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Challenges in the theoretical investigations of lipid membrane configurations

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Chinese Physics B 2013年第2期22卷 36-44页

作者：涂展春 department of Physics Beijing Normal University Kavli institute for Theoretical Physics china Chinese Academy of Sciences

We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field,which involve（i）the exact solutions to the shape equation of lipid vesicles,（ii）the exact solutions to the governing equations of open lipid membranes,（iii）the neck condition of two-phase vesicles in the budding state,（iv） the nonlocal theory of membrane elasticity,and（v）the relationship between the symmetry and the magnitude of the free energy.

关键词： configuration lipid membrane

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

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Chinese Annals of mathematics,Series B 2003年第4期24卷 501-508页

作者： CHEN ZONGXUAN department of mathematics, Jiangxi Normai University, Nanchang 330027, china. institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, beijing 100080, china. department of mathematics Jiangxi Normal University Nanchang 330027 institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080

The author investigates the hyper order of solutions of the higher order linear equation, andimproves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].

关键词： Differential equation Entire function Hyper order

Global asymptotic stability of a two species competitive system with stage structure and harvesting

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 81-87页

作者： Xinyu SONG and Lansun CHEN department of mathematics, Xinyang Teachers College, Henan 464000, china institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, beijing 100080, china department of mathematics Xinyang Teachers College Henan 464000 China institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

The dynamics of a two species competitive system, where the species one has two stages, a immature stage and a mature stage with harvesting, and the growth of the species two is of Lotka-Volterra nature, is modelled by a system of retarded functional differential equations. We obtain the conditions for global asymptotic stability of three nonnegative equilibria and the threshold of harvesting mature population. The effect of the delay on the population at equilibrium and the optimal harvesting of mature population are also considered.

关键词： optimal harvesting stage structure competitive system global asymptotic stability.

The information entropy of a static dilaton black hole

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Science china(Physics,Mechanics & Astronomy) 2008年第2期51卷 113-125页

作者： LIU ChengZhou institute of Theoretical Physics, Binzhou University, Binzhou 256600, china department of Physics, beijing Normal University, beijing 100875, china institute of Theoretical Physics Binzhou University Binzhou China department of Physics Beijing Normal University Beijing China

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

关键词： black hole entropy holographic principle non-commutative quantum field theory event horizon loop quantum gravity

CRITICAL　BIRTH　ORDER　RATIO　CONTROL　AND　ATTAINABLE　SET　OF　A　DISCRETE　AGE－DEPENDENT　PARITY　PROGRESSION　POPULATION　SYSTEM

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Systems Science and Mathematical Sciences 1994年第4期7卷 302-311页

作者： GUO Baozhu(department of Applied mathematics,beijing institute of Technolopy, beijing100080, china) 北京理工大学应用数学系北京

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ＣＲＩＴＩＣＡＬＢＩＲＴＨＯＲＤＥＲＲＡＴＩＯＣＯＮＴＲＯＬＡＮＤＡＴＴＡＩＮＡＢＬＥＳＥＴＯＦＡＤＩＳＣＲＥＴＥＡＧＥ－ＤＥＰＥＮＤＥＮＴＰＡＲＩＴＹＰＳＯＧＲＥＳＳＩＯＮＰＯＰＵＬＡＴＩＯＮＳＹＳＴＥＭＧＵＯＢａｏｚｈｕ（Ｄｅｐａｒｔｍｅｎｔｏｆ...

关键词： Population dynamics parity progression model female parity ratio attainable set stability

Characterization for commutators of n-dimensional fractional Hardy operators

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Science china mathematics 2007年第10期50卷 1418-1426页

作者： Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1+) Hong-bin WANG~3 ~1 School of Mathematical Sciences,beijing Normal University,beijing 100875,china ~2 department of mathematics,Linyi Normal University,Linyi 276005,china ~3 department of mathematics,china University of Mining and technology (beijing),beijing 100083,china School of Mathematical Sciences Beijing Normal University Beijing China department of mathematics Linyi Normal University Linyi China department of mathematics China University of Mining and Technology (Beijing) Beijing China

In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^... 详细信息

关键词： n-dimensional fractional Hardy operator, commutator, C(M)O function, homogeneous Herz space

Weighted estimation of single index models with right censored responses

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Science china mathematics 2011年第3期54卷 479-514页

作者： WANG YanHua1, LI XiaYan2, WANG QiHua3 & HE ShuYuan4 1School of Sciences, beijing institute of technology, beijing 100081, china 2department of mathematics, University of Science and technology of china, Hefei 230026, china 3Chinese Academy of mathematics and System Science, beijing 100080, china 4School of Mathematical Sciences, Capital Normal University, beijing 100048, china School of Sciences Beijing Institute of Technology Beijing China department of mathematics University of Science and Technology of China Hefei China Chinese Academy of mathematics and System Science Beijing China School of Mathematical Sciences Capital Normal University Beijing China

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

关键词： single index models random censorship central limit theorem law of the iterated logarithm weighted least squares unknown link function

Precise Asymptotics of Error Variance Estimator in Partially Linear Models

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Acta Mathematicae Applicatae Sinica 2008年第1期24卷 59-74页

作者： Shao-jun Guo, Min Chen, Feng Liu Academy of mathematics and Systems Science, Chinese Academy of Sciences, beijing 100080, china department of Statistics, Chongqing institute of technology, Chongqing 630000, china Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China department of Statistics Chongqing Institute of Technology Chongqing China

In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression models, yi = xiτβ+ g(ti) +εi, 1≤i≤n, {εi,i = 1,…, n} are i.i.d random errors with mean 0 and positive finite varianceσ2. Following the ideas of Allan Gut and Aurel Spatarut and Zhang, on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.

关键词： Precise asymptotics partially linear models error variance estimator

Solving the input data in error correc-tion of optical fabrication by finite Fourier coefficient algorithm

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Science china(Technological Sciences) 2006年第1期49卷 50-60页

作者： CHENG Haobo1,2, SUN Guozheng3 & FENG Zhijing2 1. department of Optical Engineering, beijing institute of technology, beijing 100081, china 2. department of Precision Instruments and Mechanology, Tsinghua University, beijing 100084, china 3. china North Industries Group Corporation, beijing 100089, china department of Optical Engineering Beijing Institute of Technology Beijing China department of Precision Instruments and Mechanology Tsinghua University Beijing China china North Industries Group Corporation Beijing China

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability nec-essary to perform precisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influ-ence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.

关键词： optical fabrication, computer controlled optical surfacing, free-form lens, finite Fourier coefficient, error correction.