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2015年吕梁学院数学系学术会议花絮、摘要
2015-07-23 18:57  吕梁学院数学系

开幕式:吕梁学院数学系主任,刘方教授致开幕词

                                                   参会人员

                                       

半线性微分方程振动理论新进展

俞元洪,中国科学院

摘要:通过建立广义黎卡提不等式证明了若干新的泛函微分方程振动理论,将半线性微分方程的若干振动结果,推广和改进为Emden-Fowler型泛函微分方程。这些结果将最近发表在SCI索引的刊物上,介绍的结果尚未公布。

微分包含和微分包含系统的控制

寇春海,东华大学应用数学系

摘要:微分包含可以看成是微分方程在集合值映射中的推广。最先出现在20世纪30年代。介绍微分包含理论研究的几个主要问题,简要地介绍凸系统的研究成果。介绍两类研究比较多的微分包含控制系统:多胞体系统和鲁里叶系统。目前对这两类系统研究的主要成果。

ConvergenceAccelerationTechniquesIn Partial Differential Equations

Jun-Sheng DuanSchool of Sciences, Shanghai Institute of Technology

Abtracts:We review the recent results such as the time- and space-fractional partial differential equation, the similarity solution of the fractional diffusion equation, the eigenvalue problems for the fractional ordinary differential equations with the Dirichlet, Neumann, Robin boundary conditions and the periodic boundary condition, the periodic solution of Stokes’ second problem for viscoelastic fluids as characterized by a fractional constitutive equation, etc. For nonlinear fractional ordinary differential equations, we consider the fractional power series combined with convergence acceleration techniques, such as the diagonal Padé approximants and the iterated Shanks transforms.

High-Order Algorithms for Riesz Derivatives and Riesz-type Partial Differential Equations

Changpin Li,Shanghai University

Abtracts: Generally speaking, the Laplacian in convection-diffusion equations, reaction-diffusion equations, and dispersion equations can well characterize the normal diffusion phenomena and dispersion phenomena in space. But it can not truthfully reflect spatial anomalous diffusion and dispersion. However, Riesz derivatives can practically depict such global anomalous phenomena in space. In this talk, we focus on deriving several kinds of high-order algorithms for Riesz derivatives. Then we simply present the modeling of anomalous diffusion and dispersion. Especially, by applying these established schemes to the Riesz-type partial differential equations, the high-order numerical methods are constructed, where the stability and convergence are displayed.

Error estimates of finite element method for linear space-fractional partialdifferential equations

Yubin Yan,University of Chester

Abtracts: Finite element methods for solving linear space-fractional partial differential equations are considered in one-dimensional case. The space-fractional derivative is defined as Riesz fractional derivative. The L2-norm error estimates in the semidiscrete case are proved by two different methods and the error bounds depend on the regularities of the exact solutions of the space-fractional partial differential equations.
 1. One method is by using a duality argument and the error bounds contain the norm kutkL2(0,1) of the time derivative of the exact solution.
 2. Another method is by using the approximate solution operator of the corresponding fractional elliptic problem and the error bounds contain the norm kutkH0 α(0,1), 1/2 < α ≤ 1 of the time derivative of the exact solution.

关于英文学术论文书写的一些体会

张广,天津商业大学理学院

摘要:主要就数学学术论文的选题、书写、投稿等事宜谈一些自己的体会。

   

动态网络上传染病动力学建模与分析

刘桂荣,山西大学

摘要:复杂网络上传染病动力学是近年来国内外学者广泛关注的一个研究方向, 但绝大多数工作是基于静态网络去研究的。事实上,疾病传播过程中,要考虑个体的迁移或流动;特别对于长期反复出现的传染病,还要考虑个体的出生与死亡。 这些因素会导致疾病传播网络结构随时间的演化。此外,疾病信息导致的减少外出、隔离、接种等行为也会导致网络结构的演化。因此,疾病传播网络是一个动态的复杂网络。该报告首先介绍动态网络上传染病动力学建模与研究的国内外动态,然后介绍基于动态网络上具有出生与死亡的SIS传染病动力学分析。

复杂网络中的SIS传染病模型稳定性和分支分析

王振国   吕梁学院数学系  

摘要:主要研究一类具有非线性传染率的SIS网络传染病模型的动力学行为,给出传播阈值,分析无病平衡点局部稳定;进一步考虑特征值出现零根时,系统Transcritical分支情况.  

具有尺度结构的非线性害兽种群模型的最优不育控制        

         刘荣  吕梁学院数学系          
                             
摘要:首先通过考虑模型的可分离形式的解,利用冻结系数法及不动点理论证明了模型的适定性,其次应用不等式理论证明模型解关于控制变量的连续依赖性,接着应用柯尓莫戈洛夫定理及极值化序列证明最优策略的存在性,最后借助共轭系统及切锥法锥给出最优性条件          
                                       
       二维空间上齐次moran集的Hausdorff维数            
           党云贵   吕梁学院数学系                    
摘要:介绍了分形几何的研究对象和研究方法,在正方形中,通过分割方式,选取位置,选取个数的变化,产生不同的Moran集,应用质量分布原理和位势理论研究出它们的Hausdorff维数。并将两种特殊情形推广到三维空间。最后提出将来可研究内容。                  

Afinite element method for the time fractional partial differential equations

                 HuYe   Department of Mathematics ,luliang university    

Abstracts: In this paper, we will consider the finite element method for the time fractional partial differential equations.The existence and uniqueness of the solutions have been proved by using Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach.The fully discrete scheme has been considered by using finite element method and the optimal convergence error estimates have been obtained. The numerical examples show that the experiment results are consistent with the theoretical results.

社交网络的实证分析研究

呼文军   吕梁学院数学系

                                     
摘要:首先介绍了社交网络的基本概念,其次介绍了朋友关系网络的实证研究。构建了4个节点相同但随着亲密程度的改变拓扑结构发生变化的朋友网络,经过统计性质饿研究发现,普通朋友网络是一个小世界网络,随着亲密程度的增加,网络拓扑结构由连通到不连通,平均度和聚类系数在减少,而平均路径长度增加。最后对社交网络的进一步研究做了一些设想。                    

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