problem, in which the bound of the relay selecting region is determined as a pre-processing. Utilizing the primal-dual algorithm, a cross-layer framework with pre-processing optimizes both the relay terminal selection and power allocation with quick convergence. The simulation results prove the effectiveness of the proposed algorithm.

关键词： cooperative relay cross-layer optimization pre-processing multicast

Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced transient birefringence

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Light(Science & Applications) 2020年第1期9卷 707-716页

作者： Hang Zhao Yong Tan Liangliang zhang Rui zhang Mostafa Shalaby Cunlin zhang Yuejin Zhao xi-cheng zhang Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology School of Optics and PhotonicsBeijing Institute of TechnologyBeijing 100081China Beijing Advanced Innovation Center for Imaging Technology and Key Laboratory of Terahertz Optoelectronics(MoE) Department of PhysicsCapital Normal UniversityBeijing 100048China Shenzhen Institutes of Advanced Technology Chinese Academy of SciencesShenzhen 518055China The Institute of Optics University of RochesterRochesterNY 14627USA

The fundamental properties of water molecules,such as their molecular polarizability,have not yet been *** hydrogen bond network is generally considered to play an important role in the thermodynamic properties of *** terahertz(THz)Kerr effect technique,as a novel tool,is expected to be useful in exploring the low-frequency molecular dynamics of liquid ***,we use an intense and ultrabroadband THz pulse(peak electric field strength of 14.9 MV/cm,centre frequency of 3.9 THz,and bandwidth of 1–10 THz)to resonantly excite intermolecular modes of liquid *** THz field-induced transient birefringence signals are observed in a free-flowing water *** propose a hydrogen bond harmonic oscillator model associated with the dielectric susceptibility and combine it with the Lorentz dynamic equation to investigate the intermolecular structure and dynamics of liquid *** mainly decompose the bipolar signals into a positive signal caused by hydrogen bond stretching vibration and a negative signal caused by hydrogen bond bending vibration,indicating that the polarizability perturbation of water presents competing contributions under bending and stretching conditions.A Kerr coefficient equation related to the intermolecular modes of water is *** ultrafast intermolecular hydrogen bond dynamics of water revealed by an ultrabroadband THz pump pulse can provide further insights into the transient structure of liquid water corresponding to the pertinent modes.

关键词： transient dynamics liquid

L^p-gradient Estimates of Symmetric Markov Semigroups for 1 〈 p ≤ 2

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Acta Mathematica Sinica,English Series 2006年第1期22卷 101-104页

作者： Ana Bela CRUZEIRO xi cheng zhang Department Matemdtica I.S.T. Av. Rovisco Pais 1099-01 Lisboa Portugal and Grupo de Fisica-Matemdtica U.L. Lisboa Portugal Department of Mathematics Huazhong University of Science and Technology Wuahan 430074 P. R. China

For 1 〈 p ≤2, an L^p-gradient estimate for a symmetric Markov semigroup is derived in a general framework, i.e. ‖Γ^/2（Ttf）‖p≤Cp/√t‖p, where F is a carre du champ operator. As a simple application we prove that F1/2（（I- L） ^-α） is a bounded operator from L^p to L^v provided that 1 〈 p 〈 2 and 1/2〈α〈1. For any 1 〈 p 〈 2, q 〉 2 and 1/2 〈α 〈 1, there exist two positive constants cq,α,Cp,α such that ‖Df‖p≤ Cp,α‖（I - L）^αf‖p,Cq,α（I-L）^（1-α）‖Df‖q＋‖f‖q, where D is the Malliavin gradient （[2]） and L the Ornstein-Uhlenbeck operator.

关键词： Symmetric Markov semigroup Carre du champ Path space

Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding

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Light(Science & Applications) 2019年第1期8卷 680-687页

作者： Jiapeng Zhao Yiwen E Kaia Williams xi-cheng zhang Robert W.Boyd The Institute of Optics University of RochesterRochesterNY 14627USA Department of Physics University of OttawaOttawaON K1N 6N5Canada

Recently,computational sampling methods have been implemented to spatially characterize terahertz(THz)*** methods usually rely on either specialized THz devices such as THz spatial light modulators or complicated systems requiring assistance from photon-excited free carriers with high-speed synchronization among multiple optical ***,by spatially encoding an 800-nm near-infrared(NIR)probe beam through the use of an optical SLM,we demonstrate a simple sampling approach that can probe THz fields with a single-pixel *** design does not require any dedicated THz devices,semiconductors or nanofilms to modulate THz *** computational algorithms,we successfully measure 128×128 field distributions with a 62-μm transverse spatial resolution,which is 15 times smaller than the central wavelength of the THz signal(940μm).Benefitting from the noninvasive nature of THz radiation and sub-wavelength resolution of our system,this simple approach can be used in applications such as biomedical sensing,inspection of flaws in industrial products,and so on.

关键词： synchronization beam spatially

Study on products and reaction paths for synthesis of 3,4-dihydro-2H-3-phenyl-1,3-benzoxazine from phenol,aniline and formaldehyde

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Chinese Chemical Letters 2015年第3期26卷 348-352页

作者： cheng-xi zhang Yu-Yuan Deng Yi-Yang zhang Po Yang Yi Gu State Key Laboratory of Polymer Materials Engineering College of Polymer Science and EngineeringSichuan University

To study the synthesis of 3,4-dihydro-2H-3-phenyl-1,3-benzoxazine（benzoxazine）,the reaction paths of phenol,aniline and formaldehyde were investigated by analyzing the synthesis crude *** the aid of high-performance liquid chromatography（HPLC）,chromatographic column and preparative HPLC,seven compounds originated from the crude products were obtained and their chemical structures were *** reaction paths are proposed based on these *** show that Nhydroxymethyl aniline（HMA） derived from the reaction of formaldehyde and aniline is probably the key intermediate during the *** can react with itself or other reactants to form other intermediates,such as 1,3,5-triphenyl-1,3,5-triazinane and 2-（（phenylamino）methyl）phenol,and further form benzoxazine and byproducts.

关键词： aniline phenol formaldehyde itself crude originated react monomer probably claimed