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Science China(Technological Sciences) 2004年第2期47卷 216-228页

作者： BI Chuanxing CHEN Jian CHEN Xinzhao Dynamic Measuring Center Hefei University of Technology Hefei 230009 China Dynamic Measuring Center Hefei University of Technology Hefei 230009 China Dynamic Measuring Center Hefei University of Technology Hefei 230009 China

In a multi-source acoustic field, the actual measured pressure is a scalar sum of pressures from all the sources. The pressure belonging to every source cannot be separated out with the existing techniques. Consequently, routine formulas cannot be used to reconstruct the acoustic source and predict the acoustic field directly. In this paper, a novel theoretical model of reconstruction and prediction of multi-source acoustic field in the distributed source boundary point method (DSBPM) based nearfield acoustic holography (NAH) is established. Three different methods, namely combination method with single surface measurement, combination method with multi-surface measurement and elimination method with multi-surface measurement, are proposed to realize the holographic reconstruction of sources. With these methods, the problem of reconstruction and prediction of acoustic field existing multiple coherent sources synchronously is solved effectively. Using the particular solutions constructed by the DSBPM to establish the vibro-acoustic transfer matrix, the calculation time, calculation precision and calculation stability are improved. These methods are valuable in localizing acoustic source and predicting acoustic field in engineering field.

关键词： acoustic holography, boundary point, distributed source, acoustic radiation.

QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization

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Communications in Theoretical Physics 2001年第12期36卷 665-672页

作者： SU Jun-Chen SHAN Lian-You CAO Ying-Hui Center for Theoretical Physics Department of Physics Jilin University Changchun 130023 China Center for Theoretical Physics Department of Physics Jilin University Changchun 130023 China Center for Theoretical Physics Department of Physics Jilin University Changchun 130023 China

The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary time-like momentum. The correctness of the subtraction is ensured by the Ward identities which are respected in all the processes of *** considering the mass effect, the effective coupling constant and the effective quark masses derived by solving the renormalization group equations are given in improved expressions which are different from the previous *** numbers: ***, ***, 12.38.-t, 12.38.

关键词： QCD renormalization, mass-dependent subtraction, time-like renormalization point, effective cou pling constant and quark mass, exact one-loop results

On capture and acceleration of heavy ions (α-particle) in high-speed solar wind

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Science China Mathematics 2002年第3期45卷 385-393页

作者：宋礼庭肖池阶 Space Weather Laboratory Chinese Academy of Sciences Beijing 100080 China Department of Geophysics Peking University Beijing 100871 China

The α-particles and other heavy ions, as well as a few protons are observed to be faster than the main part of protons by about the local Alfven speed in the high-speed solar wind. It is suggested that when the velocity of the solar wind is equal to the local Alfven velocity, another low-frequency kinetic Alfven wave will be excitated, and trap all the a-particles and a few protons, so these ions have a local Alfven velocity faster than the other parts of the solar wind. The undamping kinetic Alfven waves change into low-frequency Alfven solitons in the solar wind. This model can explain the observation and give the conditions of wave excitated and ions trapped.

关键词： high-speed solar wind, kinetic Alfven wave, Alfven point, Alfven-soliton.

Ritt's theorem and the Heins map in hyperbolic complex manifolds

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Science China Mathematics 2005年第Z1期48卷 238-243页

作者： Marco Abate Filippo Bracci Dipartimento di Matematica Università di Pisa Largo Pontecorvo 556127 PisaItalyDipartimento di Matematica Università di Roma "Tor Vergata"Via della Ricerca Scientifica00133 RomaItaly

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic self-map f: X →X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.

关键词： holomorphic self-map, fixed point, Wolff point, Ritt's theorem, Heins map, Stein manifold.

Repelling periodic points of given periods of rational functions

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Science China Mathematics 2006年第9期49卷 1165-1174页

作者： CHANG Jianming FANG Mingliang Department of Mathematics Changshu Institute of Technology Changshu 215500 China Department of Applied Mathematics South China Agricultural University Guangzhou 510642 China

Let R(z) be a rational function of degree d ≥ 2. Then R(z) has at least one repelling periodic point of given period k ≥ 2, unless k = 4 and d=2, or k= 3 and d ≤ 3, or k=2 and d≤8. Examples show that all exception... 详细信息

关键词： rational function, iterate, fixed point, periodic point, repelling periodic point.

