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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

Boundedness for commutators of fractional Hardy operators on Herz spaces

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Progress in Natural Science:Materials International 2007年第1期17卷 20-25页

作者： FU Zunwei, LIU Zongguang and LU Shanzhen ( school of mathematical sciences, Beijing Normal university, Beijing 100875, china Department of Mathematics, Linyi Normal university, Linyi 276005, china Department of Mathematics, china university of Mining and Technology, Beijing 100083, china) [a]school of mathematical sciences Beijing Normal University Beijing China [b]Departhent of Mathematics Linyi Normal University Linyi China [c]Departhent of Mathematics China University of Mining and Technology Beijing China

Some boundedness results are established for commutators generated by classical fractional Hardy operators and one-sided CMO functions on the homogeneous Herz spaces, which extends some known results.

关键词： fractional Hardy operator Hardy’s integral inequality commutator one-sided CMO function homogeneous Herz space.

Problems in wavelet analysis of hydrologic series and some suggestions on improvement

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Progress in Natural Science:Materials International 2007年第1期17卷 80-86页

作者： WANG Hongrui, YE Letian, LIU Changming, YANG Chi and LIU Peng ( College of Water sciences, Beijing Normal university, Beijing 100875, china Key Laboratory for Water and Sediment sciences, Ministry of Education, Beijing 100875, china school of mathematical sciences, Peking university, Beijing 100089, china College of Engineering sciences, university of Region, Canada) [a]College of Water sciences Beijing Normal University Beijing China [b]Key Laboratory for Water and Sediment sciences Ministry of Education Beijing China [c]school of mathematical sciences Peking University Beijing China [d]College of Engineering sciences University of Region Canada

Applying the wavelet theory and methods to investigate the hydrologic processes such as precipitation and runoff is a hot field. However, several aspects in research are usually ignored: the effect of admissible condition of wavelet functions and the disturbance of noises for the detection of periods, the effect of the length of a hydrologic time-series on the final result, and the choice between the anomaly and the original time series for wavelet analysis. In this paper, these issues are fully discussed. Precipitation data from Lanzhou Precipitation Station are taken for case study. The result indicates that in the wavelet analysis of hydrologic series, denoise methods should be used to eliminate the influence of noises. The MexHat wavelet function satisfies the admissible condition, which ensures that the periodic properties of hydrologic processes can be well represented by using the MexHat wavelet for decomposition. The affected range of hydro-logic series which should be discarded before analysis is given. It is also suggested that the anomaly series should be used to highlight the actual undulation of the hydrologic series.

关键词： wavelet analysis hydrologic process admissible condition noise period.

On several families of elliptic curves with arbitrary large Selmer groups

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Science china Mathematics 2010年第9期53卷 2329-2340页

作者： LI Fei & QIU DeRong school of mathematical sciences,Institute of Mathematics and Interdisciplinary Science,Capital Normal university,Beijing 100048,china 1. school of mathematical sciences Institute of Mathematics and Interdisciplinary Science Capital Normal University Beijing 100048 China

In this paper,we calculate the ()-Selmer groups S()(E/Q) and S()(E/Q) of elliptic curves y2 = x(x + εpD)(x + εqD) via the descent *** particular,we show that the Selmer groups of several families of such ell... 详细信息

关键词： elliptic curve Selmer group Mordell-Weil group

Optimal mixed-level supersaturated design with general number of runs

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Optimal mixed-level supersaturated design with general numbe...

VARIABILITY SETS AND HAMILTON SEQUENCES

2007均匀试验设计学术交流会

作者： Jie Chen,Min-Qian Liu Department of Statistics,school of mathematical sciences and LPMC,nankai university,tianjin 300071,china

Supersaturated design has received much interest because of its potentialin factor screening *** studies mainly focused on *** paper considers supersaturated designs with general numbersof *** lower bounds of theχ2 proposed by Yamada and Lin(1999)andE(fNOD)proposed by Fang,Lin and Liu(2003b)are obtained along with thesu?cient and necessary conditions for achieving them ***-more some construction methods for mixed-level supersaturated designs withgeneral number of runs are proposed.

关键词： Balanced design Coincidence number Orthogonal array Super-saturated design

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 543-550页

作者： SUN NA WU SHENGJIAN Key Laboratory of Pure and Applied Mathematics School of Mathematical Sciences Peking University Beijing 100871 China.

This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.

关键词： Quasiconformal mapping Point shift differentials Hamilton sequence Extremal mapping

Convergence rates for reversible Markov chains without the assumption of nonnegative definite matrices

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Science china Mathematics 2010年第8期53卷 1979-1988页

作者： MAO Yong-Hua school of mathematical sciences,Beijing Normal university,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,china 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China

Explicit convergence rates in geometric and strong ergodicity for denumerable discrete time Markov chains with general reversible transition matrices are obtained in terms of the geometric moments or uniform moments of the hitting times to a fixed *** way by Lyapunov's drift conditions is also used to derive these convergence *** a typical example,the discrete time birth-death process(random walk) is studied and the explicit criteria for geometric ergodicity are presented.

关键词： Markov chain spectral theory convergence rate geometric ergodicity strong ergodicity Lyapunov’s condition

Development and application of ergodicity model with FRCM and FLAR for hydrological process

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Science china(Technological sciences) 2009年第2期52卷 379-386页

作者： WANG HongRui1, FENG QiLei2, LIN Xin3 & ZENG WenYi4 1 College of Water Science, Key Laboratory for Water and Sediment sciences of the Ministry of Education, Beijing Normal university, Beijing 100875, china 2 school of Science, Beijing Institute of Education, Beijing 100011, china 3 school of mathematical sciences, Beijing Normal university, Beijing 100875, china 4 College of Information Science and Technology, Beijing Normal university, Beijing 100875, china 1. College of Water Science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing 100875 China 2. school of Science Beijing Institute of Education Beijing 100011 China 3. school of mathematical sciences Beijing Normal University Beijing 100875 China 4. College of Information Science and Technology Beijing Normal University Beijing 100875 China

In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951―2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.

关键词： hydrological process ergodic autocorrelogram fuzzy-rough c-means clustering fuzzy least absolute regression

Proper holomorphic self-maps of smooth bounded Reinhardt domains in C^2

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Science china Mathematics 2008年第1期51卷 93-100页

作者： CHEN ZhiHua~1 & PAN YiFei~(2,3+) 1 Department of Mathematics, Tongji university, Shanghai 200092, china 2 Department of mathematical sciences, Indiana university-Purdue university Fort Wayne, Fort Wayne, IN 46805-1499, USA 3 school of Mathematics and Information sciences, Jiangxi Normal university, Nanchang 330022, china Department of Mathematics Tongji University Shanghai China Department of mathematical sciences Indiana University-Purdue University Fort Wayne Fort Wayne USA school of Mathematics and Information sciences Jiangxi Normal University Nanchang China

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in C^2 is an automorphism.

关键词： Reinhardt domain proper holomorphic maps