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BAnDED TOEPLITz PRECOnDITIOnERS FOR TOEPLITz MATRICES FROM SInC METHODS

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Journal of Computational Mathematics 2012年第5期30卷 533-543页

作者： zhi-ru Ren LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We give general expressions, analyze algebraic properties and derive eigenvalue bounds for a sequence of Toeplitz matrices associated with the sinc discretizations of various orders of differential operators. We demonstrate that these Toeplitz matrices can be satisfactorily preconditioned by certain banded Toeplitz matrices through showing that the spectra of the preconditioned matrices are uniformly bounded. In particular, we also derive eigen- value bounds for the banded Toeplitz preconditioners. These results are elementary in constructing high-quality structured preconditioners for the systems of linear equations arising from the sinc discretizations of ordinary and partial differential equations, and are useful in analyzing algebraic properties and deriving eigenvalue bounds for the correspond- ing preconditioned matrices. numerical examples are given to show effectiveness of the banded Toeplitz preconditioners.

关键词： Toeplitz matrix Banded Toeplitz preconditioner Generating function Sincmethod Eigenvalue bounds.

Uniform Convergence of Wavelet Solution to the Sideways Heat Equation

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Acta Mathematica Sinica,English Series 2010年第10期26卷 1981-1992页

作者： Jin ru WAnG Department of Applied Mathematics Beijing University of Technology Beijing 100124 P. R. China

We consider the problem uxx（x, t） = ut（x, t）, 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g（t） is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g（t） can produce a big alteration on its solution （if it exists）. We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren＇t stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1].

关键词： Sideways heat equation multi-resolution analysis Meyer wavelet solution

Stochastic Equations for Two-type Continuous-state Branching Processes with Immigration

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Acta Mathematica Sinica,English Series 2013年第2期29卷 287-294页

作者： ru Gang MA School of Mathematical Sciences Beijing Normal University

A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.

关键词： Continuous-state branching process immigration stochastic integral equation comparison property strong solution

Scattering Problem for Klein–Gordon Equation with Cubic Convolution nonlinearity

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Acta Mathematica Sinica,English Series 2014年第5期30卷 827-836页

作者： ru Ying XUE Department of Mathematics Zhejiang University

The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the sc... 详细信息

关键词： Asymptotic of solution Klein–Gordon equation scattering operator

Ising Model on an Infinite Ladder Lattice

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Communications in Theoretical Physics 2007年第3X期48卷 553-562页

作者： GAO Xing-ru CCAST (World Laboratory) P.O. Box 8730 Beijing 100080 China Department of Physics and Institute of Theoretical Physics Beijing Normal University Beijing 100875 China Fundamental Teaching Department Beijing Union University Beijing 100101 China

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.

关键词： Ising model general transfer matrix phase transition Glauber dynamics critical slow down

Effective　Depletion　Potential　of　Colloidal　Spheres

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Chinese Physics Letters 2004年第6期21卷 1175-1178页

作者： LIWei-Hua MAHong-ru InstituteofTheoreticalPhysics ShanghaiJiaoTongUniversityShanghai200240

A new semianalytical method, which is a combination of the density functional theory with Rosenfeld density functional and the Ornstein-zernike equation, is proposed for the calculation of the effective depletion potentials between a pair of big spheres immersed in a small hard sphere fluid. The calculated results are almost identical to the integral equation method with the Percus-Yevick approximation, and are also in agreement well with the Monte Carlo simulation results.

关键词： Soft matter liquids and polymers Condensed matter: electrical magnetic and optical Chemical physics and physical chemistry

Effect of vegetation on soil bacteria and their potential functions for ecological restoration in the Hulun Buir Sandy Land,China

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Journal of Arid Land 2020年第3期12卷 473-494页

作者： YAn ru FEnG Wei Yanchi Research Station School of Soil and Water ConservationBeijing Forestry UniversityBeijing 100083China Engineering Research Center of Forestry Ecological Engineering of the Ministry of Education Beijing Forestry UniversityBeijing 100083China

