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Extremal eigenvalues of measure differential equations with fixed variation

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Science china Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2 1 department of Mathematical Sciences,tsinghua university,beijing 100084,china 2 Zhou Pei-Yuan Center for Applied Mathematics,tsinghua university,beijing 100084,china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

Maximal regularity of second order delay equations in Banach spaces

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Science china Mathematics 2010年第1期53卷 51-62页

作者： BU ShangQuan ? & FANG Yi department of Mathematical Sciences, tsinghua university, beijing 100084, china department of Mathematical Sciences, tsinghua university, beijing 100084, china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China

We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(*** ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).

关键词： maximal regularity second order delay equations Lebesgue-Bochner spaces Besov spaces Triebel-Lizorkin spaces

Numerical Simulation of Nonlinear Radiation Water Surface Wave Caused by Large-Amplitude Oscillation of A Cylinder

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 24-28页

作者： Wuzhou HE (department of Hydraulic Engineering, tsinghua university, beijing 100084, china) department of Hydraulic Engineering Tsinghua University Beijing 100084 China

The BEM combined with the time-stepping scheme is employed in the nonlinear numerical simulation of the development process of radiation wave profile and hydrodynamic force caused by large amplitude oscillating cylinder. To ensure stability and accuracy of the simulation, special consideration is paid on a series of difficulties in numerical modeling, such as the compatibility of free surface and body surface conditions at the intersection point and the open boundary condition problem. Numerical calculation is carried out for some study cases of different shaped cylinders undergoing large amplitude oscillating motions with distinct modes, the results show. some nonlinear phenomena and indicate the feasibility of the numerical approach.

关键词： 2-D water surface wave boundary element method time-stepping scheme

Electronic properties of multi-defected zigzag carbon nanotubes

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Science china(physics,Mechanics & Astronomy) 2010年第1期53卷 11-15页

作者： QIAN HaiYun& ZHOU Taodepartment of physics, tsinghua university, beijing 100084, china 1. department of physics Tsinghua University Beijing 100084 China

Electronic properties of multi-defected zigzag single-walled carbon nanotubes are investigated by use of the tight-binding Green's function method. The Stone-Wales defects and the vacancies are considered. We find that the conductance sensitively depends on the realistic defect configurations for the metallic zigzag carbon nanotubes. Interestingly, the electronic transport properties of the nanotubes with three vacancies can be considered as the sum effect of two double-vacancies, while those with Stone-Wales defects can not. The electron interference along the longitudinal axis and the transport blocking are observed, which may be useful for understanding the electron transport behavior of carbon nanotube in experiments.

关键词： electronic transport multi-defected carbon nanotube defect configuration electron interference transport blocking

REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 187-198页

作者： ZENG YUNBO department of Applied Mathematics, tsinghua university, beijing 100084, china. TSING HUA UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy

Study on the two and three-parameter working stability regions of 3Y-TZP suspension

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Science china(Technological Sciences) 2006年第5期49卷 547-568页

作者： CHEN Youqiang1, 2, ZHANG Xinni3, CHEN Sha’ou3 & QI Ping3 1. department of Chemistry, Qingdao university, Qingdao 266071, china 2. department of Chemistry, tsinghua university, beijing 100084, china 3. department of physics, Qingdao university, Qingdao 266071, china 1. department of Chemistry Qingdao University Qingdao 266071 China 2. department of Chemistry Tsinghua University Beijing 100084 China 3. department of physics Qingdao University Qingdao 266071 China

