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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,{3.,{4. 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.

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong department of mathematics, beijing Normal university,{3.,{4. department of mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

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.{3. 2. department of Materials Science and Engineering, beijing Normal university, beijing 100875, china 3. Testing and Analytical Center, beijing Normal university, beijing 100875,{3. 4. department of Physics, beijing Normal university, beijing 100875, china 5. Key Laboratory For atomic and Molecular Nanosciences, Tsinghua university, beijing 100084.{3. Key Laboratory For Quantum Information and Measurements Department of Physics 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 Key Laboratory for Atomic and Molecular Nanosciences Tsinghua University Beijing 100084 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

ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(department of mathematics, beijing Normal university,{3.,{4..) 北京师范大学北京 100875

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.

CORRELATION BETWEEN STRESS COMPONENTS AND STRESS CORROSION CRACKS IN BRASS Lecturer,department of Materials Physics,university of Science and Technology beijing,beijing 10008{4.china

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Acta Metallurgica Sinica(English Letters) 1992年第9期5卷 178-182页

作者： QIAO Lijie LIU Rui XIAO Jimei university of Science and Technology beijing,beijing,{3.

The effects of stress components on nucleation sites and propagation directions of stress cor- rosion cracks in brass were investigated with specimens under mode Ⅱ and mode Ⅲ loadings. The results indicated that under mode Ⅱ loading,stress corrosion cracks nucleated on the site with maximum normal stress component and propagated along the plane perpendieular to the maximum normal stress,under mode Ⅲ loading,the stress corrosion crack was not evident on the 4.°plane due to the general corrosion in aqueous solution with high NH_4.H concentra- tion,while stress corroded in aqueous solution with low NH_4.H concentration, numerous cracks with spacings of 10—150μm were found on the 4.°plane with maximum normal stress and no stress corrosion cracks was observed on the plane with maximum shear stress.

关键词： stress corrosion cracking stress compoonent brass ammonia solution

The Principal Eigenvalue for Jump Processes

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Acta Mathematica Sinica,English Series 2000年第3期16卷 361-368页

作者： Mufa Chen department of mathematics,beijing Normal university,beijing {4.,P.R.china department of mathematics Beijing Normal University Beijing 100875 P. R. China

A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is *** result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov... 详细信息

关键词： Principal eigenvalue Jump processes Variational formula for Dirichlet form

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,{3.,{4. department of mathematics Beijing Normal University 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

Multi-parameter infinite-dimensional(r,δ)-OU process

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Chinese Science Bulletin 1999年第5期44卷 418-423页

作者： WANG ZikunInstitute of mathematics, Shantou university, Shantou 515063. china {3., beijing Normal university, beijing 100875, china Institute of mathematics Shantou University Shantou China department of mathematics Beijing Normal University Beijing China

The definition of n-parameter infinite-dimensional (r, δ) -Ornstein-Uhlenbeck process {X_t (·)}((r,δ)-OUP_n~∞ for short) is given. The absolute continuity of distribution μ_t of X_t(·) and the limit of X_t(·) w... 详细信息

关键词： multi-parameter (r δ)-OUPn∞ absolute continuity in hierarchy.

Linear estimation and distribution of the limit cycles bifurcated from a kind of degenerate polycycles

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Science china mathematics 2007年第3期50卷 334-344页

作者： Li-qin ZHAO department of mathematics, beijing Normal university,{3.,{4. department of mathematics Beijing Normal University Beijing China

In this paper, we investigate the number and the distribution of the limit cycles bifurcated from a kind of degenerate planar polycycles through three singular points: a saddle-node P 0, a fine saddle P 1 with finite order m ∈ N, a contractive (attracting) saddle P 2 with the hyperbolicity ratio q 2(0) ? Q. The connection between P 0 and P 1 is of hh-type and the connection between P 0 and P 2 is of hp-type. It is assumed that the connections between P 0 to P 2 and P 0 to P 1 keep unbroken. We obtain that the cyclicity of this polycycle is not more than 3. + 1, which is linearly dependent on the order of the resonant saddle P 1. We also show that the cyclicity is not more than m + 3.if q 2(0) > m, and that the nearer q 2(0) is close to 1, the more the limit cycles are bifurcated.

关键词： degenerate polycycle cyclicity finitely-smooth normal form transition map 3.C05 3.C23 58F14