This chapter introduces the various processes by which the Song government obtains resources from its people to pay for its expenses, and also how the Song state, in pursuit of its interests, is able to manage economic activities. After outlining the dynamics of Song society and the economy, it introduces tensions generated by the various goals the fiscal administration pursued at different political and military periods. The third and main section of the chapter offers an overview of the different taxes and tax mechanisms that the state used to extract revenues from the various sectors of the economy. Emphasis is placed on the state tea and wine monopolies which were crucial both for public finance and for guidance of the Song economy. The conclusion offers some answers to the problems raised by the tensions within this system.

The first topics of study in many courses in graph theory are matchings, paths, and cycles in graphs. We introduce basic graph theoretic methods and focus on extremal aspects of these topics. We start with k-cores and maximum cuts in graphs, and move on to Hall’s Theorem and Tutte’s 1-Factor Theorem, the Tutte–Berge Formula, and the extremal problem for matchings. We study the extremal problem for paths in graphs, covering the Erdős–Gallai Theorem and the Erdős–Sós Conjecture, Perles’ proof via geometric graphs, Kopylov’s Theorem, the Pósa’s Rotation Lemma, and theorems on hamiltonian graphs such as Dirac’s Theorem and the Bondy–Chvátal closure theorem, and the Smith–Thomason theorem on uniquely hamiltonian graphs.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Australia and New Zealand, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, we reflect on influential factors that are either facilitating or inhibiting the study of PoR, including publication options, topical emphases, practitioners, orientations, methodologies, and professional organizations.

We offer opinions concerning future development topics that are emerging as important in the immediate future and/or are perennially important in order to stimulate creative and useful research including Western theoretical relevance, the extent to which Western PoR theories may or may not contain reasonable expectations and concepts for this region, contextual nuances, Indigenous theoretical concerns, collaborative research opportunities, and common faux pas – reflections on what people unfamiliar with this region commonly and incorrectly assume about conducting PoR work in this context.

This chapter explores how Indigenous relationships with Country and Indigenous knowledge systems can profoundly reshape mainstream societies’ understanding of place and planet. Using reflections from Gumbaynggirr and Awabakal Country, it demonstrates how Indigenous conceptions of Country embody deep kinship ties to land, waters, environment, and community, extending far beyond Western notions of land as property or resource. Dreaming stories illustrate sophisticated understandings of long-term environmental change and offer crucial lessons in sustainability, custodianship, and adaptation. The chapter also highlights the transformative role of universities, particularly through positions such as Pro Vice-Chancellor (Indigenous), in embedding Indigenous knowledge across all disciplines, building bicultural competence, and reshaping curricula to reflect Aboriginal perspectives. This integration enriches both teaching and research, while fostering respectful and reciprocal engagement with Indigenous communities. Ultimately, such approaches promote collective responsibility for Country and advance more sustainable, just, and enduring futures.

Empirical tests are necessary for the advancement of theories. Clear theoretical definitions enable researchers to find or create instances of the abstract concepts. Empirical tests can be done using a variety of methodologies. Some empirical tests supply more information than others based on how many alternatives interpretations for the results can be ruled out. Stronger tests are those that offer more precise predictions. Replications of tests are important for the advancement of theory. We differentiate between empirical replications, which use the exact same measurements to test a theory and theoretical replications, which use differing operationalizations to test a theory. Both types of replication are important and rely on researchers making their reasoning and test materials publicly available.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Ghana, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, we reflect on influential factors that are either facilitating or inhibiting the study of PoR, including publication options, topical emphases, practitioners, orientations, methodologies, and professional organizations.

We offer opinions concerning future development topics that are emerging as important in the immediate future and/or are perennially important in order to stimulate creative and useful research including Western theoretical relevance, the extent to which Western PoR theories may or may not contain reasonable expectations and concepts for this region, contextual nuances, Indigenous theoretical concerns, collaborative research opportunities, and common faux pas – reflections on what people unfamiliar with this region commonly and incorrectly assume about conducting PoR work in this context.

Urban development in colonial societies like Australia and the United States often results in disconnected car-based subdivisions lacking focal points, identity, or a true sense of place. Yet examples of intentional “complete communities” show alternative possibilities. Ellenbrook, established in Perth, Western Australia in 1994, has for over 30 years demonstrated leadership in creating connected, walkable neighbourhoods around a transit-ready, mixed-use town centre. In 2015, FIABCI, the International Real Estate Federation, recognised Ellenbrook as the world’s best master-planned community. Its design draws on Western Australia’s mid-20th-century planning culture, influenced by pioneers such as Margaret Feilman OBE, who emphasised neighbourhoods reflecting culture, climate, and biodiversity, and Prof George Seddon, who introduced “sense of place” into environmental design. Both shaped the timeless principles applied at Ellenbrook. This chapter explores Ellenbrook’s features that create a tangible sense of “there,” and considers opportunities to revive the art of town founding and planning across Australia’s metropolitan growth areas.

