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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,{2.,hangzhou 31002.,China 2.epartment of mathematics,university of California at Los Angeles,CA 90095,USA 3Center of Mathematical Sciences,{2.,hangzhou 31002.,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

REMARKS ON h-TRANSFORM AND DRIFT

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Chinese Annals of mathematics,Series B 1998年第4期19卷 473-478页

作者： YING JIANGANG (Department of mathematics, {2., hangzhou 31002., China.) zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2. and improves their result by a diffe... 详细信息

关键词： Right processes Revuz measures h-transform

Almost sure central limit theorems for random functions

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Science China mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun School of mathematics and Statistics, zhejiang university of Finance and Economics, {2. 310018, China Department of mathematics, zhejiang university, hangzhou 31002., China 1. School of mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China 2. Department of mathematics Zhejiang University Hangzhou 310028 China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12.= 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞2.= 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| 2.) a.s., or Rn = O(n1/2.2.) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

Circular β ensembles,CMV representation,characteristic polynomials

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Science China mathematics 2009年第7期52卷 1467-1477页

作者： SU ZhongGen Department of mathematics,{2.,hangzhou 31002.,China 1. Department of mathematics Zhejiang University Hangzhou 310027 China

In this note we first briefly review some recent progress in the study of the circular β ensemble on the unit circle,where β > 0 is a model *** the special cases β = 1,2.and 4,this ensemble describes the joint probability density of eigenvalues of random orthogonal,unitary and sympletic matrices,*** general β,Killip and Nenciu discovered a five-diagonal sparse matrix model,the CMV *** representation is new even in the case β = 2.and it has become a powerful tool for studying the circular β *** then give an elegant derivation for the moment identities of characteristic polynomials via the link with orthogonal polynomials on the unit circle.

关键词： characteristic polynomials circular β ensembles CMV representation moment identity 15A52

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science China mathematics 2010年第3期53卷 719-738页

作者： KONG DeXing 1 , LIU KeFeng 2.& WANG YuZhu 3, 1 Department of mathematics, {2., hangzhou 31002., China 2.Department of mathematics, university of California at Los Angeles, CA 90095, USA 3 Department of mathematics, Shanghai Jiao Tong university, Shanghai 2.02.8, China 1. Department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Department of Mathematics Shanghai Jiao Tong University Shanghai 200248 China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition Cauchy problem smooth solution

A New (t, n) Threshold Signature Scheme Withstanding the Conspiracy Attack

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Wuhan university Journal of Natural Sciences 2005年第1期10卷 107-110页

作者： XIE Qi 1,2. YU Xiu-yuan 3 1.Department of mathematics, {2., hangzhou 31002., zhejiang,China 2.School of Information and Engineering, hangzhou Teachers College, hangzhou 310012. zhejiang, China 3.hangzhou Teachers College, hangzhou 310012. zhejiang, China zhejiang university Department of Mathematics Hangzhou China (GRID:grid.13402.34) (ISNI:***) Hungzhou Teachers College School of Information and Engincering Hangzhou China (GRID:grid.13402.34) hangzhou Teachers College Hangzhou China (GRID:grid.13402.34)

A ccmspiracy attack is proposed to show that Wang-Li's scheme is instcure,because any t or more group members can impersonate other t member to sign any message withoutholding the responsibility. To avoid the conspiracy attack, this paper prestentsa new (t,n)threshold signature scheme with traceablt signers. A (t. n) threshold signature scheme allows t ormore group members of the group lo generate a signature on behalf of the group, Any less than tmembers cannot generate a valid signature, andany set of the group cannot impersonate another set ofmembers to sign any message without holding the responsibility. In case of disputes., the thresholdsignature can be opened, so that the original signers ean be traced without repealing the secretkeys.

关键词： cryptography threshold signature conspiracy attack identifier tracing

Strong uniqueness of best approximations in spaces of bounded linear operators

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Science China mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu Department of mathematics, {2. hangzhou 31002., China Department of mathematics, zhejiang Normal university Jinhua 32.004, China 1. Department of mathematics Zhejiang University 310027 Hangzhou China 2. Department of mathematics Zhejiang Normal University 321004 Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

Effects of Ca substitution and surface treatment on electrochemical performances of Ml_(1.0-x) Ca_xNi_(4.0) Co_(0.6) Al_(0.4) hydrogen storage alloy electrodes

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中国有色金属学会会刊：英文版 1999年第3期9卷 487-492页

作者： Chen Weixiang(陈卫祥) 1, Qi Jianqin(祁建琴) 1, Chen Changpin(陈长聘) 2.1. Department of Physics 2. Department of Materials Science and Engineering, {2., hangzhou 31002., P. R. China zhejiang Univ Dept Phys Hangzhou 310027 Peoples R China zhejiang Univ Dept Mat Sci & Engn Hangzhou 310027 Peoples R China

The influences of Ca substitution for Ml and surface treatment on electrochemical performances of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 hydrogen storage alloy electrode were investigated. Ca substitution with x 2.for Ml could improve its discharge capacity, but Ca substitution with x >0.2.could decrease the capacity. It was also found that Ca substitution deteriorates the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode. In order to improve these properties of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 alloy electrode, the alloy was treated in 6 mol/L KOH+0.02.mol/L KBH 4 solution. The results showed that the surface treatment improves the electrochemical performances such as the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode. :The influences of Ca substitution for Ml and surface treatment on electrochemical performances of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 hydrogen storage alloy electrode were investigated. Ca substitution with x 2.for Ml could improve its discharge capacity, but Ca substitution with x >0.2.could decrease the capacity. It was also found that Ca substitution deteriorates the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode. In order to improve these properties of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 alloy electrode, the alloy was treated in 6 mol/L KOH+0.02.mol/L KBH 4 solution. The results showed that the surface treatment improves the electrochemical performances such as the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode.

关键词： hydrogen storage alloy electrode Ca substitution surface modification

Rigidity for rational maps with Cantor Julia sets

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Science China mathematics 2008年第1期51卷 79-92页

作者： ZHAI Yu Department of mathematics, {2., hangzhou 31002., China Department of mathematics Zhejiang University Hangzhou 310027 China

In this paper, we prove that two rational maps with the Cantor Julia sets are quasicon- formally conjugate if they are topologically conjugate.

关键词： Cantor Julia set rigidity puzzle piece bounded shape quasiconformally conjugate 37F12