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The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china {1. 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1.2. & GUO Maozheng~(1.3) 1. School of Mathematical Sciences,Peking University,Beijing 1.0871.{1. 2. department of mathematics,Yantai University,Yantai 2.4005,{1. 3. LMAM,Peking University,Beijing 1.0871.{1. 1. School of Mathematical Sciences Peking University 100871 Beijing China 2. department of mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2. )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2. ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

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Science china(Physics,Mechanics & Astronomy) 2004年第1期47卷 8-16页

作者： TANG Zhilie1. XING Da2.& LIU Songhao2.1. department of Physics, South china Normal University, {2. 51.631. china 2. School for Information and Optoelectronic Science and Engineering, South china Normal University, {2. 51.631. china Correspondence should be addressed to Tang Zhilie (email: tangzhl@***) Received April 2., 2.03 1. department of Physics South China Normal University 510631 Guangzhou China 2. School for Information and Optoelectronic Science and Engineering South China Normal University 510631 Guangzhou China

The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single- and two-photon confocal microscopy.

关键词： second harmonic generation, third harmonic generation, confocal microscopy, three-dimensional point spread function.

Quasirational dynamic system

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Chinese Science Bulletin 2000年第14期45卷 1277-1279页

作者： SUN Daochun & YANG Lo1. department of {1., South{2. Normal University, guangzhou 51.631.{2. 2. Institute of {1., Academy of {1. and System Sciences, Chinese Academy of Sciences, Beijing 1.0080,{2. department of {1. South China Normal University Guangzhou China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Using the iterations of quasirational mappings, the theorems on dynamic system are generalized to the quasirational dynamic system. Some different results are also obtained.

关键词： quasirational mapping dynamic system covering surface.

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1.*, HAN Rushan2.and CHEN Nanxian1.1. {1. of Physics, Tsinghua University, Beijing 1.0084, china 2. {1. of Physics, Peking University, Beijing 1.0871. china) department of Physics Tsinghua University Beijing 100084 China department of Physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

Analysis on cohesive crack opening displacement considering the strain softening effect

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Science china(Physics,Mechanics & Astronomy) 2006年第1期49卷 88-101页

作者： WANG Limin1. XU Shilang2.& ZHAO Xiqiang3 1. Mechanics {1., Shandong University of Technology, Zibo 2.5049, china 2. Civil Engineering {1., Dalian University of Technology, Dalian 1.602., china 3. mathematics {1., Ocean University of china, Qingdao 2.6071. china Mechanics department Shandong University of Technology Zibo 255049 China Civil Engineering department Dalian University of Technology Dalian 116024 China mathematics {1. Ocean University of China Qingdao 266071 China

In order to investigate the crack propagation in quasi-brittle materials like rock, ceramic and concrete, Hillerborg and his co-researchers abstracted the fracture process zone in front of a stress free crack in terms of a “fictitious crack zone”. On the fictitious crack zone, cohesive stresses distribute following a given softening relationship of stress vs. crack opening. Based on the polynomial or power series expression of cohesive crack opening displacement, the relationship of the cohesive stress vs. the crack opening displacement is established using elastic theory and integral equation, and some unknown physics variables are obtained using variation approach. The calculation results gained in this paper are close to the experimentally test ones.

关键词： cohesive crack, softening, dissipation work, variation approach.

Discovery of Permian island-arc basalts in the Cenxi area and the tectonic significance──A piece of evidence for the paleo-Tethyan tectonic belt in western Guangdong and eastern Guangxi

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Chinese Science Bulletin 1998年第21期43卷 1838-1842页

作者： ZHANG Boyou 1. ZHAO Zhenhua 1. SHI Manquan 1. YANG Shufeng 2.and CHEN Hanlin 2.1. guangzhou Institute of Geochemistry, Chinese Academy of Sciences, guangzhou 51.640,{2. 2. department of Earth Sciences, Zhejiang University, Hangzhou 31.02.,{2. guangzhou Institute of Geochemistry Chinese Academy of Sciences Guangzhou China department of Earth Sciences Zhejiang University Hangzhou China

Cenxi Permian basalts are the late Palaeozoic island-arc type basalts first found in South china. REE and trace element characteristics and distribution patterns show that this volcanic formation, which has been isotopically dated at {1.1.MaB.P. by the 39Ar/ 40Ar method, is of an active continental marginal island arc type, and that the tectonic environment at that time was an island-arc marginal sea or minor ocean basin related with the paleo-Tethyan tectonic belt in western Guangdong-eastern Guangxi.

关键词： spilite-keratophyre pillow lava Permian continental margin paleo-Tethyan evolution.

Density functional study on enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine

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Science china Chemistry 2006年第4期49卷 296-307页

作者： LI Ming1. ZHENG Wenxu2.& TIAN Anmin2.1. department of Chemistry, Southwest-china Normal University, Chongqing 40071.,{2. 2. department of Chemistry, Sichuan University, Chengdu 61.064,{2. 1. department of Chemistry Southwest-China Normal University Chongqing 400715 China 2. {1. of Chemistry Sichuan University Chengdu 610064 China

The enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine is discussed by the density functional theory (DFT) method. The main intermediates and transition states for this reaction are optimized completely at the B3LYP/6-31.(d) level, and the transition states are verified by vibrational modes. As shown, the chirality-controlled steps for this re- action are the hydride transfer from borane to carbonyl carbon and oxime carbon of keto oxime ether, and the chirality for the reduced products is determined in these two reaction steps. In all examined reaction paths, the first hydride is transferred via a six-membered ring and the second hydride via a five-membered ring or a four-membered ring.

关键词： keto oxime ether, oxazaborolidine, enantioselective reduction, DFT.

SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION

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Acta Mathematica Scientia 2007年第3期27卷 581-601页

作者：姚正安周文书 department of {1. Zhongshan University

In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also... 详细信息

关键词： Degenerate and singular diffusion equation weak solution existence asymptotic behavior

Parameter estimation for whole-body kinetic model of FDG metabolism

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Progress in Natural Science:Materials International 2006年第11期16卷 1164-1170页

作者： CUI Yunfeng~1. BAI Jing~1.*, CHEN Yingmao~2.and TIAN Jiahe~2.1. department of Biomedical Engineering, Tsinghua University, Beijing 1.0084, china 2. department of Nuclear Medicine, General Hospital of PLA, Beijing 1.0853, china) [a]department of Biomedical Engineering Tsinghua University Beijing China [b]department of Nuclear Medicine General Hospital of PLA Beijing China

Based on the radioactive tracer [ ~ 1. F]2.fluoro-2.deoxy-D-glucose （FDG）, positron emission tomography （PET）, and compartment model, the tracer kinetic study has become an important method to investigate the glucose metabolic kinetics in human body. In this work, the kinetic parameters of three-compartment and four-parameter model for the FDG metabolism in the tissues of myocardium, lung, liver, stomach, spleen, pancreas, and marrow were estimated through some dynamic FDG-PET experiments. Together with published brain and skeletal muscle parameters, a relatively complete whole-body model was presented. In the liver model, the dual blood supply from the hepatic artery and the portal vein to the liver was considered for parameter estimation, and the more accurate results were obtained using the dual-input rather than the single arterial-input. The established whole-body model provides the functional information of FDG metabolism in human body. It can be used to further investigate the glucose metabolism, and also be used for the simulation and visualization of FDG metabolic process in human body.

关键词： compartment model FDG PET parameter estimation.