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linear estimation and distribution of the limit cycles bifurcated from a kind of degenerate polycycles

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Science china mathematics 2007年第3期50卷 334-344页

作者： li-qin ZHAO department of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

In this paper, we investigate the number and the distribution of the limit cycles bifurcated from a kind of degenerate planar polycycles through three singular points: a saddle-node P 0, a fine saddle P 1 with finite order m ∈ N, a contractive (attracting) saddle P 2 with the hyperbolicity ratio q 2(0) ? Q. The connection between P 0 and P 1 is of hh-type and the connection between P 0 and P 2 is of hp-type. It is assumed that the connections between P 0 to P 2 and P 0 to P 1 keep unbroken. We obtain that the cyclicity of this polycycle is not more than 3m + 1, which is linearly dependent on the order of the resonant saddle P 1. We also show that the cyclicity is not more than m + 3 if q 2(0) > m, and that the nearer q 2(0) is close to 1, the more the limit cycles are bifurcated.

关键词： degenerate polycycle cyclicity finitely-smooth normal form transition map 34C05 34C23 58F14

The Star Chromatic Numbers of Some Planar Graphs Derived from Wheels

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Acta Mathematica Sinica,English Series 2002年第1期18卷 173-180页

作者： li De Ming department of mathematics. capital normal university. beijing 100037. P. R. china department of mathematics Capital Normal University Beijing P. R. China

The notion of the star chromatic number of a graph is a generalization of the chromatic number. In this paper. we calculate the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel by subdivisions. their star chromatic numbers being 2+2/(2n + 1). 2+3/(3n + 1)and 2+3/ (3n - 1), respectively. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n. which is a generalization of one resnlt of Gao et al.

关键词： (k,d)-coloring Star chromatic number Planar graph

Output-back fuzzy logic systems and equivalence with feedback neural networks

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Chinese Science Bulletin 2000年第7期45卷 592-596页

作者： li Hongxingdepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing China

A new idea, output-back fuzzy logic systems, is proposed. It is proved that output-back fuzzy logic systems must be equivalent to feedback neural networks. After the notion of generalized fuzzy logic systems is defined, which contains at least a typical fuzzy logic system and an output-back fuzzy logic system, one important conclusion is drawn that generalized fuzzy logic systems are almost equivalent to neural networks.

关键词： output-back fuzzy logic systems generalized fuzzy logic systems feedforward neural networks feedback neural networks.

Superprocesses arising from interactive stochastic flows

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Science china mathematics 2006年第4期49卷 451-476页

作者： YAN Guojun & li Zhanbing Medical School, Shantou university, Shantou 515063, china department of mathematics, Bejing normal university, beijing 100875, china Medical School Shantou University Shantou 515063 China department of mathematics Bejing Normal University Beijing 100875 China

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also g... 详细信息

关键词： superprocess, interactive stochastic flows, martingale problem, dual processes.

POINTWISE CONVERGENCE OF FOURIER-JACOBI SERIES

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Analysis in Theory and Applications 1995年第4期11卷 58-77页

作者： Zhongkai li (capital normal university, beijing, china) 1. department of mathematics Capital Normal University 100037 Beijing PRC

The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1lized translation in terms of Jacobi polynomials, pointwise convergence theorems of the (C,δ) means for δ>α+1/2 and equiconvergence theorems for - 1lished.

关键词： POINTWISE CONVERGENCE OF FOURIER-JACOBI SERIES Math lim

Pointwise estimates for the maximal multilinear singular integral operators

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Science china mathematics 2005年第12期48卷 1696-1706页

作者： HU Guo’en, li Dengfeng & LU Shanzhen department of Applied mathematics, university of Information Engineering, P. O. Box 1001 -747, Zhengzhou 450002, china College of Mathematical and Information Sciences, Henan university, Kaifeng 475001, china department of mathematics, beijing normal university, beijing 100875, china 1. department of Applied mathematics University of Information Engineering P.O.Box 1001-747 450002 Zhengzhou China 2. College of Mathematical and Information Sciences Henan University 475001 Kaifeng China 3. department of mathematics Beijing Normal University 100875 Beijing China

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) est... 详细信息

关键词： multilinear singular integral,maximal operator,BMO (Rn),BLO (Rn).

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 1. School of Sciences Beijing Institute of Technology Beijing 100081 China2. Department of Mathematics University of Science and Technology of China Hefei 230026 China3. Chinese Academy of Mathematics and System Science Beijing 100080 China4. School of Mathematical Sciences Capital Normal University Beijing 100048 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

Noise helped manifestation of intrinsic frequency:A case study in the mesoscopic hormone signaling system

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Progress in Natural Science:Materials International 2009年第10期19卷 1209-1214页

作者： lin Ji a,,Yuanyuan Zhang a,Xiufeng Lang b,Wenxiang Hu a,Qianshu li c a department of Chemistry,capital normal university,beijing 100048,china b School of Science,beijing university of Aeronautics and Astronautics,beijing 100191,china c The Institute for Chemical Physics,beijing Institute of Technology,beijing 100081,china [a]department of Chemistry Capital Normal University Beijing 100048 China [b]School of Science Beijing University of Aeronautics and Astronautics Beijing 100191 China [c]The Institute for Chemical Physics Beijing Institute of Technology Beijing 100081 China

The selective sustainment of nonlinear systems to signals is of great significance to signal transduction in living *** take hormone signaling as an example,and investigate the sustainment of internal and external *** results prove that signals with "intrinsic frequency",no matter if it is noise induced or external injected,can be selectively sustained by exploiting internal and/or external *** the internal and external noise can optimize the noise-induced signals,and the optimization is rather robust to the disturbance of external signals with other *** results are of significance for weak signal detection and transduction in the presence of external signals.

关键词： Noise Intrinsic frequency Mesoscopic system

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

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Acta Mathematica Sinica,English Series 1998年第1期14卷 67-76页

作者： li Xiaochun Lu Shanzhen department of mathematics, beijing normal university, beijing 100875, china

Let 01, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

关键词： Strongly singular convolution operator Hardy space