Generalisation : graphs and colourings

The interaction between practice and theory in mathematics is a central theme. Many mathematical structures and theories result from the formalisation of a real problem. Graph Theory is rich with such examples. The graph structure itself was formalised by Leonard Euler in the quest to solve the problem of the Bridges of Königsberg. Once a structure is formalised, and results are proven, the mathematician seeks to generalise. This can be considered as one of the main praxis in mathematics. The idea of generalisation will be illustrated through graph colouring. This idea also results from a classic problem, in which it was well known by topographers that four colours suffice to colour any map such that no countries sharing a border receive the same colour. The proof of this theorem eluded mathematicians for centuries and was proven in 1976. Generalisation of graphs to hypergraphs, and variations on the colouring theme will be discussed, as well as applications in other disciplines.peer-reviewe

Frequency planning optimisation in real mobile networks

Due to the annual increase of cellular subscribers, there is a growing interest by the network operators, in how to deploy the network infrastructure to achieve maximum capacity. A key point is the channel or frequency assignment, which implies efficiently assigning frequencies from a limited set, to each cell, while satisfying the electromagnetic compatibility constraints.Peer ReviewedPostprint (published version

The mobile commerce technologies: Generations, standards and protocols

Mobile Commerce has staged a remarkable come-back. Driven by the technological innovations in the field of telecommunications, it is showing signs of a healthy recovery. The collapse of the dot-com boom in 2001/2002 had dealt a severe blow not only to Electronic Commerce but also to Mobile Commerce, which was just about developing at that time. In addition to a general lack of customer demand for mobile, location-based, services, it suffered heavily under the technical deficiencies of end-devices, slow data transmission and unripe technological standards. These factors in turn had a negative impact on the customer acceptance of mobile services and whatever little demand was available, was rendered useless. Many of the environmental conditions have changed since then. Technology innovations have reduced many barriers to acceptance. Increasing globalization has led to more mobility and therefore to greater demand for mobile, ubiquitios services that can be consumed anytime, anywher. This paper examines different telecommunication technologies regarding their suitablilty and deficiencies. It provides an overview over the historical development of mobile technologies while pointing towards the expected future scenario. --Mobile Commerce,M-Commerce,UMTS,WLAN,3G