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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,{2.,china 2.0},University of California at Los Angeles,CA 90095,USA 3Center of Mathematical Sciences,zhejiang University,{2.,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

ω-Gorenstein injective modules and dimensions

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Science china mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2.& DING NanQing3 1department of mathematics, zhejiang University, zhejiang 310027, china 2.0}, zhejiang University of Technology, zhejiang 31002., china 3department of mathematics, Nanjing University, Nanjing 2.0093, china 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module

A HOMOCLINIC ORBIT FOR LAGRANGIAN SYSTEMS

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Systems Science and Mathematical Sciences 1995年第1期8卷 75-81页

作者： WU Shaoping (department of mathematics, zhejiang University, {2., china) 浙江大学数学系浙江杭州

ＡＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＦＯＲＬＡＧＲＡＮＧＩＡＮＳＹＳＴＥＭＳＷＵＳｈａｏｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ３１００２７，Ｃｈｉ... 详细信息

ＡＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＦＯＲＬＡＧＲＡＮＧＩＡＮＳＹＳＴＥＭＳＷＵＳｈａｏｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ３１００２７，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｗｅｐｒｏ...

关键词： Homoclinic orbit Lagrangian system Mountain Pass Lemma.

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

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Chinese Annals of mathematics,Series B 2003年第2期24卷 249-260页

作者： WANG WENSHENG LIN ZHENGYAN department of mathematics, zhejiang University, {2. 31002., china. department of mathematics, {2. Teacher’s College, {2. 310012. china. E-mail: wswang@*** department of mathematics, zhejiang University, {2. 31002., china. zhejiang Univ Dept Math Hangzhou 310028 Peoples R China hangzhou Teachers Coll Dept Math Hangzhou 310012 Peoples R China

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of th... 详细信息

关键词： Ornstein-Uhlenbeck processes Stationary Gaussian processes Modulus of continuity Law of the iterated logarithm

Lp integrability of trigonometric series with special varying coefficients

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Applied mathematics:A Journal of Chinese Universities 2009年第4期24卷 402-410页

作者： WEI Bao-rong department of mathematics,hangzhou Normal University,{2. 310036,china department of mathematics Hangzhou Normal University Zhejiang 310036 China

Very recently,Yu,Le and Zhou introduced the so called Δ*B1 and Δ*B2.conditions,which are generalizations of the monotone *** applying these two new conditions,the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric *** fact,the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series,where coefficients may have diffierent signs.

关键词： Lp integrability trigonometric series special varying coefficients

Physically based simulation of Buddha Glory

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Progress in Natural Science:Materials International 2006年第6期16卷 656-662页

作者： LIU Shiguang, WANG Zhangye, GONG Zheng, WANG Changbo and PENG Qunsheng (State Key Laboratory of CAD&CG, zhejiang University, hangzhou 310027, {2. department of mathematics, zhejiang University, hangzhou 310027, {2. department of Structure Engineering, Tongji University, Shanghai 2.0092. {2.) [a]State Key Laboratory of CAD&CG Zhejiang University Hangzhou China [b]department of mathematics Zhejiang University Hangzhou China [c]department of Structure Engineering Tongji University Shanghai China

This paper proposes a novel method of photorealistic simulation of Buddha Glory, a natural phenomenon of great visual beauty which can be observed in the area of famous Buddhism Holy Lands in china. This phenomenon is mainly caused by back-scattering of water droplets in fog or cloud. To simulate the glory, we first calculate the spectral scatter intensity of glory rings using Mie scattering theory. We then present a new shadow model to determine the deformed shape of the head and body of "Buddha" within the glory ring. The affect of atmospheric parameters such as the solar elevation angles, the density and size of water droplet in fog or cloud on the shape and color of Buddha Glory is also calculated. For rendering, we adopt the method of path scattering integral to generate the whole attenuated scene of Buddha Glory. Compared with the photographs of real Buddha Glory displays, our synthetic results are quite satisfactory.

关键词： natural phenomenon Buddha Glory back-scattering physically based simulation.

The decomposition of K_v into K_2.× K_5's

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Science china mathematics 2007年第10期50卷 1382-1388页

作者： Yang LI~1 Jian-xing YIN~1 Ru-cong ZHANG~2.Gen-nian GE~(2.) ~1 department of mathematics,Suzhou University,Suzhou 2.5006,china ~2.department of mathematics,zhejiang University,hangzhou 310027,china 1. department of mathematics Suzhou University Suzhou 215006 China 2. department of mathematics Zhejiang University Hangzhou 310027 China

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2.and c = 5, and show that such a de... 详细信息

关键词： decomposition, the complete graph Kv, product graph Kr×Kc, DNA library screening

POLYMERIZATION OF γ-STEARYL-α,l-GLUTAMATE N-CARBOXYANHYDRIDE USING RARE EARTH COORDINATION CATALYSTS

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Chinese Journal of Polymer Science 2000年第4期18卷 369-372页

作者： Xiao-ping Hu Jian Wu Zhi-kang Xu Lin-xian Feng Institute of Polymer Science, zhejiang University, hangzhou 310027, {2. department of Chemistry, zhejiang University, hangzhou 310027, {2. zhejiang Univ Dept Chem Hangzhou 310027 Peoples R China zhejiang Univ Inst Polymer Sci Hangzhou 310027 Peoples R China

A rare earth coordination system was first investigated as a new type of catalyst for the ring-openingpolymerization of α-amino acid N-carboxyanhydrides (NCAs). The results for the polymerization of γ-stearyl-α,L-glutamate(SLG) NCA using neodymium acetylacetonate (Nd(acac)_3)- or neodymium tris(2.ethylhexylphosphonate) (Nd(P_(2.4))_3)-triethylaluminum-water as catalysts were compared with those using conventional catalysts. It was found that the helicalpoly(γ-stearyl-L-glutamate) with high molecular weight as well as narrow molecular weight distribution can be obtained inthe presence of Nd(acac)_3/AlEt_3-1/2._2.. The polymer obtained was characterized by IR and NMR spectroscopy.

关键词： Rare earth coordination catalyst Ring-opening polymerization Polypeptide Poly(γ-stearyl-α,L-glutamate)

Preparation and Conductivity of Triheteropoly Tungstozincoaluminic Acid

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Rare Metals 2001年第4期20卷 221-223页

作者： Qingyin Wu department of Chemistry, zhejiang University, {2., china zhejiang Univ Dept Chem Hangzhou 310027 Peoples R China

The ternary undecatungstozincoaluminic heteropoly acid H-7[Al(H2.)ZnW11O39](.)12.(2.O was prepared by the ion exchanging-cooling method. The optimal proportion of solutions of the component elements and the pH of the synthesis reaction were given. The product was characterized by chemical analysis, potentiometric titration, IR, UV, XRD and TG-DTA. AC impedance measurement results show that its proton conductivity is 1.37x10(-4) S/cm at 18 degreesC.

关键词： heteropoly acid tungstozincoaluminic acid protonic conductivity