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On a class of weak Landsberg metrics

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Science china Mathematics 2007年第4期50卷 573-589页

作者： Ben-ling LI & Zhong-min SHEN Department of Mathematics, zhejiang university, hangzhou 310028, china Department of mathematical sciences, Indiana university Purdue university Indianapolis (IUPUI), 402 N. Blackford Street, Indianapolis, IN 46202-3216, USA center of mathematical sciences, zhejiang university, hangzhou 310027, china 1. Department of Mathematics Zhejiang University Hangzhou 310028 China 2. Department of mathematical sciences Indiana University Purdue University Indianapolis (IUPUI) 402 N. Blackford Street Indianapolis IN 46202-3216 USA 3. center of mathematical sciences Zhejiang University Hangzhou 310027 China

In this paper, we discuss a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We characterize weak Landsberg metrics in this class and show that there exist weak Landsberg metrics whi... 详细信息

关键词： Finsler metric weak Landsberg metric (α,β)-metric 53B40

Behaviour of an Oscillatory Singular Integral on Weighted Local Hardy Spaces

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Acta Mathematica Sinica,English Series 1997年第3期13卷 305-320页

作者： Chen Liyuan (Department of Economics,Hangszhou university,hangzhou 310028,china)Sun Qiyu (center for mathematical sciences,zhejiang university,hangzhou 310027,china) Department of Economics Hangszhou University center for mathematical sciences Zhejiang University

The boundedness on weighted local Hardy spaces h1,pw of the oscillatory singular integral Tf（x）=∫Rn eiQ（x,y）K（x,y）f（y）dy is considered when Q（x,y）=P（x-y）for some real-valued polynomial P with its degree not less than *** a sufficient and necessary condition on polynomial Q on Rn × Rn such that T maps h1,pw to the weighted integrable function space L1w is found.

关键词： Oscillatory singular integral Weighted local Hardy spaces Muckenhoupt weight

GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD

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Acta Mathematica Scientia 2007年第3期27卷 611-618页

作者：谢纳庆许洪伟 Institute of Mathematics Fudan University center of mathematical sciences Zhejiang University

This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.

关键词： Submanifolds second fundamental form pinched Riemannian manifold

Influence of viscosity on the phase transformation of amorphous calcium carbonate in fluids:An understanding of the medium effect in biomimetic mineralization

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Science china Chemistry 2010年第10期53卷 2208-2214页

作者： XIE YiDong, XU XuRong & TANG RuiKang center for Biomaterials and Biopathways and Department of Chemistry, zhejiang university, hangzhou 310027, china 1. center for Biomaterials and Biopathways and Department of Chemistry Zhejiang University Hangzhou 310027 China

Biological mineral generation via an amorphous precursor is a topic of great current interest. Various factors such as the temperature, solution composition and presence of organic molecules can influence this important inorganic process. Here we demonstrate that this mineral transformation can actually readily be regulated by solution viscosity, a fundamental but often overlooked property. In our experiment, amorphous calcium carbonate (ACC), a key model compound in biomimetic mineralization studies, is synthesized and dispersed into inert dispersants with different viscosities and the crystallization process is examined by using FT-IR spectroscopy and XRD. It is found that the inhibition of the transformation of ACC becomes more significant with increasing fluid viscosity. This phenomenon can be explained by the differences in ion diffusion in different media. Furthermore, the resulting crystals always have different morphologies and size distributions although they all have the calcite structure. This study implies that the importance of the fluid medium cannot be ignored in building a complete understanding of biological control of biomimetic crystallizations.

关键词： mineralization amorphous calcium carbonate transformation viscosity

Time-periodic solutions of the Einstein's field equations II:geometric singularities

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Science china Mathematics 2010年第6期53卷 1507-1520页

作者： KONG DeXing1,LIU KeFeng2,& SHEN Ming3 1Department of Mathematics,zhejiang university,hangzhou 310027,china 2Department of Mathematics,university of California at Los Angeles,CA 90095,USA 3center of mathematical sciences,zhejiang university,hangzhou 310027,china 1. Department of Mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China

In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,*** singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.

