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A Principal Theorem of Normal Discretization Schemes for Operator Equations of the First Kind

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Wuhan University Journal of Natural Sciences 2001年第4期6卷 767-768页

作者： Du Nai lin 1, Wang Hannah 2.1.school of Mathematics and statistics, Wuhan University, Wuhan 43.072.{2. 2. school of Foreign Languages and Literature,Wuhan University,Wuhan 43.072.china Wuhan University School of Mathematics and Statistics Wuhan China (GRID:grid.49470.3e) (ISNI:***) Wuhan University School of Foreign Languages and Literature Wuhan China (GRID:grid.49470.3e) (ISNI:***)

The authors announce a newly-proved theorem of theirs. This theorem is of principal significance to numerical computation of operator equations of the first kind.

关键词： operator equation of the first kind normal discretization scheme pure pseudoinverse

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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Acta Mathematica Scientia 2010年第5期30卷 1819-1836页

作者：吴臻消华 school of Mathematics Shandong University school of Mathematics and statistics Shandong University at Weihai

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关键词： backward stochastic differential equations comparison theorem local time

Superconductivity of small metal grains

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 431-441页

作者： ZHENG Renrong1 CHEN Zhiqian2.& ZHU Shunquan1,3.1. Department of Physics, Shanghai Normal University, Shanghai 2.02.4,{3. 2. Department of Physics, Southwest Normal University, Chongqing 400715,{3. 3. Department of Computer and Electric Technology, Shanghai Business {2., Shanghai 2.1400,{3. 1. Department of Physics Shanghai Normal University 200234 Shanghai China 2. Department of Physics Southwest Normal University 400715 Chongqing China 3. Department of Computer and Electric Technology Shanghai Business School 201400 Shanghai China

The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关键词： size effect, superconductivity enhancements, small metallic grains.

The steady-state solution of dendritic growth from the undercooled binary alloy melt with the far field flow

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Science china(Technological Sciences) 2009年第8期52卷 2280-2287页

作者： CHEN MingWen1,2. WANG ZiDong2.& XU JianJun2.3.4 1 {3. of Applied Sciences, University of Science and Technology Beijing, Beijing 100083. china {2. of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083. china 3.{3. of Mathematical Sciences, Nankai University, Tianjin 3.0071, china 4 Department of Mathematics and statistics, McGill University, Montreal H3. 2.6, Canada school of Applied Sciences University of Science and Technology Beijing Beijing 100083 China school of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China school of Mathematical Sciences Nankai University Tianjin 300071 China Department of Mathematics and statistics McGill University Montreal H3A 2K6 Canada

The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the steady-state solution for the case of the large Schmidt number, in terms of the multiple variable expansion method. The changes of the temperature and concentration fields, the morphology of the interface, the normalization parameter and the Peclet number of the system induced by uniform external flow are derived. The results show that, compared with the system of dendritic growth from undercooled pure melt, the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface. Nevertheless, the shape of the interface still remains nearly a paraboloid.

关键词： binary alloy melt convection dendritic growth interfaces steady-state solution multiple variable expansion method

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

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Science china(Physics,Mechanics & Astronomy) 2004年第3期47卷 365-380页

作者： CHENG Chuanfu1, 2. SONG Hongsheng2. LIU Chunxiang2. REN Xiaorong2. ZHANG Ningyu3. TENG Shuyun1 & XU Zhizhan1 1. Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P. O. Box 800-2.1, Shanghai 2.1800, china 2. Department of Physics, Shandong Normal University, Jinan 2.0014, china 3. Shandong Institute of Architecture and Engineering, Jinan 2.0014, china 1. Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences P. O. Box 800-211 201800 Shanghai China 2. Department of Physics Shandong Normal University 250014 Jinan China 3. Shandong Institute of Architecture and Engineering 250014 Jinan China

From Helmholtz equation of the harmonic electromagnetic waves, the integral equations of the light field at the medium boundaries are obtained by use of the Green's theorem and are discretized into linear equation set with the values of the light field and its derivative as the unknowns. On solving the linear equation set, we realize the rigorous computations of the light fields at the boundaries. Then the intensities of the light waves scattered by the random self-affine fractal surfaces in the optical near-field are calculated, and the propagation characteristics, the evolutions of the contrast and the intensity probability density function of the near-field speckles are studied in detail. The near-field speckles are much different from the conventional speckles in the diffraction regions and in the imaging systems. There are obvious local fluctuations in the intensity distributions of the near-field speckles and such fluctuations disappear after propagating a distance of one wavelength from the medium surfaces. For the random surfaces with smaller lateral correlation lengths, the speckle contrasts approach the saturation values and the speckle fields approach Gaussian distribution within the near-field, while for the random surfaces with larger lateral correlation lengths, such evolutions become comparatively slow.

