We prove that a solution to the 3D Navier–Stokes or magneto-hydrodynamics equations does not blow up at t = T provided $\displaystyle \limsup_{q \to \infty} \int_{\mathcal{T}_q}^T \|\Delta_q(\nabla \times u)\|_\infty \, dt$ is small enough, where u is the velocity, $\Delta_q$ is the Littlewood–Paley projection and $\mathcal T_q$ is a certain sequence such that $\mathcal T_q \to T$ as $q \to \infty$. This improves many existing regularity criteria.

We study a specific practice of predatory lending: Borrowers being rejected and approved in rapid succession by the same lender. We show that in such cases borrower and contract characteristics and ex post performance are consistent with predatory steering. Steered borrowers are associated with groups with lower financial sophistication. They are more likely to enter non-amortizing contracts with high profit margins that are quickly securitized. Steered borrowers default less in boom years when refinancing is easy. However, their performance deteriorates sharply once falling prices trap them in contracts with rising payments, reflecting the long-term costs of predatory lending.

A robust literature on the professional advancement of Chinese officials has paid comparatively little attention to an important elite group: the foreign policy bureaucracy. We introduce original data documenting over 11,000 career assignments of 1,357 senior officials in the foreign ministry from 1949 to 2023 and leverage these data to offer the first systematic analysis of who rises to the top of China’s foreign affairs system. We find that diplomats who spend a greater share of their careers in postings abroad are less likely to be promoted to higher ranks than diplomats who remain at home – and that these patterns persisted even after the professionalization of the foreign affairs bureaucracy. Meanwhile, the analysis finds only mixed evidence that diplomatic performance assists promotion. The data and analysis draw attention to the unique challenges of professional advancement in bureaucracies charged with managing China’s foreign relations.

This article explores the representation of women electric guitarists on Instagram. It examines the ways in which their practices as electric guitarists are represented and surveys the spectrum of gender expressions represented on Instagram. It also considers the interconnectedness between these representations and their significance. The research findings are based on textual analysis of the Instagram content of sixteen electric guitarists of varying ages, success levels, and career stages. The findings show that Instagram is a platform through which a multiplicity of representations of women electric guitarists can be observed that can contribute to a deeper, more nuanced understanding and narrative. This article demonstrates that Instagram is an important site of analysis in its ability to contribute to shaping the discourses around gender and the electric guitar and the normalisation of diverse individuals occupying this role.

A random temporal graph is an Erdős-Rényi random graph $G(n,p)$, together with a random ordering of its edges. A path in the graph is called increasing if the edges on the path appear in increasing order. A set $S$ of vertices forms a temporal clique if for all $u,v \in S$, there is an increasing path from $u$ to $v$. Becker, Casteigts, Crescenzi, Kodric, Renken, Raskin and Zamaraev [(2023) Giant components in random temporal graphs. arXiv,2205.14888] proved that if $p=c\log n/n$ for $c\gt 1$, then, with high probability, there is a temporal clique of size $n-o(n)$. On the other hand, for $c\lt 1$, with high probability, the largest temporal clique is of size $o(n)$. In this note, we improve the latter bound by showing that, for $c\lt 1$, the largest temporal clique is of constant size with high probability.

Music streaming platforms are complex socio-technical infrastructures that co-construct cultural production, distribution, and reception. Different contributions have highlighted that artists, producers, and operators may implement optimisation processes, based on their algorithmic imaginaries, to align their music to the modes of listening and categorisation imposed by algorithmic media. Drawing on thirty-nine semi-structured interviews with producers, songwriters, recording industry professionals, and listeners who are heavy users of streaming platforms, this paper reconstructs the social life of a platform-optimised song. Bridging perspectives from science and technology studies and media studies, we investigate the network of relations between human and non-human actors that contribute to the circulation of a platform-optimised song during a four-phase life cycle: creation, industry mediation, platform mediation, and reception. The findings highlight multiple forms of power asymmetries at each stage, recursive dynamics, the erosion of artistic autonomy, and the collaboration of humans and non-human agents to transform music tracks into datafied products.

This article reappraises the early intellectual formation of the medieval “lex mercatoria” thesis: the idea that the international merchants of medieval Europe (or perhaps beyond) enjoyed a universal, autonomous, and customary body of commercial law created and administered by themselves. The debate over its existence, raging for at least 120 years, shows no signs of slowing, in part because the idea is of undoubted usefulness to both proponents (so-called “mercatorists”) and critics. The article offers a new account of the origins of this idea and looks to disaggregate different mercatorist conceptions. Revising the conventional genealogy that traces the theory through the work of Berthold Goldman to the nineteenth-century German scholar Levin Goldschmidt, who is much misunderstood in Anglophone scholarship, it argues that the idea’s powerful re-emergence in the second half of the twentieth century was mediated through two distinct channels, one centred around the British-German jurist Clive Schmitthoff and the other around the British historian William Mitchell. The latter yoked Goldschmidt’s emphasis on the medieval merchant class as a source of legal innovation to a thoroughly Anglophone concept: the “law merchant”. Critics, however, have engaged primarily with Schmitthoff’s conception, whose “strong” mercatorist argument was not only unusually forthright but reoriented the debate to focus on commercial law’s supposed autonomy from the law of territorial states, an even less plausible proposition in historical terms.

The two-spined deepwater cardinalfish, Epigonus bispinosus Okamoto & Gon 2018 is documented for the first time from the Arabian Sea (n= 2) (137.4–151.1 mm SL). The specimens were caught by a demersal shrimp trawl operated along the Kerala coast at a depth of 250–420 m. This species was previously recorded in South Africa and northern Madagascar regions. The present study also provides the first molecular information on E. bispinosus based on mitochondrial cytochrome oxidase subunit I and 16S ribosomal RNA genes. Detailed taxonomic identification, and molecular and phylogenetic analysis are described.

English words and phrases have been creatively adopted, adapted, and appropriated by Persian speakers, resulting in a Persianized form of English that is widely used in daily conversations in Iran. This article aims to identify and describe various English loanwords and phrases commonly integrated into everyday Persian discourse, reflecting Iran’s sociolinguistic globalization. The research is guided by two key questions: How do Iranians Persianize English words and phrases in daily conversations? And what broader patterns emerge in this Persianization process? To address these questions, a qualitative analysis was conducted to examine the prevalence and patterns of English loanwords in Iranian discourse. The findings suggest that Persianized English creates a hybrid mode of expression that blends Persian linguistic traditions with contemporary English influences, shaping identity and communication within Iranian society. The study concludes by recommending further research on the effects of Persianized English on public discourse, media, education, and the daily cultural practices of Iranians.