To date,much of research on revegetation has focused on soil microorganisms due to their contributions in the formation of soil and soil remediation ***,little is known about the soil bacteria and their functions respond to the diverse vegetational types in the process of vegetation *** of dominated vegetation,i.e.,Artemisia halodendron Turcz Ex Bess,Caragana microphylla Lam.,Hedysarum fruticosum *** Pinus sylvestris *** bacterial community structures and their potential functions in the Hulun Buir Sandy Land,China were determined using high-throughput 16S rRnA gene sequencing and phylogenetic investigation of communities by reconstruction of unobserved states(PICruSt)in *** the dominant phyla of soil bacterial community among different types of vegetation,including Proteobacteria,Actinobacteria,Acidobacteria,Bacteroidetes and Firmicutes,were similar,the relative abundance of these dominant groups significantly differed,indicating that different types of vegetation might result in variations in the composition of soil bacterial *** addition,functional genes of bacterial populations were similar among different types of vegetation,whereas its relative abundance was significantly *** carbon fixation genes showed a high relative abundance in ***,*** carbon decomposition genes in ***,suggesting the variations in carbon cycling potential of different types of *** of assimilatory nitrate reduction genes was the highest in ***,*** nitrate reduction and nitrate reductase genes in ***,indicating higher nitrogen gasification loss and lower nitrogen utilization gene functions in *** structures and functional genes of soil bacterial community showed marked sensitivities to different plant species,presenting the potentials for regulating soil carbon and nitrogen cycling.

关键词： bacterial taxonomic composition functional gene vegetational type soil carbon and nitrogen 16S rRnA

Antimonene-based saturable absorber for a soliton mode-locked and Q-switched fiber laser in the 2 μm wavelength region

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Chinese Physics B 2023年第6期32卷 259-269页

作者： H Ahmad B nizamani M z Samion n Yusoff M F Ismail Photonics Research Centre Universiti Malaya50603 Kuala LumpurMalaysia Physics Department Faculty of ScienceUniversiti Malaya50603 Kuala LumpurMalaysia Distinguished Visiting Professor Universiti Kuala Lumpur British Malaysian Institute(UniKL BMI)Batu 8Jln Sungai Pusu53100SelangorMalaysia

We demonstrate antimonene as a saturable absorber(SA) to generate an ultrafast mode-locked and Q-switched laser in the 2 μm wavelength region. The two antimonene-based SAs were prepared and inserted separately in a thulium–holmiumdoped fiber laser to produce the pulsed laser. Antimonene was coated onto a tapered fiber to generate soliton mode-locked pulses and used in thin-film form for the generation of Q-switched pulses. The mode-locking was stable within a pump power of 267 m W–511 m W, and the laser operated at a central wavelength of 1897.4 nm. The mode-locked laser had a pulse width of 1.3 ps and a repetition rate of 12.6 MHz, with a signal-to-noise ratio of 64 d B. Q-switched laser operation was stable at a wavelength of 1890.1 nm within a pump power of 312 m W–381 m W. With the increase in pump power from 312 m W to 381 m W, the repetition rate increased to a maximum of 56.63 k Hz and the pulse width decreased to a minimum value of 2.85 μs. Wide-range tunability of the Q-switched laser was also realized within the wavelength range of1882 nm–1936 nm.

关键词： mode-locking Q-switched fiber laser optical saturable absorber

Parameterizing Stellar Spectra Using Deep neural networks

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Research in Astronomy and Astrophysics 2017年第4期17卷 49-56页

作者： Xiang-ru Li ru-Yang Pan Fu-Qing Duan School of Mathematical Sciences South China Normal University College of Information Science and Technology Beijing Normal University

Large-scale sky surveys are observing massive amounts of stellar spectra. The large number of stellar spectra makes it necessary to automatically parameterize spectral data, which in turn helps in statistically exploring properties related to the atmospheric parameters. This work focuses on designing an automatic scheme to estimate effective temperature （Tee）, surface gravity （log g） and metallicity [Fe/H] from stellar spectra. A scheme based on three deep neural networks （Dnns） is proposed. This scheme consists of the following three procedures： first, the configuration of a Dnn is initialized using a series of autoencoder neural networks; second, the Dnn is fine-tuned using a gradient descent scheme; third, three atmospheric parameters Tefr, log 9 and [Fe/H] are estimated using the computed Dnns. The constructed Dnn is a neural network with six layers （one input layer, one output layer and four hidden layers）, for which the number of nodes in the six layers are 3821, 1000, 500, 100, 30 and 1, respectively. This proposed scheme was tested on both real spectra and theoretical spectra from Kurucz＇s new opacity distribution function models. Test errors are measured with mean absolute errors （MAEs）. The errors on real spectra from the Sloan Digital Sky Survey （SDSS） are 0.1477, 0.0048 and 0.1129 dex for log 9, log Tefr and [Fe/H] （64.85 K for Teff）, respectively. Regarding theoretical spectra from Kurucz＇s new opacity distribution function models, the MAE of the test errors are 0.0182, 0.0011 and 0.0112 dex for log 9, log Teff and [Fe/H] （14.90 K for Tdf）, respectively.

关键词： methods: statistical - methods data analysis - stars fundamental parameters - stars atmospheres - stars abundances - techniques spectroscopic