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Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

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Chinese Annals of mathematics,Series B 2011年第5期32卷 771-780页

作者： Yi ZHOU 11 key laboratory of mathematics for Nonlinear Sciences,Ministry of Education,{3. Shanghai key laboratory for Contemporary applied mathematics School of Mathematical Sciences,Fudan University,Shanghai 20043.,{3.. key laboratory of mathematics for Nonlinear Sciences Ministry of Education China Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic *** the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in *** ***.,Vol.169,2003.pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

关键词： Cauchy problem Global classical solution Partially dissipativequasilinear hyperbolic system

Prediction of Tumor Outcome Based on Gene Expression Data

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Wuhan University Journal of Natural Sciences 2004年第2期9卷 177-182页

作者： Liu Juan 1,2, Hitoshi Iba 3.1. School of Computer, Wuhan University, Wuhan 43.072, hubei, china 2. State key {3. of Software Engineering, Wuhan 43.072, hubei, china 3. Department of Frontier Informatics, University of Tokyo, Tokyo 113.8656, Japan Wuhan University School of Computer Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) State key laboratory of Software Engineering Wuhan Hubei China (GRID:grid.49470.3e) University of Tokyo Department of Frontier Informatics Tokyo Japan (GRID:grid.26999.3d) (ISNI:***)

Gene expression microarray data can be used to classify tumor types. We proposed a new procedure to classify human tumor samples based on microarray gene expressions by using a hybrid supervised learning method called MOEA+WV (Multi-Objective Evolutionary Algorithm+Weighted Voting). MOEA is used to search for a relatively few subsets of informative genes from the high-dimensional gene space, and WV is used as a classification tool. This new method has been applied to predicate the subtypes of lymphoma and outcomes of medulloblastoma. The results are relatively accurate and meaningful compared to those from other methods. key words bioinformatics - tumor classification - Pareto optimization - MOEA CLC number Q 786 - TP 181 Foundation item: Supported by the National Natural Science Foundation of china (603.1009), the Foundation of Young Scholars of Ministry of Education of china (150118) and Chenguang Project of Wuhan City (211121009).Biography: Liu Juan (1970-), female, Associate Professor, Postdoctoral, research direction: bioinformatics, data mining, machine learning.

关键词： bioinformatics tumor classification Pareto optimization MOEA

Convergence analysis of the adaptive finite element method with the red-green refinement

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Science china mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3., HU Jun 2,? & SHI ZhongCi 1 1 State key laboratory of Scientific and Engineering Computing, Institute of Computational mathematics and Scientific/Engineering Computing, Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, china 2.key laboratory of mathematics and applied mathematics (Peking University), Ministry of Education and School of Mathematical Sciences, Peking University, Beijing 100871, china 3.Graduate University of Chinese Academy of Sciences, Beijing 100190, china 1. State key laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

A novel method for evaluating and improving the 1H-MRSI glioma data quality

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Progress in Natural Science:Materials International 2005年第8期15卷 765-768页

作者： YUAN Kehong 1,2, LU Hongyu2, BAO Shanglian2*, CHEN Qiansheng1, LI Shaowu3.and DUAN Chaijie2(1. key laboratory of Pure and applied {3., School of Mathematical Sciences, Beijing 100871, china 2. The Research Center for Tumor Diagnosis and Therapeutical Physics & the Beijing key laboratory of Medical Physics and Engineering, Peking University, Beijing 100871, china 3. The Tian Tan Hospital, Beijing 100050, china) key laboratory of Pure and applied {3. School of Mathematical Sciences Beijing 100871 China. The Research Center for Tumor Diagnosis and Therapeutical Physics & the Beijing key laboratory of Medical Physics and Engineering Peking University Beijing 100871 China. The Tian Tan Hospital Beijing 100050 China

Metabolic information obtained by proton magnetic resonance spectroscopic imaging (1H-MRSI) has been approved to be a powerful tool to identify either benign or malignant glioma, as well as to confirm the tumor level. However, 1H-MRSI data are affected by various factors, such as the thermal noise, eddy currents, susceptibility artifacts, and rigid body motion. To get accurate quantitative metabolic information, the key problem is to assess the 1H-MRSI data quality. In this paper, we introduce a new evaluating system to filter the data, and a new method, called wavelet denoising method, to improve the data quality under the evaluating system. Experimental results on 1H-MRSI glioma data demonstrate that preprocessing is prerequisite and the proposed algorithm with evaluating system is effective.

