Exploring the ‘hollow’ character of middle-class status in contemporary Kenya, this article shows how upwardly mobile young Kenyans struggle to cope with the expectations for distribution that their displays of achievement create. Focusing on the urbanizing peripheries of Nairobi, it shows how accusations of envy (wivu) made about poorer friends and relatives reflect their anxieties about failing to act as the providers they are expected to be. Anticipation of the disappointment and resentment of their would-be dependants encourages them to withdraw from friendships and kinship relations in their home neighbourhoods, and seek instead an impersonal life in new urban enclaves closer to Nairobi. The avoidance of obligation is justified through discourses of individual effort and achievement, while poorer peers and relations are criticized for looking to rely on others. The article shows how such tensions over obligation and desires for withdrawal illuminate the fragility of Kenya’s emerging middle class and the ‘ironies of accomplishment’ – that their very precarity denies these Kenyans the respect and status they desire in their neighbourhood homes.

Law plays an important role in reshaping and enforcing governance efforts in radical shifts and can function as a catalyst for transitioning governance towards sustainability. This article assesses the capacity of law to facilitate decarbonization as a radical societal shift. It argues that decarbonization demands fundamental and systemic restructuring in law and legal thinking. This should also be reflected in legal scholarship and, most importantly from the point of view of this article, in the methodological choices and approaches that legal scholarship relies on to study societal challenges. To that end, the article develops a new methodological approach (disciplinary comparison) through which to study law's capacities in respect of decarbonization as a radical societal shift. Disciplinary comparison can be used to gain information on both the friction and the synergies between legal disciplines. This new methodological approach will contribute to increasing insight into law's capacities for the radical, cross-sectoral change necessitated by the need to decarbonize societies.

The following theorems appear in [1, pp. 62-63]: Theorem 1 If similar triangles A1B0C0, A0B1C0, A0B0C1 are erected externally on the sides of ΔA0B0C0, then the circumcircles of these three triangles have a common point, F.

This review explores the evolution of dietary protein intake requirements and recommendations, with a focus on skeletal muscle remodelling to support healthy ageing based on presentations at the 2023 Nutrition Society summer conference. In this review, we describe the role of dietary protein for metabolic health and ageing muscle, explain the origins of protein and amino acid (AA) requirements and discuss current recommendations for dietary protein intake, which currently sits at about 0⋅8 g/kg/d. We also critique existing (e.g. nitrogen balance) and contemporary (e.g. indicator AA oxidation) methods to determine protein/AA intake requirements and suggest that existing methods may underestimate requirements, with more contemporary assessments indicating protein recommendations may need to be increased to >1⋅0 g/kg/d. One example of evolution in dietary protein guidance is the transition from protein requirements to recommendations. Hence, we discuss the refinement of protein/AA requirements for skeletal muscle maintenance with advanced age beyond simply the dose (e.g. source, type, quality, timing, pattern, nutrient co-ingestion) and explore the efficacy and sustainability of alternative protein sources beyond animal-based proteins to facilitate skeletal muscle remodelling in older age. We conclude that, whilst a growing body of research has demonstrated that animal-free protein sources can effectively stimulate and support muscle remodelling in a manner that is comparable to animal-based proteins, food systems need to sustainably provide a diversity of both plant and animal source foods, not least for their protein content but other vital nutrients. Finally, we propose some priority research directions for the field of protein nutrition and healthy ageing.

Savings groups are an important feature of life in rural Uganda and elsewhere. They have been celebrated as an ‘alternative’, community-based approach to economic development with a particular focus on empowering women. In this article we offer a more critical perspective, showing how a savings group in a village in eastern Uganda informs more general experiences of financialization. Joining the group was not really an ‘alternative’ to other forms of finance and was often a first step to securing loans from moneylenders, microfinance institutions and commercial banks. We show how poorer members of the group, typically women, ‘rented out’ their membership to wealthier villagers. Members also used the Friday meetings to socialize and to build political careers, and to reflect critically on experiences of financialization. ‘Money looks for money’, a phrase new to the area, interrogates these socialities and inequalities, as part of the seemingly inexorable pull of loans, interest and financialized debt.

On 21 December 2020 the night sky offered a beautiful astronomical treat for stargazers worldwide. An exceptionally rare conjunction of Jupiter and Saturn brought them to 0.1 degrees of angular separation – a fifth of the full moon’s diameter. It marked their closest approach since 1623 and the closest visible conjunction since 1226 (almost 800 years ago!). Astronomy enthusiasts crossed their fingers for clear skies and waited eagerly for this event. The internet and social media were inundated with pictures and news reports, celebrating the great conjunction of our solar system’s two most extensive and majestic planets.

The unprecedented COVID-19 pandemic has caused restrictive measures to be established in many sectors including the legal and judicial sector; an example is the use of electronic litigation systems and video-conferencing facilities for trials. With the implementation of changes in the legal and judicial sector to adapt to restrictions arising from the pandemic, there is the question of whether the current rules governing civil-court proceedings are designed to accommodate these changes. This article seeks to explore the measures taken by courts in response to the pandemic with a focus on Asia, notably Singapore. The article will outline the legal basis for the use of live video links for the purpose of witness evidence-taking under Singapore law and the possible implications will be reviewed taking Singapore’s civil proceedings as an example in comparison with other jurisdictions.

An explicit transformation for the series $\sum \limits _{n=1}^{\infty }\displaystyle \frac {\log (n)}{e^{ny}-1}$, or equivalently, $\sum \limits _{n=1}^{\infty }d(n)\log (n)e^{-ny}$ for Re$(y)>0$, which takes y to $1/y$, is obtained for the first time. This series transforms into a series containing the derivative of $R(z)$, a function studied by Christopher Deninger while obtaining an analog of the famous Chowla–Selberg formula for real quadratic fields. In the course of obtaining the transformation, new important properties of $\psi _1(z)$ (the derivative of $R(z)$) are needed as is a new representation for the second derivative of the two-variable Mittag-Leffler function $E_{2, b}(z)$ evaluated at $b=1$, all of which may seem quite unexpected at first glance. Our transformation readily gives the complete asymptotic expansion of $\sum \limits _{n=1}^{\infty }\displaystyle \frac {\log (n)}{e^{ny}-1}$ as $y\to 0$ which was also not known before. An application of the latter is that it gives the asymptotic expansion of $ \displaystyle \int _{0}^{\infty }\zeta \left (\frac {1}{2}-it\right )\zeta '\left (\frac {1}{2}+it\right )e^{-\delta t}\, dt$ as $\delta \to 0$.

Given a polynomial equation x3 + ax2 + bx + c = 0 of degree 3 with real coefficients, we may translate the variable by replacing x with x − to make the quadratic term vanish. We then obtain a simpler equation x3 + px + q = 0 where Therefore, in order to solve a polynomial equation of degree 3, it is sufficient to solve equations of the form x3 + px + q = 0.