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An extension of Schwick's theorem for normal families

Yasheng YeXuecheng PangLiu Yang — 2015

Annales Polonici Mathematici

In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.

Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks

Yang LiuJianquan LuBo Wu — 2014

ESAIM: Control, Optimisation and Calculus of Variations

This paper investigates the output controllability problem of temporal Boolean networks with inputs (control nodes) and outputs (controlled nodes). A temporal Boolean network is a logical dynamic system describing cellular networks with time delays. Using semi-tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems. Some necessary and sufficient conditions on the output controllability two kinds of inputs are obtained by providing corresponding...

Blow-up of a nonlocal p-Laplacian evolution equation with critical initial energy

Yang LiuPengju LvChaojiu Da — 2016

Annales Polonici Mathematici

This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

The uniqueness of meromorphic functions ink-punctured complex plane

Hong Yan XuSan Yang Liu — 2017

Open Mathematics

The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).

Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

Yang LiuRongjiang YangJianquan LuBo WuXiushan Cai — 2013

International Journal of Applied Mathematics and Computer Science

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous...

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