关键词： Einstein’s field equations time-periodic solution Riemann curvature tensor singularity event horizon

STEREOCHEMICAL CONTROL IN PROPYLENE POLYMERIZATION CATALYZED BY UNBRIDGED METALLOCENE CATALYSTS

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Chinese Journal of Polymer Science 2001年第4期19卷 407-413页

作者： yin-bang Zhu Zhi-qiang Fan Tariq Yasin Lin-xian Feng Department of Polymer Science and Engineering zhejiang university hangzhou 310027, china zhejiang Univ Dept Polymer Sci & Engn Hangzhou 310027 Peoples R China

Two unbridged metallocene catalysts, bis(2,4,7-trimethylindenyl)zirconium dichloride (met-I) and bis(2,4,6-trimethylindenyl)zirconium dichloride (met-II), which are different in the position of substituents on the six-membered ring of the indenyl ligands were synthesized. The effect of substituents in the two metallocenes on the propylene polymerization was studied in the presence of methylaluminoxane (MAO) and triisobutylaluminium (TIBA). From the analysis of microstructure determined by C-13-NMR, it was demonstrated that the polymers produced by met-II have higher [mmmm] isotactic sequences than that of met-I. Using a mechanism based on model statistical analysis, it was found that chain-end model was dominant for met-I. However, met-II obeys the concurrent two-sites model during polymerization, which can be attributed to the existence of 'racemic-like' conformer in its system.

关键词： unbridged metallocene propylene polymerization elastomeric polypropylene stereochemical mechanism

Surface electromagnetic modes contribution to the anomalous terahertz transmission through double-layered metal hole array

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Science china(Information sciences) 2012年第1期55卷 90-97页

作者： RAO Lei1&YANG DongXiao1,2 1Department of Information Science and Electronic Engineering,zhejiang university,hangzhou 310027,china 2Research center for Terahertz Technology,zhejiang university,hangzhou 310027,china 1. Department of Information Science and Electronic Engineering Zhejiang University Hangzhou 310027 China2. Research Center for Terahertz Technology Zhejiang University Hangzhou 310027 China

Terahertz transmission spectra through both single-layered and double-layered sub-wavelength metal hole arrays were calculated using rigorous mode-matching *** dispersion relations of the single-layered and double-layered metal hole arrays were obtained by FDTD *** are three anomalous peaks in the spectrum of the double-layered metal hole array,which arise from the three surface electromagnetic modes appearing in the dispersion *** comparing the transmission spectra and the dispersion relations of the single-layered and double-layered metal hole arrays,it was found that the two surface electromagnetic modes at higher frequencies are introduced by the single-layered metal hole array,while the one at lower frequencies is introduced by the double-layered metal hole *** validity of the analysis was qualitatively verified by the experimental *** structure can be finely designed for potential applications,such as wideband filtering.

关键词： surface electromagnetic modes double-layered metal hole array terahertz

Polylogarithms and multiple zeta values from free Rota-Baxter algebras

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Science china Mathematics 2010年第9期53卷 2239-2258页

作者： GUO Li1,2 & ZHANG Bin3,1center of mathematical sciences,zhejiang university,hangzhou 310027,china 2Department of Mathematics and Computer Science,Rutgers university,Newark,NJ 07102,USA 3Yangtze center of Mathematics,Sichuan university,Chengdu 610064,china 1. center of mathematical sciences Zhejiang University Hangzhou 310027 China2. Department of Mathematics and Computer Science Rutgers University Newark NJ 07102 USA3. Yangtze Center of Mathematics Sichuan University Chengdu 610064 China

We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara,Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one *** apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single *** also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.

关键词： multiple zeta values polylogarithms Rota-Baxter algebras

AN EXPERIMENTAL STUDY ON THE FLOW FIELDS OF THE WEST LAKE BY ELECTRO-HYDRODYNAMIC ANALOGUE METHOD

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Journal of Hydrodynamics 1991年第3期3卷 65-67页

作者： Shao Chu-yin Jin Wei Wang Zi-xun, Mechanics Department, zhejiang university, hangzhou 310027, P.R.china zhejiang Univ Hongzkou China

Electro hydrodynamic analogue (EHA) method is applied to study the flow fields in the West Lake. It gives out a satisfactory result on water velocities and discharges of the bridge openings.

关键词： Lake AN EXPERIMENTAL STUDY ON THE FLOW FIELDS OF THE WEST LAKE BY ELECTRO-HYDRODYNAMIC ANALOGUE METHOD West