in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

Voluntary acts are assumed to be initiated by their anticipated sensoric consequences. This old assumption (James, 1890/1981) was taken up recently by new models of Artificial Life and Psychology which share the notion of a close linkage between perception and action. The models of both disciplines stress the importance of the ability of a cognitive system to act and the importance of being sit...

The classical reduction techniques of bifurcation theory, Liapunov–Schmidt reduction and centre manifold reduction, are investigated where symmetry is present. The symmetry is given by the action of a finite or continuous group. The symmetry is exploited systematically by using the algebraic structure of the module of equivariant polynomial tuples. We generalize the concept of SAGBI-bases to mo...

The exterior algebra over the centre of a Lie algebra acts on the cohomology of the Lie algebra in a natural way. Focusing on nilpotent Lie algebras, we explore the module structure afforded by this action. We show that for all two-step nilpotent Lie algebras, this module structure is non-trivial, which partially answers a conjecture of Cairns and Jessup [4]. The presence of free submodules ind...

This paper describes a smart bushfire monitoring system that can provide an early warning message in case of a bushfire. The system utilises short message service through global system for mobile (GSM) communication technology as a medium of communication. The device is composed of a temperature and humidity sensors that are connected to a microcontroller. The microcontroller also interfaces wi...

Lerch’s formulae for Euler quotients in the rings Z and Fq[t] have already been studied. In this paper, we extend the study of these quotients to number fields and the Carlitz module. In the number fields case, we prove a version of Lerch’s formula for OKHil , the ring of integers of the Hilbert class field of a number field K. In the Fq[t] case, we replace the usual multiplication in Fq[t] wit...

This paper focuses on an overview of an autonomous navigation system in maritime transportation that is supplied with intelligent guidance to avoid collision, while respecting the COLREGs rules and regulations and using expert knowledge in navigation for close quarter’s manoeuvres. The proposed collision avoidance process consists of two modules: a fuzzy logic based parallel decision making mod...

The Lawrence-Krammer representation of the braid groups recently came to prominence when it was shown to be faithful by myself and Krammer. It is an action of the braid group on a certain homology module H2(C̃) over the ring of Laurent polynomials in q and t . In this paper we describe some surfaces in C̃ representing elements of homology. We use these to give a new proof that H2(C̃) is a free mod...