Pacemaker dynamics in the full Morris–Lecar model

This article reports the finding of pacemaker dynamics in certain region of the parameter space of the three-dimensional version of the Morris–Lecar model for the voltage oscillations of a muscle cell. This means that the cell membrane potential displays sustained oscillations in the absence of an external electrical stimulation. The development of this dynamic behavior is shown to be tied to the strength of the leak current contained in the model. The approach followed is mostly based on the use of linear stability analysis and numerical continuation techniques. In this way it is shown that the oscillatory dynamics is associated to the existence of two Hopf bifurcations, one subcritical and other supercritical. Moreover, it is explained that in the region of parameter values most commonly studied for this model such pacemaker dynamics is not displayed because of the development of two fold bifurcations, with the increase of the strength of the leak current, whose interaction with the Hopf bifurcations destroys the oscillatory dynamics.     

代数连续映象的零点定理及其应用

在Hausdorff拓扑线性空间X及其超1维线性子空间V中,提出并证明了代数连续映象F：X→V^#的一个零点定理,作为应用,讨论了一类广义保号的散度型二阶椭圆方程和一类退化的Fichera-Keldys型二阶抛物方程的弱解存在的问题,推广和改进了现有的结论和现有的证法。     

L∞‐solutions for the ultra‐slow reaction‐diffusion equation

The existence and uniqueness of solutions for a reaction‐diffusion ultra‐slow equation are proved. We also show that they can be extended up a maximal time and are stable as long as they exist. Symmetric and positive solutions are also proved to exist.     

Homoclinic Solutions for A Class of Second Order Neutral Functional Differential Systems

By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.     

连续化方法求解一般无界非凸规划的K-K-T点

给出了求解无界非凸规划的K-K-T系统的一种连续化方法,在适当的条件下,得到了连接可行域内部任意给定的点和非凸规划的K-K-T点的同伦路径存在性的构造性证明,从而构建了可数值实现的全局收敛性算法.数值算例进一步验证了本文结果的有效性.     

On the ferromagnetic Ising model in noninteger spatial dimension

Using the necessary and sufficient conditions in terms of the high-field series coefficients that the Yang-Lee theorem holds, we prove rigorously by counterexample that it cannot be extended to general noninteger dimension, when such models are defined by the natural analytic continuation.Work supported in part by the US DOE.     

带常系数的Cauchy型奇异积分方程的快速方法

Petrov-Galerkin 方法是研究Cauchy型奇异积分方程的最基本的数值方法. 用此方法离散积分方程可得一系数矩阵是稠密的线性方程组. 如果方程组的阶比较大, 则求解此方程组所需要的计算复杂度则会变得很大. 因此, 发展此类方程的快速数值算法就变成了必然. 该文将就对带常系数的Cauchy型奇异积分方程给出一种快速数值方法. 首先用一稀疏矩阵来代替稠密系数矩阵, 其次用数值积分公式离散上述方程组得到其完全离散的形式,然后用多层扩充方法求解此完全离散的线性方程组. 证明经过上述过程得到方程组的逼进解仍然保持了最优阶, 并且整个过程所需要的计算复杂度是拟线性的. 最后通过数值实验证明结论.     

渐近非扩张半群公共不动点迭代逼近的CQ方法

该文在Hilbert空间中,利用CQ方法证明了修正渐近非扩张半群的Ishikawa迭代序列的强收敛性,此结果推广并改进了一些相关结论.