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Entropy number and non-linear approximations on multivariate Besov space by manifolds of finite pseudo-dimension

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Progress in Natural science:Materials International 2006年第3期16卷 260-265页

作者： LONG Jingfan and FANG Gensun (School of Mathematical sciences, beijing normal university, beijing 100875,{3. Department of Computer science, Information technology Institute, beijing 100101,{3.) [a]School of Mathematical sciences Beijing Normal University Beijing China [b]Department of Computer science Information Technology Institute Beijing China

We determine the asymptotic order of entropy number and optimal non -linear approximations of anisotropic periodic Besov class of Bpθr(Td') (1≤p≤∞,1≤0≤∞) by manifolds of finite pseudo-dimension in the metric Lq... 详细信息

关键词： Pseudo-dimension anisotropic Besov class of functions entropy number nonlinear width.

Implementation of a multiple round quantum dense coding using nuclear magnetic resonance

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science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 706-715页

作者： ZHANG Jingfu1, XIE Jingyi2, WANG Chuan1, DENG Zhiwei3. LU Zhiheng4, & LONG Guilu1,5 1. Key Laboratory For Quantum Information and Measurements of MOE, Department of Physics, Tsinghua university, beijing 100084,china 2. Department of Materials {3. and Engineering, beijing normal university, beijing 100875, china 3. Testing and Analytical Center, beijing normal university, beijing 100875,china 4. Department of Physics, beijing normal university, beijing 100875, china 5. Key Laboratory For atomic and Molecular Nano{3.s, Tsinghua university, beijing 100084,china 1. Key Laboratory For Quantum Information and Measurements of MOE Department of Physics Tsinghua University 100084 Beijing China 2. Department of Materials science and Engineering Beijing Normal University 100875 Beijing China 3. Testing and Analytical Center Beijing Normal University 100875 Beijing China 4. Department of Physics Beijing Normal University 100875 Beijing China 5. Key Laboratory For Atomic and Molecular Nanosciences Tsinghua University 100084 Beijing China

A multiple round quantum dense coding scheme based on the quantum phase estimation algorithm is proposed and implemented in a three qubit nuclear magnetic resonance (NMR) quantum computer. Using an m + 1 qubit system, Bob can transmit one of 2m+1 messages to Alice, through manipulating only one qubit and exchanging it between Alice and Bob for m rounds. The information capacity is enhanced to m + 1 bits as compared to m bits in a classical scheme. The scheme has been demonstrated in NMR system, and the experimental results show a good agreement between theory and experiment.

关键词： quantum dense coding, multiple round, nuclear magnetic resorance

Quasi-critical ring of a primitive ring with nonzero socle

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Chinese science Bulletin 1997年第3期42卷 189-192页

作者： JIANG ZimeiDepartment of Mathematics, beijing normal university, beijing 100875, china Department of Mathematics Beijing Normal University Beijing China

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠{0} if and only if there is a pair of dual vector spaces (M,M’) over a division ring ... 详细信息

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠3. if and only if there is a pair of dual vector spaces (M,M’) over a division ring Δ such that S=F(M, M’)(?) R(?)(?)(M, M’), where (?)(M, M’)-{ω∈Ω|ωM’(?)M’, Ω is the complete ring of linear transformations of M over Δ}, F(M, M’) is the set of all linear transformations of (?)(M, M’) of finite rank. After that, some people reproved this theorem by using different methods such as those in refs. [2, 3.. In

关键词： primitive ring socle conjugate space total subspace of conjugate space.

Dense coding scheme using superpositions of Bell-states and its NMR implementation

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science china(Physics,Mechanics & Astronomy) 2005年第1期48卷 57-67页

作者： ZHANG Jingfu, XIE Jingyi, DENG Zhiwei & LU Zhiheng Key Laboratory for Quantum Information and Measurements, Department of Physics, Tsinghua university, beijing 100084, china Center for Quantum Information, Tsinghua university, beijing 100084, china Department of Materials science and Engineering, beijing normal university, beijing 100875, china Testing and Analytical Center, beijing normal university, beijing 100875, china Department of Physics, beijing normal university, beijing 100875, china 1. Key Laboratory for Quantum Information and Measurements Department of Physics Tsinghua University 100084 Beijing China 2. Center for Quantum Information Tsinghua University 100084 Beijing China 3. Department of Materials science and Engineering Beijing Normal University 100875 Beijing China 4. Testing and Analytical Center Beijing Normal University 100875 Beijing China 5. Department of Physics Beijing Normal University 100875 Beijing China

Dense coding using superpositions of Bell-states is proposed. The generalized Grover's algorithm is used to prepare the initial entangled states, and the reverse process of the quantum algorithm is used to determine the entangled state in the decoding measurement. Compared with the previous schemes, the superpositions of two Bell-states are exploited. Our scheme is demonstrated using a nuclear magnetic resonance (NMR)quantum computer. The corresponding manipulations are obtained. Experimental results show a good agreement between theory and experiment. We also generalize the scheme to transmit eight messages by introducing an additional two-state system.

关键词： dense coding, superpositions of Bell-states, generalized Grover's algorithm, nuclear magnetic res-onance, quantum computer.

