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Refraction of light in media

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Science china(Physics,Mechanics & Astronomy) 2007年第5期50卷 591-600页

作者： ZHANG Tao Key Laboratory of Beam Technology and Material Modification of Ministry of Education, Institute of Low Energy Nuclear Physics, beijing Normal University, beijing 100875. china beijing radiation center, beijing 100875. china Key Laboratory of Beam Technology Material Modification of Ministry of Education Institute of Low Energy Nuclear Physics Beijing Normal University Beijing 100875 China beijing radiation center Beijing 100875 China

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dBM/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the elec- tron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work.

关键词： refractive index, light, speed, medium, propagation

STUDY OF Ag DIFFUSION INTO Cu SINGLE CRYSTALS BY RUTHERFORD BACKSCATTERING SPECTROMETRY

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Acta Metallurgica Sinica(English Letters) 2003年第5期16卷 332-334页

作者： R.Wang 1) Key Laboratory of Beam Technology and Materials Modification, Ministry of Education, beijing 100875. china2) Institute of Low Energy Nuclear Physics, beijing Normal University, beijing 100875. china3) beijing radiation center, beijing 100875. china Key Laboratory of Beam Technology and Materials Modification Ministry of Education Beijing 100875China Institute of Low Energy Nuclear Physics Beijing Normal University Beijing 100875 China beijing radiation center Beijing 100875 China

4.0Me V 7Li++ RBS was used for investigations of thermal diffusion of Ag in Cu single crystals. The annealing of samples was carried out in vacuum in the temperature range from 498K to 613K. The element depth concentration profiles transformed from RBS spectra indicate that the diffusion of Ag into Cu is a typical volume diffusion. The Arrhenius parameters corresponding to the diffusion were obtained.

关键词： Ag diffusion single crystal

A Remark on Multilinear Oscillatory Singular Integrals

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Acta Mathematica Sinica,English Series 2000年第4期16卷 655-668页

作者： Shanzhen Lu Dunyan Yan Department of Mathematics, beijing Normal University, beijing 100875. P. R. china Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper we study multilinear oscillatory singular integrals with rough kernel and give a criterion of certain boundedness for this kind of operator

关键词： Multilinear oscillatory integrals Calderon-Zygmund kernel BLO 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.

A Construction of Characteristic Tilting Modules

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Acta Mathematica Sinica,English Series 2002年第1期18卷 129-136页

作者： DENG Bang Ming Department of Mathematics. beijing Normal University. beijing 100875. P. H. china Department of Mathematics Beijing Normal University Beijing P. R. China

Associated with each finite directed quiver Q is a quasi-hereditary algebra. the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endonorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual.

关键词： Quasi-hereditary algebra Characteristic tilting module Ringel dual

Nash Inequalities for Markov Processes in Dimension One

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Acta Mathematica Sinica,English Series 2002年第1期18卷 147-156页

作者： MAO Yong Hua Department of Mathematics. beijing Normal University. beijing 100875. P. R. china Department of Mathematics Beijing Normal University Beijing P. R. China

In this paper. we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. As a by-product. we prove that for these processes. transience implies that the semigroups P(t) ... 详细信息

关键词： Nash inequalities Hardy type inequality Birth-death process Diffusion

Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line

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Acta Mathematica Sinica,English Series 2002年第3期18卷 417-436页

作者： Mu Fa CHEN Department of Mathematics. beijing Normal. University. beijing 100875. P. R. china Department of Mathematics Beijing Normal University Beijing P. R. China

Motivated from the study on logarithmic Sobolev. Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined.

关键词： Variational formula Poincare inequality Logarithmic Sobolev inequality Orliez space

Functional central limit theorem for super α-stable processes

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Science china Mathematics 2004年第6期47卷 874-881页

作者： HONG WenmingDepartment of Mathematics, beijing Normal University, beijing 100875. china 1. Department of Mathematics Beijing Normal University 100875 Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

On asymptotics of t-type regression estimation in multiple linear model

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Science china Mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of Mathematics, beijing Normal University, beijing 100875. china 1. Department of Mathematics Beijing Normal University 100875 Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.