As documented exhaustively through human art, architecture, gardens, music, histories, myths, legends, poetry and prose, our species does not merely ‘exist’ within a physical environment; we interact with it and derive important meaning from it. Indigenous Peoples, artists and Western environmental psychologists alike appreciate that landscapes, places and buildings are more than just props in our lives; they are imbued with meaning, collective memory and resonance (Altman, 1975; Cole et al., 2024).

The method of hypergraph containers is a modern incarnation of a classical proof technique concerned with enumerating certain classes of graphs. Perhaps the origins of the method lie in a paper of Kleitman and Winston about enumerating the number of n-vertex graphs containing no 4-cycle. The full generality and power of this approach became evident only in the past decade when very general theorems were proved with wide applicability to a host of questions. These results are concerned with counting the number of independent sets in a hypergraph. Two essentially equivalent approaches were developed by Saxton and Thomason and by Balogh, Morris, and Samotij, and our goal is to state one of these results and give some applications.

The Epilogue draws out the broader implications for the rise of the Atlantic world in the early modern public sphere, demonstrating, first, that what happened in and across the ocean mattered to people at home, and, second, why managing news became a concern for authorities who gradually lost their information monopoly regarding developments across the Atlantic. It reflects on the historiographical repercussions for the fields of Atlantic history and the history of news – making fresh connections to the transoceanic exchange of people, commodities, values, and ideas.

In this chapter, we deal with extremal problems for uniform hypergraphs that are motivated by Turán’s graph theorem. These extremal problems are substantially more difficult than for graphs, and indeed the extremal problem for hypergraph cliques remains unsolved, even asymptotically as the number of vertices grows. Perhaps the most notorious conjecture is the Turán conjecture from 1941 about the maximum density of a triple system on n points that contains no copy of the tetrahedron. This chapter explores a variety of Turán-type problems for hypergraphs while introducing the important methods in this area.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in United Kingdom, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, we reflect on influential factors that are either facilitating or inhibiting the study of PoR, including publication options, topical emphases, practitioners, orientations, methodologies, and professional organizations.

We offer opinions concerning future development topics that are emerging as important in the immediate future and/or are perennially important in order to stimulate creative and useful research including Western theoretical relevance, the extent to which Western PoR theories may or may not contain reasonable expectations and concepts for this region, contextual nuances, Indigenous theoretical concerns, collaborative research opportunities, and common faux pas – reflections on what people unfamiliar with this region commonly and incorrectly assume about conducting PoR work in this context.

From this chapter on, we study graded quotients of upper ramification subgroups. In this chapter we prove that the graded quotients are abelian and annihilated by p. The proof is by reduction to the classical case where the extension is totally ramified. The geometric fact behind this property is that the closed fiber of the covering of stable integral models is étale. Other tools used in the proof of the reduction are the first homology group of the cotangent complex and the Tor group of the module of relative differential forms.

Providing a cohesive reference for advanced undergraduates, graduate students, and even experienced researchers, this text contains both introductory and advanced material in extremal graph theory, hypergraph theory, and Ramsey theory. Along the way, this book includes many modern proof techniques in the field, such as the probabilistic method and algebraic methods. Several recent breakthroughs are presented with complete proofs, for example, recent results on the sunflower problem, and off-diagonal and geometric Ramsey theory. It is perhaps unique in containing material on both hypergraph regularity and containers.

Featuring an extensive list of exercises, this book serves as a valuable teaching resource for a variety of courses in extremal combinatorics. Each of the two parts can form the basis of separate courses, and the majority of sections are designed to match the length of a single lecture.

The surge in archaeological activity since the 1950s has led to the discovery of a large number of Song burials in northern China, adorned with pictorial scenes and architectural motifs. This chapter investigates the decoration of these tombs, shifting our focus from the elaborate tombs themselves to the individuals who constructed them. By emphasizing the significance of burial practices during the Song dynasty, it becomes clear that tombs not only continued to reflect principles of filial piety and ancestral reverence but also became a critical force in shaping cultural values and social order. These tombs can be interpreted as a form of self-expression by the wealthy class, emerging from the interplay between ritual regulations and regional social customs, while simultaneously serving as focal points for family bonds, ancestor veneration, and belief systems.

I present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Egypt, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, I reflect on influential factors that are either facilitating or inhibiting the study of PoR, including publication options, topical emphases, practitioners, orientations, methodologies, and professional organizations.

I offer opinions concerning future development topics that are emerging as important in the immediate future and/or are perennially important in order to stimulate creative and useful research including Western theoretical relevance, the extent to which Western PoR theories may or may not contain reasonable expectations and concepts for this region, contextual nuances, Indigenous theoretical concerns, collaborative research opportunities, and common faux pas – reflections on what people unfamiliar with this region commonly and incorrectly assume about conducting PoR work in this context.