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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 College of Water Science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing China School of Science Beijing Institute of Education Beijing China School of Mathematical Sciences Beijing Normal University Beijing China College of Information Science and Technology Beijing Normal University Beijing 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

Functional central limit theorem for super α-stable processes

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Science china Mathematics 2004年第6期47卷 874-881页

作者： HONG WenmingDepartment of Mathematics, beijing normal University, beijing 100875, china Department of Mathematics Beijing Normal University Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α 2α (0 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d 2α, the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

On asymptotics of t-type regression estimation in multiple linear model

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Science china Mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of Mathematics, beijing normal University, beijing 100875, china Department of Mathematics Beijing Normal University Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 375-388页

作者： ZHOU XIANYIN(Depatment of Mathematics, beijing normal University beijing 100875, china) Department of Mathematics Beijing Normal University Beijing 100875 China

It is proved that φ(s) = s2 log |logs| is the correct function to give the Hausdorff measureof a sample path of the Westwater process.

关键词： Hausdorff measure Wiener process Westwater process Sojourn time

Quasi-critical ring of a primitive ring with nonzero socle

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Chinese Science Bulletin 1997年第3期42卷 189-192页

作者： JIANG ZimeiDepartment of Mathematics, beijing normal University, beijing 100875, china Department of Mathematics Beijing Normal University Beijing China

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠{0} if and only if there is a pair of dual vector spaces (M,M’) over a division ring ... 详细信息

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠2 if and only if there is a pair of dual vector spaces (M,M’) over a division ring Δ such that S=F(M, M’)(?) R(?)(?)(M, M’), where (?)(M, M’)-{ω∈Ω|ωM’(?)M’, Ω is the complete ring of linear transformations of M over Δ}, F(M, M’) is the set of all linear transformations of (?)(M, M’) of finite rank. After that, some people reproved this theorem by using different methods such as those in refs. [2, 3]. In

关键词： primitive ring socle conjugate space total subspace of conjugate space.

Cytotoxicity, apoptosis induction, and mitotic arrest by a novel podophyllotoxin glucoside, 4.PG, in tumor cells

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Acta Pharmacologica Sinica 2005年第8期26卷 1000-1008页

作者： Yi-lin QI~(2,4., Fan LIAO~(2,4., Chang-qi ZHAO~2, Yong-da LIN~2, Ming-xue ZUO~(2,3,5) ~2 College of Life Sciences, beijing normal University, beijing 100875 china ~3 Key Laboratory for Molecular Biology and Gene Engineering Drugs of beijing, beijing 100875, china College of Life Sciences Beijing Normal University Beijing China Key Laboratory for Molecular Biology and Gene Engineering Drugs of beijing Beijing China

Aim: To define the in vitro cytotoxic activities of 4.demethyl-picropodophyllotoxin 7'-O-β-D-glucopyranoside （4.PG）, a new podophyllotoxin glucoside. Methods: Antiproliferation activity was measured in several tumor cell lines by using the microculture tetrazolium MTT assays. Cell cycle distribution was analyzed using flow cytometry and mitosis index assays. Furthermore, transmission electron microscopy, TUNEL, DNA agarose electrophoresis, and activated caspase-3 were used to analyze the induction of apoptotic cell death. Moreover, intracellular changes in the cytoskeleton were detected using immunocytochemistry. Results: 4.PG effectively inhibited the proliferation of cancer cells （HeLa, CNE, SH-SY5Y, and K562 cell lines）. For the K562 cell line, the antiproliferation effect of 4.PG was much more potent than that of etoposide (IC50value: 7.79x10（-9） mol/L for 4.PG vs 2.23x 10（-5） mol/L for etoposide). Further, 4.PG blocked the cell cycle in the mitotic phase. The induction of apoptosis and elevated levels of activated caspase-3 were confirmed in cells treated with 4.PG. The microtubule skeleton of HeLa cells was disrupted immediately after treatment with 4.PG. Conclusion: The cytotoxicity of 4.PG is due to its inhibition of the microtubule assembly of cancer cells at a low concentration, thus inducing apoptosis. These properties qualify 4.PG to be a potential antitumor drug.

关键词： 4.demethyl-picropodophyllotoxin 7’-O-β-D-glucopyranoside podophyllotoxin flow cytometry microtubulin apoptosis

SINGLE BIRTH PROCESSES

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(Department of Mathematics,beijing normal University,beijing 100875,china) Department of Mathematics Beijing Normal University Beijing 100875 China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

Reaction-diffusion processes

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Chinese Science Bulletin 1998年第17期43卷 1409-1420页

作者： CHEN Mufa beijing normal University beijing 100875, china beijing normal University Beijing China

The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statistical physics and consist of an important class of interacting particle systems which is currently an active research field in probability and mathematical physics. The models are concrete but as a part of the infinite-dimensional mathematics, the topic is quite hard. It is explained how new problems arise, and how some new ideas and new mathematical tools are introduced. Surprisingly, the mathematical tools produced from the study on the simple models then turn to have a lot of powerful applications not only in probability theory but also in other branches of mathematics. Nevertheless, the story is still far from finished, and some important open problems are proposed for further study.

关键词： Reaction-diffusion process ergodicity phase transitions coupling.

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun Department of Mathematics, beijing normal University, beijing 100875, china Department of Mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.