关键词： 1H-MRSI evaluating system glioma data quality wavelet denoising

Gene flow from transgenic oilseed rape (Brassica napus L.) to cruciferous weeds under mentor pollen inducement

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Progress in Natural Science:Materials International 2007年第11期17卷 1284-1289页

作者： Zhao Xiangxiang1,2, Luo Yuming1, Lu Weiping2, Qi Cunkou3. Pu Huiming3.and Wang Youping2(1. Biotechnology key laboratory of Eco-agriculture in Hongze Lake Region, Jiangsu province, Huaiyin Normal College, Huai'an 223.01, {3. 2. Jiangsu Provincial key laboratory of Crop Genetics and Physiology, Yangzhou University, Yangzhou 225009, {3. 3. Institute of Industrial Crops, Jiangsu Academy of Agricultural Sciences, Nanjing 210014, {3.) Biotechnology key laboratory of Eco-agriculture in Hongze Lake Region Jiangsu Province Huaiyin Normal College Huai'an 223001 China Jiangsu Provincial key laboratory of Crop Genetics and Physiology Yangzhou University Yangzhou 225009 China Institute of Industrial Crops Jiangsu Academy of Agricultural Sciences Nanjing 210014 China

The alien gene flow between genetically modified glyphosate-resistant rapeseed variety Q3.(Brassica napus L.) and four cruciferous weeds was studied under mentor pollen inducement. The results showed that when Thlaspi arvense L., Capsella bursa-pastoris (L.) Medic, Cardamine hirsuta L. and Rorippa palustris (L.) Besser were pollinated with mentor pollen, the mixed Q3.and the weed, pollen grains aggregated largely and germinated quickly, and the numbers of pollen tubes penetrating into the style and the ovary were greatly increased as compared with corresponding self-pollination groups. Twenty four to forty eight hours after pollination, several pollen tubes were observed to penetrate into the ovule via micropyle in each mentor combination. However, when the mentor progenies were analyzed by PCR, all of them showed negative for the Q3.herbicide-resistant gene. Collectively, these results indicated that crossing between T. arvense, C. bursa-pastoris, C. hirsuta, R. palustris (as female) and Q3.(as male) was highly incompatible and the herbicide-resistant gene could not flow from Q3.to these four weeds.

关键词： herbicide-resistant rapeseed cruciferous weeds mentor pollination aniline blue fluorescence gene flow

A Series of Soliton-like and Double-like Periodic Solutions of a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

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Communications in Theoretical Physics 2004年第11期42卷 655-660页

作者： CHEN Yong,~(1,3.4, WANG Qi~(2,4) LI Biao~(2,4) ~1Department of mathematics,Ningbo University,Ningbo 3.5211,china ~2Department of applied mathematics,Dalian University of Technology,Dalian 116024,china ~3.epartment of Physics,Shanghai Jiao Tong University,Shanghai 20003.,china ~4key laboratory of mathematics Mechanization~ the Chinese Academy of Sciences,Beijing 100080,china key laboratory of mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China

We generalize the algebraic method presented by Fan [***.A:***.3. (2003. 7009)] to uniformlyconstruct a series of soliton-like solutions and double-llke periodic solutions for nonlinear partial differential equations(NPDE),As an application of the method,we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equa-tion and successfully construct new and more general solutions including a series of nontraveling wave and coefficientfunctions’ soliton-like solutions,double-like periodic and trigonometric-like function solutions.

