Conjugation-invariant means

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Invariant Means on Chart Groups

The purpose of this paper is to give a stream-lined proof of the existence and uniqueness of a right-invariant mean on a CHART group. A CHART group is a slight generalisation of a compact topological group. The existence of an invariant mean on a CHART group can be used to prove Furstenberg’s fixed point theorem.

Means to Achieve Sustained Release of Synergistic Drugs by Conjugation

Two Means of Compensating Fiber Nonlinearity Using Optical Phase Conjugation

The growing demand of higher capacity over longer transmission distances has seen fiber nonlinearity as a major limiting factor in modern optical transmission systems [1, 2]. Among the methods under investigation, nonlinearity compensation using optical phase conjugation (OPC) has emerged as an effective means of suppressing the nonlinear impairments [3, 4, 5]. This paper shall discuss two type...

On the Inversion Invariance of Invariant Means

An invariant mean on a group G is a normalized, positive, translation invariant linear functional defined on the space of all bounded complex valued functions on G. Some groups possess an invariant mean (or are said to be amenable), while others do not. In particular, all abelian groups are amenable [2, §17.5]. An invariant mean on a group need not be inversion invariant. It is quite easy to sh...