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On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3.1. Department of applied Mathematics, {2. {2. of Technology, {2. 100081, China 2. Department of Mathematics, Yunnan University, Kunming 650091, China 3. {2. of applied Mathematics, C Department of applied Mathematics Beijing Institute of Technology Beijing China Department of Mathematics Yunnan University Kunming China institute of applied Mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

A three-dimensional variational ocean data assimilation system:Scheme and preliminary results

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Science China Earth Sciences 2006年第11期49卷 1212-1222页

作者： ZHU Jiang1,2. ZHOU Guangqing1, YAN Changxiang1, FU Weiwei1 & YOU Xiaobao1,3.1. International Center for Climate and Environment Sciences, institute of Atmospheric Physics, Chinese Academy of Sciences,{2., China 2. Jiangsu Key Laboratory of Meteorological Disaster, Nanjing University of Information Science and Technology, Nanjing 2.0044, China 3. beijing institute of applied meteorology,{2., China 1. International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China 2. Jiangsu Key Laboratory of Meteorological Disaster Nanjing University of Information Science and Technology Nanjing 210044 China 3. beijing institute of applied meteorology Beijing 100029 China

A new 3.VAR-based Ocean Variational Analysis System (OVALS) is developed. OVALS is capable of assimilating in situ sea water temperature and salinity observations and satellite altimetry data. As a component of OVALS, a new variational scheme is proposed to assimilate the sea surface height data. This scheme considers both the vertical correlation of background errors and the nonlinear temperature-salinity relationship which is derived from the generalization of the linear balance constraints to the nonlinear in the 3.VAR. By this scheme, the model temperature and salinity fields are directly adjusted from the altimetry data. Additionally, OVALS can assimilate the temperature and salinity profiles from the ARGO floats which have been implemented in recent years and some temperature and salinity data such as from expendable bathythermograph, moored ocean buoys, etc. A 2.-year assimilation experiment is carried out by using OVALS and the Tropical Pacific circulation model. The results show that the assimilation system may effectively improve the estimations of temperature and salinity by assimilating all kinds of observations. Moreover, the root mean square errors of temperature and salinity in the upper depth less than 42. m reach 0.63. and 0.3. psu.

关键词： data assimilation, 3.VAR, sea surface height, ARGO floats.

A new DNA algorithm to solve graph coloring problem

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Progress in Natural Science:Materials International 2007年第6期17卷 733-738页

作者： Jiang Xingpeng1, Li Yin2. Meng Ya3.and Meng Dazhi2.1. National Laboratory of Pattern Recognition,institute of Automation, Chinese Academy of Sciences, {2. 100080, China 2. College of {2. Sciences, {2. University of Technology, beijing 10002., China 3. School of Science, {2. institute of Technology, {2. 100081, China) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China College of applied Sciences Beijing University of Technology Beijing 100022 China School of Science Beijing Institute of Technology Beijing 100081 China

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).

关键词： DNA computing NP-hard problem graph coloring problem.

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 Mathematics, beijing Normal University, beijing 100875, China 2. {2. of {3. Mathematics, Chinese Academy of Sciences, beijing 100080, China 3. {2. of Systems Science, Chi Department of Mathematics Beijing Normal University Beijing China institute of applied Mathematics 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.

Optimal reactions for the synthesis of superheavy nucleus ^(2.0)Hs

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Science China(Physics,Mechanics & Astronomy) 2006年第6期49卷 641-648页

作者： LIU Zuhua1,3.& BAO Jingdong1,2.1. Key Laboratory of Beam Technology and Material Modification of Ministry of Education, beijing Normal University, beijing 100875, China 2. Physics Department, beijing Normal University, beijing 100875, China 3. China institute of Atomic Energy, beijing 102.13. China Key Laboratory of Beam Technology Material Modification of Ministry of Education Beijing Normal University Beijing 100875 China Physics Department Beijing Normal University Beijing 100875 China China institute of Atomic Energy Beijing 102413 China

The superheavy nucleus 2.0Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 2.8Cm(2.Mg,4n)2.0Hs, 2.4Pu(3.Si,4n)2.0Hs, 2.0}U(3.S,4n)2.0Hs and 2.6Ra(48Ca,4n)2.0Hs using a two-parameter Smoluchowski equation. It is found from our results that 2.6Ra(48Ca,4n)2.0Hs and 2.0}U(3.S,4n)2.0Hs are two optimal reactions for the synthesis of the superheavy nucleus 2.0Hs due to their large negative Q-values.

