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NUMErICAL DISSIpATION FOr THrEE-pOINT DIFFErENCE SCHEMES TO HYpErBOLIC EQUATIONS WITH UNEVEN MESHES

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Journal of Computational Mathematics 2003年第4期21卷 519-534页

作者： Zi-niu Wu(department of Engineering Mechanics, tsinghua university, beijing 100084, china) department of Engineering Mechanics Tsinghua University Beijing 100084 China

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. The numerical dissipation due to these interfaces is studied here for three-point difference approximations of a hyperbolic equation. It will be shown that if the wave moves in the fine-to-coarse direction then the dissipation is positive (stabilizing), and if the wave moves in the coarse-to-fine direction then the dissipation is negative (destabilizing).

关键词： refined interfaces Numerical dissipation Three-point difference approxima-tion Hyperbolic equation.

rational points and zeta functions of some curves over finite fields

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Science china Mathematics 2010年第11期53卷 2855-2863页

作者： WANG Long1, & LUO JinQuan2,3 1department of mathematical sciences, tsinghua university, beijing 100084, china 2School of mathematical sciences, Yangzhou university, Yangzhou 225002, china 3Division of mathematical sciences, School of physical and mathematical sciences, Nanyang Technology university, 637371, Singapore 1. department of mathematical sciences Tsinghua University Beijing 100084 China2. School of Mathematical Sciences Yangzhou University Yangzhou 225002 China3. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technology University Singapore 637371 Singapore

In this paper we study the number of rational points on some curves over finite fields. Moreover, zeta functions of the associated function fields are evaluated explicitly.

关键词： exponential sum rational point rational place zeta function

THE MEASUrEMENT OF pLASTIC DEFOrMATION AND CrACK GrOWTH IN CrACKED SpECIMENS BY SAM

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Acta Mechanica Solida Sinica 1994年第4期7卷 347-353页

作者： Sun Xuewei Li Mingzheng (department of Engineering Mechanics,tsinghua university,beijing 100084,p.r.china) department of Engineering Mechanics Tsinghua University Beijing 100084 China

In this paper,scanning acoustic microscope(SAM) was used to obtain some characteristic photographs which explain the mesoscopic information of several cracked *** results on subsurface information of steel,nickel and aluminium were *** deformation and crack initiation were observed and *** length of crack propagation was *** is particularly suited to the study of many mesoscopic phenomena in material science because it can image mesoscopic subsurface feature without *** is revealed that SAM has a bright future in the field of mesomechanics.

关键词： SAM(scanning acoustic microscope) experiment mesomechanics crack

Closed and endoreversible chemical oscillation

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Chinese Journal of Chemistry 1994年第3期12卷 199-205页

作者： LI, ru-Shengdepartment of Chemistry, tsinghua university, beijing 100084, china department of Chemistry Tsinghua University Beijing 100084 China

Based on a simple nonideal chemical reaction model, the closed system with reversible nonideal reactions and illumination is shown to be able to exhibit sustained oscillation. The essential points in the occurrence of such oscillations are the nonideality of reacting media, which gives rise to multiple chemical equilibria, and the energy flow through illumination and heat conduction, which gives rise to spontaneous transitions repeatedly between the multiple equilibrium states. During the oscillation, reacting media undergo only reversible chemical transformation and all irreversibilities are restricted to the coupling of the system to external world. This oscillation provides an example of the so-called endoreversible machine and a possible way to convert radiation energy of the light directly into mechanical energy.

关键词： Chemical oscillation closed system nonideality endoreversible machine illumination.

Multiple time step molecular dynamics simulation for interaction between dislocations and grain boundaries

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Acta Mechanica Sinica 2005年第4期21卷 371-379页

作者： X.Y.Li W.Yang department of Engineering Mechanics,tsinghua university,beijing 100084.china department of Engineering Mechanics Tsinghua University Beijing 100084 China

A multiple time step algorithm, called reversible reference system propagator algorithm, is introduced for the long time molecular dynamics simulation. In contrast to the conventional algorithms, the multiple time method has better convergence, stability and efficiency. The method is validated by simulating free relaxation and the hypervelocity impact of nano-clusters. The time efficiency of the multiple time step method enables us to investigate the long time interaction between lattice dislocations and low-angle grain boundaries.

关键词： Multiple time step Molecular dynamics ,Dislocation Grain boundary

Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields

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Chinese Science Bulletin 1998年第10期43卷 824-826页

作者： LIU Tong department of Applied Mathematics, tsinghua university, beijing 100084, china department of Applied Mathematics Tsinghua University Beijing China

Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, Zhang Xianke from 1948 to 1988.

关键词： real cyclic sextic number fields class number fundamental relative unit.

A measurement error model for microarray data analysis

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progress in Natural Science:Materials International 2005年第7期15卷 614-620页

作者： ZHOU Yiming and CHENG Jing ( department of Biological sciences and Biotechnology, tsinghua university, beijing 100084, china State Key Laboratory of Biomembrane and Membrane Biotechnology, tsinghua university, beijing 100084, china National Engineering research Center for beijing Biochip Technology, 18 Life Science parkway, beijing 102206, china) department of Biological sciences and Biotechnology Tsinghua University Beijing 100084 China. State Key Laboratory of Biomembrane and Membrane Biotechnology Tsinghua University Beijing 100084 China. National Engineering research Center for beijing Biochip Technology 18 Life Science Parkway Beijing 102206 China

Microarray technology has been widely used to analyze the gene expression levels by detecting fluorescence intensity in a high throughput fashion. However, since the measurement error produced from various sources in microarray experiments is heterogeneous and too large to be ignored, we propose here a measurement error model for microarray data processing, by which the standard deviation of the measurement error is demonstrated to be linearly increased with fluorescence intensity. A robust algorithm, which estimates the parameters of the measurement error model from a single microarray without replicated spots, is provided. The model and algorithm for estimating of the parameters from a given data set are tested on both the real data set and the simulated data set, and the result has been proven satisfactory. And, combining the measurement error model with traditional Z-test method, a full statistical model has been developed It can significantly improve the statistical inference for identifying differentially expressed genes.

关键词： microarray measurement error model parameter estimation differentially expressed genes.

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.

Multiparty quantum secret sharing of classical and quantum messages

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progress in Natural Science:Materials International 2007年第1期17卷 26-31页

作者： CHEN pan, DENG Fuguo and LONG Guilu ( Key Laboratory for Quantum Information and Measurements, and department of physics, tsinghua university, beijing 100084, china Key Laboratory of Beam Technology and Material Modification, MOE, Institute of Low Energy Nuclear physics, and department of Material Science and Engineering, beijing Normal university, beijing 100875, china beijing radiation Center, beijing 100875, china Key Laboratory for Atomic and Molecular Nano-sciences, tsinghua university, beijing 100084, china) [a]Key Laboratory for Quantum Information and Measurements and Department of Physics Tsinghua University Beijing China [b]Key Laboratory of Beam Technology and Material Modification MOE Institute of Low Energy Nuclear Physics and Department of Material Science and Engineering Beijing Normal University Beijing China [c]beijing radiation Center Beijing China [d]Key Laboratory for Atomic and Molecular Nano-sciences Tsinghua University Beijing China

A scheme for multiparty quantum secret sharing of classical and quantum messages is proposed by using entanglement swapping. This scheme can distribute not only the classical information but also the quantum informati... 详细信息

关键词： quantum secret sharing classical message quantum message Epr pair.