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A MODIFIED ALGORITHM OF FINDING AN ELEMENT OF CLARKE GENERALIZED GRADIENT FOR A SMOOTH COMPOSITION OF MAX-TYPE FUNCTIONS A MODIFIED ALGORITHM OF FINDING AN ELEMENT OF CLARKE GENERALIZED GRADIENT FOR A SMOOTH COMPOSITION OF MAX-TYPE FUNCTIONS

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Journal of Computational Mathematics 2000年第5期18卷 513-520页

作者： Yan Gao (Department of Basic Science, china university of Mining and Technology-{2., beijing 100083. china) （北京）中国矿业大学北京 100083

This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxj∈J1 f1j(x),''', maxj∈Jm fmj(x)), where x ∈Rn, Ji, i = 1,''',m are finite index sets, g and fij,j ∈ Ji, i = 1,... )m, are continuously differentiable on Rm+n and Rn, respectively. In a previous paper) we proposed an algorithm of finding an element of Clarke generalized gradient for f, at a point. In that paper, finding an element of Clarke generalized gradient for f, at a point, is implemented by determining the compatibilities of systems of linear inequalities many times. So its computational amount is very expensive. In this paper) we will modify the algorithm to reduce the times that the compatibilities of systems of linear inequalities have to be determined.

关键词： Nonsmooth optimization Clarke generalized gradient Max-type function.

Prediction of Rock Burst with Deep Mining Excavation in Linglong Gold Mine

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Journal of university of Science and Technology beijing 2001年第4期8卷 241-243页

作者： Meifeng Cai, Jinan Wang, Shuanghong Wang Civil and Environmental Engineering School, university of Science and Technology beijing,{2. Civil and Environmental Engineering School University of Science and Technology Beijing Beijing 100083 China

To predict rock burst in deep mining excavation in Linglong gold mine, systematical laboratory tests of mechanical properties of rock, in situ stress measurement and 3-D FEM analysis on energy distribution in rock mass surrounding deep mining rooms were carried out. According to various prediction criteria of rock burst, it is concluded that rock burst is liable to occur during deep mining excavation in the mine.

关键词： rock burst prediction deep mining excavation Linglong gold mine

Cu(Ⅱ) Potentiation of Alzheimer Aβ1-40 Cytotoxicity and Transition on its Secondary Structure

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Acta Biochimica et Biophysica Sinica 2006年第11期38卷 765-772页

作者： Xue-Ling DAI~1 Ya-Xuan SUN~2.Zhao-Feng JIANG~2. 1 College of Life Science,Capital Normal university,beijing 100037,{2. 2.College of Applied Sciences and Humanities,beijing Union university,beijing 100083.{2. College of Life Science Capital Normal UniversityBeijing 100037 China College of Applied Sciences and Humanities Beijing Union UniversityBeijing 100083 China

Mounting evidence has shown that dyshomeostasis of the redox-active biometals such as Cuand Fe can lead to oxidative stress,which plays a key role in the neuropathology of Alzheimer's disease（AD）.Here we demonstrate that with the formation of Cu（Ⅱ）·Aβ1-40 complexes,copper markedly potentiatesthe neurotoxicity exhibited by β-amyloid peptide （Aβ）.A greater amount of hydrogen peroxide was releasedwhen Cu（Ⅱ）·Aβ1-40 complexes was added to the xanthine oxidase/xanthine system detected by potassiumiodide *** bound to Aβ1-40 was observed by electron paramagnetic resonance（EPR） *** dichroism （CD） studies indicated that copper chelation could cause a structuraltransition of Aβ.The addition of copper to Aβ introduced an increase on β-sheet as well as α-helix,whichmay be responsible for the aggregation of Aβ.We hypothesized that Aβ aggregation induced by copper maybe responsible for local injury in *** interaction between Cu2.and Aβ also provides a possible mechanismfor the enrichment of metal ions in amyloid plaques in the AD brain.

关键词： Alzheimer’s disease Cu(Ⅱ)·Aβ1-40 complex neuron injury Aβ secondary structure

The refined theory of transversely isotropic piezoelectric rectangular beams

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Science china(Physics,Mechanics & Astronomy) 2006年第4期49卷 473-486页

作者： GAO Yang1 & WANG Minzhong2.1. College of Science, china Agricultural university,{2. 2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engi- neering Science, Peking university, beijing 100871, china College of Science China Agricultural University Beijing China State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science Peking University Beijing China

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur'e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.

关键词： rectangular beams, the refined theory, piezoelectric, transversely isotropic.

Theorems for Testing Local Activity of CNN and Application to Cardiac Purkinje Equations

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International Journal of Minerals,Metallurgy and Materials 2000年第2期14卷 139-146页

作者： Lequan Min(Applied Science School, university of Science and Technology beijing,{2.) Applied Science School University of Science and Technology Beijing Beijing 100083 China

The theorems for testing the local in one-port cellular neural/inear network (CNN) cells with four local state variables are presented. Using the theorems computes the bifurcation diagrams of the cardiac Purkinje fiber (CPE) equations Which describethe long-lasting action and pace-maker potentials of the Purkinje fiber of the heart. The computer simulation shows that periodic trajectories or convergent trajectories of the CPF Equations can be foun if the cormsponing cell Parameters are located in a positive domainbut nearby edge of chaos. In particular a heart with approximate normal frequency of heartbeat but non-normal electrocardiogram maysuddenly stop by slightly perturbing the parameters of the corresponding CPF Equations when the Paramders are located nearby the edge of chaos in the bifurcation diagrams. This research seems to interpret reasonbly the phenomena that patients with cardiac diseases might suddenly die without warning.

