In this article, the authors contend that three blades, archaeometrically identified as made of obsidian from the Nemrut Dağ source in eastern Anatolia, were recovered from bona fide archaeological contexts at two sites in Poland. This is supported by somewhat contentious contextual evidence, which is thoroughly reviewed. If the findspots are accepted as genuine, these artefacts would mark the furthest western distribution of Nemrut Dağ obsidian, approximately 2200 km away from the source, more than three times the previously recorded western distribution of this material. The known history of recovery and curation of these artefacts, their techno-typological features, and their raw material source (based on EDXRF analysis) are assessed, and an interpretation of this unusual material is offered.

We provide a presymplectic characterization of Liouville sectors introduced by Ganatra–Pardon–Shende in [10, 12] in terms of the characteristic foliation of the boundary, which we call Liouville σ-sectors. We extend this definition to the case with corners using the presymplectic geometry of null foliations of the coisotropic intersections of transverse coisotropic collection of hypersurfaces, which appear in the definition of Liouville sectors with corners. We show that the set of Liouville σ-sectors with corners canonically forms a monoid that provides a natural framework for considering the Künneth-type functors in the wrapped Fukaya category. We identify its automorphism group that enables one to give a natural definition of bundles of Liouville sectors. As a byproduct, we affirmatively answer a question raised in [10, Question 2.6], which asks about the optimality of their definition of Liouville sectors in [10].

While the Common European Framework of Reference (CEFR) for languages was originally developed for the European context, its influence has extended to other regions. The present paper highlights this growing influence by reporting on revisions to grammar in South Korea’s National English Curriculum based on CEFR criteria and the related CEFR-based English Grammar Profile resource. Specifically focusing on Appendix 4 of the 2015 curriculum, which consists of example sentences of language forms for communication (e.g. Kate is from London), the revising process based on CEFR and the English Grammar Profile involved two steps: 1) adding grammatical categories for the example sentences, and 2) reorganizing the school level where the grammatical categories are recommended to be taught. The resulting changes were implemented in the 2022 Korean National English Curriculum, which began being applied nationwide to English education in 2024.

We examine hidden orders usage by algorithmic traders (ATs) and nonATs. ATs extensively use hidden orders but of smaller size than nonATs, who are the primary contributors to hidden volume. ATs’ relative share of hidden volume decreases with volatility, adverse selection costs, and the relative tick-size. Proprietary ATs (HFTs), who differ from agency ATs (AATs) in their information sets and potential gains from trade, hide orders to reduce competition for liquidity provision, whereas AATs use hidden orders to conceal information in their more informed orders and manage picking-off risk. Finally, superior technology provides limited benefit for hidden order execution.

Courts in England ordinarily grant anti-suit injunctions when proceedings are (or will soon be) initiated in a foreign court in breach of clauses which subject disputes to the exclusive jurisdiction of courts, or refer them to arbitration, in England. Would they, however, grant such relief in support of foreign dispute-resolution clauses? In UniCredit Bank v RusChemAlliance, the Supreme Court of the United Kingdom answered this question in the affirmative, thus expanding the English courts’ power to issue anti-suit injunctions. This article seeks to assess the likely extent of this expansion and the future implications it could have for the law on anti-suit injunctions in England. The article also examines the Supreme Court’s pronouncements on the other significant issue in the case concerning the law governing arbitration agreements and their potential effect following the enactment of the Arbitration Act 2025.

In an earlier note in this journal, I located a contradiction in On Liberty. On the one hand, Mill describes piecework as a self-regarding “private concern” between employees and employers, one that does not harm other workers. On the other, he says that the competitors in economic markets harm each other. But workers compete in the labor market, and Mill does not deny that for some workers to accept payment by the piece may set back the interests of others. Jonathan Riley’s recent reply fails to demonstrate that Mill does not contradict himself. Riley’s argument depends on showing that in On Liberty Mill is presupposing that employers are employing a very specific model of piecework, one which Riley claims is self-regarding. However, Riley fails to establish that Mill is making this presupposition. Moreover, an employer’s choice to adopt piecework would not be self-regarding even if they did employ Riley’s model.

Deep-sea trawl samples collected from the west coast of India have revealed several previously undetected species inhabiting the deep waters. This study reports the first record of Bathycongrus nasicus from the western Indian waters and the second record from the entire western Indian Ocean. A single specimen of B. nasicus was collected from the Neendakara fishery harbour in southern Kerala. The species identity was confirmed morphometrically by comparing it with previous records, and the study provides the first molecular identification of this rare congrid eel. The presence of B. nasicus in the western Indian waters suggests its potential distribution throughout the northern Indian Ocean, with prior records from the Bay of Bengal and the western Arabian Sea. This new record indicates that there might be occurrences of several previously unknown fish species in the non-commercial fishery of this region, underscoring the importance of survey collections of non-commercial fishes, which play a crucial role in marine ecosystems.

In this article, we show that any $\mathbb {A}^2$-fibration over a discrete valuation ring which is also an $\mathbb {A}^2$-form is necessarily a polynomial ring. Further, we show that separable $\mathbb {A}^2$-forms over principal ideal domains are trivial.