Theoretical and experimental investigation of holographic reconstruction and prediction of multi-source hybrid acoustic field

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Science China(Physics,Mechanics & Astronomy) 2005年第3期48卷 282-299页

作者： BI Chuanxing CHEN Jian CHEN Xinzhao YU Fei LI Weibing Dynamic Measuring Center Hefei University of Technology Hefei 230009 China Dynamic Measuring Center Hefei University of Technology Hefei 230009 China Dynamic Measuring Center Hefei University of Technology Hefei 230009 China Dynamic Measuring Center Hefei University of Technology Hefei 230009 China Dynamic Measuring Center Hefei University of Technology Hefei 230009 China

Study on a multi-source hybrid acoustic field is very important for nearfield acoustic holography (NAH) to be applied in the practical engineering field. In this paper, two methods based on the distributed source boundary point method (DSBPM) for holographic reconstruction and prediction of multi-source hybrid acoustic field, namely combination method with single surface measurement and combination method with multi-surface measurement, are proposed. Then, an experiment on two coherent speakers is carried out. By comparison of the reconstructed and predicted results and the actual measured results, the validity of the two methods and the superiority of the combination method with multi-surface measurement are proved. Considering the high sensitivity of the reconstructed results to measurement errors, the Tikhonov regularization method is proposed to stabilize the reconstruction procedure and restrict the influence of errors. And then, the optimal reconstructed results can be obtained and the reliability of holographic reconstruction and prediction is assured.

关键词： acoustic holography, boundary point, distributed source, acoustic radiation, regularization.

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

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Science China Mathematics 2003年第4期46卷 506-515页

作者：郭志明庾建设 Department of Applied Mathematics Hunan University Changsha 410082China Department of MathematicsTaiyuan Normal CollegeTaiyuan 030012China Department of Applied Mathematics Hunan University Changsha 410082China

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.

关键词： superlinear difference equation, periodic solution, subharmonic solution, critical point, linking.

Non-wandering points and the depth for graph maps

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Science China Mathematics 2007年第12期50卷 1818-1824页

作者： Jie-hua MAI~1 Tai-xiang SUN~(2+) ~1 Institute of Mathematics,Shantou University,Shantou 515063,China ~2 College of Mathematics and Information Sciences,Guangxi University,Nanning 530004,China Institute of Mathematics Shantou University Shantou China College of Mathematics and Information Sciences Guangxi University Nanning China

Let G be a graph and f:G→G be *** by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f ***Ω_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈*** minimal m∈NU {∞} such thatΩ_m(f)=Ω_(m+1)(f) is called the depth of *** this paper,we show thatΩ_2 (f)=(?) and the depth of f is at most ***,we obtain some properties of non-wandering points of f.

关键词： graph map, non-wandering point, the depth of a graph map

The topology of Julia sets for polynomials

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Science China Mathematics 2002年第8期45卷 1020-1024页

作者：尹永成 Centre of Mathematical Sciences Zhejiang University Hangzhou China

We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for t... 详细信息

关键词： critical point, non-recurrent, Julia set.

Anisotropy of the horizontal velocity fluctuation field in the large wavenumber region

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Science China Earth Sciences 2003年第3期46卷 210-216页

作者：吴永富徐寄遥 Laboratory for Space Weather Center for Space Science and Applied Research Chinese Academy of SciencesBeijing 100080 China

This paper utilizes meridional and zonal velocity data measured by chaff rockets at a high resolution of 25 m in the 67—96 km region during the MAC/SINE campaign to study the char-acteristics of the spectra of the meridional and zonal velocity fluctuations. Results suggest that the mean vertical wavenumber spectra have a forked point near vertical wavenumber k = 0.001 m-1. In the vertical wavenumber region smaller than the forked point, the spectra of the meridional and zonal velocities have approximately the same spectral slope, amplitude, and characteristic vertical wavelength, and agree well with the linear saturated spectral model. In the vertical wavenumber region larger than the forked point, however, the meridional and zonal spectra are inconsistent not only in both slope and amplitude, but also in spectral structure. The differences between the observed meridional and zonal spectra provide observational evidence of azimuthal anisotropy of the velocity fluctuation field in the large vertical wavenumber region in mean sense.

关键词： velocity fluctuation spectra, forked point, anisotropy, large wavenumber.