关于“Several Inequalities of Matrix Traces一文的几点意见

本文指出了《数学季刊》第十卷第二期中发表的一篇文章“Several Inequalities of Matrix Traces”中的几点失误。     

Hyperbolic metric and normal family

In this paper, we study the normality of the family of meromorphic functions from the viewpoint of hyperbolic metric. Then, a new sufficient and necessary condition is obtained, which can determine a given family of meromorphic functions is normal or not.     

A contact process with a semi-infected state on the complete graph

In this paper, we are concerned with a contact process with a semi-infected state on the complete graph C_n with n vertices. Our model is a special case of a general model introduced by Schinazi in 2003. In our model, each vertex is in one of three states, namely, “healthy,” “semi-infected,” or “fully-infected.” Only fully-infected vertices can infect others. A healthy vertex becomes semi-infected when being infected while a semi-infected vertex becomes fully-infected when being further infected. Each (semi- and fully-) infected vertex becomes healthy at constant rate. Our main result shows a phase transition for the waiting time until extinction of the fully-infected vertices. Conditioned on all the vertices are fully-infected when t = 0, we show that fully-infected vertices survive for exp?{O(n)} units of time when the infection rate λ > 4 while they die out in O(log?n) units of time when λ < 4.     

Search strategies investigation in brain storm optimization

The canonical brain storm optimization (BSO) employs clustering, creating and selecting operators, which are all connected and have great impacts on the optimization performance. In this paper, the state-of-the-art search strategies are introduced and the potential strengths and weaknesses of these strategies in the BSO algorithm are analyzed and compared from the perspective of the analytical model rather than any metaphors. The numerical experiments are carried out to artificially amplify and highlight the performance of various strategies. Finally, the progressive directions of the BSO algorithm are discussed for further research.     

Coderivatives of the generalized perturbation maps

This paper is devoted to considering the coderivatives of the generalized perturbation maps in general Banach spaces. Under some mild conditions, the upper estimate of coderivatives of the generalized perturbation maps are obtained. Their exact calculus rules are obtained under some additional conditions. Furthermore, the generalized perturbation maps are shown to be differentiably regular under some strong conditions.     

Smooth solutions for a stochastic hydrodynamical equation in Heisenberg paramagnet

In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.     

Comment on “On the Neumann function and the method of images in spherical and ellipsoidal geometry”

In this note, we point out two errors in the article “On the Neumann function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed.