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Rational points and zeta functions of some curves over finite fields

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science China mathematics 2010年第11期53卷 2855-2863页

作者： WANG Long1, & LUO JinQuan2,3.1Department of mathematical sciences, Tsinghua university, Beijing 100084, China 2{3. of mathematical sciences, Yangzhou university, Yangzhou 225002, China 3.ivision of mathematical sciences, school of physical and mathematical sciences, nanyang Technology university, 63.3.1, singapore 1. Department of mathematical sciences Tsinghua University Beijing 100084 China2. School of Mathematical Sciences Yangzhou University Yangzhou 225002 China3. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technology University Singapore 637371 Singapore

In this paper we study the number of rational points on some curves over finite fields. Moreover, zeta functions of the associated function fields are evaluated explicitly.

关键词： exponential sum rational point rational place zeta function

Application of splitting scheme and multigrid method for TV-Stokes denoising

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science China(Information sciences) 2011年第4期54卷 745-756页

作者： CHANG QianShun 1,TAI XueCheng 2 & XING LiLi 3.1 Institute of Applied mathematics,Academy of mathematics and Systems sciences,Chinese Academy of sciences,Beijing 100190,China 2 Department of mathematics,university of Bergen,Bergen 5007,Norway school of physical and mathematical sciences,nanyang technological university,63.798,singapore 3.school of mathematics and computational science,China university of petroleum (East China),dongying 257061,China 1. Institute of Applied mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100190 China2. Department of Mathematics University of Bergen Bergen 5007 Norway3. School of Mathematics and Computational Science China University of Petroleum (East China) Dongying 257061 China

Based on some previous work on the connection between image restoration and fluid dynamics,we apply a two-step algorithm for image *** the first step,using a splitting scheme to study a nonlinear Stokes equation,tangent vectors are *** the second step,an image is restored to fit the constructed tangent *** apply a fixed point iteration to solve the total variation-based image denoising problem,and use algebraic multigrid method to solve the corresponding linear *** results demonstrate that our algorithm is efficient and robust,and boundary conditions are satisfactory for image denoising.

关键词： image denoising total variation Stokes equation algebraic multigrid method

Complete solving of explicit evaluation of Gauss sums in the index 2 case

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science China mathematics 2010年第9期53卷 2525-2542页

作者： YANG Jing1,2 & XIA LingLi3.1Department of mathematical sciences,Tsinghua university,Beijing 100084,China 2Division of mathematical sciences,school of physical and mathematical sciences,nanyang technological university,63.3.1,singapore 3.asic Courses Department,Beijing Union university,Beijing 100101,China 1. Department of mathematical sciences Tsinghua University Beijing 100084 China2. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 637371 Nanyang Singapore3. Basic Courses Department Beijing Union University Beijing 100101 China

Let p be a prime number,N be a positive integer such that gcd(N,p) = 1,q = pf where f is the multiplicative order of p modulo *** χ be a primitive multiplicative character of order N over finite field *** paper studies the problem of explicit evaluation of Gauss sums G(χ) in the "index 2 case"(i.e.[(Z/NZ):] = 2).Firstly,the classification of the Gauss sums in the index 2 case is ***,the explicit evaluation of Gauss sums G(χλ)(1 λ N-1) in the index 2 case with order N being general even integer(i.e.N = 2r·N0,where r,N0 are positive integers and N0 3.is odd) is ***,combining with the researches before,the problem of explicit evaluation of Gauss sums in the index 2 case is completely solved.

关键词： Gauss sum Stickelberger’s theorem Stickelberger congruence Davenport-Hasse lifting formula Davenport-Hasse product formula

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 school of Applied sciences, university of {3. and Technology Beijing, Beijing 100083. China 2 school of Materials {3. and Engineering, university of {3. and Technology Beijing, Beijing 100083. China 3.school of mathematical sciences, Nankai university, Tianjin 3.0071, China 4 Department of mathematics and Statistics, McGill university, Montreal H3. 2K6, 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

A Comparative Study of Boron and Phosphorus Doping Effects in SiC: H Films Prepared by ECR-CVD

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Journal of Materials science & Technology 1998年第1期14卷 65-71页

作者： S.F. Yoon (school of Electrical and Electronic Engineering, nanyang technological university, nanyang Avenue,{3. 63.798, Rep. of {3.) nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

Hydrogenated silicon carbide films (SiC:H) were deposited using the electron cyclotron resonance chemical vapour deposition (ECR-CVD) technique from a mixture of methane, silane and hydrogen, and using diborane and phosphine as doping gases. The effects of changes in the microwave power on the deposition rate and optical bandgap were investigated, and variations in the photoand dark-conductivities and activation energy were studied in conjunction with film analysis using the Raman scattering technique. In the case of boron-doped samples, the conductivity increased rapidly to a maximum, followed by rapid reduction at high microwave power. The ratio of the photo- to dark-conductivity (σph/σd) peaked at microwave power of ~600 W. Under conditions of high microwave power, Raman scattering analysis showed evidence of the formation and increase in the silicon microcrystalline and diamond-like phases in the films, the former of which could account for the rapid increase and the latter the subsequent decrease in the *** the case of phosphorusdoped SiC:H samples, it was found that increase in the microwave power has the effect of enhancing the formation of the silicon microcrystalline phase in the films which occurred in correspondence to a rapid increase in the conductivity and reduction in the activation energy The conductivity increase stabilised in samples deposited at microwave power exceeding 500 W probably as a result of dopant saturation. Results from Raman scattering measurements also showed that phosphorus doping had the effect of enhancing the formation of the silicon microcrystals in the film whereas the presence of boron had the effect of preserving the amorphous structure.

