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Remarks on Hard Lefschetz conjectures on Chow groups Dedicated in celebration of SCIENCE china on the occasion of its 60th birthday

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Science china Mathematics 2010年第1期53卷 105-114页

作者： FU BaoHua institute of Mathematics, academy of Mathematic and Systems Science, chinese academy of sciences, beijing 100190, china institute of Mathematics Academy of Mathematic and Systems Science Chinese Academy of Sciences Beijing China

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are equivalent to the well-known conjectures of Beauville and Murre.

关键词： Chow groups abelian varieties Bloch-Beilinson conjectures Beauville conjecture Murre conjecture

STUDY ON THE SYNTHESIS AND PROPERTIES OF POLY(ESTER-IMIDEETHER)MULTIBLOCK COPOLYMERS

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chinese Journal of Polymer Science 2000年第1期18卷 9-13页

作者： Zu-yao Shan Zhen-yi Li institute of chemistry, chinese academy of sciences, beijing 100080, china chinese Acad Sci Inst Chem Beijing 100080 Peoples R China

A new class of poly(ester-imide-ether) multiblock copolymers was synthesized by transes-terification and melt copolymerization of dimethyl terephthalate (DMT) and N-(4-carbomethoxyphenyl)-4-(carbomethoxy)-phthalimide with ethylene glycol (EG) and polytetramethylene glycol (PTMG). The structure of the above copolymers was characterized by H-1-NMR and IR spectroscopy. Some properties of the coplymers were also examined. It was found that their mechanical properties and heat stability, compared with poly(ether-ester) copolymers, were obviously improved.

关键词： N-(4-carbomethoxyphenyl)-4-(carbomethoxy)-phthalimide polyester-polyether copolymer poly-(ester-imidether) multiblock copolymer imide modification

Holomorphic invariant forms of a bounded domain

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Science china Mathematics 2008年第11期51卷 1945-1964页

作者： LU QiKeng institute of Mathematics, academy of Mathematics and Systems Science, chinese academy of sciences, beijing 100190, china institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Given a complete ortho-normal system ? = (?0,?1,?2,…) of L 2 H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2 1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2 of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2 differs from ds 2 only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 32A36 32A65

Spectrophotometric determination of cationic surfactants by formation of ternary complexes with Fe(Ⅲ) and chrome azurol S

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chinese Journal of chemistry 1996年第3期14卷 228-234页

作者： SONG, Ming LIANG, Shu-Quan institute of chemistry, chinese academy of sciences, beijing 100080, china institute of chemistry Chinese Academy of Sciences Beijing 100080 China

An extraction-free spectrophotometric method for the determination of cationic surfactants, such as cetylpyridinium chloride, cetyltrimethylammonium bromide and zephiramine is proposed, which is based on the formation of ternary complexes with Fe(Ⅲ) and chrome azurol S. The molar ratio of the complex is 2:1:1 (Fe(Ⅲ):chrome azurol S:cationic surfactant). The method is simple, rapid and sensitive, giving an apparent molar absorptivity of 4.5×104 ***-1 and a linear range of 0.1-6.0 umol/L cationic surfactants. The total cationic surfactant content can be determined directly in aqueous solutions by measuring the absorbance at 680 nm (pH 5.8). The method has been successfully applied to water samples.

关键词： Cationic surfactant determination spectrophotometry ternary complex Fe(Ⅲ) chrome azurol S

MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE-Ⅱ SUPERCONDUCTORS

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Journal of Computational Mathematics 1997年第4期15卷 365-384页

作者： Zhi-ming Chen (institute of Mathematics, chinese academy of sciences, beijing, china) 中科院数学所北京

In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy *** also report on some numerical results at the end of the paper.

