具有时滞的一般型脉冲神经网络的指数稳定性

讨论具有时滞的一般性脉冲神经网络的稳定性.在不假定激励函数有界或可导的前提下,利用非光滑分析和Lyapunov泛函,得到了这类神经网络系统平衡点的存在唯一性和全局指数稳定性判别准则.作为特例,得到了Hopfield神经网络,时滞细胞神经网络,双向联想记忆神经网络的平衡点的存在唯一性和全局指数稳定性判定定理.     

Clarification of the role of protein in carbonmonoxy myoglobin by investigating electronic states

This article reports the proton tautomerization effects of distal histidine residues in carbonmonoxy myoglobin according to the density functional calculations of the whole protein. The electron eigenstates and electrostatic potential (ESP) distributed around heme and its pocket vary significantly depending on the protonation positions of the distal histidine residues. To investigate the range over which the electronic structures are affected by the proton tautomerization, the quantum mechanics/molecular mechanics (QM/MM) method is applied to probe the QM size to reproduce the atomic partial charges and ESP around the active center. Consequently, we show that these properties converged for the 300 pm QM/MM system in this study. During the analysis, we also find that amino residues such as Phe43, Val68, and Phe138 interact strongly with heme through orbital mixing, indicating that the protein is a medium not only interacting with the reaction center, but also buffering on electrons. © 2013 Wiley Periodicals, Inc.     

Branching Numbers for Euclidean Projections onto Convex Polyhedra

The purpose of this note is to give a short proof of the theorem of Ralph in Linear Algebra Appl. 178 (1993), 249–260, on the geometry of projection maps. This theorem implies that the so-called normal maps derived from projections satisfy a general geometric criterion for bijectivity of piecewise affine maps given by Kuhn and Löwen in Linear Algebra Appl. 96 (Section 5.3), (1987), 109–129. As a consequence, one obtains Robinson's characterization of bijectivity of normal maps.     

Generalized Alexandroff Duplicates and CD 0(K) spaces

We define and investigateCD _Σ,Γ(K, E)-type spaces, which generalizeCD ₀-type Banach lattices introduced in [1]. We state that the space CD _Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].     

Topological classification of linear hyperbolic cocycles

In this paper linear hyperbolic cocycles are classified by the relation of topological conjugacy. Roughly speaking, two linear cocycles are conjugate if there exists a homeomorphism which maps their trajectories into each other. The problem of classification of discrete-time deterministic hyperbolic dynamical systems was investigated by Robbin (1972). He proved that there exist 4d classes ofd-dimensional deterministic discrete hyperbolic dynamical systems. We obtain a criterion for topological conjugacy of two linear hyperbolic cocycles and show that the number of classes depends crucially on the ergodic properties of the metric dynamical system over which they are defined. Our result is a generalization of the deterministic theorem of Robbin.     

关于Teichmuller空间中一个问题的注记

本文指出了Ara Basmajian在美国数学会出版的“Contemporary Mathematics”第221卷中提出的一个关于Teichmuller空间的问题的答案是完全否定的。     

Actions of finitely generated groups on the universal Menger curve

We prove that every finitely generated group acts effectively on the universal Menger curve.

     

tvs锥度量空间上同胚映射的可扩性

设$f$是紧tvs锥度量空间上同胚映射. 本文证明了$f$是tvs锥可扩的当且仅当$f$有生成元. 进一步, 如果$f$是tvs锥可扩的,则具有收敛半轨的点集是可数集. 本文的这些结果改进了拓扑动力系统的一些可扩同胚定理, 将有助于研究tvs锥度量空间上同胚映射的动力性质.     

On the topological equivalence of flows of Brouwer homeomorphisms

We prove that the set of all regular points of a flow of Brouwer homeomorphisms is invariant under topological equivalence of flows. We also show that a similar result holds for the first prolongational limit set.     

平均跟踪与伪轨跟踪

证明了紧致度量空间中有伪轨跟踪的distal同胚不具有平均跟踪性,并给出了有平均跟踪性的同胚是极小的一个充分条件。