6A Radiation as a photon gas

In the nineteenth century, physicists applied classical electromagnetic theory to explain the experimental results of black body radiation but were unable to provide an adequate explanation. This was a major problem to the physicists as classical theory predicted an infinite amount of energy of the radiation emitted from a black body. This gross disagreement was called the “ultraviolet catastrophe”. Max Planck presented a paper on December 14, 1900, in which he guessed the answer to this problem of black body radiation. This guess marked the very beginning of quantum mechanics.

The electromagnetic radiation inside a black body chamber exists as patterns of standing waves or modes. A single mode is like a standing wave on a guitar string and is characterized by a frequency. Planck made a bold hypothesis that the energy of such a mode is quantized, ithat is, only certain energies of these oscillation modes are allowed. Thus, the energy 𝐸𝑛 of 𝑛th mode is given by 𝐸𝑛 = (𝑛 + 12 ) ℏ𝜔 = (𝑛 + 12 ) ℎ𝜈, where 𝜈 is the oscillation frequency, ℎ is Planck's constant, and 𝑛 is an integer starting with 0. Thus, each oscillation mode can exist in any one of an infinite number of energy states whose energies are equally separated by the energy ℏ𝜔. In the discussion of the properties of the photon gas, for the time being, we shall ignore 12 in the expression for 𝐸𝑛 as it has no effect on the results we seek. Therefore, we take 𝐸𝑛 = 𝑛ℏ𝜔 as the energy of the 𝑛th mode whose (angular) frequency is 𝜔. When the energy of a mode is 𝐸𝑛, we say that there are 𝑛 photons in the mode. Each photon has energy equal to ℏ𝜔. Thus, according to the prescription of Max Planck, a black body radiation chamber consists of a number of photons in various energy states with different amounts of energy.

Background

Madhesh, a region rich in culture and history and the heartland of the ancient Mithila kingdom, is celebrated as the birthplace of revered figures such as Sita and Gargi, women who embody wisdom, power, and empowerment. As daughters of Mithila, their legacy should have been one of empowerment for all Madheshi women, fostering a sense of strength and agency among those residing in their homeland. Yet, contrary to this legacy, Madheshi women today find themselves marginalized in their own land, treated as outsiders both by their own patriarchal society and by the nationalist discourse of the Nepali state, which views Madhesh as a peripheral and contested space. This dual marginalization places Madheshi women in a complex state of “otherness,” where they are not only excluded from the mainstream narratives of Nepali identity but also subjected to restrictive patriarchal norms within their own community (Gautam 2008; Ghimire 2018). To understand this paradox, we must delve into the forces that have conspired to marginalize these women and examine why the legacy of empowerment has not been passed down to the women of Mithila, that is, “Madhesh.”

In the sociopolitical landscape of Nepal, Madheshi women endure a unique form of intersectional oppression that intertwines gender-based and ethnic discrimination. They face the multidimensional nature of marginalization that includes patriarchal constraints within their community and systemic exclusion from the broader nationalist discourse. As a result, Madheshi women find themselves “doubly othered,” experiencing dual layers of discrimination that render their struggles distinct within Nepal's feminist and social justice movements.

This chapter offers an overview of how artificial intelligence (AI) systems are being used (and could potentially be used) within the context of public courts to help predict legal outcomes, generate content such as motions and other court documents, make recommendations to legal stakeholders regarding positions to adopt (including whether to go forward with a suit) or become a substitute to human judges in the decision-making process. Looking at all these potential scenarios, the authors present the pros and cons of relinquishing a portion of legal stakeholders’ autonomy to AI systems, focusing on underlying risks linked to bias, datasets and a pervasive misunderstanding of what AI system are, and what they can do. The chapter suggests that, while the use of AI can, in many instances, positively affect impediments to access to public courts such as delays, and cost, legal stakeholders need to better understand how this can impact fundamental legal tenets.

In this chapter, we restrict our attention to the Hilbertian framework and get some estimates of the essential norms involving the Nevanlinna counting functions. In particular we get (or recover) characterizations of the compactness of composition operators.

