In February 1744 in Paris, the Swedish physician Abraham Bäck (1713–95), better known as Carl Linnaeus’s best friend, dissected the cadaver of an unidentified sub-Saharan man. In contrast to the widespread exploitation of the enslaved dead in North America, cadavers of dark-skinned Africans remained rare in the anatomical theatres of eighteenth-century Europe. Scarcity not only increased their market value in medical circles interested in skin colour: in Europe, empirical anatomists often used these rare remains for building their medical authority. This article explores the rise of an empiricist social culture of racial anatomy in the European Enlightenment by following the case of Bäck, whose research on ‘black’ skin also provides a little-known counterpart to Linnaeus’s racial anthropology. Bäck’s case illustrates not only how European anatomists often wrote accounts of skin colour which best showcased their medical skills but also how the production of racial pseudoscience became increasingly driven by the authoritative rise of empiricism, the expansion of the slave trade, and the Enlightenment’s fascination with human differences.

Vapour-driven solutal Marangoni effects have been studied extensively due to their potential applications, including mixing, coating, and droplet transport. Recently, the absorption of highly volatile organic liquid molecules into water droplets, which drives Marangoni effects, has gained significant attention due to its intricate and dynamic physical behaviours. To date, steady-state scenarios have been considered mainly by assuming the rapid establishment of vapour–liquid equilibrium. However, recent studies show that the Marangoni flow arises even under uniform vapour concentration, and requires a considerable time to develop fully. It indicates that the vapour–liquid equilibrium takes longer to establish than was previously assumed, despite earlier studies reporting that vapour molecules instantly adsorb on the interface, highlighting the importance of observing transient flow patterns. Here, we experimentally and numerically investigate time-dependent flow structures throughout the entire lifetime of a droplet in ethanol vapour environments. Under two distinct vapour boundary conditions of uniform and localised vapour distributions, a significant flow structure change consistently occurs within the droplet. The time-varying ethanol vapour mass flux from numerical simulation reveals that the flow transition is caused by the high vapour absorption flux at the droplet contact line, due to the geometric singularity there. Based on the detailed analysis of the surface tension gradient along the droplet interface, we identify that the flow transition occurs before and after the vapour–liquid equilibrium is achieved at the droplet contact line, which induces the flow direction change near the contact line.

This article is part of Religious Studies’ initiative to publish a series of interviews with distinguished philosophers of religion. Each interview explores the personal and academic background of the interviewee and discusses their core philosophical views. The aim is to inspire students and scholars and to provide an overview of some of the most important works developed by contemporary philosophers of religion. In this interview, Chris Tweedt interviews Jonathan Kvanvig, covering such topics as his upbringing, his educational and career trajectory, and his views on philosophical methodology, epistemic humility, divine providence, faith, and hell.

We determine the average size of the $3$-torsion in class groups of G-extensions of a number field when G is any transitive $2$-group containing a transposition, for example $D_4$. It follows from the Cohen–Lenstra–Martinet heuristics that the average size of the p-torsion in class groups of G-extensions of a number field is conjecturally finite for any G and most p (including $p\nmid |G|$). Previously this conjecture had only been proven in the cases of $G=S_2$ with $p=3$ and $G=S_3$ with $p=2$. We also show that the average $3$-torsion in a certain relative class group for these G-extensions is as conjectured, proving new cases of the Cohen–Lenstra–Martinet heuristics. Our new method also works for many other permutation groups G that are not $2$-groups.