We determined the variation tendency of viscosity (η) at various solids load- ing (α) for 3Y-TZP suspension as a function of dispersant concentration (Cw) using vis- cosity measurement, measured the diameter of particles as a function of Cw in very dilute suspension using light scattering method, and obtained the surface features of the sedi- ment of suspension with different Cw using SEM. We also discussed the influence of the microstructure of adsorbed polymer layers on particles and their interactions in the dis- persing medium on the stability of suspension. Then two different stable states and two different unstable states for 3Y-TZP suspension were given. Accordingly, the (Cw, η), (Cw, α), and (α, η) two-parameter, and (Cw, α, η) three-parameter stability maps were con- structed. Based on the DLVO theory calculations, the dispersant concentration, particle distance (r), and interparticle potential energy (VT) maps with various solids loading for 3Y-TZP aqueous suspension were also constructed. In (Cw, r) two-parameter coordinate system, the stable motion region map for particles was established. The Cw, α, and VT,max (the highest potential energy) surface of the potential barrier map was obtained through calculation and simulation on the basis of the surfaces of Cw, r, VT maps introduced above. The (Cw, α) two-parameter stability map was then obtained from the Cw, α, VT,max map. The results showed that this theoretical map can qualitatively prove the experimentally obtained results—the existence of different dispersed states of particles in suspension system and the variation tendency of suspension stability with changing each parame- ter—were reasonable.

关键词： 3Y-TZP, suspension, stability, DLVO theory, interparticle potential energy.

Three types of maximally entangled states for a two-particle system

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Science china(physics,Mechanics & Astronomy) 2004年第1期47卷 36-41页

作者： RUAN Manqi, XU Gang & ZENG Jinyan department of physics, tsinghua university, beijing 100084, china department of physics, Peking university, beijing 100871, china Correspondence should be addressed to Zeng Jinyan (email: jyzeng@***) Received June 16, 2003 1. department of physics Tsinghua University 100084 Beijing China 2. department of physics Peking University 100871 Beijing China

For a two-particle (spin 1/2) system, three fundamental forms of complete sets of commuting observables (CSCO) composed of two-body operatorsσ 1α σ 2α are given. The corresponding simultaneous eigenstates constitute three types of maximally entangled states, one of which is the well known Bell basis. This paper discusses the possible pairs of spin observables whose simultaneous measurement outcomes are definitely correlated in probabilistic fashion.

关键词： spin entangled state, complete set of commuting observables, two-body operator.

Two mode photon bunching effect as witness of quantum criticality in circuit QED

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Science china(physics,Mechanics & Astronomy) 2009年第12期52卷 1898-1905页

作者： AI Qing1,WANG YingDan2,LONG GuiLu1,3 & SUN ChangPu4 1 department of physics,tsinghua university,beijing 100084,china 2 department of physics,university of Basel,Klingelbergstrasse 82,4056 Basel,Switzerland 3 tsinghua National Laboratory for Information Science and Technology,beijing 100084,china 4 Institute of Theoretical physics,Chinese Academy of Sciences,beijing 100080,china 1. department of physics Tsinghua University Beijing 100084 China 2. department of physics University of Basel Klingelbergstrasse 82 4056 Basel Switzerland 3. tsinghua National Laboratory for Information Science and Technology Beijing 100084 China 4. Institute of Theoretical physics Chinese Academy of Sciences Beijing 100080 China

We suggest a scheme to probe critical phenomena at a quantum phase transition (QPT) using the quantum correlation of two photonic modes simultaneously coupled to a critical system. As an experimentally accessible physical implementation,a circuit QED system is formed by a capacitively coupled Josephson junction qubit array interacting with one superconducting transmission line resonator (TLR). It realizes an Ising chain in the transverse field (ICTF) which interacts with the two magnetic modes propagating in the TLR. We demonstrate that in the vicinity of criticality the originally independent fields tend to display photon bunching effects due to their interaction with the ICTF. Thus,the occurrence of the QPT is reflected by the quantum characteristics of the photonic fields.

关键词： quantum phase transition photon bunching circuit QED

Modularity of Calabi-Yau varieties and conformal field theory

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Science china Mathematics 2008年第6期51卷 1135-1146页

作者： TAN FuCheng department of Mathematical Sciences,tsinghua university,beijing 100084,china department of Mathematical Sciences Tsinghua University Beijing 100084 China

We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of *** express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.

关键词： L-function Calabi-Yau variety Gepner model 53C80