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On Browkin's conjecture about the elements of order five in K_2(Q)

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Science china mathematics 2007年第1期50卷 116-120页

作者： Ke-jian XU department of mathematics, qingdao university, qingdao 266071, china department of mathematics Qingdao University Qingdao China

Based on the work of Lenstra, a succinct proof of Browkin’s conjecture about the elements of order five in K2(Q) is given.

关键词： K2 group cyclotomic polynomial lattice binary quartic form.

Low friction under ultrahigh contact pressure enabled by self-assembled fluorinated azobenzene layers

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Friction 2024年第7期12卷 1434-1448页

作者： Dandan XUE Zhi XU Linyuan GUO Wendi LUO Liran MA Yu TIAN Ming MA qingdao ZENG Ke DENG Wenjing ZHANG Yichun XIA Shizhu WEN Jianbin LUO State Key Laboratory of Tribology in Advanced Equipment Tsinghua UniversityBeijing 100084China National Center for Nanoscience and Technology Beijing 100190China

Extensive efforts have been made to pursue a low-friction state with promising applications in many fields,such as mechanical and biomedical *** which,the load capacity of the low-friction state has been considered to be crucial for industrial ***,we report a low friction under ultrahigh contact pressure by building a novel self-assembled fluorinated azobenzene layer on an atomically smooth highly-oriented pyrolytic graphite(HOPG)*** friction coefficients could be as low as 0.0005 or even lower under a contact pressure of up to 4 *** demonstrates that the low friction under ultrahigh contact pressure is attributed to molecular *** fluorination leads to effective and robust lubrication between the tip and the self-assembled layer and enhances tighter rigidity which can reduce the stress concentration in the substrate,which was verified by density functional theory(DFT)and molecular dynamics(MD)*** work provides a new approach to avoid the failure of ultralow friction coefficient under relatively high contact pressure,which has promising potential application value in the future.

关键词： ultrahigh contact pressure self-assembled layer fluorination robust lubrication

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 department of Chemistry Qingdao University Qingdao China department of Chemistry Tsinghua University Beijing China department of Physics Qingdao University Qingdao 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.

ON RAYLEIGH QUOTIENT MATRICES: THEORY ANDAPPLICATIONS

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Journal of Computational mathematics 1999年第6期17卷 629-638页

作者： Xin-guo Liu(department of Applied mathematics Ocean university of qingdao, qingdao 266003, china) 青岛海洋大学应用数学系山东青岛 266003

Many authors have studied the Rayleigh quotient and Rayleigh quotient matrix. This paper consists of two parts. First, generalizations of some results on the Rayleigh quotient are proved. Second, we give some applicat... 详细信息

关键词： Rayleigh quotient matrix eigenvalue approximation

On the torsion in K_2 of a field

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Science china mathematics 2008年第7期51卷 1187-1195页

作者： XU KeJian & LIU Min College of mathematics,qingdao university,qingdao 266071.china College of mathematics Qingdao University Qingdao China

For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(x) is the n-th cyclotomic *** first,by using Faltings' theorem on Mordell conjecture it is proved that if F is a number field and if n = 4,8,12 is a positive integer having a square factor then Gn(F) is not a subgroup of K2(F),and then by using the results of Manin,Grauert,Samuel and Li on Mordell conjecture theorem for function fields,a similar result is established for function fields over an algebraically closed field.

关键词： number field function field torsion Milnor K2-group Mordell conjecture

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

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Journal of Computational mathematics 2003年第2期21卷 201-206页

作者： Xinguo Liu Zhengjian Bai (department of mathematics, Ocean university of china, qingdao 266071) Departmenl of mathematics Ocean University of China Qingdao 266071

In this note, we consider the backward errors for more general inverse eigenvalue problems by extending Sun's approach. The optimal backward errors are defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution, and the upper and lower bounds are derived for the optimal backward errors. The results may be useful for testing the stability of practical algorithms.

关键词： Inverse eigenvalue problem Optimal backward error Upper bound Lower bound

The Electrochemical Characteristics of Multilayer Assembly of Hemoglobin and Polystyrene Sulfonate at Self-assembled MonolayerSurface

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Chinese Chemical Letters 2000年第1期11卷 81-84页

作者： Hong SUN (department of Chemistry, Textile College, qingdao university, qingdao 266071) department of Chemistry Textile College Qingdao University Qingdao 266071 China

A multilayer film of hemoglobin (Hb) molecules and polyelectrolyte sulfonate were fabricated on a thiol self-assembled monolayers (SAMs) by electrostatic force. The Hb maintains electroactive property in the multilayer film, methylene blue (MB) incorporated into the multilayer can enhance the electron transfer rate between the Hb and the electrode surface.

关键词： multilayer film hemoglobin methylene blue

The advancement of oscillation theory of functional differential equations

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Chinese Science Bulletin 1998年第12期43卷 974-982页

作者： ZHANG Binggen department of Applied mathematics, Ocean university of qingdao, qingdao 266003, china department of Applied mathematics Ocean University of Qingdao Qingdao China

The oscillation theory of functional differential equations (FDEs) is surveyed including (ⅰ) formulation of oscillation problems; (ⅱ) a brief history of the oscillation theory of FDEs; (ⅲ) main topics in the oscill... 详细信息

关键词： functional differential equations oscillation theory.

Classification of (2, 2)-Stable Unfoldings of Map Germs with Codimensions (?) 4

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Acta Mathematica Sinica,English Series 1996年第4期12卷 415-432页

作者： Xiong Jianfei Institute of Applied mathematics qingdao university, 266071.china Institute of Applied mathematics Qingdao University China

In this paper we classify (2,2)-stable unfoldings of map germs with codimensions ≤4 by means of the algorithm given in [4] by Wassermann.

关键词： Classification of Stable Unfoldings of Map Germs with Codimensions Map