We provide an overview of interatomic potentials, explaining their components and significance. Moving from simple to complex formalisms, we discover pair-wise potentials and multi-body potentials, demonstrating their importance in modelling atomic interactions. We then focus on interatomic potentials for metals, exploring their specific characteristics and applications. Additionally, we discuss force fields and machine learning approaches, highlighting their role in enhancing accuracy and efficiency. Finally, we outline the essential requirements for developing high-quality interatomic potentials.

The Introduction establishes the aims and bounds of the study, which examines attitudes towards, and uses of, the written word in Kent, Mercia and Wessex from the 830s to the 920s. The Introduction provides an overview of scholarship that has informed the study, as well as the new perspectives that it seeks to provide. The structure of the study is also explained.

Perimenopause is a period of heightened risk of onset and relapse of mental illnesses including depressive disorders, schizophrenia spectrum disorders and bipolar affective disorder, as well as a time of increased risk of psychological symptoms including low mood, cognitive problems and anxiety. Perimenopausal depression can be seen as a distinct diagnostic entity with specific clinical features and treatment pathways. The risk of suicide in the perimenopause is widely reported and we look at the nuances of this association and other possible confounding factors. Perimenopause may be a particularly challenging time for women with pre-existing severe mental illness; women with severe mental illness are at risk of substandard menopause education and care, and there maybe diagnostic overshadowing, with menopausal symptoms not being identified, exacerbation of psychiatric symptoms due to perimenopausal symptoms, and an impact of ovarian hormones on psychopharmacology. We explore the evidence base behind psychological, pharmacological and hormonal treatment strategies (including hormone replacement therapy and selective oestrogen receptor modulators) proposed for treatment of perimenopausal mental illnesses.

The move towards social innovation is gaining momentum with the UN’s post-2030 Sustainable Development Goals. Upcycling encourages social innovation by transforming discarded materials into value-added inventions, making them socially useful and sustainable in the long run. Conversely, patent laws protect inventions that meet specific criteria, such as novelty. Patent law not only safeguards new inventions but also covers new uses of existing products. While this can support social innovation as well, it may pose challenges for developing upcycled inventions. Although there are no standard approaches to upcycled and transformative uses under patent law in both the EU and the US, there is a growing body of cases laws on altered use of patented products that could have implications for value added transformation of existing inventions. This chapter explores the foundations of upcycling and its implications for patent law. In doing so, it examines the concept of ‘novelty’ as a requirement under patent law and its effect on upcycling. It further analyzes judicial discussions and case studies from a European and comparative perspective at the intersection of patent law and reconstructive uses, thereby highlighting the role of patent law in fostering social innovation.

This paper delves into the viability of artificial intelligence (AI) as a legal decision-maker through a controlled experiment involving two advanced language models: GPT-4o and Llama 3.1. Using a real-world Colombian arbitration case centred on contract disputes exacerbated by the COVID-19 pandemic, the authors test each model’s ability to generate legally sound arbitration awards. The experiment unfolds in two scenarios: the first provides only the factual background of the case and the second includes the legal arguments of both parties. Each model’s output is evaluated against Colombian legal standards to determine whether the resulting decisions could withstand annulment proceedings. The findings show that GPT-4o closely mirrors the reasoning and outcome of the actual arbitral award, applying doctrines like imprevisión and good faith with legal coherence. Llama 3.1, while capable of reproducing basic legal reasoning, displays limitations, particularly when limited to factual inputs. The results demonstrate that state-of-the-art AI can, under proper conditions, replicate complex legal reasoning and generate decisions unlikely to be overturned. The paper concludes that AI has the potential to serve as a decision-maker in certain adjudicatory contexts, warranting further exploration into its regulated use in arbitration and beyond.

