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CONVERGENCE PROPERTIES OF A MODIFIED BFGSALGORITHM FOR MINIMIZATION WITHARMIJO-GOLDSTEIN STEPLENGTHS

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Journal of Computational Mathematics 1999年第6期17卷 645-652页

作者： Nai-yang Deng Zheng-feng Li(Department of Mathematics, beijing agricultural engineering university, beijing 100083.china) 北京农业工程大学数学系北京 100083 北京农业工程大学数学系北京

The line search strategy is crucial for an efficient unconstrained optimization algorithm. One of the reason why the Wolfe line searches is recommended lies in that it ensures positive definiteness of BFGS updates. When gradient information has to be obtained costly, the Armijo-Goldstein line searches may be preferred. To maintain positive difiniteness of BFGS updates based on the Armijo-Goldstein line searches, a slightly modified form of BFGS update is proposed by I.D. Coope and C.J. Price (Journal of Computational Mathematics, 13 (1995), 156-160), while its convergence properties is open up to now. This paper shows that the modified BFGS algorithm is globally and superlinearly convergent based on the Armijo-Goldstein line searches.

关键词： BFGS methods convergence superlinear convergence

Theoretical analysis of alloy multiplying factor by the empirical electron theory of solids and molecules

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Science china(Technological Sciences) 2007年第6期50卷 807-814页

作者： SONG YuePeng1,2, LIU GuoQuan2, LI ZhiLin3, FENG ChengMing1 1 Mechanical and Electronic engineering college, Shandong agricultural university, Tai’an 271018, china 2 college of Materials Science and engineering, university of Science and Technology, beijing 100083. china 3.college of Material Science and engineering, beijing university of Chemical Technology, beijing 100029, china Mechanical and Electronic engineering college Shandong Agricultural University Tai’an China college of Materials Science and engineering University of Science and Technology Beijing China college of Material Science and engineering Beijing University of Chemical Technology Beijing China

By introducing the distribution probability of structural units in austenite contain- ing alloying elements and considering its effects on phase transformation, this paper establishes a calculation model of distribution probability of structural units. A new valence electron structure (VES) parameter-transformation effect coefficient of alloying elements (HL), is defined and then studied both theoretically and ex- perimentally. The relationship between the parameter HL and the multiplying factor (the quenching capability factor) of alloying elements is studied. The results indi- cate that the two parameters (HL and the quenching capability factor) have the same variation characteristic and substance feature. Therefore, the multiplying factor virtually expresses the relative quantity of structural units in the alloying elements-containing austenite.

关键词： multiplying factor (the quenching capability factor), empirical electron theory of solids and molecules, transformation effect coefficient of alloying elements, structural units in austenite containing alloying elements

Mixed boundary conditions for piezoelectric plates

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Science china(Physics,Mechanics & Astronomy) 2009年第5期52卷 755-761页

作者： GAO Yang 1 ,XU SiPeng 2 &ZHAO BaoSheng 3 1college of Science,china agricultural university,beijing 100083.china 2college of engineering,Ocean university of china,Qingdao 266071,china 3 School of Mechanical engineering,university of Science and Technology of Liaoning,Anshan 114044,china college of Science China Agricultural University Beijing China college of engineering Ocean University of China Qingdao China School of Mechanical engineering University of Science and Technology of Liaoning Anshan China

For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order.A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the *** the case of axisymmetric bending and stretching of a circular plate,these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate *** are then used for the correct formulation of boundary conditions for the interior solution.

关键词： boundary conditions piezoelectric plates mixed data bending problems stretching problems

Boundary conditions for the bending of a piezoelectric beam

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Science china(Physics,Mechanics & Astronomy) 2008年第7期51卷 847-856页

作者： GAO Yang1, XU SiPeng2 & ZHAO BaoSheng3 1 college of Science, china agricultural university, beijing 100083. china 2 college of engineering, Ocean university of china, Qingdao 266071, china 3 School of Mechanical engineering, university of Science and Technology Liaoning, Anshan 114044, china college of Science China Agricultural University Beijing China college of engineering Ocean University of China Qingdao China School of Mechanical engineering University of Science and Technology Liaoning Anshan China

For beam bending in transversely isotropic piezoelectric media, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the beam of general edge geometry and loadings. By generalizing the method developed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. The prescribed edge-data of the beam must satisfy these conditions in order that they could generate a decaying state within the beam. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions for the case of bending deformation of piezoelectric beam are derived explicitly. They are then used for the correct formulation of boundary conditions for the beam theory solution (or the interior solution). Besides, an analytical solution of elastic beam is formulated to verify validity of our boundary conditions. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two sets of mixed edge-data are obtained for the first time.

关键词： boundary conditions beam bending piezoelectric media decaying states regular states

Multi-objective dynamic detection of seeds based on machine vision

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Progress in Natural Science:Materials International 2007年第2期17卷 217-221页

作者： XUN Yi, ZHANG Junxiong, LI Wei and CAI Weiguo ( college of engineering, china agricultural university, beijing 100083. china college of Science, Dalian Fisheries university, Dalian 116023, china) college of engineering China Agricultural University Beijing 100083 China college of Sciences Dalian Fisheries University Dalian 116023 China

An approach to inspecting massive numbers of moving seeds was studied based on the techniques of dynamic inspection and machine vision. A progressive scanning CCD camera with external trigger function was used for real-time capture of dynamic images of seeds. The methods based on R channel of RGB (Red, Green and Blue) and region-dependent segmentation were adopted to reduce the data size of image processing and improve the efficiency of seeds inspection. All the seeds were sorted into four grades according to their morphological characteristics, such as surface area, perimeter, major axis, minor axis, circularity and eccentricity. The detection experiments indicated that the eligible ratio of the classifications was about 81.90% by this real-time inspection system.