关键词： cellular neural network local activity cardiac Purkinje fiber heartbeat

The refined theory of deep rectangular beams based on general solutions of elasticity

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Science china(Physics,Mechanics & Astronomy) 2006年第3期49卷 291-303页

The problem of deducing one-dimensional theory from two-dimensional the- ory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the re- fined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two ex- amples, it is shown that the new theory provides better results than Levinson’s beam the- ory when compared with those obtained from the linear theory of elasticity.

关键词： deep rectangular beams,the refined theory,Papkovich-Neuber solution,Lur'e method,governing equation

The mathematical model of wetting angle of heterogeneous nucleation

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Science china(Technological Sciences) 2004年第4期47卷 391-397页

作者： HUANG Cheng1, SONG Bo1, MAO Jinghong2.& ZHAO Pei3 1. School of Metallurgical and Ecological Engineering, university of Science and Technology beijing,{2. 2. School of Material Science, university of Science and Technology beijing,{2. 3. Central Iron and Steel Research Institute, beijing 100081, china School of Metallurgical and Ecological Engineering University of Science and Technology Beijing Beijing China School of Material Science University of Science and Technology Beijing Beijing China Central Iron and Steel Research Institute Beijing China

The heterogeneous nucleation has been analyzed in terms of the thermodynamic theory, and the mathematical model of wetting angle of heterogeneous nucleation has been developed based on the dynamic requirements of hetero- and homogeneous nucleation. With the wetting angel model, the wetting angles of different catalysts in liquid iron have been calculated. The result shows that the wetting angle of most catalysts is smaller than 40, and the value of f() is far less than 1. The wetting angles of TiN, TiC and RE2.3 are smaller, while the wetting angle of MnO is bigger among the ordinary nucleation catalysts. The wetting angles calculated by this model are in agreement with the results of other research work.

关键词： heterogeneous nucleation, mathematical model, wetting angle, undercooling.

Based on the Spectral Variation of Vegetation Monitoring the Heavy Metal Pollution of Soil

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地学前缘 2009年第S1期16卷 86-87页

作者： Li Mi School of Information Engineering,china university of {2.(beijing),beijing 100083.china.

Heavy metal pollution of soil is one of serious problems of *** easy to break down, heavy metal was enriched and became the pollutants. It would not only destroy the normal function of soil and impede the growth of crops,but also through the food chain cause the harm to human *** the impact of heavy metal pollution of soil,the vegetation is also very easy to be *** the vegetation has been contaminated,its internal structure,

关键词： heavy metal pollution chlorophyll spectral variation red valley parameters

Geochemical characteristics and tectonic implications of HP-UHP eclogites and blueschists in southwestern Tianshan, china

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Progress in Natural Science:Materials International 2006年第6期16卷 624-632页

作者： AI Yongliang, ZHANG Lifei, LI Xuping and QU Junfeng (MOE Key Laboratory of Orogenic Belt and Crust Evolution, School of Earth and Space Sciences, Peking university, beijing 100871, {2. School of geosciences and Resources, {2. university of geosciences, beijing 100083. china) MOE Key Laboratory of Orogenic Belt and Crust Evolution School of Earth and Space Sciences Peking University Beijing 100871 China School of geosciences and Resources China University of Geosciences Beijing 100083 China

Four rock assemblages in correspondence with two different tectonic settings have been recognized in the NEE-SWW extending HP-UHP metamorphic belt in southwestern Tianshan, northwest china. Eclogite assemblage EC1 is geochemically akin to alkaline within-plate oceanic island basalt (OIB). EC2.shows affinity to enriched mid-oceanic ridge basalt (EMORB). Rare earth element (REE) and other immobile trace element characteristics of blueschist assemblage BS1 resemble those of normal mid-oceanic ridge basalt (NMORB). These three assemblages are likely formed on a seamount setting, and the prevalent presence of carbonate minerals and om-phacite quartzite stripes/gobbets suggests ancient pelagic sediments including marls are probably developed upon the basaltic seamount. Whereas the geochemical characteristics of BS2.assemblage are of volcanic arc basalt-type. The seamount with the pelagic sediments on it is brought into the subduction zone, and volcanic arc basalts formed on the active continental margin and trench sediments are eroded and enwrapped in the subducting mass, they are altogether subjected to high to ultrahigh pressure metamorphism and subsequent exhumation towards surface. The HP-UHP metamorphic belt is thus interpreted as a subduct ion-accretionary complex formed by tectonic juxtaposition and imbrication of seamount, seafloor, trench and volcanic arc sequences during oceanic crust subduction.

关键词： southwestern Tianshan HP-UHP metamorphic belt snbduction-accretion complex trace element geochemistry.