We prove the formula

\begin{equation*} \text{cat}_G(X\vee Y)=\max \{\text{cat}_G(X),\text{cat}_G(Y)\} \end{equation*}

$X\vee Y$

$\bigvee _{i=1}^m X_i$

$G$

$X_i$

$G$

$i=1,\ldots ,m$

$X/A$

$G$

$X$

$A$

$A\hookrightarrow X$

$G$

$\overline {x_0}\,:\,A\to X$

$x_0\in X^G$

\begin{align*} \text{TC}_G(X\vee Y)&=\max \{\text{TC}_G(X),\text{TC}_G(Y),\text{cat}_G(X\times Y)\},\\ \text{TC}^G(X\vee Y)&=\max \{\text{TC}^G(X),\text{TC}^G(Y),_{X\vee Y}\text{cat}_{G\times G}(X\times Y)\}, \end{align*}

$G$

$G$

$X$

$Y$

To explore the longitudinal associations between an Chinese healthy diet and the progression of cardiometabolic multimorbidity (CMM) development among Chinese adults. A prospective analysis was conducted utilizing data from 18,720 participants in the China Health and Nutrition Survey, spanning from 1997 to 2018. Dietary data were collected by three consecutive 24-hour dietary recalls combined with weighing method. An Chinese healthy diet score was developed by assigning scores to various food components. CMM was defined as the coexistence of two or more cardiometabolic diseases (CMDs), including myocardial infarction, stroke, and type 2 diabetes, diagnosed through blood indicators and clinical diagnosis. We employed a multistate model to examine the associations between the Chinese healthy diet and the longitudinal progression from being free of CMDs to first cardiometabolic disease (FCMD), then to CMM. Quantile G-computation was utilized to evaluate the relative contribution of each food component. Over a median follow-up period of 7.3 years, 2,214 (11.8%) participants developed FCMD, 156 (0.83%) progressed to CMM. Comparing participants in the highest quintile of dietary scores to those in the lowest, we observed a 55% lower risk of transitioning from baseline to CMM (HR = 0.45, 95% CI: 0.23 - 0.87), and a 60% lower risk of transition from FCMD to CMM (HR = 0.40, 95% CI: 0.20 - 0.81). Fresh fruits contributed to 42.8% and 43.0% for delaying CMM and transition from FCMD to CMM, respectively. Our study revealed that greater adherence to the Chinese healthy diet is negatively associated with the risk of CMM.

In this paper we solve a long-standing problem which goes back to Laurent Schwartz’s work on mean periodic functions. Namely, we completely characterize those locally compact Abelian groups having spectral synthesis. So far a characterization theorem was available for discrete Abelian groups only. Here we use a kind of localization concept for the ideals of the Fourier algebra of the underlying group. We show that localizability of ideals is equivalent to synthesizability. Based on this equivalence we show that if spectral synthesis holds on a locally compact Abelian group, then it holds on each extensions of it by a locally compact Abelian group consisting of compact elements, and also on any extension to a direct sum with a copy of the integers. Then, using Schwartz’s result and Gurevich’s counterexamples, we apply the structure theory of locally compact Abelian groups to obtain our characterization theorem.

This paper presents an analytical method for modelling the acoustic field radiation from a semi-infinite elliptic duct in the presence of uniform subsonic flow. In contemporary aircraft design, elliptic ducts play crucial roles as inlets for advanced blended wing body configurations owing to their capacity to maximise the pre-compression effect of the fuselage and enhance the stealth performance of aircraft. The method uses Mathieu functions to describe the incident and scattered sound in the elliptic cylindrical coordinates. An analytical Wiener–Hopf technique is developed in this work to derive near- and far-field solutions. Numerical simulations based on a finite element method are conducted to validate the accuracy of the analytical method, revealing a strong correspondence with analytical predictions. A parametric study is conducted to explore the influence of the elliptic cross-section shape on noise directivity. Moreover, we investigate reflections within the duct via an extended derivation of the analytical model. The proposed method can be used to examine the acoustic characteristics of elliptic ducts with inflow mean flows, which holds relevance for noise control and optimisation of turbofan engine inlets and blended wing body applications.