关键词： Math QT MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE SUPERCONDUCTORS

Plastic deformation of nanocrystalline nickel

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Science china(Technological sciences) 2009年第8期52卷 2216-2221页

作者： WU XiaoLei State Key Laboratory of Nonlinear Mechanics, institute of Mechanics, chinese academy of sciences, beijing 100190, china State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing 100190 China

A high-resolution electron microscopy study has uncovered the plastic behavior of accommodating large strains in nanocrystalline (NC) Ni subject to cold rolling at liquid nitrogen temperature. The activation of grain-boundary-mediated-plasticity is evidenced in NC-Ni, including twinning and formation of stacking fault via partial dislocation slips from the grain boundary. The formation and storage of 60? full dislocations are observed inside NC-grains. The grain/twin boundaries act as the barriers of dislocation slips, leading to dislocation pile-up, severe lattice distortion, and formation of sub-grain boundary. The vicinity of grain/twin boundary is where defects preferentially accumulate and likely the favorable place for onset of plastic deformation. The present results indicate the heterogeneous and multiple natures of accommodating plastic strains in NC-grains.

关键词： nanocrystalline metal plastic deformation deformation twinning dislocation microstructure

Simulation of aerodynamic performance affected by vortex generators on blunt trailing-edge airfoils

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Science china(Technological sciences) 2010年第1期53卷 1-7页

作者： YANG Ke1,2,ZHANG Lei1,3 & XU JianZhong1,2 1 institute of Engineering Thermophysics,chinese academy of sciences,beijing 100190,china 2 Key Laboratory of Wind Energy Utilization,chinese academy of sciences,beijing 100190,china 3 Graduate School of chinese academy of sciences,beijing 100190,china 1. institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Wind Energy Utilization Chinese Academy of Sciences Beijing 100190 China3. Graduate School of Chinese Academy of Sciences Beijing 100190 China

An investigation was carried out by numerical simulation on a wind turbine airfoil and a blunt trailing-edge airfoil with and without vortex generators (VGs), and the performance of the airfoils was analyzed. By the simulation of airfoil DU 91-W2-250 it was verified that the numerical method and model were credible. Based on this airfoil, a new one with a blunt trailing edge of 6% chord was blended by symmetrically adding thickness, and its characteristics curves were obtained through computing at key angles of attack. Additionally, the pressure distribution on blended airfoil was analyzed by comparing to the airfoil without blend. The interaction of streamwise vortices induced by VGs with trailing vortex or separation vortex was considered, followed by the uncovery of how VGs can suppress the boundary layer separation.

关键词： vortex generators airfoil blunt trailing-edge

PHASE STRUCTURE AND PROPERTIES OF EPOXY RESIN MODIFIED BY POLYSILOXANE BEARING PENDANT AMINO GROUPS

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chinese Journal of Polymer Science 2000年第2期18卷 133-138页

作者： Bing Zhang Xiang-luan Liu Ying Huang Center of Molecular sciences, institute of chemistry, chinese academy of sciences, beijing 100080, china chinese Acad Sci Inst Chem Ctr Mol Sci Beijing 100080 Peoples R China

Polysiloxane-modified epoxy resins were prepared through the reaction of epoxy resin with polydimethylsiloxanes bearing pendant N-(beta-aminoethyl)-gamma-aminopropyl groups. The morphology and properties of the cured epoxy resins modified by the polysiloxanes were investigated. It was found that the phase structure and properties of the cured epoxy resins depend mainly on the amino group content in the polydimethylsiloxane and the level of the modifier. The change of phase structure in the cured epoxy resin systems was responsible for the dramatic change in their mechanical and surface properties.

关键词： phase structure polysiloxane epoxy resin mechanical property

Poisson kernel and Cauchy formula of a non-symmetric transitive domain

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Science china Mathematics 2010年第7期53卷 1678-1683页

作者： LU Qi-Keng institute of Mathematics, academy of Mathematics and System Science, chinese academy of sciences, beijing 100190, china 1. institute of Mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100190 China

In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2 ∈Cq×m|2i1( Z-Z+)-Z1Z1′-Z2′Z2>0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2→Z2 transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2 which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2 when it acts on the Poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the Poisson formula.

关键词： Poisson kernel Cauchy formula