Almost all magnetically ordered materials involve 3d or 4f elements. The late 3d metals and their alloys, including interstitial alloys and intermetallic compounds, are frequently ferromagnetic. Large magnetocrystalline anisotropy in 3d–4f inter-metallics, due mainly to the rare-earth, gives useful hard magnets. Conversely, the anisotropy can be reduced practically to zero in certain 3d alloys and, when magnetostriction is also vanishingly small, perfect soft ferromagnetism results. Oxides and other ionic compounds are usually insulators with localized electrons. There, anti-ferromagnetic superexchange coupling leads to antiferromagnetic or ferrimagnetic order. Some oxides, however, are metals, with the d-electrons forming a conduction band. Occasionally the 3d band is half-metallic. 44 representative materials are described, and some data is provided on 300 others. A few examples are included of magnetically-ordered materials that include neither 3d nor 4f electrons.

A magnetic material must first be grown in a form appropriate for the measurement — crystalline or amorphous, bulk, thin film or particulate, and characterized structurally by X-ray or electron diffraction. Central to most magnetic measurements is the generation and detection of magnetic fields. Atomic-scale magnetic structure is best probed by neutron diffraction, while other atomic-scale element-specific information is provided by spectroscopic methods, especially using synchrotron radiation. Domain-scale magnetization measurements are made by magneto-optic methods or magnetic force microscopy, whereas macroscopic measurements of magnetization are made in open or closed circuit by a variety of methods. Spin-wave and other excitations are best explored by inelastic neutron scattering. Numerical methods of investigation are of growing importance for understanding the static and dynamic behavior of real magnetic materials and magnetic systems.

This chapter explores the definition of Chinese and introduces the field of linguistics and its key sub-disciplines, the two fundamental concepts that set the stage for a study of Chinese linguistics. Chinese is then situated in its geographic and linguistic landscape, elucidating its genetic and contact relationships. The history behind the establishment of Modern Standard Chinese is presented, along with some of its linguistic features. The chapter concludes with a preview of the contents of the rest of the textbook.

This Chapter provides a close reading of the Declaration’s text. Supporters of the thirteen independent nations argument rely almost entirely on the Declaration’s assertion about “Free and Independent States.” Yet, this assertion is far less compelling than is often claimed, and the relevant passage can be read quite differently (as declaring the independence of the “United Colonies”). More importantly, other passages in the Declaration strongly support a “one nation” argument, including the document’s opening reference to “one People” and its conspicuous failure to identify any state by name. The Chapter also focuses on the importance of the capitalization of “United Colonies” and “Free and Independent States” as well as the “United States of America” (phrases where the Dunlap broadside differs from the ceremonial parchment, an issue that prior historians have often bungled).

Many scholars believe 1804 marks the beginning of Blake’s composition process for Milton: A Poem, a work whose plates were subsequently repurposed several times. This chapter reads Milton’s celebrated vortex passages as a response to the emergence of time-critical media in the early Romantic period. For Wolfgang Ernst, time-criticality refers to the temporalizing functions of media or the introduction of new temporal logics that transform how we interact with the signals such media produce. I highlight a gap between a cultural analysis of history in Milton: A Poem and a media archaeological analysis of the poem’s time-criticality by reading the poem in both senses. In addition to representing the history of Blake’s ideological relationship to history and time in 1804, I suggest that attention to the poem’s media materiality adds to our historical understanding of the first decade of the nineteenth century. Overall, my work emphasizes Blake’s history as a construction of temporal and archival techniques by delineating how time is produced by the infrastructures mediating Blake’s poem.

This chapter sets out the argument for Bingham’s conception of the rule of law. First, it exposes the political roots of the legal positivist ‘thin’ conception of the rule of law. Second, it shows that examples on which the thin conception relies, notably slavery and apartheid South Africa, when properly examined, both support the thick conception and illustrate the important connection between the procedural and the substantive dimensions of the rule of law. That connection raises the issue of the status of international law and it shows, third, how the UK dualist tradition is merely the way that the UK manages its commitment to international law, understood as part of its commitment to the rule of law. Finally, the chapter shows that the common good lawyers’ conception of sovereignty is one of executive, not parliamentary sovereignty.

The independence number of a hypergraph H is the maximum size of an independent set of vertices of H – a set of vertices containing no edges of H. The problem of determining the maximum size of an independent set in an r-uniform hypergraph with a prescribed number of vertices and edges is equivalent to the notorious Turán problem for hypergraphs. In this chapter, we consider the fundamental problem of lower bounds on the independence number of H when H is an n-vertex r-uniform linear hypergraph of average degree d, with an illustration of applications to the Erdős–Heilbronn triangle problem and to lower bounds on extremal numbers for bipartite graphs. In particular, we give a novel proof of the Ajtai–Komlós–Pintz–Spencer– Szemerédi Theorem, giving large independent sets in uncrowded hypergraphs.

The proliferation of artificial intelligence (AI) technologies has introduced a profound paradox: while AI promises efficiency, automation and insight, its growing energy consumption, computational demands and infrastructural dependencies increasingly strain ecological and technological limits. This chapter addresses the behavioural and systemic dynamics that shape the sustainability of AI itself – not only in terms of ethics or outcomes, but in terms of its continued viability in a resource-constrained world. Drawing from systems theory, behavioural modelling and computational sustainability, we examine how AI behaves as a system-of-systems, how those behaviours accumulate energy and material costs and what design principles might render AI more compatible with long-term environmental and economic thresholds. By analysing patterns such as runaway model scaling, overfitting to hardware architectures and unsustainable data pipelines, the chapter outlines a Behavioural Data Science approach to understanding and modifying AI’s systemic impact. Through case studies and modelling strategies, it argues that AI’s future must be governed not only by performance metrics, but by its capacity to sustain itself – ecologically, computationally and institutionally – within the planetary boundaries.

An r-sunflower is a collection of sets such that there is a set C (possibly the empty set) called the core, for which every two of the sets have intersection exactly C. Sunflowers are one of the most important structures in extremal set theory since they are the only configuration that one is guaranteed to contain in any sufficiently large collection of k-elements sets. The simple structure of a sunflower enables one to prove many theorems in combinatorics and beyond. This chapter considers the basic theory of sunflowers, culminating in recent breakthroughs.

This chapter explores the use of natural language processing and large databases of digitised text to make inferences about the psychology of authors, including their emotional state, cognitive abilities and beliefs. By analysing longitudinal data, researchers can investigate how behaviour, psychology and culture change over time. The chapter addresses various research questions, including how language evolves, how mental health and rationality change over time and the relationship between mental suffering and artistic output. The chapter aims to provide readers with an understanding of the methodologies, workflows and resources used to conduct this type of research, as well as potential pitfalls and ways to avoid them. It also highlights exceptional work in this field. The chapter emphasises that natural language processing and behavioural insights are allowing researchers to answer questions about human psychology and culture at an unprecedented scale.