As the first article in its March 1889 issue, The Classical Review published a short piece jointly authored by Henry Sidgwick and John Grote: a dialogue between Socrates and friends and John’s brother, George Grote. This brief but complex and playful dialogue is a microcosm of a broader discussion between a group of friends, colleagues, and relatives in the third quarter of the nineteenth century about individual happiness, justice and the good of the community. This article introduces the dialogue and places it in the context of two important wider debates in order to show how this brief dialogue illuminates the intellectual milieu of the time and the personalities involved. The first is a debate about how to read and engage with Plato’s philosophical dialogues. The second is a debate about utilitarianism, the nature of happiness, and the correct end of human actions.

This article situates the work of famous “skeptical environmentalist” Bjørn Lomborg in current environmental debates, arguing that he represents a shift from a “market” to a “planning” orientation within promethean environmental discourse taking place since the early 2000s. Instead of seeing self-correcting markets as a panacea for all societal ills, “planning” prometheanism aims to address environmental problems such as climate change through public policy, state investment, and technology development. We investigate the genesis of Lomborg’s “planning” prometheanism and locate its key sources of inspiration in the works of American economists Julian Simon, William Nordhaus, and Thomas Schelling. Moreover, we argue that Lomborg’s approach is characterized by a technocratic skepticism toward democracy which derives from his reliance on rational-choice theory. Finally, highlighting the adaptability of promethean discourse, we suggest that Lomborg’s “planning” prometheanism represents a renaissance of 1950s promethean thought at a time when a post-neoliberal world is taking shape.

Secondary fragmentation of an impulsively accelerated drop depends on fluid properties and velocity of the ambient flow. The critical Weber number $(\mathit{We}_{cr})$, the minimum Weber number at which a drop undergoes non-vibrational breakup, depends on the density ratio $(\rho )$, the drop $(\mathit{Oh}_d)$ and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. The current study uses volume-of-fluid based interface-tracking multiphase flow simulations to quantify the effect of different non-dimensional groups on the threshold at which secondary fragmentation occurs. For $\mathit{Oh}_d \leqslant 0.1$, a decrease in $\mathit{Oh}_d$ was found to significantly influence the breakup morphology, plume formation and $\mathit{We}_{cr}$. The balance between the pressure difference between the poles and the periphery, and the shear stresses on the upstream surface, was found to be controlled by $\rho$ and $\mathit{Oh}_o$. These forces induce flow inside the initially spherical drop, resulting in deformation into pancakes and eventually the breakup morphology of a forward/backward bag. The evolution pathways of the drop morphology based on their non-dimensional groups have been charted. With inclusion of the data from the expanded parameter space, the traditional $\mathit{We}_{cr}-\mathit{Oh}_d$ diagram used to illustrate the dependence of the critical Weber number on $\mathit{Oh}_d$ was found to be inadequate in predicting the minimum initial $\mathit{We}$ required to undergo fragmentation. A new non-dimensional parameter $C_{\textit{breakup}}$ is derived based on the competition between the forces driving the drop deformation and the forces resisting the drop deformation. Tested using available experimental data and current simulations, $C_{\textit{breakup}}$ is found to be a robust predictor for the threshold of drop fragmentation.

This article examines the role of religious law in the context of modern state formation in the Arabian Gulf sheikhdoms. It focuses on Qatar, where a dual legal system emerged out of contestations over political community in the aftermath of imperialism and oil. From the mid-twentieth century onward, the ruling family empowered both a sharia and a civil judiciary without fully clarifying the jurisdictional boundaries between the two judiciaries. Until the 2003 unification of the judiciary, litigants were seemingly free to take civil and criminal cases to a court of their choice. I suggest that the appeal of Qatar’s Sharia Courts lay primarily in the socially embedded nature of Islamic legal practice, the extra-legal functions fulfilled by sharia judges, and the transnational networks of Islamic institutions. While the appeal of the sharia was partly produced by the state, Islamic legal institutions also drew force from their oppositional stance toward modern state power. The Qatari case shows how legal actors can secure state recognition by positioning themselves as authentic cultural mediators against the alienating structures of modern bureaucracy when they offer an alternative model of justice grounded in a dense network of social relations and the provision of a wide range of services.