The Fourier analysis is applied to the deviations from divisibility, so that readers experience the first instances of mathematical dualities. Through this duality, we are able to see the congruence issues much better than solely dealing with them naively. The theory of quadratic binary equations yields the quadratic reciprocity law. Gauss’ eight proofs, save for the fifth, of it, as well as Legendre’s, are fully explained from various angles, which, as a whole, indicates the modern algebraic number theory and signifies the theory of primes in arithmetic progressions. We shall also be led inevitably to the history of the theory of algebraic equations, which will be presented with some concrete examples.

Matching available health resources to consumer needs is challenging. Governments and health bureaucracies with finite resources face increasing demands from their client populations, which often have complex health issues. No country prioritises resources to meet every single health need of every citizen; consequently, effective health service planning is critical to maximising population health outcomes and ensuring value for the available money. Due to the inherent contradictions existing between the high demand for and the limited responsive supply capacity by health services, health service planning is often characterised by negotiation, lobbying and compromise among various interest groups. A consensus can best be achieved if stakeholders agree upon a set of core values, and all involved in the process endorse principles and the procedures of planning. This chapter focuses on the practice of health service planning.

This chapter is essentially a treatise on the subject. We shall give all basic material on today’s theory of the distribution of prime numbers; note that we restrict ourselves to asymptotic study, as it is more basic. Thus all deep prime number theorem (Vinogradov’s, Huxley’s, Bombieri’s, Linnik’s) will be presented with complete proofs; analytic means as well are developed with full details. The sieve mechanism stemmed from Linnik and Selberg will be seen as the main mover of our discussion. In the final section, we shall deal with a recent astounding discovery on bounded gaps between prime numbers; our presentation is introductory but will suffice for readers to proceed to the full details.

This chapter offers a fresh reconstruction of the (legal) power to act punitively in torts that is respectful of the wrongdoer–victim perspective and, more particularly, to the substantive content of the victim’s punitive responses to categories of reprehensible wrongdoing. It challenges the assumption that criminal law and the criminal procedure are the exclusively valid institutional venues for the imposition of punishment by suggesting that Relational Retribution be a viable and valuable mode of institutional moral communication between the private parties that is proper of the role of the victim in tort law and its bilateral structure. It recognizes the special position of the victim herself to personally provide sufficient reasons for the court to exercise its power and impose a punitive sanction on the reprehensible wrongdoer. Ultimately, the idea underlying this chapter is that, if we care about individuals’ ability to engage meaningfully with their peers, we should ensure the availability of legitimate, official channels for institutional expression, one that tort lawsuits provide.

The urbanization process has been long intertwined with environmental problems. Human settlements and their growth create demands on the local resource base often resulting in depletion and degradation of these materials. Urban development and attempts to resolve these issues impact the everyday needs and activities of residents of these places and create stresses and crises. The objective of this chapter is to present the conditions through which these stresses and crises emerge and the associated inefficiencies and inequities typically embedded in these processes. These stresses and crises can take place when resources are both brought into cities and distributed around cities, and when waste generated from these practices is managed. Basic factors that mediate these conditions including population, level of wealth, social organization, and access to technology are introduced. The role of choice and what factors enable or constrain choice are explored and examples are presented. How choice is socially constructed and by whom and in whose interests are significant issues examined. The unintended consequences emerging from interim environmental solutions embedded within policy choices are richly detailed in the urban environmental literature and play a significant role in the chapter’s overarching aim.

Congruence theory is the same as the study of the deviations from divisibility. With this view, here a basis of modern number theory is constructed. It is built, however, on the availability of prime power decomposition of moduli, save for the linear case. We shall show this aspect can be reverted to an extent so that the integer factorization, one of the fundamental issues in whole mathematics and also in our digital life, can be discussed with certain success. Our approach also yields a description of a quantum factorization algorithm solely with plain mathematical terms. Further, we shall hint at another great issue, the general reciprocity among power residues, from which the modern algebraic number theory stemmed.

