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

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, {1. university,{3., china 2. department of Chemistry, Tsinghua university, Beijing 1.0084, china 3. department of Physics, {1. university,{3., china 1. department of Chemistry Qingdao University Qingdao 266071 China 2. department of Chemistry Tsinghua University Beijing 100084 China 3. {1. of Physics Qingdao University Qingdao 266071 China

We determined the variation tendency of viscosity (η) at various solids load- ing (α) for 3.-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 3.-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 3.-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： 3.-TZP, suspension, stability, DLVO theory, interparticle potential energy.

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Analysis on cohesive crack opening displacement considering the strain softening effect

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Science china(Physics,Mechanics & Astronomy) 2006年第1期49卷 88-101页

作者： WANG Limin1. XU Shilang2 & ZHAO Xiqiang3.1. Mechanics {1., Shandong {1. of Technology, Zibo 255049, china 2. Civil Engineering {1., Dalian {1. of Technology, Dalian 1.6024, china 3. mathematics department, ocean university of china, qingdao 266071, china Mechanics department Shandong University of Technology Zibo 255049 China Civil Engineering department Dalian University of Technology Dalian 116024 China mathematics{1. Ocean University of China Qingdao 266071 China

In order to investigate the crack propagation in quasi-brittle materials like rock, ceramic and concrete, Hillerborg and his co-researchers abstracted the fracture process zone in front of a stress free crack in terms of a “fictitious crack zone”. On the fictitious crack zone, cohesive stresses distribute following a given softening relationship of stress vs. crack opening. Based on the polynomial or power series expression of cohesive crack opening displacement, the relationship of the cohesive stress vs. the crack opening displacement is established using elastic theory and integral equation, and some unknown physics variables are obtained using variation approach. The calculation results gained in this paper are close to the experimentally test ones.

关键词： cohesive crack, softening, dissipation work, variation approach.

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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{1., ocean university of china,{3.) 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

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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{1. ocean {3. of qingdao, qingdao 266003. china) ocean Univ{1. Dept Appl Math Ocean Qingdao 266003 Peoples R China

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

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The extension of the first main theorem for π-blocks

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Science china{1. 2006年第5期49卷 620-625页

作者： HAI Jinke department of{1., qingdao {3., qingdao 266071, china College of{1. ,Shandong {3., Jinan 2501.0, china department of{1. Qingdao University Qingdao 266071 China College of mathematics Shandong University Jian 250100 China

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

关键词： π-block, π-separable group, π-regular classes, defect group.

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CMC surfaces in the hyperbolic 3.space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1. 2 and LI Zhenqi 1. 3.1. Institute of {1., Fudan {1., Shanghai 20043., china 2. {3. of {1.,Sichuan Union {1., Chengdu 61.064, china 3. {3. of {1., Nanchang {1., Nanchang 3. nstitute of Mathemalics Fudan University Shanghai China department of{1. Sichuan Union University Chengdu China department of{1. Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1.are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

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

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Science china{1. 2007年第1期50卷 116-120页

作者： Ke-jian XU department of{1., qingdao {3., qingdao 266071, china 1. department of{1. Qingdao University Qingdao 266071 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.

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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{1., ocean {3. of qingdao, qingdao 266003. china department of Applied{1. 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.

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Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1. 2, WANG Mingxin 3. XIE Chunhong 1.1. {1. of {1., Nanjing university, Nanjing 21.093. {3. 2. {1. of {1., Henan university, Kaifeng 475001. {3. 3. {1. of Applied {1., Southeast university, department of Mathernntics Nanjing University Nanjing China department of{1. Henan University Kaifeng China department of Applied{1. Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

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A maximum entropy distribution for wave heights of non-linear sea waves

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Progress in Natural Science:Materials International 2007年第11期17卷 1318-1326页

作者： Zhou Liangming1. Xu Delun1. Wang Aifang1. Chen Zhengshou2 and Yan Xiuhua1.1. Physical oceanography Laboratory,{1., qingdao 2661.0,{3. 2.Engineering College,{1., qingdao 266071, {3.) Physical oceanography Laboratory Ocean University of China Qingdao 266100China 2.Engineering College Ocean University of China Qingdao 266071 China

Based on the maximum entropy principle,a probability density function (PDF) for the zero-crossing wave height (H) of random waves is derived as the simple form fn(H)=αHγe-βHn (n is a selectable positive integer) through solving a variational problem subject to some quite general constraints. This PDF maximizes the information entropy of H, and its parameters α, γ and β are expressed explicitly in terms of the distribution moments m, m=1.2,…,n, so it is well competent for describing the distribution of H of nonlinear sea waves with large uncertainty, and its parameters can be simply determined from available data. Comparisons between the PDF with n=3.and n=4 and the observed distributions of H from wave records measured in the East {1. Sea and in a wind-wave tunnel show fairly satisfying agreements.

关键词： sea waves the maximum entropy principle probability density function

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