Outer synchronization between drive-response networks with nonidentical nodes and unknown parameters

In this paper, through designing some proper controllers and adaptive updating laws, the outer synchronization between drive-response networks with nonidentical topological structure and unknown parameters are achieved and the unknown parameters are identified under given assumption. Several sufficient conditions for achieving outer synchronization are derived. Numerical simulations are provided to verify the effectiveness of the proposed methods.     

The conservation laws and self-consistent sources for a super-Yang hierarchy

In the present paper, a super-extension of the Yang hierarchy is proposed by super-matrix Lie algebras, and the super-Yang hierarchy with self-consistent sources is established. Furthermore, we establish infinitely many conservation laws of the super-integrable hierarchy. The methods presented by us can be generalized to other nonlinear equation hierarchies with self-consistent sources.     

Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces

In this paper, we consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. We construct a system of recurrence relations for the methods, and based on it, we prove an existence–uniqueness theorem that shows the R-order of the methods.     

A note on commutators of Hardy operators

Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample.     

Mean width inequalities for isotropic measures

In this paper, we establish Barthe’s mean width inequalities for continuous isotropic measures by a direct approach rather than using the Brascamp–Lieb inequality. The following results are obtained: among the convex hulls of the support of isotropic measures on S ^n–1, the regular simplex inscribed in the Euclidean unit ball has maximal ?-norm; in the dual situation, there is a reverse result for their polar bodies. Moreover, the case of even isotropic measures is also investigated.     

Hirota-Satsuma方程的N-孤子解(英文)

In this work,using the Hirota bilinear method,N-soliton solution is obtained for Hirota-Satsuma nonlinear evolution equation:u_t - u_xxt - 3u_xu_t + u_x = 0.     

Computation of matrix functions with deflated restarting

A deflated restarting Krylov subspace method for approximating a function of a matrix times a vector is proposed. In contrast to other Krylov subspace methods, the performance of the method in this paper is better. We further show that the deflating algorithm inherits the superlinear convergence property of its unrestarted counterpart for the entire function and present the results of numerical experiments.     

内PN*-群的结构(英文)

若有限群G的每个极小子群及4阶循环子群在G中正规,则称G为PN~*-群.本文给出了有限群的每个真子群都是PN~*-群但其本身不是PN~*-群的完全分类.     

Chan-Vese模型的共轭梯度算法

随着图像采集设备的发展和对图像分辨率要求的提高,人们对图像处理算法在收敛速度和鲁棒性方面提出了更高的要求.从优化的角度对Chan-Vese模型进行算法上的改进,即将共轭梯度法应用到该模型中,使得新算法有更快的收敛速度.首先,简单介绍了Chan-Vese模型的变分水平集方法的理论框架;其次,将共轭梯度算法引入到该模型的求解,得到了模型的新的数值解方法;最后,将得到的算法与传统求解Chan-Vese模型的最速下降法进行了比较.数值实验表明,提出的共轭梯度算法在保持精度的前提下有更快的收敛速度.