Since the advent of ChatGPT in November 2022, public discourse has intensified regarding the intersection of artificial intelligence and intellectual property rights, particularly copyright. Large language models (LLMs) like ChatGPT and Gemini have sparked debates about what deserves copyright protection and what constitutes copyright infringement. Key questions arise: Are LLM-generated outputs original enough to merit copyright protection? And do they infringe upon existing copyrighted works used in their training data? This chapter delves into these issues, examining the legal and ethical implications of training LLMs on copyrighted material. The chapter also explores the concept of fair use, the potential for transformative use of copyrighted works, and the evolving landscape of copyright law in the age of AI.

Lack of compassion among health service staff has been identified as a concern around the world. High-profile scandals and inquiries in the United Kingdom have suggested that health systems and services ‘are struggling to provide safe, timely, and compassionate care’. In the United States, only half of patients and staff surveyed believed the health system provides compassionate care. Similarly, a recent study in Australia identified a gap between the intentions of organisational leadership to provide consistently high-quality care and the ability of staff to do so at point of care. Healthcare managers are looking for proven ways to support staff to recognise and provide compassionate care.

This chapter examines the theoretical foundations of intellectual property law in the United States, setting the stage for understanding the challenges posed by artificial intelligence. The chapter focuses on utilitarianism as the dominant theoretical framework for US IP law, contrasting it with non-consequentialist theories. It provides a brief overview of the four major IP regimes:

Patent patent and copyright, which are explicitly grounded in the Constitution’s mandate to "promote the Progress of Science and useful Arts"; Trademark, which aims to reduce consumer search costs and ensure fair competition by protecting source identifiers; and Trade secret, which has a more convoluted history but has increasingly focused on promoting innovation and protecting confidential business information. The chapter emphasizes that US IP law prioritizes practical, societal outcomes over moral or philosophical considerations. It sets the stage for subsequent chapters that explore how AI’s emergence challenges these traditional theoretical underpinnings and the practical functioning of each IP regime.

A 2021 report on a study of workplace conflict in the United Kingdom concludes that, in 2018–19, more than 35 per cent of respondents reported workplace conflict, with an estimated 485 000 employees resigning as a result. Managers need to understand that conflict does not resolve itself; rather, it tends to gather intensity and energy. Gupta, Boyd and Kuzmits have found that ‘employees spend as much as 42 percent of their time engaging in or attempting to resolve conflict and 20 percent of managers’ time is taken up by conflict-related issues’. Managing conflict is one of the primary responsibilities of managing staff and teams, particularly in multicultural work environments. Understanding what is ‘culturally normative in terms of self-worth, confrontation, emotional expression, and managerial intervention can help [staff] involved in workplace conflict understand what they are experiencing’. Additionally, it can help managers intervene appropriately. In this chapter, different types and origins of conflict are discussed, as well as approaches to managing and resolving conflict.

Finally, Chapter 6, ‘From permissive consensus to persistent critique’, turns to the most recent past of the Convention. It shows how the critique of the eighties became unsustainable by an unforeseen event: the end of the Cold War. This galvanized the earlier hesitant governments into accepting permanent supranational oversight. However, the signatory states’ caution had not suddenly disappeared. The concerns of the 1980s may have been briefly interrupted in the 1990s, but remained a constant factor.

The Convention also became a topic of public debate in the Netherlands from 2010 onwards: in order for that debate to flourish, a fundamental change in the previous, rather self-evident acceptance of human rights as inherently desirable was brokered, as the Court got caught up in wider debates surrounding national identity and migration.

Finally, the chapter sheds light on the persistent challenges the Convention keeps posing to the Kingdom. Caught between Dutch and Caribbean unwillingness, sensitivities and financial limitations, human rights standards occasionally lose out. The Convention has come to serve as a reminder of the shared responsibility of all in addressing those problems, but remains tied to historical grown discrepancies.