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CHARACTERIZATIONS OF PROPER EFFICIENT SOLUTIONS IN TERMS OF SADDLE POINTS AND DUALITY

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Systems Science and Mathematical Sciences 1992年第1期5卷 9-18页

作者： LI Shizheng (shandong normal university,jinan 2.0014,china) 山东师范大学山东济南

In this paper we characterize the proper efficient solution of a mul-tiobjective programming problem(P)in terms of the saddle point criterion of anew problem(S)and establish a pair of dual problems(S_α)and(D_α)in order todecide the proper efficient solution by the strong *** also give methodof characterization in terms of the saddle point criterion of(P).Finally,we provethat every efficient solution of the matrix linear programming problem is a properefficient solution.

关键词： Efficient solution proper efficient solution saddle point criterion duality perturbation function matrix linear programming problem

STUDY ON SPATIAL LANDSCAPE PATTERN OF YANTAI CITY BASED ON RS AND GIS

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Chinese Geographical Science 2003年第3期13卷 254-258页

作者： WU Quan-yuan (Department of Geography, shandong normal university, jinan 2.0014, P. R. china) Department of Geography Shandong Normal University Jinan P. R. China

Influenced by artificial factors, landscape pattern of Yantai City, shandong Province changes continuously. Revealing its landscape pattern and its changing process has a practical significance for the urban development and layout. Zhifu District, Development Zone, Laishan District and Fushan District in Yantai City were selected to study the landscape pattern. Remote sensing technology was used to obtain landscape information of different periods. Under the support of Geographic Information System (GIS), the spatial landscape pattern of Yantai City was analyzed and simulated by using various special quantitative analysis models. The analysis shows that built-up area lies in the center of Yantai City, the outside is vegetable land, irrigated land, dry land, garden land and woodland.

关键词： landscape remote sensing geographic information system yantai city

Mutual Conversion of Land Use between Urban and Rural Area in the Process of Urbanization: A Case Study of shandong Province

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Chinese Journal of Population,Resources and Environment 2007年第2期5卷 93-96页

作者： Xu Hong College of Population, Resource and Environment, shandong normal university, jinan shandong 2.0014, china College of Population Resource and Environment Shandong Normal University

Urbanization is one of the driving forces for the land use change in type and structure, and its prominent effect is to convert rural land to urban land. This paper takes Shan-dong Province as an example to analyze the current situation of the mutual conversion between the urban and rural areas from the aspects of the structure of land use, the decreasing tendency of the cultivated land, the changes of land use in urban and rural residential areas. It points out that cultivated land is converted to residential area land, industrial and/or mining area land. The relationship between the urban area land and the cultivated land is more direct; meanwhile, the changes of rural residential area lag behind obviously. The decrease of the cultivated land and the decline of soil quality will be the two difficult problems in the process of urbanization.

关键词： mutual conversion of land use between urban and rural areas structure of land use flow of the cultivated land

Bifurcation of Nonlinear Problems Modeling Flows Through Porous Media

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Acta Mathematica Sinica,English Series 1998年第1期14卷 125-134页

作者： liu Xiyu Department of Mathematics, shandong normal university, jinan 2.0014, china

This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for ope... 详细信息

关键词： Bifurcation Continua Operator theory Flow through porous media

Simulation and analysis of aerodynamics for high speed face milling cutters

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Science china(Technological Sciences) 2010年第9期53卷 2575-2580页

作者： JI ChunHui,liu ZhanQiang & liu LuNing School of Mechanical Engineering,shandong university,jinan 250061,china School of Mechanical Engineering Shandong University

In high speed face milling,noise can be broadly categorized as idling noise and cutting *** noise mainly consists of aerodynamic noise.A mathematical model is developed based on the Ffowcs Williams-Hawkings *** noise predicted with the mathematical model compares well with the experimental *** characteristics of aerodynamic noise with the different model parameters (number of teeth,tooth spacing) and locations of observation points are *** directivity of noise is found and the peak value of sound power can be moved from the rotating frequency to higher *** investigation can provide theoretical foundation for the design of face milling cutters with low noise.

