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American Journal of Computational Mathematics 2016年第1期6卷 49-54页

作者： R. B. Ogunrinde T. E. Olaosebikan Department of Mathematical Sciences Ekiti State University Ado Ekiti Nigeria

In this paper, we developed a new numerical scheme which aimed to solve some initial value problems of ordinary differential equations. The full breakdown of this new numerical scheme derivation is presented. While in our subsequent research, we shall fully examine the characteristics of the scheme such as consistency, convergence and stability. Also, the implementation of this new numerical scheme shall be worked-on and comparison shall also be made with some existing methods.

关键词： Numerical Scheme ordinary differential equation Scheme Development

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GLOBAL ANALYSIS TO A KIND OF COMPETITION MODEL OF E-COMMERCE SITES

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Annals of differential equations 2003年第3期19卷 325-333页

作者：李艳会朱思铭 Dept. of Applied Math. Zhongshan University Guangzhou 510275

In this paper, we present a competition modei of e-commerce sites with the property of 'better for better'. Then we qualitatively analyze the special case of two dimensions. So we prove that there does not exist limit... 详细信息

关键词： e-commerce sites competition model ordinary differential equation qualitative analysis

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An Improved Explicit Integration for Nonrigid Simulation

International Journal of Systems and Control

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International Journal of Systems and Control 2008年第1期 48-56页

作者： HU Xinrong, LI Dehua Institute for Pattern Recognition and Artificial Intelligence, State Education Commission Laboratory for Image Processing and Intelligence Control,HuaZhong Univ. of Science&Technology, Wuhan 430074,China

Nonrigid simulation is a hard but challengeable work to all graphics researchers. A satisfied nonrigid simulation should be general, accurate, efficient and stable. Explicit, implicit and semi-implicit integration methods have contributed to large performance enhancements in the field of nonrigid simulation. Cloth is the most representative nonrigid object. In this paper, we propose an improved explicit integration--embedded Runge-Kutta method to solve the nonrigid simulation that takes cloth for example based on classical spring-mass model. Traditional embedded Runge-Kutta methods generally apply some optimized coefficients to solve ordinary differential equations of nonrigid simulation. Most of them tend to concentrate on the efficiency of the simulation process, and not the fidelity of the simulation result. We investigate and determine the extent to which the overall quality must be compromised in order for the stable conditions to be satisfied. The improved integration method proposed in our paper incorporates the fixed timestep and adaptive timestep in solving cloth motion equations to achieve a controllable error evaluation. Compared with the other Runge-Kutta methods, the proposed method has some advantages for nonrigid simulation: controllable error evaluation without extra computations, excellent efficiency, good stability and satisfied precision. Experiment demonstrates that this method results in simulation efficiency improvements and is considerable practicable.

关键词： Nonrigid simulation Explicit integration ordinary differential equation Spring-mass model Timestep

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On the equivalence classes of linear non-autonomous systems

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Progress in Natural Science:Materials International 2001年第3期 26-33页

作者：武际可黄克服林文卉 Beijing 100871 China Department of Mechanics and Engineering Science Peking University

In this paper, the equivalence classification of the linear non-autonomous dynamic systems near singularities is given. Under some conditions their equivalence classes are the same as the autonomous ones. Using a seri... 详细信息

关键词： linear autonomous systems equivalence class ordinary differential equation qualitative theory bifurcation.

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Linearization of Emden differential equation via the Generalized Sundman Transformations

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Advances in Pure Mathematics 2021年第3期11卷 163-168页

作者： Joel Mvendaga Orverem Yusuf Haruna Bala Ma’aji Abdulhamid Magaji Yunbunga Adamu Department of Mathematical Sciences Federal University Dutsin-Ma Katsina State Nigeria Department of Mathematical Sciences Abubakar Tafawa Balewa University Bauchi Nigeria

The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.

关键词： Emden differential equation Second Order ordinary differential equation Generalized Sundman Transformation Linearization

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Building and Simulation of Mitotic Regulatory Network

Building and Simulation of Mitotic Regulatory Network

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第五届全国生物信息学与系统生物学学术大会暨国际生物信息...

作者： Yiran Wu Ziwei Dai Jia Lv Luhua Lai College of Chemistry and Molecular Engineering Peking University Center for Quantitative Biology Peking University College of Engineering Peking University

Background:Mitosis is the key step in eukaryotic cell cycle at which the mother cell divided into two daughter *** failure causes chromosome mis-segregation and aneuploidy,thus may lead to apoptosis or *** recent years,the regulatory mechanism of mitosis is much *** mitotic kinases,including cyclindependent kinase 1,Aurora kinases,and polo-like kinase 1,have been considered as targets for anti-cancer drug *** these kinases regulates different processes in mitosis, combinations of their inhibitors were considered as more effective treatment of *** the therapeutic window of anti-cancer drugs are often narrow,quantitative study of mitosis is necessary. Methods:The mitosis network was constructed according to published information. The network dynamic was simulated using ordinary differential *** reactions were described using sigmoid ***-blot and F(o|¨)ster resonance energy transfer data from literature were used for data fitting to determine parameters used in the *** adjustment and parameter sensitivity analysis were done using an in-house program. Results:The mitotic regulatory network we built contains the main processes of mitosis: mitotic entry,spindle assembly checkpoint,and the effect of anaphase-promoting complex (ubiquitin ligase).Only the major interactions of the key regulators are included in the *** the regulation of cyclin dependent kinase 1,Aurora kinase A and B,and pololike kinase 1 are *** model contains 13 substances and 24 *** sets of parameters have been obtained by fitting to experimental *** analysis of the distribution of the parameter sets and parameter sensitivity analysis are under investigation. Conclusions:A simplified network model of the mitosis regulation was built and parameters were estimated by fitting to experimental *** model is being used to study the dynamics property of mitosis process and to s

关键词： mitosis biological network simulation ordinary differential equation mitotic kinases

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