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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. Institute of Technology, {2. 100081,{3. 2. Department of Mathematics, Yunnan University, Kunming 650091,{3. 3. Institute 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, beijing 10002.,{2. 2. Jiangsu Key Laboratory of Meteorological Disaster, Nanjing University of Information Science and Technology, Nanjing 2.0044,{2. 3. {3. Institute of applied meteorology, beijing 10002.,{2. 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 {2. 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, beijing 100080,{2. 2. College of applied Sciences, beijing University of Technology, beijing 10002.,{2. 3. School of Science, beijing Institute of Technology, beijing 100081,{2.) 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. Institute of {3. Mathematics, Chinese Academy of Sciences, beijing 100080, china 3. Institute 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.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of Mathematics, beijing Normal University, beijing 100875,{2. 2. Institute of {3. Physics and Computational Mathematics, beijing 100080,{2. 1. Department of Mathematics Beijing Normal University Beijing 100875 China 2. Institute of applied Physics and Computational Mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

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

Prediction method for October 2.03.solar storm

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Science china(Technological Sciences) 2006年第5期49卷 629-640页

作者： XIE Yanqiong1, 2. 3. WEI Fengsi1, FENG Xueshang1 & ZHONG Dingkun1, 2.1. State Key Laboratory of Space Weather, Center for Space Science and applied Research, Chinese Academy of Sciences, {2. 100080, china 2. Graduate School, Chinese Academy of Sciences, {2. 10003., china 3. Institute of meteorology, PLA University of Science and Technology, Nanjing 2.1101, china State Key Laboratory of Space Weather Center for Space Science applied Research Chinese Academy of Sciences Beijing 100080 China Graduate School Chinese Academy of Sciences Beijing 100039 China Institute of meteorology PLA University of Science Technology Nanjing 211101 China

Aiming at two intense shock events on October 2. and 2., 2.03. this paper presents a two-step method, which combines synoptic analysis of space weather ——“observing” and quantitative prediction ——“palpating”, and then uses it to test predictions. In the first step of “observing”, on the basis of observations of the solar source surface magnetic field, interplanetary scintillation (IPS) and ACE spacecraft, we find that the propagation of the shocks is asymmetric relative to the normal direction of their solar sources, and the Earth is located near the direction of the fastest speed and the greatest energy of the shocks. As the two fast ejection shock events, the fast explosion of coronal mass of the extremely high temperature, the strong magnetic field, and the high speed background solar wind are also helpful to their rapid propagation. In the second step of “palpating”, we adopt a new membership function of the fast shock events for the ISF method. The predicted results show that for the onset time of the geomagnetic disturbance, the relative errors between the observational and the predicted results are 1.8% and 6.7%; and for the magnetic disturbance magnitude, the relative errors are 4.1% and 3.1%, re- spectively. Furthermore, the comparison among the predicted results of our two-step method with those of five other prevailing methods shows that the two-step method is advantageous. The results tell us that understanding the physical features of shock propagation thoroughly is of great importance in improving the prediction precision.

关键词： solar storm, interplanetary shock, interplanetary scintillation, two-step method, ISF method.

A tentative study for the prediction of the CME related geomagnetic storm intensity and its transit time

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Science china(Technological Sciences) 2005年第6期48卷 648-668页

作者： ZHAO Xinhua1,2.& FENG Xueshang1,3.1. SIGMA Weather Group, Key Laboratory of Space Weather, Center for Space Science and applied Re-search, Chinese Academy of Sciences, {2. 100080, china 2. Graduate School of the Chinese Academy of Sciences, {2. 10003., china 3. School of Geophysics and Geoinformation Systems, china University of Geosciences, {2. 100083. china 1. SIGMA Weather Group Key Laboratory of Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences 100080 Beijing China 2. Graduate School of the Chinese Academy of Sciences 100039 Beijing China 3. School of Geophysics and Geoinformation Systems China University of Geosciences 100083 Beijing China

Using 80 CME-ICME events during 1997.1―2.02.9, based on the eruptive source locations of CMEs and solar magnetic field observation at the photosphere, a current sheet magnetic coordinate (CMC) system is established in order to study the propagation of CME and its geoeffectiveness. In context of this coordinate system, the effect of the eruptive source location and the form of heliospheric current sheet (HCS) at the eruptive time of CME on the geomagnetic storm intensity caused by CME and the CME’s transit time at the Earth is investigated in detail. Our preliminary conclusions are: 1) The geomagnetic disturbances caused by CMEs tend to have the so-called “same side-opposite side effect”, i.e. CMEs erupt from the same side of the HCS as the earth would be more likely to arrive at the earth and the geomagnetic disturbances associated with them tend to be of larger magnitude, while CMEs erupting from the opposite side would arrive at the earth with less probability and the corresponding geomagnetic disturbance magnitudes would be relatively weaker. 2. The angular separation between the earth and the HCS affect the corresponding disturbance intensity. That is, when our earth is located near the HCS, adverse space weather events occur most probably. 3. The erupting location of the CME and its nearby form of HCS will also affect its arrival time at the earth. According to these conclusions, in this context of CMC coordinate we arrive at new prediction method for estimating the geomagnetic storm intensity (Dstmin) caused by CMEs and their transit times. The application of the empirical model for 80 CME-ICME events shows that the relative error of Dst is within 3.% for 59% events with Dstmin≤?50 nT, while the averaged absolute error of transit time is lower than 10 h for all events.

关键词： coronal mass ejections, current sheet magnetic coordinate system, geomagnetic storm intensity, transit time, prediction method.

Integrated precise orbit determination of Shenzhou IV unmanned spacecraft

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Science china(Technological Sciences) 2004年第5期47卷 518-525页

作者： L Congmin1,2. GU Yidong3. LIN Baojun3.& GUO Jiong3.1. Center for Space Science and applied Research, Chinese Academy of Sciences, beijing 100080, china 2. Graduate School of the Chinese Academy of Sciences, beijing 10003., china 3. General Establishment of Space Science and Application, Chinese Academy of Sciences, beijing 100080, china Correspondence should be addressed to L Congmin 1. Center for Space Science and applied Research Chinese Academy of Sciences 100080 Beijing China 2. Graduate School of the Chinese Academy of Sciences 100039 Beijing China 3. General Establishment of Space Science and Application Chinese Academy of Sciences 100080 Beijing China

Considering the characteristic orbit of Shenzhou IV spacecraft and the advantages and disadvantages of several types of domestic orbit measurements, a scheme of IPOD is determined, which uses GPS, SLR and USB observation data jointly plus precise ionosphere corrections to GPS observation data. IPOD system and mathematic models of OD are introduced. The results of different joint OD are analyzed using true observation data, and show that radial accuracy is better than 2.m.

关键词： Shenzhou IV unmanned spacecraft integrated precise orbit determination GPS SLR USB.