关键词： machine vision seed sorting multi-objective morphological parameter.

Integrating MODFLOW and GIS technologies for assessing impacts of irrigation management and groundwater use in the Hetao Irrigation District,Yellow River basin

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Science china(Technological Sciences) 2009年第11期52卷 3257-3263页

作者： XU Xu1,2, HUANG GuanHua1,2 & QU ZhongYi3 1 Center for Agriculture Water Research, china agricultural university, beijing 100083. china 2 Chinese-Israeli International Center for Research and Training in Agriculture, china agricultural university, beijing 100083. china 3 Water Conservancy and Civil engineering college, Inner Mongolia agricultural university, Hohhot 010018, china Center for Agriculture Water Research China Agricultural University Beijing China Chinese-Israeli International Center for Research and Training in Agriculture China Agricultural University Beijing China Water Conservancy and Civil engineering college Inner Mongolia Agricultural University Hohhot China

Due to severe water scarcity, water resources used in agricultural sector have been reduced markedly in Hetao irrigation district. Application of water-saving practices (WSPs) is required for the sustainable agricultural development. The human activities including WSPs and increase of groundwater abstraction can lower down the groundwater table, which is helpful to the salinity control. Meanwhile, an excessively large groundwater table depth may result in negative impact on crop growth and fragile ecological environment. In this paper, the Jiefangzha irrigation system in Hetao irrigation district was selected as a typical area, a groundwater flow model based on ArcInfo Geographic Information System (GIS) was developed and implemented to quantify the effect of human activities on the groundwater system in this area. The preand post-processing of model data was performed efficiently by using the available GIS tools. The time-variant data in boundary conditions was further edited in Microsoft Excel with programs of Visual Basic for Application (VBA). The model was calibrated and validated with independent data sets. Application of the model indicated that it can well describe the effect of human activities on groundwater dynamics in Jiefangzha irrigation system.

关键词： groundwater flow modeling MODFLOW GIS water-saving practices irrigation district

Phase relationship of complex multi-component system in chromate cleaner production

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Progress in Natural Science:Materials International 2007年第7期17卷 845-850页

作者： Ge Xinlei~1 Wang Xidong~(1,3**) Zheng Shili~2 Zhang Mei~1 Zhang Yi~2 (1.Department of Physical Chemistry,university of Science and Technology beijing,beijing 100083.china 2.Institute of Process engineering,Chinese Academy of Sciences,beijing 100080,china 3.college of engineering,Peking university,beijing 100871,china) Department of Physical Chemistry University of Science and Technology Beijing Beijing 100083 China college of engineering Peking University Beijing 100871 China Institute of Process engineering Chinese Academy of Sciences Beijing 100080 China

The phase relationships of the complex multi-component systems in the liquid-phase oxidization and separation process related with the chromate cleaner production are investigated theoretically and *** phase diagram of main system Fe- Cr2O4-KOH-O2of oxidization process and the relationship of its standard Gibbs free energy change with temperature are calculated.A se- ries of phase diagrams of the separation process at different temperatures,such as K（Na）OH-K（Na）2CrO4-H2O,KOH-KAlO2-H2O, K（Na）OH-K（Na）2CO3-H2O,K（Na）OH-K（Na）HCO3-H2O and K（Na）HCO3-K（Na）2CrO4-H2O have also been *** ex- periments are carried out to verify the calculated *** results showed that the sub-molten salt media are suitable for the oxidization and separation processes;FeCr2O4can be oxidized across a wide range of temperature;K（Na）2CrO4can be separated from K（Na）AlO2system at appropriate temperature and proper concentration;the crystallization of carbonate is easier than that of K（Na）2CrO4.

关键词： chromite chromate system thermodynamics calculation phase diagram

Nanostructured Sulfide Composite Coating Prepared by Atmospheric Plasma Spraying

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材料工程 2006年第Z1期34卷 281-284页

作者： GUAN Yao-hui~1,XU Yang~1,ZHENG Zhong-yu~2,TONG Xiao-hui~2(1 engineering college of china agricultural university,beijing 100083.china 2 beijing Research Institute of Mechanical & Electrical Technology,beijing 100083.china) engineering college China Agricultural University Beijing 100083 China beijing Research Institute of Mechanical and Electrical Technology Beijing 100083 China

Nanostructured FeS-SiC coating was deposited by atmospheric plasma spraying（APS）.The microstructure and phase composition of the coating were characterized with SEM and XRD,*** addition,the size distribution of the reconstituted powders and the porosity of the coating have been *** was found that the reconstitiuted powers with sizes in the range of 20 to 80 μm had excellent flowability and were suitable for plasma spraying *** as-sprayed FeS-SiC composite coating exhibited a bimodal distribution with small grains（30～80nm） and large grains（100～200nm）.The coating was mainly composed of FeS and SiC,a small quantity of Fe1-xS and oxide were also *** porosity of the coating was approximately 19%.

关键词： plasma spraying nanostructured FeS-SiC composite coating

The refined theory of deep rectangular beams for symmetrical deformation

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Science china(Physics,Mechanics & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2 1 college of Science, china agricultural university, beijing 100083. china 2 State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace engineering, 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 Aerospace engineering Peking University Beijing China

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur'e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams.

关键词： deep rectangular beams the refined theory symmetrical deformation the Papkovich-Neuber solution the Lur’e method