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Exploring the evolution mechanism of function module in the biological networks

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Exploring the evolution mechanism of function module in the ...

Stability analysis of the fractional differential systems with Miller-Ross sequential derivative

第十三届全国非线性振动暨第十届全国非线性动力学和运动稳定性学术会议

作者： Junjun Hao1,Zengrong Liu1,2(1.Institute of System Biology,shanghai university,shanghai,200444,china 2.department of mathematics,shanghai university,shanghai 200444,china)

In the process of biological evolution,it is indispensable for duplication and divergence to the module *** a network consisted with several isolated sub-networks,duplication can only cause to local expand,while it can not produce the connection with biological functions,such as module *** provides linkages with other potential isolated parts,but it can not contribute with the scale of network *** taking into account these two factors,we can describe effectively the biological evolution mechanism of the network module.

关键词： Biological network Duplication and divergence Functional module

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Stability analysis of the fractional differential systems wi...

Top 10 Influential Events in carbon neutrality and climate change response for 2023

第十三届全国非线性振动暨第十届全国非线性动力学和运动稳定性学术会议

作者： QIAN De-liang1 LI Chang-pin2(1.College of Science,Zhongyuan university,Henan 450007,china 2.department of mathematics,shanghai university,shanghai 200444,china)

Because of lacking of the semigroup property of Riemann-Liouville derivative and Caputo one,the Miller-Rose sequential fractional derivative operator,which in the sense of this two types of fractional derivatives,has been proposed,which often appears in a nature way in the formulation of various applied problems in physics and applied *** this paper,by using the Laplace transform,the solutions of the systems with the Miller-Ross sequential derivative in the sense of the Riemann-Liouville derivative and the Caputo one are derived *** on the asymptotical expansion of the Mittag-Leffler function,the stability criteria of the fractional differential systems with Miller-Ross sequential fractional derivative are given,where two cases are included:the homogenous case and the non-homogenous one.

关键词： Miller-Ross sequential fractional derivative Mittag-Leffler function stability fractional differential system Caputo derivative Riemann-Liouville derivative

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Frontiers in Energy 2024年第1期18卷 1-3页

作者： Research Institute of Carbon Neutrality of shanghai Jiao Tong university Research Institute of Carbon Neutrality Shanghai Jiao Tong UniversityShanghai 200240China

In 2023, the global community intensified its efforts towards achieving carbon neutrality and addressing climate change, witnessing several impactful events. Research Institute of Carbon Neutrality, shanghai Jiao Tong university compiled the Top 10 Events (in chronological order) in the field of global carbon neutrality and climate change response for 2023, to share with readers these significant moments that document the ongoing ambition and collective efforts of human society.

关键词： neutral collective intensified

Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(Physics,Mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2 & DING Hu2 1 department of Mechanics, shanghai university, shanghai 200444, china 2 shanghai Institute of Applied mathematics and Mechanics, shanghai 200070, china department of Mechanics Shanghai University Shanghai 200444 China shanghai Institute of Applied mathematics and Mechanics Shanghai 200070 China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation

On two transverse nonlinear models of axially moving beams

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Science china(Technological Sciences) 2009年第3期52卷 743-751页

作者： DING Hu1 & CHEN LiQun1,2 1 shanghai Institute of Applied mathematics and Mechanics, shanghai university, shanghai 200072, china 2.department of Mechanics, shanghai university, shanghai 200444, china 1. shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China 2. department of Mechanics Shanghai University Shanghai 200444 China

Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.

关键词： axially moving beam nonlinearity transverse vibration finite difference method differential quadrature method

Isotropic bodies and Bourgain's problem

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Science china mathematics 2005年第5期48卷 666-679页

作者： HE Binwu & LENG Gangsong department of mathematics, shanghai university, shanghai 200444, china 1. department of mathematics Shanghai University 200444 Shanghai China

Let K (?) Rn be a convex body of volume 1 whose barycenter is at the origin, LK be the isotropic constant of K. Finding the least upper bound of LK , being called Bourgain's problem, is a well known open problem in the local theory of Banach space. The best estimate known today is LK 2 (?) K (?) r2Bn2,(r1≥1/2, r2≤(?)/2), then (?) ≤ (?) and find the conditions with equality. Further, the geometric characteristic of isotropic bodies is shown.

关键词： convex body isotropic body isotropic constant Bourgain’s problem spherical section function.

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of mathematics, shanghai Normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

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Journal of Computational mathematics 2003年第5期21卷 625-636页

作者： Jin-yan Fan (department of mathematics, shanghai Jiaotong university, shanghai 200240, china) department of mathematics Shanghai Jiaotong University 上海 200240

Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.

关键词： Singular nonlinear equations Levenberg-Marquardt method Trust region al- gorithm Quadratic convergence.

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, shanghai Normal university, shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.