The Stable Class of the Augmentation Ideal

In [F.E.A. Johnson, Stable Modules and the D(2)-Problem, LMS Lecture Notes In Mathematics, vol. 301, CUP (2003)], for finite groups G, we gave a parametrization of the stable class of the augmentation ideal of Z[G] in terms of stably free modules. Whilst the details of this parametrization break down immediately for infinite groups, nevertheless one may hope to find parallel arguments for restricted classes of infinite groups. Subject to the restriction that Ext¹(Z, Z[G]) = 0, we parametrize the minimal level in Ω₁(Z) by means of stably free modules and give a lower estimate for the size of Ω₁(Z).     

一类时滞多组传染病模型的全局稳定性分析

本文研究具有变量分离发生率的具时滞的多组传染病模型.首先,分别针对强连通和非强连通情形,得到基本再生数$R_0$. 然后运用Lyapunov泛函方法和LaSalle不变集原理分别分析了当$R_0<1$时无病平衡点$P_0$ 的全局渐近稳定性以及$R_0>1$时地方病平衡点$P^*$的全局渐近稳定性.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

Uniform dimension results of multi-parameter stable processes

The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic Hölder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, ifZ is a stable (N,d, α)-process and αN ?d, then $\forall E \subseteq \mathbb{R}_ + ^N , \dim Z\left( E \right) = \alpha \cdot \dim E$ holds with probability 1, whereZ(E) = {x : ?t ∈E,Z _t =x} is the image set ofZ onE. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results.     

Evolutionary games

This paper deals with a mathematical game. As the name implies, the game concept is formulated with biological evolution in mind. An evolutionary game differs from the usual game concepts in that the players cannot choose their strategies. Rather, the strategies used by the players are handed down from generation to generation. It is the survival characteristics of a strategy that determine the outcome of the evolutionary game. Players interact and receive payoffs according to the strategies they are using. These interactions, in turn, determine the fitness of players using a given strategy. The survival characteristics of strategy are determined directly from the fitness functions. Necessary conditions for determining an evolutionarily stable strategy are developed here for a continuous game. Results are illustrated with an example.Dedicated to G. LeitmannThis work was supported by NSF Grant No. INT-82-10803 and The University of Western Australia (Visiting Fellowship, Department of Mathematics, 1983).     

Global stability of a multi‐group model with distributed delay and vaccination

A delayed multi‐group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number plays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable when , while the endemic equilibrium exists uniquely and is globally asymptotically stable when . For the proofs, we exploit a graph‐theoretical approach to the method of Lyapunov functionals. Our results show that distributed delay has no impact on the global stability of equilibria, and the results improve and generalize some known results. Copyright © 2016 John Wiley & Sons, Ltd.     

Global stability of a generalized epidemic model

The competitive exclusion principle is one of the most interesting and important phenomena in both theoretical epidemiology and biology. We show that the equilibrium in which only the strain with the maximum basic reproductive number exists is globally asymptotically stable by using an average Lyapunov function theorem and some dynamical system theory. This result is anticipated by H.J. Bremermann and H.R. Thieme (1989) [6] where they showed that the equilibrium is locally stable — the global result has not been established previously.     

RELAXATION SOLVERS FOR IDEAL MHD EQUATIONS-A REVIEW

We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH.     

Bifurcation in the stable manifold of a chemostat with general polynomial yields

A three‐dimensional chemostat with nth‐ and mth‐order polynomial yields, instead of the particular ones such as A+BS, A+BS², A+BS³, A+BS⁴, A+BS² + CS³, and A+BSⁿ, is proposed. The existence of limit cycles in the two‐dimensional stable manifold, the Hopf bifurcation, and the stability of the periodic solution created by the bifurcation is proved. Copyright © 2009 John Wiley & Sons, Ltd.     

Level Sets of Multiparameter Stable Processes

We establish the correct Hausdorff measure function for the level sets of additive strictly stable processes derived from strictly stable processes satisfying Taylor’s condition (A). This leads naturally to a characterization of local time in terms of the corresponding Hausdorff measure function of the level set.