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Small Random Perturbations of One-Dimensional Diffusion Processes

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Acta Mathematica Sinica,English Series 1998年第1期14卷 35-40页

作者： Xi Fubao department of Applied mathematics, beijing institute of technology, beijing 100081, china

In the present paper we consider the small random perturbations of one-dimensional diffosion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistic... 详细信息

关键词： Diffusion processes Small random perturbations Exit times

On the Iteration of Holomorphic Self Maps of C

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Acta Mathematica Sinica,English Series 1998年第1期14卷 139-144页

作者： Fang Liping department of Applied mathematics, beijing institute of technology, beijing 100081, china

Let f be a holomorphic self-map of the punctured plane C~*=C\{0} with essentially singular points 0 and ∞. In this note, we discuss the sets I_O(f)={z∈C~*: f^n(z)→0,n→∞} and I_∞(f)={z∈C~*: f^n(z)→∞,n→∞}.We try to find the relation between I_O(f), I_∞(f) and J(f). It is proved that both the boundary of I_O(f) and the boundary of I_∞(f) equal to J(f), I_O(f) ∩J(f)≠ 0 and I_∞(f)∩J(f)≠. As a consequence of these results, we find both I_O(f) and I_∞(f) are not doubly-bounded.

关键词： Iteration Julia set

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

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Acta Mathematica Sinica,English Series 2001年第4期17卷 649-656页

作者： Zuo Xin GAN Wei Gao GE institute of Systems Science, Chinese Academy of Sciences, beijing 100080, P. R. china department of Applied mathematics, beijing institute of technology, beijing 100081, P. R. china institute of Systems Science Chinese Academy of Sciences Beijing 100080 P. R. China department of Applied mathematics Beijing Institute of Technology Beijing 100081 P. R. China

In this paper, the problenl of absohlte stability for general Lurie control systems with multi- nonlinear feedback terms is investigated. From the Lyapunov function approach. new necessary and sufficient conditious and some practical sufficient conditions of absolute stability are derived. which improve the absolute stability for the set. A numerical examplc illustrates the effectiveness of the proposed results.

关键词： General Lurie system Multi-nonlinear feedback Absolute stability

SUPERCONVERGENCES OF THE ADINI'S ELEMENT FORSECOND ORDER EQUATION

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Journal of Computational mathematics 1999年第6期17卷 569-574页

作者： Ping Luo(department of Computer Science and technology, Qinghua University, beijing 100084,china)Qun Lin(institute of Systems Science, Academia Sinica, beijing, 100080, china) 清华大学计算机系北京 100084 中科院系统科学所北京 100080

n this papers the asymptotic error expansions of Adini's element for the secondorder imhomogeneous Neumann problem are given and the superconvergence estimations are obtained. Moreover, a numerical example to support ... 详细信息

关键词： Adini's element Superconvergence estimation Asymptotic expansion.

BOUNDED SOLUTIONS AND PERIODIC SOLUTIONS OF VISCOUS POLYTROPIC GAS EQUATIONS

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Chinese Annals of mathematics,Series B 1997年第1期18卷 89-98页

作者： LUO TAO institute of mathematics, Academia Sinica,beijing 100080, china department of Applied mathematics Tsinghua University Beijing 100084 China

A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, t... 详细信息

关键词： Viscous polytropic gas Uniformly bounded solution Periodic solution

Experiment Study of LD Pumped Solid State of Dual-Frequency Laser

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Chinese Journal of Lasers 2000年第2期9卷 97-102页

作者： LU Congcong WEI Guanghui ZHAO Changming WU Keying MA Yu (department of Optical Engineering, beijing institute of technology, beijing 100081, china ) 北京理工大学北京

Dual-frequency laser resulting from fine detuning twisted-mode cavity is discussed in this paper. Two measurement systems, a Fabry-Perot etalon and a confocal spherical interferometer, are adopted. The former reflects directly the interferogram of multimode and single mode. The latter can judge accurately the mode spectrum of single frequency and dual-frequency laser. Moreover, the experimental results provide the relationship between frequency difference and the angle of the relative rotation of the two quarter-wave plates and agree well with the theoretical analyses. The range of difference frequency is from 50 MHz to 1 GHz.

关键词： dual-frequency laser twisted-mode cavity of fine detuning diode-pumped solid-state laser (DPSL)

Cutting Performance and Mechanism of RE Carbide Tools

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Rare Metals 2001年第3期20卷 197-201页

作者： Jianbing Cheng, Yufang Wu, Qixun Yu 1) department of Mechanical Engineering, beijing technology and Business University, beijing 100037, china 2) College of Mechanical Engineering and Automation, beijing institute of technology beijing 100081, china 北京工商大学北京 100037 北京理工大学北京 100081

The research of rare earth elements (RE), added into cemented carbide tools, is one of the recent developments of new types of tool materials in china. Systematic experiments about RE carbides YG8R. (K30), YT14R (P20) and, YW1R (M10) were made to study on the cutting performance in comparison with non-RE carbides YG8, YT14 and YW1. The cutting experiments were as follows: tool life, cutting force, tool-chip friction coefficient and interrupted machining. The action of RE on the carbide materials and the cutting mechanism of the RE carbide tools in the cutting process were verified with the aid of SEM and energy spectrum analysis. Experimental results show that the RE carbide tools have a good overall performance.

关键词： rare earth elements cemented carbide tool cutting performance cutting mechanism

NONEQUILIBRIUM STATISTICAL FOUNDATION OF FATIGUE FRACTURE

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Acta Mechanica Sinica 1990年第1期6卷 35-44页

作者： Xing Xiusan, department of Applied Physics, beijing institute of technology, beijing, 100081, china department of Applied Physics Beijing Institute of Technology Beijing China

The physical foundation of statistical law of fatigue fracture is discussed. The universal forms of the microcrack growth rate, fluctuation growth coefficient and distribution function and fatigue life distribution fu... 详细信息

关键词： microcrack evolution equation microscopic mechanism microcrack distribution function fatigue life distribution function

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2 1. department of mathematics, beijing Normal University, beijing 100875, china 2. institute of Applied Physics and Computational mathematics, beijing 100080, china department of mathematics Beijing Normal University Beijing China institute of Applied Physics and Computational mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.