This chapter shows that, while there is reason to be skeptical about the value of public admiration in general, there is one kind of admiration – heroising admiration – that stands out as particularly problematic. Heroising admiration is public admiration of an individual’s or a groups’ supposed heroism. The main issue has to do with the way heroising admiration obscures its targets’ moral status as human beings, by overwriting it with heroic social status. The two are fundamentally in conflict. The imposition of hero status partially deprives targets of their moral status as fellow human beings within a socio-normative realm, so that that they are no longer as eligible for other people’s help or even sympathy, as they were before. It centrally contains depriving people of their social recognisability as human beings who potentially need other people’s help or solidarity. It is argued that there is perfect duty not to contribute to such deprivation.

The last chapter contrasts separation and integration at the highest ends of oppositional self-other hierarchization. The focus is on formal representations of Iran’s religious state authority (whether through marjaʿiyat or rahbari) and non-Iranian lay organizations with transsectarian tendencies supporting the Islamic Republic. The former (e.g., the Islamic Centre of England in London and the Imam Ali Centres of Hamburg and Vienna) have moderated abrasive expressions of oppositional hierarchy while the latter (e.g., Siddiqui’s London-founded Muslim Parliament and the ‘Kaplan Gemeinde’ in Cologne) thrived publicly on unapologetic Islamic supremacism. Only a trace remains of the transsectarian current of Muslim segregation in Europe, whereas Shiʿism’s state-bound, sectarian institutionalization has flourished — even while overtly ecumenist and opposed to self-isolation. Its treatment is prefaced by a reading of multicultural secularism as seeking assimilation in reverse. Among the cases of institutionalization is Germany’s national Shiʿite representation, the IGS Gemeinschaft, which is led by Khomeinists who also advocate Muslims’ European integration. Some entryist strategies are documented around regimist integration discourse serving the Shiʿite indigenisation of Europe, which are increasingly recognized and countered by European (supra-)state institutions. The text ends on a counterpoint with the exceptional case of Ayatollah Qāʾem-Maqāmi, a regime representative who also developed a ‘theology of integration’ inviting Muslims to engage positively with Europe as it is.

Background

Bala Krishna Sama (1902–1981), the doyen of Nepali drama, wrote an epic entitled Chiso Chulho (1958), or “cold hearth.” This epic is woven around the theme of a silent but very strong love relationship between Gauri, a so-called high caste girl, and Sante, a Dalit young man. Sama has chosen to write an epic on the theme of inter-caste love, which was not accepted by the traditional Nepali society. In this epic Sama has dramatized the moments and conditions of alterity. Sama chooses the epic genre to write about othering in a caste-ridden society that he experienced and inherited because this genre gives him space to play at once with tradition and individuality. Sama has chosen to describe the agony of the characters by giving them poetic elevation, thereby deconstructing the canonical norm, which requires that the hero of the epic should be one who hails from the upper echelon or caste of society. By selecting a Dalit or the so-called low-caste male character named Sante, who tailors clothes as part of his traditional occupation, Sama has used all the accoutrements of the epic genre in this oeuvre.

Sante's love for the higher-caste woman Gauri has introduced an unsolved theme that reverberates even in today's Nepali society, which claims to have made achievements in terms of eliminating the excesses of casteism and improving the conditions of women. We can imagine what would have happened if Gauri and Sante had taken a rebellious stand nearly seven decades ago. As a reminder, we can take the widely reported and discussed tragic incident resulting in the death of several young men of Rukum Karnali that happened on May 20, 2020, perpetrated to foil the love between a high-caste girl and a Dalit boy.

Deficits and excesses in emotional experience and behavior are central transdiagnostic features of mental illness. This chapter examines how culture shapes the impact of mental illness on emotional functioning. It draws on insights from clinical psychology, affective science, and cultural psychology, and identifies areas ripe for integration and interdisciplinary work. Despite differences in levels of analysis, target populations, theories, and methodologies, these fields are united in their efforts to understand how people interpret bottom-up changes (e.g., subjective reports of emotions and symptoms, physiological reactivity) using top-down categorical judgments that are consensually shared within local cultural contexts (e.g., culturally salient forms of distress). These processes in turn shape experiences of distress. It synthesizes empirical research to examine how patterns of emotional functioning give rise to both culturally divergent and convergent experiences of mental illness, with implications for both the treatment of mental illness and mental health education.