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A quasi-local mass for 2-spheres with negative Gauss curvature

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science china mathematics 2008年第9期51卷 1644-1650页

作者： ZHANG Xiao Institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We extend our previous definition of quasi-local mass to 2-spheres whose Gauss curvature is negative, and prove its positivity.

关键词： general relativity quasi-local mass positivity 53C27 53C50 83C60

Fiducial inference in the pivotal family of distributions

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science china mathematics 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying Department of mathematics, beijing Institute of Technology, beijing 100081, china academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of mathematics Beijing Institute of Technology Beijing China academy of mathematics and systems science Chinese Academy of Sciences Beijing China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

Relations between Lipschitz functions and convex functions

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science china mathematics 2005年第5期48卷 703-710页

作者： RUAN Yingbin Department of mathematics, Fujian Normal University, Fuzhou 350007, china academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of mathematics Fujian Normal University Fuzhou China academy of mathematics and systems science Chinese Academy of Sciences Beijing China

We discuss the relationship between Lipschitz functions and convex functions. By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differenti... 详细信息

关键词： Lipschitz functions convex functions the Frechet differentiability.

Nonlinear autoregressive models with heavy-tailed innovation

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science china mathematics 2005年第3期48卷 333-340页

作者： JIN Yang & AN Hongzhi School of Statistics, Renmin University of china, beijing 100872, china academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Sch. of Statistics Renmin Univ. of China Beijing 100872 China Acad. of mathematics and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.

关键词： nonlinear autoregressive model, innovation, tail probability.

A note on noncommutative moment problems

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science china mathematics 2005年第8期48卷 1144-1151页

作者： MA Xiujuan School of sciences, Hebei University of Technology, Tianjin 300130, china mathematics Institute, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china School of sciences Hebei University of Technology Tianjin China mathematics Institute Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.

关键词： moment, free product, state, group C*-algebra.

Monomial Hopf algebras over fields of positive characteristic

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science china mathematics 2006年第3期49卷 320-329页

作者： LIU Gongxiang & YE Yu Institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of mathematics, University of science and Technology of china, Hefei 230026, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of mathematics University of Science and Technology of China Hefei China

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n)are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.

关键词： monomial coalgebra, Gaussian binomial coefficient, monomial Hopf algebra.

NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

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chinese Annals of mathematics,Series B 2003年第2期24卷 239-248页

作者： FENG SHAOJI FENG DEXING academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china. E-mail: fengshaoji0164@sina.comacademy of mathematics and systems science, chinese academy of sciences, beijing 100080, china. E-mail: dxfeng@*** academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China

The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.

关键词： Wave equations Nonlinear boundary feedback Exponential decay Asymptotic decay Riemannian manifold

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

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science china mathematics 2006年第10期49卷 1392-1404页

作者： XU Yichao,CHEN Minru & MA Songya academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china College of mathematics and Information sciences, Henan University, Kaifeng 475001, china academy of mathematics and systems science Chinese Academy of Sciences Beijing China College of mathematics and Information sciences Henan University Kaifeng China

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso (D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN,F)) and Iso (D(VN, F))(0), where G(0) is the unit connected component of the Lie group G.

关键词： holomorphic automorphism group, homogeneous Siegel domain, normal Siegel domain, complex homogeneous bounded domain.

Review on the study of entanglement in quantum computation speedup

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chinese science Bulletin 2007年第16期52卷 2161-2166页

作者： DING ShengChao1,3 & JIN Zhi1,2,1 Institute of Computing Technology,chinese academy of sciences,beijing 100080,china 2 academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china 3 Graduate University of chinese academy of sciences,beijing 100080,china Institute of Computing Technology Chinese Academy of Sciences Beijing China Graduate University of chinese academy of sciences Beijing China academy of mathematics and systems science Chinese Academy of Sciences Beijing China

The role the quantum entanglement plays in quantum computation speedup has been widely disputed. Some believe that quantum computation's speedup over classical computation is impossible if entan-glement is absent,while others claim that the presence of entanglement is not a necessary condition for some quantum algorithms. This paper discusses this problem systematically. Simulating quantum computation with classical resources is analyzed and entanglement in known algorithms is reviewed. It is concluded that the presence of entanglement is a necessary but not sufficient condition in the pure state or pseudo-pure state quantum computation speedup. The case with the mixed state remains open. Further work on quantum computation will benefit from the presented results.

关键词：量子论量子纠缠量子计算加速模拟