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JACOBI SPECTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of Computational Mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(Department of Mathematics, Shanghai normal university, Shanghai 200234, china)(COM2MAC, Pohang university of Science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science china Mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 Department of Mathematics,Zhejiang normal university,Jinhua 321004,china 2 Department of Mathematics,Tongji university,Shanghai 200092,china 1. Department of Mathematics Zhejiang Normal University Jinhua 321004 China2. Department of Mathematics Tongji University Shanghai 200092 China

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-Pick estimate holomorphic function Taylor expansion

p-th moment exponential stability of stochastic differential equations with impulse effect

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Science china(Information Sciences) 2011年第8期54卷 1702-1711页

作者： SHEN LiJuan 1,2 & SUN JiTao 11 Department of Mathematics, Tongji university,Shanghai 200092,china 2 Department of Mathematics,Luoyang normal university, Luoyang 471022,china 1. Department of Mathematics Tongji University Shanghai 200092 China2. Department of Mathematics Luoyang Normal University Luoyang 471022 China

The p-th moment exponential stability of stochastic differential equations with impulse effect is *** employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are *** addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential *** examples are also discussed to illustrate the effectiremess of the results obtained.

关键词： stochastic differential equations impulse p-th moment exponential stability vector Lyapunov functions

ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational Mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (Department of Mathematics, East china normal university, Shanghai 200062, china) E china normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number

Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

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Science china(Physics,Mechanics & Astronomy) 2004年第1期47卷 8-16页

作者： TANG Zhilie1, XING Da2 & LIU Songhao2 1. Department of Physics, South china normal university, Guangzhou 510631, china 2. School for Information and Optoelectronic Science and Engineering, South china normal university, Guangzhou 510631, china Correspondence should be addressed to Tang Zhilie (email: tangzhl@***) Received April 23, 2003 1. Department of Physics South China Normal University 510631 Guangzhou China 2. School for Information and Optoelectronic Science and Engineering South China Normal University 510631 Guangzhou China

The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single- and two-photon confocal microscopy.

关键词： second harmonic generation, third harmonic generation, confocal microscopy, three-dimensional point spread function.

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science china Mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2 1 Department of Mathematics,Fuzhou university,Fuzhou 350002,china 2 Department of Mathematics,South china normal university,Guangzhou 510631,china 1. Department of Mathematics Fuzhou University Fuzhou 350002 China 2. Department of Mathematics South China Normal University Guangzhou 510631 China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α

Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science china Mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2 1 Department of Mathematics, Zhejiang normal university, Jinhua 321004, china 2 Department of Mathematics, Kunming university of Science and Technology, Kunming 650093, china Department of Mathematics Zhejiang Normal University Jinhua 321004 China Department of Mathematics Kunming University of Science and Technology Kunming 650093 China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 34C37 34C23 74J30 58Z05

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环境影响评价听证程序实效性问题研究

河北师范大学学报（哲学社会科学版） 2008年第6期31卷 43-46页

作者： PROJECT Team(hebei university of Science and Technology,shijiazhuang,hebei 050016,china) 河北科技大学文法学院

作为公众参与的重要形式之一——听证会在我国行政管理模式中逐渐为政府所适用。就环境行政来说,首次以法律形式规定听证程序的是环境影响评价法。自圆明园湖底防渗工程听证程序后,环境影响评价行政许可听证程序逐渐在实践中被适用。但... 详细信息

作为公众参与的重要形式之一——听证会在我国行政管理模式中逐渐为政府所适用。就环境行政来说,首次以法律形式规定听证程序的是环境影响评价法。自圆明园湖底防渗工程听证程序后,环境影响评价行政许可听证程序逐渐在实践中被适用。但听证程序立法的缺失与不足,直接影响了环境影响评价行政许可行为的实施效果。而听证程序实效性研究将成为打破这一瓶颈的必然选择。

关键词：环境影响评价听证程序实效性

Hawking radiation and thermodynamics of a Vaidya-Bonner black hole

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Research in Astronomy and Astrophysics 2010年第1期10卷 33-38页

作者： Zhen-Feng Niu Wen-Biao Liu Department of Physics Hebei North University Zhangjiakou 075000 China Department of Physics Institute of Theoretical Physics Beijing Normal University Beijing 100875 China

Using Parikh＇s tunneling method, the Hawking radiation on the apparent horizon of a Vaidya-Bonner black hole is calculated. When the back-reaction of particles is neglected, the thermal spectrum can be precisely obtained. Then, the black hole thermodynamics can be calculated successfully on the apparent horizon. When a relativistic perturbation is applied to the apparent horizon, a similar calculation can also lead to a purely thermal spectrum. The first law of thermodynamics can also be derived successfully at the new supersurface near the apparent horizon. When the event horizon is thought of as a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be based on the event horizon. It is concluded that the thermodynamics should be constructed exactly on the apparent horizon while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.

关键词： black hole physics -- relativity -- kinematics and dynamics