Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces

We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.     

Remarks on Neumann boundary problems involving Jacobians

In this note, we explore the validity of Wente-type estimates for Neumann boundary problems involving Jacobians. We show in particular that such estimates do not in general hold under the same hypotheses on the data for Dirichlet boundary problems.     

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In this paper, we extend the previous Markov-modulated reflected Brownian motion model discussed in [1] to a Markov-modulated reflected jump diffusion process, where the jump component is described as a Markov-modulated compound Poisson process. We compute the joint stationary distribution of the bivariate Markov jump process. An abstract example with two states is given to illustrate how the stationary equation described as a system of ordinary integro-differential equations is solved by choosing appropriate boundary conditions. As a special case, we also give the sationary distribution for this Markov jump process but without Markovian regime-switching.     

基于伙伴关系建构的联盟标准扩散效应

在技术标准扩散动机下,为技术标准联盟设计了一种“以公共供应商为结构洞的、由上下游企业共同组成的三元伙伴结构,分析了这种伙伴结构对于技术标准扩散的影响方式以及有效性,并讨论了共赢结果的实现条件以及稳定性,从而从技术标准联盟内部伙伴关系建构的角度,提出了新的内源性技术标准扩散机制。研究结论主要有三个:第一,技术标准联盟中以公共供应商为结构洞的长期性上下游伙伴结构对于加速技术标准扩散具有内源性促进作用,贡献度取决于以结构洞为中介的双向知识流动比率的大小;第二,共赢结果的实现条件为:三方伙伴同时遵守关于双向知识流动比率的临界值;第三,共赢结果的稳定性取决于供应商与生产商之间的技术相似程度以及生产商专有知识的价值性等因素,而且上下游伙伴之间的技术相似度越高,则供应商对于合作均衡稳定性的决定作用就越大于生产商。     

A new approximation for the generalized fractional derivative and its application to generalized fractional diffusion equation

In this paper, we derive a fourth order approximation for the generalized fractional derivative that is characterized by a scale function z(t) and a weight function w(t) . Combining the new approximation with compact finite difference method, we develop a numerical scheme for a generalized fractional diffusion problem. The stability and convergence of the numerical scheme are proved by the energy method, and it is shown that the temporal and spatial convergence orders are both 4. Several numerical experiments are provided to illustrate the efficiency of our scheme.     

On the number of eigenvalues for parameter‐dependent diffusion problem on time scales

In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given.     

Global synchronization of fractional‐order and integer‐order N component reaction diffusion systems: Application to biochemical models

This study considers the problem of control and synchronization between fractional‐order and integer‐order, N‐components reaction‐diffusion systems with nonidentical coefficients and different nonlinear parts. The control scheme is designed using the Lyapunov direct method. The results are exemplified by two significant biochemical models, namely, the fractional‐order Lengyel‐Epstein model and the Gray‐Scott model. To illustrate the effectiveness of the proposed scheme, numerical simulations are performed in one and two space dimensions using Homotopy Analysis Method (HAM).     

粘纤单丝数目自动检测系统的研究

针对化纤企业生产、检测的需要,研制了一种粘纤单丝数目自动检测系统。系统采用环形光源,从周围均匀照明经静电和高速风两次分离的粘纤,再由成像物镜将分离的粘纤清晰成像至高速面阵CCD传感器靶面上,基于Directshow技术自行编制出图像采集程序。利用自主研发的图像处理软件,处理粘纤图像信息,自动计算其单丝的数目,并给出判别结果。在图像处理方面采用分行消包络阈值分割法和连通域跟踪计数法,解决了粘纤计数中的胶丝重叠、分叉等关键技术难题,保证了计数准确率。该系统具有精度高、检测速度快等特点。     

用改进的格点哈密顿量计算2+1维QCD 0++胶球质量

用改进的格点哈密顿量和截断本征方程法计算2＋1维QCD 0^ 胶球质量,结果显示较好的标度行为。