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

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. Department of mathematics, Nanjing university, Nanjing 210093. china 2. Department of mathematics, Henan university, Kaifeng 475001, china 3. Department of Applied mathematics, Southeast university, Department of Mathernntics Nanjing University Nanjing China Department of mathematics Henan University Kaifeng China Department of Applied mathematics 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.

LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

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Journal of Computational mathematics 2002年第2期20卷 153-164页

作者： Dan-ping Yang (School of mathematics and system science, Shandong {3., Jinan 250100, china) School of mathematics and system science Shandong University Jinan 250100

Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio... 详细信息

关键词： least-squares algorithm mixed finite element nonlinear parabolic problems convergence analysis

Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes

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Progress in Natural science:Materials International 2006年第6期16卷 588-593页

作者： GAO Wenhua, YE Peixin and WANG Hui (College of mathematics and system sciences, {3., urumqi 83.046, china School of Mathematical sciences and LPMC, Nankai university, Tianjin 3.0071, china Department of mathematics, Ily Teachers' College, Yining 83.000, china College of science, Hehai university, Nanjing 210098, china) College of mathematics and system sciences Xinjiang University Urumqi 830046 China School of Mathematical sciences and LPMC Nankai University Tianjin 300071 China Department of mathematics Ily Teachers' College Yining 835000 China College of science Hehai University Nanjing 210098 China

We study the restricted Monte Carlo integration error for anisotropic Sobolev classes. Results prove that with O(log2 n) random bits we have the optimal order for the n-th minimal Monte Carlo integration error with ar... 详细信息

关键词： Monte Carlo integration random bits anisotropic Sobolev classes.

Theory of truth degrees of propositions in the logic system Ln^＊

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science in china(Series F) 2006年第4期49卷 471-483页

作者： LI Jun1,2 & WANG Guojun1,3.1. Institute of mathematics, Shaanxi Normal university, Xi’an 710062, china 2. School of {3.s, Lanzhou university of Technology, Lanzhou 73.050, china 3. Research Center for {3., Xi’an Jiaotong university, Xi’an 710049, china Institute of mathematics Shaanxi Normal University Xi’an China School of sciences Lanzhou University of Technology Lanzhou China Research Center for science Xi’an Jiaotong University Xi’an China

By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^＊ is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.

关键词： truth degree similarity degree approximate reasoning.

A study of two-dimensional magnetic polaron

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science china(Physics,Mechanics & Astronomy) 2006年第4期49卷 421-429页

作者： LIU Tao1, ZHANG Huaihong1, FENG Mang1,2 & WANG Kelin1,3.1. School of science, Southwest university of science and Technology, Mianyang 621010, {3. 2. Wuhan Institute of Physics and mathematics, Chinese Academy of sciences, Wuhan 43.070, {3. 3. Department of Modern Physics, university of science and Technology of {3., Hefei 23.026, {3. School of science Southwest University of Science and Technology Mianyang China Wuhan Institute of Physics and mathematics Chinese Academy of Sciences Wuhan China Department of Modern Physics University of Science and Technology of China Hefei China

By using the variational method and anneal simulation, we study in this paper the self-trapped magnetic polaron (STMP) in two-dimensional anti-ferromagnetic material and the bound magnetic polaron (BMP) in ferromagnetic material. Schwinger angular momentum theory is applied to changing the problem into a coupling problem of carriers and two types of Bosons. Our calculation shows that there are single-peak and multi-peak structures in the two-dimensional STMP. For the ferromagnetic material, the properties of the two-dimensional BMP are almost the same as that in one-dimensional case; but for the anti-ferromagnetic material, the two-dimensional STMP structure is much richer than the one-dimensional case.

关键词： self-trapped magnetic polaron, bound magnetic polaron, impurity potential, anti-ferromagnet.

Function S-rough sets and security-authentication of hiding law

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science in china(Series F) 2008年第7期51卷 924-935页

作者： SHI KaiQuan1,2 & ZHAO JianLi3.1 School of mathematics and Computer sciences, Longyan university, Longyan 3.4000, {3. 2 School of mathematics and system sciences, Shandong university, Jinan 250100, {3. 3.School of mathematics science, Liaocheng university, Liaocheng 252059, {3. School of mathematics and Computer sciences Longyan University Longyan China School of mathematics and system sciences Shandong University Jinan China School of mathematics science Liaocheng University Liaocheng China

Function S-rbugh sets are defined by R-function equivalence class, which have dynamic characteristic. Function S-rough sets have dynamic characteristic, law characteristic and law-hiding characteristic. Function S-rough sets can generate f-hiding law and f-hiding law. By engrafting, crossing, and penetrating between the information security theory and function S-rough sets, the security hiding and the authentication of f-hiding law and f-hiding law are given respectively in this paper. The fusion and share between function S-rough sets and information security theory is a new research direction of the application of information law in information system.

关键词： function S-rough sets law-hiding elliptic curve the security-authentication of hiding law

Approximation of dense-n/2-subgraph and table compression problems

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science china mathematics 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1 HAN Jiye~2 & DU Dongle~3.1. College of Applied sciences,Beijing university of Technology,Beijing 100022,china 2. Institute of Applied {3.,Academy of {3. and systems science,Chinese Academy of sciences,Beijing 100080,china 3. Faculty of Administration,university of New Brunswick,P.O.Box 4400,Fredericton,NB E3. 5A3.Canada College of Applied sciences Beijing University of Technology Beijing 100022 China Institute of Applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Faculty of Administration University of New Brunswick P.O. Box 4400 Fredericton NB E3B 5A3 Canada

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2-subgraph and table *** on SDP relaxation and advanced rounding techniques,we first propose 0. 5982 and 0. 5970-approximation algorithms respec- tively for the dense-n/2-subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0. 6243.and 0. 6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP *** results for TCP beat the 0. 5 bound of a simple greedy algorithm on this problem,and hence answer an open question of Anderson in an affirmative way.

关键词： dense-n/2-subgraph problem(DSP) table compression problem(TCP) SDP approximation ratio

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

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Wuhan university Journal of Natural sciences 2005年第2期10卷 339-343页

作者： HAN Hui-li 1,2 ,DU Jin-yuan 1,3.1. School of mathematics and Statistics, Wuhan university, Wuhan 43.072, Hubei, china 2. School of mathematics and Computer, Ningxia university, Yinchuan 750021, Ningxia, china 3. Department of mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, china School of mathematics and Statistics Wuhan University Wuhan Hubei China School of mathematics and Computer Ningxia University Yinchuan Ningxia China Department of Mathematies Hubei Institute for Nationalities Enshi Hubei China

We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... 详细信息

关键词： boundary value problem singular integral equation the singularities of high order