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.

Attention to human rights as a central pillar of global mental health work has shifted from a focus on the right to healthcare to a deeper examination of the quality of care received, and to the way in which people with mental health conditions are treated in all aspects of life. The QualityRights programme is the World Health Organization’s flagship guidance for promotion of rights-based approaches to mental healthcare, and a means of holding service providers to account for quality of care provided. A recent evaluation of the QualityRights e-training package demonstrates promising impact on attitude change of participants, raising the prospect of an efficient scale-up of efforts to improve dignity in services and reduce stigma and discrimination.

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.

Jespers and Sun conjectured in [27] that if a finite group G has the property ND, i.e. for every nilpotent element n in the integral group ring $\mathbb{Z}G$ and every primitive central idempotent $e \in \mathbb{Q}G$ one still has $ne \in \mathbb{Z}G$, then at most one of the simple components of the group algebra $\mathbb{Q} G$ has reduced degree bigger than 1. With the exception of one very special series of groups we are able to answer their conjecture, showing that it is true—up to exactly one exception. To do so, we first classify groups with the so-called SN property which was introduced by Liu and Passman in their investigation of the Multiplicative Jordan Decomposition for integral group rings.

The conjecture of Jespers and Sun can also be formulated in terms of a group q(G) made from the group generated by the unipotent units, which is trivial if and only if the ND property holds for the group ring. We answer two more open questions about q(G) and notice that this notion allows to interpret the studied properties in the general context of linear semisimple algebraic groups. Here we show that q(G) is finite for lattices of big rank but can contain elements of infinite order in small rank cases.

We then study further two properties which appeared naturally in these investigations. A first which shows that property ND has a representation theoretical interpretation, while the other can be regarded as indicating that it might be hard to decide ND. Among others we show these two notions are equivalent for groups with SN.

The relationship between parliaments and governments during the Covid-19 pandemic has been closely examined by various disciplines, which have typically analysed data on the laws and procedures enforced to manage the emergency. This literature generally agrees that the government dominated the management of the pandemic, often at the expense of parliamentary prerogatives. However, such data may not be sufficiently detailed to fully grasp some nuances. Above all, they may provide limited information on the factors that influenced the balance of powers between the two institutions. This article focuses on the Italian case. It complements data on legislation with the findings of semi-structured interviews conducted with members of parliament and government, as well as high-ranking bureaucrats, to gain a more in-depth understanding of these processes. The data on legislation suggest that governmental dominance was strong at every stage of the emergency, although parliament slightly regained some prerogatives over time. This recovery began under Prime Minister Giuseppe Conte, but it became more pronounced under Mario Draghi. The acquisition of knowledge about the pandemic was perceived by several interviewees as a factor that helped parliament regain some control, making it a possible outcome of a policy learning process. However, other factors also emerged as significant, such as the direct role of the prime ministers in strengthening the role of the executive and the difficulties of the technocratic members of the government in navigating parliamentary dynamics during Draghi’s tenure.