关键词： ECR A Comparative Study of Boron and Phosphorus Doping Effects in SiC H Films Prepared by ECR-CVD

Anisotropic HDDR-treated Nd_2Fe_(14)B-type powder

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science China(Physics,Mechanics & Astronomy) 2010年第9期53卷 1590-1593页

作者： LIU Min1,3.HAN BaiPing2,3.HAN GuangBing3.& GAO RuWei3.1 Department of Electronic science,Huizhou university,Huizhou 516007,China 2 College of mathematical and {3. sciences,Xuzhou Institute of Technology,Xuzhou 221008,China 3.school of Physics,Shandong university,Jinan 250100,China 1. Department of Electronic science Huizhou University Huizhou 516007 China3. School of Physics Shandong University Jinan 250100 China2. College of Mathematical and Physical Sciences Xuzhou Institute of Technology Xuzhou 221008 China

Effects of the wheel speeds v and disproportionation time during the SC-HDDR process on the properties of Nd-Fe-B magnetic powders are *** is found that the remanence Br,coercivity Hcj and energy products(BH)max of magnetic powders all first increase to the maximum at v=3.m/s,and then decrease with enhancing *** is attributed to the fact that the SC alloy flakes prepared by the wheel speed of 3.m/s display the optimized *** optimized SC alloy flakes without homogenizing treatment which carried out a short duration disproportionation treatment can prepare the evidently anisotropic *** prolonging disproportionation time,the alignment degree of anisotropy of magnetic powders gradually *** is due to the fact that a short duration disproportionation reaction is beneficial to the disproportionated microstructure displaying the lamella crystals,and the lamella disproportionated microstructure is helpful to the formation of *** results confirm that the anisotropic HDDR Nd-Fe-B magnetic powders prepared directly from the SC alloy flakes without homogenizing treatment can be obtained.

关键词： SC-HDDR process SC alloy flakes disproportionated microstructure anisotropic powders

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 {3. and Technology Beijing, Beijing 100083. China 2 school of Materials {3. and Engineering, university of {3. and Technology Beijing, Beijing 100083. China 3.school of mathematical sciences, Nankai university, Tianjin 3.0071, China 4 Department of mathematics and Statistics, McGill university, Montreal H3. 2K6, 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

Optical and Structural Properties of In_(0.52)Al_(0.48)As/InP Structures Grown at Very High Arsenic Overpressures by Molecular Beam Epitaxy

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Journal of Materials science & Technology 1998年第3期14卷 231-235页

作者： S.F. Yoon(school of Electrical and Electronic Engineering, nanyang technological university, nanyang Avenue,{3. 63.798, Rep. of {3. school of Electrical and Electronic Engineering Nanyang Technological University Nanyang Avenue Singapore 639798 Singapore

Growth of ln0.52Al0.48As epitaxial layers on lnP(100) substrates by molecular beam epitaxy at a wide range of arsenic overpressures (V/III flux ratios from 3. to 3.0) has been carried out. Analysis performed using low-temperature photoluminescence (PL) and double-axis X-ray diffraction (XRD) shows a strong and prominent dependence of the PL and XRD linewidths on the V/III flux ratio. Under our growth conditions, both the PL and XRD linewidths exhibit a minimum point at a V/III flux ratio of 150 which corresponds to a maximum in the PL intensity and XRD intensity ratio. Flux ratios exceeding 150 result in an increase in both the PL and XRD linewidths corresponding to a reduction in their associated intensities. Room temperature Raman scattering measurements show a narrowing in the lnAs-like and AlAs-like longitudinal-optic (LO)phonon linewidths which broaden at high flux ratios, while the LO phonon frequencies exhibit a gradual reduction as the flux ratio is increased. PL spectra taken at increasing temperatures show a quenching of the main emission peak followed by the evolution of a broad lower energy emission which is possibly associated with deep lying centres. This effect is more prominent in samples grown at lower V/III flux ratios. Hall effect measurements show a gradual reduction in the mobility in correspondence to an increase in the electron concentration as the flux ratio is increased.

关键词： As/InP Structures Grown at Very High Arsenic Overpressures by Molecular Beam Epitaxy InP Optical and Structural Properties of In Al

Effect of rock mass structure and block size on the slope stability——physical modeling and discrete element simulation

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science China(technological sciences) 2005年第z1期48卷 1-17页

作者： LI Shihai1, LIAN Zhenzhong1,2 & J. G. Wang3.1. Institute of Mechanics, Chinese Academy of sciences, Beijing 100080, China 2. Graduate school, Chinese Academy of sciences, Beijing 100060, China 3. Tropical Marine {3. Institute, National university of singapore, singapore 119260 Chinese Acad Sci Inst Mech Beijing 100080 Peoples R China Chinese Acad Sci Grad Sch Beijing 100060 Peoples R China Natl Univ singapore Trop Marine Sci Inst Singapore 119260 Singapore

This paper studies the stability of jointed rock slopes by using our improved three-dimensional discrete element methods (DEM) and physical modeling. Results show that the DEM can simulate all failure modes of rock slopes with different joint configurations. The stress in each rock block is not homogeneous and blocks rotate in failure development. Failure modes depend on the configuration of joints. Toppling failure is observed for the slope with straight joints and sliding failure is observed for the slope with staged joints. The DEM results are also compared with those of limit equilibrium method (LEM). Without considering the joints in rock masses, the LEM predicts much higher factor of safety than physical modeling and DEM. The failure mode and factor of safety predicted by the DEM are in good agreement with laboratory tests for any jointed rock slope.

关键词： rock masses, slope stability, DEM simulation, block size effect, joints configuration effect, limit equilibrium method.