Since its inception, evangelical Protestantism has attracted passionate converts and produced anguished deserters: people with intense conversion experiences who have later chosen to flee their churches and the peculiar stream of Christianity that once held their devotion. In past generations, a person exiting evangelicalism left community into seclusion. However, I argue that in the first quarter of the twenty-first century, post-evangelical feminists used digital media to create online post-evangelical feminist communities that alleviated isolation for those leaving conservative evangelical communities. This paper explores the invention and adoption of digital technologies in light of the evangelical history of media innovation. Using blogposts, social media posts, and interviews, it examines the experiences of twenty-first century post-evangelical feminists who participated in digital communities. The metaphor of outposts in “the wilderness,” commonly used by post-evangelical feminists, suggests that digital communities acted as havens of theologically and politically progressive sociality outside evangelical institutions. These communities provided an important function for those early twenty-first-century post-evangelical feminists who left evangelicalism but maintained a Christian faith. Those marginalized by their gender and their theological positions used digital media as a structure to forge religious belonging in a period defined by the rise of the religiously unaffiliated. This history illuminates the promises and the limitations of digital religious communities.

Let p be a fixed odd prime. We prove the following results for positive integer solutions $(x,m,n)$ of the equation $(*)\ x^2=2^m+p^n$. (i) If $p \equiv 3 \pmod 8$, then $(*)$ has only the solution $(p,x,m,n)=(3,5,4,2)$. (ii) If $p \equiv 5 \pmod 8$, then $(*)$ has only the solution $(p,x,m,n)=(5,3,2,1)$. (iii) If $p \equiv 7 \pmod 8$, then $(*)$ has at most one solution $(x,m,n)$, except for $p=7$, $(x,m,n)=(3,1,1)$ and $(9,5,2)$. Moreover, if $p=2^q-1$ is a Mersenne prime with $p>7$, where q is an odd prime with $q>3$, then $(*)$ has exactly one solution $(x,m,n)=(2^q+1,q+2,2)$. If $p \equiv 7\pmod 8$, p is not a Mersenne prime and either $p<1.5\times 10^{12}$ or $p>C$, where C is an effectively computable absolute constant, then $(*)$ has only the solutions $p=a^2-2$, where a is an odd positive integer, $(x,m,n)=(a,1,1)$. (iv) If $p \equiv 1\pmod 8$ with $p \ne 17$, then $(*)$ has at most two solutions $(x,m,n)$.

Cet article tente de mesurer les changements possibles survenus dans la structure de l’opinion publique sur la question de l’indépendance du Québec. Plus particulièrement, nous comparons deux modèles théoriques qui ont été au coeur de notre compréhension des appuis à l’indépendance, soit le modèle du choix rationnel associé aux coûts-bénéfices prospectifs de l’indépendance et le modèle socio-psychologique qui met de l’avant les griefs et revendications que le Québec ressent face au régime canadien. Notre étude permet aussi d’évaluer la pertinence de ces modèles à travers les générations entre 2014 et 2024; et de considérer de nouveaux facteurs explicatifs contemporains. Dans l’ensemble, nos résultats suggèrent une surprenante stabilité quant à l’importance des différents facteurs considérés pour comprendre les mécaniques expliquant l’appui ou non à l’indépendance du Québec. Les attitudes populistes, nativistes et autoritaristes apportent aussi un pouvoir explicatif additionnel, quoique limité.

In the second half of the 19th century, Darboux obtained determinant formulae that provide the general solution for a linear hyperbolic second-order PDE with the finite Laplace series. These formulae played an important role in his study of the theory of surfaces and, in particular, in the theory of conjugate nets. During the last three decades, discrete analogues of conjugate nets (Q-nets) were actively studied. Laplace series can be defined also for hyperbolic difference operators. We prove discrete analogues of Darboux formulae for discrete and semi-discrete hyperbolic operators with finite Laplace series.

This article examines how to increase students’ self-reported feelings of political efficacy in introductory US government courses. We test the effectiveness of civic engagement assignments, such as writing a letter to one’s member of Congress and attending a public meeting, in increasing political efficacy beyond simply taking the course. By conducting pretests and posttests in both classes with (treatment group) and without (control group), the civic engagement assignments allowed us to isolate the effect of the assignments. We find significant effects for taking the course in both the treatment and control groups, confirming existing research that taking an introductory US government course increases students’ political efficacy. We also find treatment effects for multiple elements of the standard political efficacy questionnaire. That our intervention had these affects at a state university that is both a Hispanic Serving Institution and a Minority Serving Institution indicates that these types of civic engagement assignments hold significant potential not only for increasing political efficacy among students but also for increasing it among historical marginalized groups that typically participate in politics at lower rates than white Americans.

This study revisits the relationship between second-language (L2) learners’ ability to distinguish sounds in non-native phonological contrasts and to recognize spoken words when recognition depends on these sounds, while addressing the role of methodological similarity. Bilingual Catalan/Spanish learners of English were tested on the identification of two vowel contrasts (VI) of diverging difficulty, /i/-/ɪ/ (difficult) and /ɛ/-/æ/ (easy), in monosyllabic minimal pairs, and on their recognition of the same pairs in a word-picture matching task (WPM). Learners performed substantially better with /i/-/ɪ/ in VI than in WPM, and individual scores were only weakly correlated. By replicating previous findings through a more symmetrical design, we show that an account of prior work rooted in methodological dissimilarity is improbable and provide additional support for the claim that accuracy in sound identification does not guarantee improvements in word recognition. This has implications for our understanding of L2-speech acquisition and L2 pronunciation training.