关键词： speckle, near-field optics, first order statistics, Green's function.

A Graph Theoretic Method to Handle Deadlocks in Flexible Manufacturing Cells

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武汉理工大学学报 2006年第S3期28卷 1117-1120页

作者： WANG Chunxiang~(1,2. LIU Donglin~3.(1.school of Mathematics and statistics,Wuhan University,Wuhan 43.072.{2., {3. of Mathematics and statistics,Central china Normal University,Wuhan 43.079,{2. 3.school of Electronic and Mechanical Engineering,Wuhan University of Technology,Wuhan 43.070,{2.) school of Mathematics and statistics Wuhan UniversityWuhan 430072China school of Mathematics and statistics Central China Normal UniversityWuhan 430079China school of Electronic and Mechanical Engineering Wuhan University of TechnologyWuhan 430070China

The deadlock-handling scheme is based on a bipartite graph model of the part-machine relationship in the manufac- turing cell.A distinction is made between permanent deadlock and transient *** deadlock depicts a manufactur- ing system state where parts are irrevocably blocked and where external intervention is required to resolve the deadlock,whereas a transient deadlock indicates that there is a positive probability that the deadlock will resolve itself over *** recover from dead- locks,one control policy is studied:resolve deadlocks in the manufacturing *** the policy,it is shown that it is sufficient to resolve any cycle in the set of deadlocked parts to resolve the ***,we estimate the deadlocks in flexible manufactur- ing cells.

关键词： permanent deadlock transient deadlock deadlock detection deadlock resolution graph

Normal scalar curvature and a pinching theorem in S^m×R and H^m×R

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Science china Mathematics 2011年第9期54卷 1977-1984页

作者： CHEN Qun 1,2.& CUI Qing 3.1,1 school of Mathematics and statistics,Wuhan University,Wuhan 43.079,{2. 2.International Center for Theoretical Physics,Trieste 3.100,Italy 3.school of Mathematics,Southwest Jiaotong University,Chengdu 61003.,{2. school of Mathematics and statistics Wuhan University Wuhan China International Center for Theoretical Physics Trieste Italy school of Mathematics Southwest Jiaotong University Chengdu China

We obtain an inequality in Sm×R and Hm×R which is similar to DDVV *** an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type γ×R,where γ is a g... 详细信息

关键词： product spaces DDVV conjecture pinching theorem

The evolution and morphological stability of a spherical crystal

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Science china(Technological Sciences) 2008年第3期51卷 225-243页

作者： CHEN MingWen1,2. WANG ZiDong2.& XU JianJun3.4 1 school of Applied Sciences, University of Science and Technology Beijing, Beijing 100083.{3. {2. of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083.{3. 3.school of Mathematical Sciences, Nankai University, Tianjin 3.0071,{3. 4 Department of Mathematics and statistics, McGill University, Montreal H3. 2.6, Canada 1. school of Applied Sciences University of Science and Technology Beijing Beijing 100083 China 2. school of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China 3. school of Mathematical Sciences Nankai University Tianjin 300071 China 4. Department of Mathematics and statistics McGill University Montreal H3A 2K6 Canada

The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.

关键词： solid-liquid interface spherical crystal convective flow crystal growth morphological stability

An Overview on Wavelet Software Packages

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Wuhan University Journal of Natural Sciences 2001年第Z1期6卷 593-600页

作者： Fan Qi\|bin 1, Li Hong 2.1. school of Mathematics and statistics, Wuhan University, Wuhan 43.072.{2. 2. school of Electronic Information, Wuhan University, Wuhan 43.072.{2. school of Mathematics and statistics Wuhan University Wuhan China school of Electronic Information Wuhan University Wuhan China

Wavelet analysis provides very powerful problem\|solving tools for analyzing, encoding, compressing, reconstructing, and modeling signals and images. The amount of wavelets\|related software has been constantly multiplying. Many wavelet analysis tools are widely available. This overview represents a significant survey for many currently available packages. It will be of great benefit to engineers and researchers for using the toolkits and developing new software. The beginner to learning wavelets can also get a great help from the review. If you browse around at some of the Internet sites listed in the reference of this paper, you may find more plentiful wavelet resources.

关键词： wavelet transforms image compression matching pursuit lifting MATLAB