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.

Cyber breaches pose a significant threat to both enterprises and society. Analyzing cyber breach data is essential for improving cyber risk management and developing effective cyber insurance policies. However, modeling cyber risk is challenging due to its inherent characteristics, including sparsity, heterogeneity, heavy tails, and dependence. This work introduces a cluster-based dependence model that captures both temporal and cross-group dependencies, providing a more accurate representation of multivariate cyber breach risks. The proposed framework employs a cluster-based kernel approach to model breach severity, effectively handling heterogeneity and extreme values, while a copula-based method is used to capture multivariate dependence. Our findings, validated through both empirical and synthetic studies, demonstrate that the proposed model effectively captures the statistical characteristics of multivariate cyber breach risks and outperforms commonly used models in predictive accuracy. Furthermore, we show that our approach can enhance cyber insurance pricing by generating more profitable insurance contracts.

This paper examines the likely economic consequences of a unilateral US trade policy, particularly those involving across-the-board tariffs and retreat from multilateral commitments. Drawing on computable general equilibrium (CGE) models, dynamic macroeconomic frameworks, and a rich body of empirical literature, the paper demonstrates that the static efficiency losses, estimated by standard trade models, understate the true costs of protectionism. It identifies five key amplification channels – loss of economies of scale, supply chain fragility, diminished technological spillovers, investment hold-up under policy uncertainty, and financial market reactions – that interact to depress both short-run output and long-run growth potential. The analysis estimates that comprehensive unilateral trade measures could reduce US GDP by 2–3% in the short term and lower the long-term growth trajectory by 0.4–0.7 percentage points annually. While some strategic interventions may yield resilience or national security benefits, the paper concludes that unilateralism generates systemic economic risks and should be approached with caution. The findings underscore the need for integrated policy frameworks that combine targeted trade tools with domestic support and international cooperation.