The toxicity of Cu^(2+) to Microcystis aeruginosa using dielectric spectroscopy

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science china Chemistry 2010年第3期53卷 631-636页

作者： YU YanLi1,BAI Wei1,ZHAO KongShuang1& ZHOU YunLong2 1college of Chemistry,beijing normal {3.,beijing 100875,china 2college of Life science,beijing normal {3.,beijing 100875,china 1. college of Chemistry Beijing Normal University Beijing 100875 China2. College of Life Science Beijing Normal University Beijing 100875 China

Dielectric spectroscopy(DS) was utilized to investigate the toxicity of the Cu2+ solution to Microcystis *** was found that 0.04 mM Cu2+ had no effect on dielectric increment,whereas the Cu2+ concentrations above 0.1 mM decreased the value of Δε/Δε *** toxic effect of Cu2+ on *** cells was time-dependent and *** was a threshold concentration between 0.04 mM and 0.1 mM,which affected the cell membrane,suggesting that Cu2+ at the concentrations higher than 0.1 mM caused serious plasmalemma damage to *** *** addition of 1 mM Ca2+ or Mg2+ did not protect *** cells from 1 mM Cu2+ *** study demonstrates that DS monitors cell biomass facilitating observation of the toxic effects of metal ions.

关键词： Microcystis aeruginosa dielectric spectroscopy dielectric increment cupric ion toxicity

Reaction-diffusion processes

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Chinese science Bulletin 1998年第17期43卷 1409-1420页

作者： CHEN Mufa beijing normal university beijing 100875, china beijing normal university Beijing China

The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statistical physics and consist of an important class of interacting particle systems which is currently an active research field in probability and mathematical physics. The models are concrete but as a part of the infinite-dimensional mathematics, the topic is quite hard. It is explained how new problems arise, and how some new ideas and new mathematical tools are introduced. Surprisingly, the mathematical tools produced from the study on the simple models then turn to have a lot of powerful applications not only in probability theory but also in other branches of mathematics. Nevertheless, the story is still far from finished, and some important open problems are proposed for further study.

关键词： Reaction-diffusion process ergodicity phase transitions coupling.

Key technology of mine underground mobile positioning based on LiDAR and coded sequence pattern

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中国有色金属学会会刊：英文版 2011年第S3期21卷 570-576页

作者： WANG Zhi1, 2, WU Li-xin1, 2, LI Hui-ying3.1. college of resources and Civil Engineering, Northeastern university, Shenyang 110004,{3. 2. Academy of Disaster Reduction and Emergency Management, Ministry of Civil Affairs and Ministry of Education, beijing normal university, beijing 100875,{3. 3. college of Computer science and technology, Jilin university, Changchun 13.012,{3. [a] college of resources and Civil Engineering Northeastern University Shenyang 110004 China [b] Academy of Disaster Reduction and Emergency Management Ministry of Civil Affairs and Ministry of Education Beijing Normal University Beijing 100875 China [c] college of Computer science and technology Jilin University Changchun 130012 China

Technologies of underground mobile positioning were proposed based on LiDAR data and coded sequence pattern landmarks for mine shafts and tunnels environment to meet the needs of fast and accurate positioning and navigation of equipments in the mine underground without satellite navigation signals. A coded sequence pattern was employed for automatic matching of 3. scans. The methods of SIFT feature, Otsu segmentation and fast hough transformation were described for the identification, positioning and interpretation of the coded sequence patterns, respectively. The POSIT model was presented for speeding up computation of the translation and rotation parameters of LiDAR point data, so as to achieve automatic 3. mapping of mine shafts and tunnels. The moving positioning experiment was applied to evaluating the accuracy of proposed pose estimation method from LiDAR scans and coded sequence pattern landmarks acquired in an indoor environment. The performance was evaluated using ground truth data of the indoor setting so as to measure derivations with six degrees of freedom.

关键词： LiDAR coded sequence pattern mobile positioning SLAM algorithm POSIT algorithm

Theoretical analysis of alloy multiplying factor by the empirical electron theory of solids and molecules

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science china(Technological sciences) 2007年第6期50卷 807-814页

作者： SONG YuePeng1,2, LIU GuoQuan2, LI ZhiLin3. FENG ChengMing1 1 Mechanical and Electronic Engineering college, Shandong Agricultural university, Tai’an 271018, china 2 college of Materials science and Engineering, university of science and technology, beijing 100083. china 3.college of Material science and Engineering, beijing university of Chemical technology, beijing 100029, china Mechanical Electronic Engineering college Shandong Agricultural University Tai’an 271018 China college of Materials science Engineering University of Science technology Beijing 100083 China college of Material science Engineering Beijing University of Chemical Technology Beijing 100029 China

By introducing the distribution probability of structural units in austenite contain- ing alloying elements and considering its effects on phase transformation, this paper establishes a calculation model of distribution probability of structural units. A new valence electron structure (VES) parameter-transformation effect coefficient of alloying elements (HL), is defined and then studied both theoretically and ex- perimentally. The relationship between the parameter HL and the multiplying factor (the quenching capability factor) of alloying elements is studied. The results indi- cate that the two parameters (HL and the quenching capability factor) have the same variation characteristic and substance feature. Therefore, the multiplying factor virtually expresses the relative quantity of structural units in the alloying elements-containing austenite.

关键词： multiplying factor (the quenching capability factor), empirical electron theory of solids and molecules, transformation effect coefficient of alloying elements, structural units in austenite containing alloying elements

Recovery of functions via their irregular sampling values

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Chinese science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun Department of Mathematics, beijing normal university, beijing 100875, china Department of Mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.