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On the composition operators on the Bloch space of several complex variables

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Science China Mathematics 2005年第Z1期48卷 392-399页

作者： ZHOU Zehua & CHE Renyu Department of Mathematics, Tianjin University, Tianjin 300072, China LiuHui Center for Applied Mathematics, Nankai University & Tianjin University,Tianjin 300072, China Department of Mathematics Tianjin University Tianjin China LiuHui Center for Applied Mathematics Nankai University & Tianjin University Tianjin China

In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the compositio... 详细信息

关键词： Bloch space, bounded symmetric domains, composition operator, bergman metric.

Geometric aspects of the moduli space of Riemann surfaces

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Science China Mathematics 2005年第Z1期48卷 97-122页

作者： Shing-Tung Yau Department of Mathematics Harvard University CambridgeMA 02138USA

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore,the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.

关键词： moduli space, Teichmuller space, metric, curvature.

Think ＂ Big＂ and become ＂ Big＂： On the architectureand space of an urban museum

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科学教育与博物馆 2016年第3期2卷 223-229页

作者： ZHAO Wenjun Shanghai Natural History Museum (巳ranch of Shanghai Science & Technology Museum)

Nowadays many urban museums are situated in ever-changing cities face with problems regardingspace and architecture. The main question this paper wants to discuss is how the museum could achieve accessibilityand inclusiveness to a greater extent via rethinking and reshaping its space, both physically and vir -tually,Based on practices conducted by the Museum of London since its establishment in the 20th century, Iendeavour to understand how the museum architecture was established during the negotiation and compro -mise among different individuals and parties and to extend the conception by exploring the possibilities of expanding out of the traditional realm of the museum architecture.

关键词： museum, architecture, space, extension

A global solution of the Einstein-Yang-Mills equation on the conformal space

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Science China Mathematics 2002年第3期45卷 342-355页

作者：陆启铿 Institute of Mathematics Acad. of Math. and Systems Science Chinese Academy of Sciences Beijing 100080 China

The method used to construct the SU(2) Yang-Mills field on a compactified Minkowski space-M(which is equivalent to the conformal space) is generalized to construct an SU(N)(N > 2) Yang-Mills fieldFjκ on M. It is proved that both Fjκ and the invariant metric tensor gjκ of M satisfy the Einstein-Yang-Mills equation. The case of N →∞ is also discussed.

关键词： Einstein-Yang-Mills equaton, su(N)-connection, conformal space, large N limit.

On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space

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Science China Mathematics 2002年第12期45卷 1538-1547页

作者：张文俊刘太顺 Department of Mathematics Shenzhen University Normal College Shenzhen 518060 China Department of Mathematics Univ. of Sci. and Technol. of China Hefei 230026 China

A class of biholomorphic mappings named 'quasi-convex mapping' is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the 'quasi-convexmapping' is exactly the 'quasi-convex mapping of type A' introduced by K. A. Roper and T. J. Suffridge.

关键词： Banach space, quasi-convex mapping, growth theorem, covering theorem.

The generators of Lorentz transformation in momentum space

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Science China Mathematics 2002年第2期45卷 241-245页

作者：张鹏飞阮图南 CCAST (World Lab.) P. O. Box 8730 Beijing 100080 China Natl. Synchrt. Radiation Laboratory Department of Modern Physics Univ. of Sci. and Technol. of China Hefei 230029 China

In the momentum space, the angular momentum operator and the boost vector operator,i.e. the generators for the Lorentz transformation of a particle with arbitrary spin and nonzero mass are discussed. Some new expressi... 详细信息

关键词： momentum space, angular momentum operator, boost vector operator.

Geodesic discs in Teichmüller space

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Science China Mathematics 2005年第8期48卷 1075-1082页

作者： LI Zhong LMAM & School of Mathematical Sciences Peking University Beijing 100871 China

Let T(S) be the Teichmüller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincaré disc into T(S). It is shown in this paper that for any non-Stre... 详细信息

关键词： Teichmüller space, geodesic discs.

Totally real minimal 2-spheres in quaternionic projective space

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Science China Mathematics 2005年第3期48卷 341-349页

作者： HE Yijun WANG Changping LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J,K} of complex structures on HPn satisfying IJ = -JI = K, JK = -KJ = I, KI = -IK = J. A surface M HPn is called totally real, if at each point p ∈ M the tangent plane TpM is perpendicular to I(TpM),J(TpM) and K(TpM). It is known that any surface M RPn HPn is totally real, where RPn HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in RP2m RPn HPn with 2m ≤ n. As a consequence we show that the Veronese sequences in RP2m (m ≥ 1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.

关键词： quaternionic projective space, totally real surfaces, minimal surfaces.

Experimental realization of quantum cryptography communication in free space

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Science China(Physics,Mechanics & Astronomy) 2005年第2期48卷 237-246页

作者： WANG Chuan1, ZHANG Jingfu1, WANG Pingxiao1, DENG Fuguo1, AI Qing1 & LONG Guilu1,2 1. Department of Physics, Key Laboratory for Quantum Information and Measurements, Tsinghua Univer- sity, Beijing 100084, China 2. Center for Atomic and Molecular NanoSciences, Tsinghua University, Beijing 100084, China Department of Physics Key Laboratory for Quantum Information and Measurements Tsinghua University Beijing China Atomic and Molecular NanoSciences Tsinghua University Beijing China

Utilizing linear optical devices, the principle of B92 quantum key distribution (QKD) protocol is demonstrated in free space with a distance of transmission of 2.2 meters. The faint laser pulses with 650 nm wavelength are used as the single photon sources. The experimental results show that the eavesdropping behavior in the signal transmission can be detected. We also discuss the problems and solutions in using the quantum cryptography communication practically. It is pointed out that one of the approaches to increasing the distance of the quantum communication is to overcome the attenuation of the single photon in transmission. This could not be solved by the use of single photon source, and new quantum communication protocols are needed to solve these problems.

关键词： quantum key distribution, free space, linear optics, faint pulses.