关键词： symbolic computation soliton-like solution Weierstrass and Jacobi elliptic functions periodic solution

A new family of windows——convolution windows and their applications

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Science china(Technological Sciences) 2005年第4期48卷 468-480页

作者： ZHANG Jieqiu1,2, LIANG Changhong1 & CHEN Yanpu3.1. Department of applied Math. & Phys., College of Science, Airforce Engineering University, Xi’an 710051, china 2. National key {3. of Antennas and Microwave Technology, Xidian University, Xi’an 710071, china 3. Computer Center, Xi’an Communication College, Xi’an 710106, china 1. Department of applied Math. & Phys. College of Science Airforce Engineering University 710051 Xi’an China 2. National key laboratory of Antennas and Microwave Technology Xidian University 710071 Xi’an China 3. Computer Center Xi’an Communication College 710106 Xi’an China

A new family of windows is constructed by convolutions via a few rectangular windows with same time width and is thus referred to as convolution windows. The expressions of the second-order up to the eighth-order convolution windows in both the time and frequency domains are derived. Their applications in high accuracy harmonic analysis of periodic signals are investigated. Comparisons between the proposed windows and some known windows with the same width shows that, when the synchronous deviation of data sampling is slight, the proposed ones have the least effect of spectral leakage. Therefore, the new windows are well suited for high accuracy harmonic analysis and parameter estimation for periodic signals. The error analysis and computer simulations show that the estimation errors, corresponding to frequency, amplitude and phase of every harmonic component of a signal, are proportional to the pth power of the relative frequency deviation in case of the pth-order convolution window is applied to windowing signal of approximately p cycles. By introducing real time adjustment in sampling interval, the proposed algorithm can adaptively trace signal frequency and lead to less sampling synchronous deviation. The proposed approach has the advantages of easy implementation and high measure precision and can be used in harmonic analysis of quasi-periodic signals whose fundamental frequency drifts slowly with time.

关键词： signal processing harmonic analysis window function convolution window synchronous error spoctral leakage

Simulation study of phase retrieval for hard X-ray in-line phase contrast imaging

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 450-458页

作者： YU Bin1,2, PENG Xiang1,2, TIAN Jindong1, NIU Hanben1, DIAO Luhong3.& LI Hua3.1. key laboratory of Optoelectronic Devices and Systems of Ministry of Education, Institute of Optoelec- tronics, Shenzhen University, Shenzhen 518060, china 2. State key laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 3.0072,china 3. key laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100080,china 1. key laboratory of Optoelectronic Devices and Systems of Ministry of Education Institute of Optoelectronics Shenzhen University 518060 Shenzhen China 2. State key laboratory of Precision Measuring Technology and Instruments Tianjin University 300072 Tianjin China 3. key laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences 100080 Beijing China

Two algorithms for the phase retrieval of hard X-ray in-line phase contrast imaging are presented. One is referred to as Iterative Angular Spectrum Algorithm (IASA) and the other is a hybrid algorithm that combines IASA with TIE (transport of intensity equation). The calculations of the algorithms are based on free space propagation of the angular spectrum. The new approaches are demonstrated with numerical simulations. Comparisons with other phase retrieval algorithms are also performed. It is shown that the phase retrieval method combining the IASA and TIE is a promising technique for the application of hard X-ray phase contrast imaging.

关键词： X-ray optics, phase contrast imaging, phase retrieval, angular spectrum, hard X-ray.

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear Mathematical Modeling and Methods laboratory Shanghai key laboratory for Contem- porary {3. mathematics School of Mathematical Sciences, Fudan University, Shanghai 20043., china. 2 School of Mathematical Sciences, Fudan University, Shanghai 20043., china Department of mathematics, North University of china, Taiyuan 03.051, china. Nonlinear Mathematical Modeling and Methods laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan