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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. {1. of mathematics, Fudan University, Shanghai 20043., china 2. Department of mathematics,Sichuan Union University, chengdu 61.064, china 3. Department of mathematics, Nanchang University, Nanchang 3. nstitute of Mathemalics Fudan University Shanghai China Department of mathematics Sichuan Union University Chengdu China Department of mathematics 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.

A trust region algorithm for bilevel programing problems

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chinese Science Bulletin 1998年第10期43卷 820-824页

作者： LIU Guoshan 1. HAN Jiye 2 and WANG Shouyang 3.1. Department of {1., Beijing Normal University, Beijing 1.0875, china 2. institute of Applied {1., chinese Academy of Sciences, Beijing 1.0080, china 3. institute of Systems Science, chi Department of mathematics Beijing Normal University Beijing China institute of Applied {1. Chinese Academy of Sciences Beijing China institute of Systems Science Chinese Academy of Sciences Beijing China

A trust region algorithm is proposed for solving bilevel programming problems where the lower level programming problem is a strongly convex programming problem with linear constraints. This algorithm is based on a tr... 详细信息

关键词： bilevel programming problem trust region algorithm global convergence.

Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1. XIAO Hongying2* and cHEN Qiuhui{1.1. Department of mathematics, Beijing Jiaotong University, Beijing 1.0044, china 2. {{1. of mathematics, Academy of mathematics and System Sciences, chinese Academy of Sciences, Beijing 1.0080, china {1. Department of Scientific computing and computer Applications, Zhongshan University, Guangzhou 51.275, china) Department of mathematics Beijing Jiaotong University Beijing 100044 China. institute of {1. Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. Department of Scientific computing and computer Applications Zhongshan University Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

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 {1. and Statistics, Wuhan University, Wuhan 43.072, Hubei, china 2. School of {1. and computer, Ningxia University, Yinchuan 750021. Ningxia, china 3. Department of {1., Hubei institute for Nationalities, Enshi 445000, Hubei, china Wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningxia University School of Mathematics and Computer Yinchuan Ningxia China (GRID:grid.260987.2) (ISNI:***) Wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Hubei institute for Nationalities Department of Mathematies Enshi Hubei China (GRID:grid.34418.3a) (ISNI:***)

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

The dynamical properties of Rydberg hydrogen atom near a metal surface

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Science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 667-675页

作者： GE Meihua1. ZHANG Yanhui1. WANG Dehua2, DU Mengli3.& LIN Shenglu1.1.{1.ollege of Physics and Electronics, Shandong Normal University, Jinan 25001.,{1.hina 2. Department of mathematics and Physics, Shandong {3. of Architecture and Engineering, Jinan 25001.,{1.hina 3. {3. of Theoretical Physics,{1.hinese Academy of Sciences, Beijing 1.0080,{1.hina 1. college of Physics and Electronics Shandong Normal University 250014 Jinan China 2. Department of mathematics and Physics Shandong Institute of Architecture and Engineering 250014 Jinan China 3. {1. of Theoretical Physics Chinese Academy of Sciences 100080 Beijing China

The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number as n = 20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distance d. When d is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. When d becomes smaller, there exists a critical value dc. For d > dc, the system is near-integrable and the motion is regular. While chaotic motion appears for d c, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.

关键词： Rydberg hydrogen atom, van der Waals interaction, Poincaré surface of section, closed orbit theory, chaos.

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

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Science china {1. 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1.HAN Jiye~2 & DU Dongle~3.1.{1.ollege of Applied Sciences,Beijing University of Technology,Beijing 1.0022,china 2. institute of Applied mathematics,Academy of mathematics and Systems Science,chinese Academy of Sciences,Beijing 1.0080,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 {1. 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. 624{1.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

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. {1. of mathematics, Shaanxi Normal University, Xi’an 71.062, china 2. School of Sciences, Lanzhou University of Technology, Lanzhou 73.050, china 3. Research center for Science, Xi’an Jiaotong University, Xi’an 71.049, china 1. institute of {1. Shaanxi Normal University Xi’an 710062 China 2. School of Sciences Lanzhou University of Technology Lanzhou 730050 China 3. Research{1.enter for Science Xi’an Jiaotong University Xi’an 710049 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.

^(40)Ar/^(3.)Ar dating of shear deformation of the Xianshuihe fault zone in west Sichuan and its tectonic significance

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Science china Earth Sciences 2004年第9期47卷 794-803页

作者： ZHANG Yueqiao1. cHEN Wen2, {1.& YANG Nong1.1. institute of Geomechanics, chinese Academy of Geological Sciences, Beijing 1.0081. china 2. institute of Geology, chinese Academy of Geological Sciences, Beijing 1.00{1., china {1. institute of Geology and Geophysics, chinese Academy of Sciences, Beijing 1.0029, china institute of Geomechanics Chinese Academy of Geological Sciences Beijing 100081 China institute of Geology Chinese Academy of Geological Sciences Beijing 100037 China institute of Geology and Geophysics Chinese Academy of Sciences Beijing 100029 China

Based on field geological survey, structural measurements and classical Ar/Ar dating of mica, biotite and K-feldspar, we obtain cooling ages for Miocene left-lateral shear along the Xianshuihe fault zone. The results document two thermal events during the sinistral shear. The early event (1.-1. Ma) corresponds to rapid cooling of the Zheduoshan granitic massif from above 700℃ to below 3.0℃. The late event (5-3.5 Ma) corresponds to cooling of granites intruded along the eastern side of the fault zone. These dating results provide important thermochronological constraint on the timing of late cenozoic eastward extrusion of the chuan-Dian Block in the SE Tibetan margin.

关键词： Xianshuihe fault zone, Zheduoshan granitic massif, sinistral shear deformation, 40Ar/3.Ar dating, late cenozoic.

critical slope gradient for compulsory abandonment of farmland on the hilly Loess Plateau

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chinese Science Bulletin 1998年第5期43卷 409-412页

作者： TANG Keli+1. ZHANG Keli 1.2 and LEI Aling 1.3.1. {1. of Soil and Water conservation, chinese Academy of Sciences, Yangling 71.1.0, china 2. Department of Hydraulic Engineering, Tsinghua University, Beijing 1.0084, china 3. Water Resources c institute of Soil and Water{1.onservation Chinese Academy of Sciences Yangling China Department of Hydraulic Engineering Tsinghua University Beijing China Water Resources conservation Bureau of Yangtze River Ministry of Water Resources Wuhan China

Scientific evidence for the upper limit of farmland is proposed. Shallow gully erosion is one of erosion types distributed extensively on sloping farmland in the hilly regions of the Loess Plateau. Field observation and aerial photos interpretation, as well as laboratory experiments show that the shallow gully erosion occurring on the steeper farmland in the hilly regions of the Loess Plateau is an important factor leading to intensive erosion on slope, because of its extensive distribution and intensive runoff collection. The data on the formation, development and distribution of shallow gullies on sloping farmland indicate that critical slope gradient for shallow gully initiation ranges from 1. to 20 degrees with an average of 1..2 degrees. Therefore, it is suggested that critical slope gradient for compulsory abandonment of farmland on the hilly Loess Plateau should be kept within the critical slope gradient for shallow gully initiation to prevent shallow gully formation in order to control soil loss more effectively. But as the first step, the cultivation on the slopes with slope larger than 25 degrees where the maximum erosion occurs should be strictly forbidden.

关键词： hilly region of Loess Plateau upper limitation for farmland shallow gully erosion erosion dynamic.