关键词： diffused fusion barrier,Smoluchowski equation,superheavy nuclei.

A note on n-edge chromatic number

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Chinese Science Bulletin 1997年第23期42卷 1952-1954页

作者： SUN Liang and ZHANG Zhongfu1. Department of applied Mathematics, beijing{2. of Technology, beijing 100081, China 2.{2. of applied Mathematics, Lanzhou{2. of Railway, Lanzhou 73.070, China Department of applied Mathematics Beijing Institute of Technology Beijing 100081 China

ALL graphs appearing in this note are simple. A graph with p vertices and q edges will becalled a (p, q )-graph. The maximum degree of G is denoted by Δ(G).Let n≥2.be an integer. The n-edge chromatic number X_n (G) of a simple graph G is theminimum cardinality of a set of colors with which one can assign the colors to the edges of Gsuch that the edges on a path of length less than or equal to n receive different *** aim of this note is to explore the bounds for X’_n (G) and X’_n (G) + X’_n (G). It is

关键词： graph complement n-edge chromatic number.

Solving the input data in error correc-tion of optical fabrication by finite Fourier coefficient algorithm

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Science China(Technological Sciences) 2006年第1期49卷 50-60页

作者： CHENG Haobo1,2. SUN Guozheng3.& FENG Zhijing2.1. Department of Optical Engineering, beijing {2. of Technology, beijing 100081, China 2. Department of Precision Instruments and Mechanology, Tsinghua University, beijing 100084, China 3. China North Industries Group Corporation, beijing 100089, China 1. Department of Optical Engineering Beijing Institute of Technology Beijing 100081 China 2. Department of Precision Instruments and Mechanology Tsinghua University Beijing 100084 China 3. China North Industries Group Corporation Beijing 100089 China

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability nec-essary to perform precisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influ-ence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.

关键词： optical fabrication, computer controlled optical surfacing, free-form lens, finite Fourier coefficient, error correction.

Numerical simulation of topography effects on the “00.7” severe rainfall in beijing

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Progress in Natural Science:Materials International 2005年第9期15卷 818-826页

作者： ZHANG Chaolin1**, JI Chongping1, KUO Yinghwa2. FAN Shuiyong1, XUAN Chunyi3.and CHEN Min1(1. institute of Urban {2., China Meteorological Administration, {2. 100089, China 2. Mesoscale and Microscale {2. Division, National Center for Atmospheric Research, Boulder, CO 803.7-3.00, USA 3. {2. Meteorological Bureau, {2. 100089, China) institute of Urban meteorology China Meteorological Administration Beijing 100089 China. Mesoscale and Microscale meteorology Division National Center for Atmospheric Research Boulder CO 80307-3000 USA. beijing Meteorological Bureau Beijing 100089 China

In an effort to study the severe rainfall event of 4—5th July 2.00 in beijing (with 2.h accumulated precipitation of 2.0 mm), we perform numerical simulations to investigate this event using the MM5v3.6 model. The model is initialized with the MM5/WRF 3.VAR analysis, which incorporates the ground-based GPS precipitable water vapor, automatic and conventional meteorological observations in its assimilation step. For 2. h accumulated precipitation forecast, the threat scores are 0.72. 0.76, 0.67 and 0.63. for thresholds of 1, 5, 10, and 2. mm, respectively. Holding other factors unchanged, sensitivity experiments were conducted with different topographic resolutions of 110, 50 and 3.7 km to investigate the topographic effects on precipitation over the beijing area. In these sensitivity experiments, we attempt to preserve the realistic orographic distribution in the model topography under the condition of keeping the dynamic-thermodynamic consistency of the initial model atmosphere to the extent possible. Results indicate that the unique topographic distribution and variations in the beijing area play an important role in determining the location, distribution and intensity of heavy precipitation.

关键词： topography heavy rainfall 3.VAR ground-based GPS numerical simulation.

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,{2. University of Technology,{2. {3.,China 2. institute of applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,{2. 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. 62.3.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