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Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate

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Science China Mathematics 2017年第8期60卷 1371-1398页

作者： LIU ZhiHua YUAN Rong school of mathematical sciences Beijing Normal University

An infection-age structured epidemic model with a nonlinear incidence rate is *** formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the *** analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.

关键词： infection-age structured epidemic non-densely defined stability normal form zero-Hopf bifurcation

On the Largest Prime Factor of Shifted Primes

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Acta Mathematica Sinica,English Series 2017年第3期33卷 377-382页

作者： Feng Juan CHEN Yong Gao CHEN school of mathematical sciences Soochow University school of mathematical sciences and Institute of Mathematics Nanjing Normal University

For any integer n ≥ 2, let P（n） be the largest prime factor of n. In this paper, we prove 1 This that the number of primes p 〈 x with P（p- 1） ≥ pC is more than （1 -c＋o（1））π（x） for 0 〈 c 〈 1/2 extends... 详细信息

关键词： Prime factor shifted prime

New approximate solution for time-fractional coupled KdV equations by generalised differential transform method

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Chinese Physics B 2010年第11期19卷 41-47页

作者：刘金存侯国林 school of mathematical sciences Inner Mongolia University

In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.

关键词： fractional coupled KdV equations Caputo fractional derivative differential transform method approximate analytic solution

Reduced-order finite element method based on POD for fractional Tricomi-type equation

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Applied Mathematics and Mechanics(English Edition) 2016年第5期37卷 647-658页

作者： Jincun LIU Hong LI Yang LIU Zhichao FANG school of mathematical sciences Inner Mongolia University

The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.

关键词： reduced-order finite element method (FEM) proper orthogonal decompo-sition (POD) fractional Tricomi-type equation unconditionally stable error estimate

Monogamy relations in tripartite quantum system

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Chinese Physics B 2010年第10期19卷 94-99页

作者：李姣姣王志玺 school of mathematical sciences Capital Normal University

This paper presents monogamy relations for three-qubit quantum states by using convex-roof extended negativity, which inspires studying the difference between the three entanglement measures, concurrence, negativity and convex- roof extended negativity. It finds that the convex-roof extended negativity is a stronger entanglement measure than concurrence in multipaxtite higher-dimensional quantum system.

关键词： concurrence monogamy relation convex-roof extended negativity

FINDING THE TOPOLOGY OF IMPLICITLY DEFINED TWO ALGEBRAIC PLANE CURVES

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Journal of Systems Science & Complexity 2012年第2期25卷 362-374页

作者： Ben GAO Yufu CHEN school of mathematical sciences Graduate University of Chinese Academy of Sciences

An algorithm is given for computing in a very efficient way the topology of two real algebraic plane curves defined *** authors preform a symbolic pre-processing that allows us later to execute all numerical computati... 详细信息

关键词： Algebraic curves cylindrical algebraic decomposition generic position subresultantssequence topology.

Global existence and decay of smooth solutions for the 3-D MHD-type equations without magnetic diffusion

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Science China Mathematics 2016年第10期59卷 1949-1974页

作者： REN XiaoXia XIANG ZhaoYin ZHANG ZhiFei school of mathematical sciences Peking University school of mathematical sciences University of Electronic Science and Technology of China

We study the large time behavior of a 3-D MHD(magneto-hydrodynamical)-type system without magnetic diffusion introduced by Lin and Zhang(2014). By using the elementary energy method and interpolation technique, we pro... 详细信息

关键词： global existence decay estimates magneto^hydrodynamical equations zero magnetic diffusion

Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

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Chinese Physics B 2011年第12期20卷 264-272页

作者：齐高娃侯国林阿拉坦仓 school of mathematical sciences Inner Mongolia University

The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.

关键词： operator matrix Hamiltonian operator symplectic orthogonal eigenfunction system completeness

Strain-stress relation in macromolecular microsphere composite hydrogel

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Applied Mathematics and Mechanics(English Edition) 2016年第11期37卷 1539-1550页

作者： Hui ZHANG school of mathematical sciences Beijing Normal University

This paper investigates the strain-stress relation for the macromolecular microsphere composite （MMC） hydrogel. The novel point is to present the strain-stress model, which is based on the microscopic mixed entropy set up in the previous work and the Flory-Rehner elastic energy. Then, the numerical result of the strain-stress model is shown, which is completely consistent with the chemical experiment. Moreover, the theoretical relation of the strain-stress depends on the microscopic parameters of the MMC hydrogel. Therefore, it is a way to investigate the relation of macroscopic properties and microscopic structures of soft matters. This approach can be extended to other soft matters,

关键词： strain-stress model large deformation free energy functional microscopicparameter