关键词： face milling cutter aerodynamic noise numerical simulation

Exponential sums over primes in short intervals

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Science china Mathematics 2006年第5期49卷 611-619页

作者： liu Jianya, Lu Guangshi & ZHAN Tao Department of Mathematics, shandong university, jinan 250100, china Department of Mathematics Shandong University Jinan China

In this paper we establish one new estimate on exponential sums over primes in short intervals. As an application of this result, we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N = p12+p22+p32+p42+p52, with |pj-(N/5)^(1/2)|≤U = N1/2.1.20+ε, where pj are primes. This result is as good as what one can obtain from the generalized Riemann hypothesis.

关键词： exponential sums over primes circle method Waring-Goldbach problems.

The Ambient Gas Effects on Pulsed Laser Ablation of Target

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光电子·激光 1996年第1期7卷 12-15页

作者： Gongtang Wang Xiangtai Wang Baoyuan Mian(Department of physics,shandong normal university,jinan 2.0014)Bingzhang Xu Liangmo Mei(Department of physics.shandong university,jinan 250100) 山东师范大学物理系山东济南山东大学物理系山东济南

ＴｈｅＡｍｂｉｅｎｔＧａｓＥｆｆｅｃｔｓｏｎＰｕｌｓｅｄＬａｓｅｒＡｂｌａｔｉｏｎｏｆＴａｒｇｅｔ￥ＧｏｎｇｔａｎｇＷａｎｇ；ＸｉａｎｇｔａｉＷａｎｇ；ＢａｏｙｕａｎＭｉａｎ（Ｄｅｐａｒｔｍｅｎｔｏｆｐｈｙｓｉｃｓ，... 详细信息

ＴｈｅＡｍｂｉｅｎｔＧａｓＥｆｆｅｃｔｓｏｎＰｕｌｓｅｄＬａｓｅｒＡｂｌａｔｉｏｎｏｆＴａｒｇｅｔ￥ＧｏｎｇｔａｎｇＷａｎｇ；ＸｉａｎｇｔａｉＷａｎｇ；ＢａｏｙｕａｎＭｉａｎ（Ｄｅｐａｒｔｍｅｎｔｏｆｐｈｙｓｉｃｓ，ＳｈａｎｄｏｎｇＮｏｒｍａｌＵｎｉ...

关键词： Al￣+ ion mean projected range laser ablation ambient gas effect.

On the Distribution of Integral Ideals and Hecke Grssencharacters

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Chinese Annals of Mathematics,Series B 2010年第3期31卷 385-392页

作者： Huixue LAO School of Mathematical Sciences Shandong Normal University Jinan 250014 China.

The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and G... 详细信息

关键词： Dedekind zeta-function Integral ideal Grossencharacters

Determination of reaction heat on the hydrolytic polymerization of chromium(Ⅲ) ion by microcalorimetric method

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Chinese Journal of Chemistry 1996年第3期14卷 286-288页

作者： YU, Xiu-Fang ZHANG, Hong-LinDepartment of Chemistry, Qufu normal university, Qufu, shandong 273165, chinaLU, Cheng-Xue SUN, Si-XiuDepartment of Chemistry, shandong university, jinan, shandong 250100, china Department of Chemistry Qufu Normal University Qufu Shandong 273165 China Department of Chemistry Shandong University Jinan Shandong 250100 China

Thermochemistry is the study of the energy changes which occur during a chemi-cal reaction. For example, in the hydrolytic polymerization of Cr, Cr[Cr（OH）],Cr[Cr（OH）]and Cr[Cr（OH）]were formed at concentration ra... 详细信息

关键词： Chromium(Ⅲ) hydrolytic polymerization reaction heat thermodynamical function