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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, {3. 100080, China {2.,{3., beijing 10002., China 3. School of Science, {3. Institute of technology, {3. 100081, China) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China college of applied {2. 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.

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 {2.,{3. university of technology,{3. 10002.,China 2. Institute of applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of {2.,{3. 100080,China 3. Faculty of Administration,university of New Brunswick,P.O.Box 4400,Fredericton,NB E3. 5A3.Canada college of applied {2. 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

Simultaneous variable selection for heteroscedastic regression models

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Science China Mathematics 2011年第3期54卷 515-530页

作者： ZHANG ZhongZhan1 & WANG DaRong2.1college of applied {2.,{3., beijing 10012., China 2.he Pilot college,{3., beijing 101101, China 1. college of applied {2. Beijing University of Technology Beijing 100124 China2. The Pilot College Beijing University of Technology Beijing 101101 China

In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.

关键词： variable selection heteroscedastic regression models adjusted profile log-likelihood AIC BIC

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science China Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. college of applied {2.,{3. university of technology,{3. 10002.,China 2. Department of Mathematics,Hong Kong Baptist university,Hong Kong,China 1. college of applied {2. Beijing University of Technology 100022 Beijing China 2. Department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

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, beijing Institute of {2., beijing 100081, China 2. Department of Mathematics, Yunnan university, Kunming 650091, China 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.

Cu(Ⅱ) Potentiation of Alzheimer Aβ1-40 Cytotoxicity and Transition on its Secondary Structure

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Acta Biochimica et Biophysica Sinica 2006年第11期38卷 765-772页

作者： Xue-Ling DAI~1 Ya-Xuan SUN~2.Zhao-Feng JIANG~2. 1 college of Life Science,Capital Normal {3.,{2. 10003.,China 2.college of applied sciences and Humanities,{2. Union {3.,{2. 100083.China college of Life Science Capital Normal UniversityBeijing 100037 China college of applied {2. and Humanities Beijing Union UniversityBeijing 100083 China

Mounting evidence has shown that dyshomeostasis of the redox-active biometals such as Cuand Fe can lead to oxidative stress,which plays a key role in the neuropathology of Alzheimer's disease（AD）.Here we demonstrate that with the formation of Cu（Ⅱ）·Aβ1-40 complexes,copper markedly potentiatesthe neurotoxicity exhibited by β-amyloid peptide （Aβ）.A greater amount of hydrogen peroxide was releasedwhen Cu（Ⅱ）·Aβ1-40 complexes was added to the xanthine oxidase/xanthine system detected by potassiumiodide *** bound to Aβ1-40 was observed by electron paramagnetic resonance（EPR） *** dichroism （CD） studies indicated that copper chelation could cause a structuraltransition of Aβ.The addition of copper to Aβ introduced an increase on β-sheet as well as α-helix,whichmay be responsible for the aggregation of Aβ.We hypothesized that Aβ aggregation induced by copper maybe responsible for local injury in *** interaction between Cu2.and Aβ also provides a possible mechanismfor the enrichment of metal ions in amyloid plaques in the AD brain.

关键词： Alzheimer’s disease Cu(Ⅱ)·Aβ1-40 complex neuron injury Aβ secondary structure

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2.and Cheng Caozong1(1. college of applied {2.,{3., beijing 10002., China 2. Center for Nonlinear Studies, Institute of applied Physics and Computational Mathematics, beijing 100088, China) college of applied {2. Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

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 {3. 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.

The mathematical model of wetting angle of heterogeneous nucleation

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Science China(Technological sciences) 2004年第4期47卷 391-397页

作者： HUANG Cheng1, SONG Bo1, MAO Jinghong2.& ZHAO Pei3.1. School of Metallurgical and Ecological Engineering, university of Science and technology {2., {2. 100083. China 2. School of Material Science, university of Science and technology {2., {2. 100083. China 3. Central Iron and Steel Research Institute, {2. 100081, China 1. School of Metallurgical and Ecological Engineering University of Science and Technology Beijing 100083 Beijing China 2. School of Material Science University of Science and Technology Beijing 100083 Beijing China 3. Central Iron and Steel Research Institute 100081 Beijing China

The heterogeneous nucleation has been analyzed in terms of the thermodynamic theory, and the mathematical model of wetting angle of heterogeneous nucleation has been developed based on the dynamic requirements of hetero- and homogeneous nucleation. With the wetting angel model, the wetting angles of different catalysts in liquid iron have been calculated. The result shows that the wetting angle of most catalysts is smaller than 40, and the value of f() is far less than 1. The wetting angles of TiN, TiC and RE2.3.are smaller, while the wetting angle of MnO is bigger among the ordinary nucleation catalysts. The wetting angles calculated by this model are in agreement with the results of other research work.

关键词： heterogeneous nucleation, mathematical model, wetting angle, undercooling.