When writing the first edition of this book the procedural bent of judicial review in England and Wales could scarcely be exaggerated. The model of rationality, and more specifically what may be termed ‘process review’ on the basis that the decision has been reached in the wrong way, went in tandem with natural justice or procedural fairness. The Wednesbury umbrella of legal factors bearing on the exercise of administrative discretion and centred on purpose and relevancy thus lay at the heart of doctrinal analysis. Conceptually speaking at one with the traditional distinction between appeal and review, a distinctive and restricted focus on process rather than substance reflected and reinforced a more restrained judicial role than is currently fashionable.

In this chapter, we consider which regular polygons can be constructed by ruler and compasses. This requires more than the material of . Indeed, the chapter can be seen as an extended exercise of the theory ofto , together with the theory of 𝑝-groups and soluble groups. We need one more ingredient.

In any legal system, certain entities, whether they be individuals or companies, will be regarded as possessing rights and duties enforceable at law. Thus, an individual may prosecute or be prosecuted for assault and a company can sue for breach of contract. They are able to do this because the law recognises them as ‘legal persons’ possessing the capacity to have and to maintain certain rights, and being subject to perform specific duties. Just which persons will be entitled to what rights in what circumstances will depend upon the scope and character of the law. But it is the function of the law to apportion such rights and duties to such entities as it sees fit. Legal personality is crucial. Without it institutions and groups cannot operate, for they need to be able to maintain and enforce claims. In municipal law individuals, limited companies and public corporations are recognised as each possessing a distinct legal personality, the terms of which are circumscribed by the relevant legislation. It is the law which will determine the scope and nature of personality. Personality involves the examination of certain concepts within the law such as status, capacity and competence, as well as the nature and extent of particular rights and duties. The status of a particular entity may well be determinative of certain powers and obligations, while capacity will link together the status of a person with particular rights and duties. The whole process operates within the confines of the relevant legal system, which circumscribes personality, its nature and definition. This is especially true in international law. A particular view adopted of the system will invariably reflect upon the question of the identity and nature of international legal persons.

In this chapter, we discuss the essential ingredients of a wireless communications system. While we focus on these radio systems, the underlying concepts apply to a wide range of communications systems, including those that communicate via acous-tics, wires, and fiber optics. We introduce the idea of a communications link that uses the electromagnetic spectrum. We discuss sources of data that we communicate. We introduce the idea of the theoretical limit on data rates, given the communications channel, and provide an introduction to the characteristics of a simple channel, including propagation loss and noise. We provide an overview of the basic components of a radio system for the transmitter and receiver. We review the meaning of the Nyquist rate, and how we group signal energy into the overlapping ideas of samples, chips, symbols, or channel usage.

Lawyers tend to focus on procedural conceptions of administrative justice as the provision of appropriate machinery to arbitrate disputes between individuals and the state. This limited interpretation – what Creyke calls its ‘minimum meaning’ – is natural, since lawyers tend to see administrative law through the lens of the practitioner, whose function it is to provide legal redress for clients. A common starting point for a study of administrative justice is very much this perspective: a ‘top down’ view, in which courts retain the important prescriptive and standard-setting functions that many see as its core function and tribunals offer a less costly alternative to courts.

Suppose first that 𝑓 ∈ ℚ[𝑥]. As we have seen, we may factorize 𝑓 in an essentially unique way into irreducible factors. Further, 𝑓 can be written as λg, where λ ∈ ℚ and 𝑔 is a primitive element of ℤ[𝑥].