For each pair $j,n$ with $n>j$, we consider the subgroup of the multiplicative group mod n of residues with order dividing $n-j$. We generalise some results in the case $j=1$ due to Erdős and the current author [‘On the number of false witnesses for a composite number’, Math. Comp. 46 (1986), 259–279]. The case $j=0$ is of particular interest.

Red alder, Alnus rubra Bongard (Betulaceae), is a keystone hardwood tree species of great ecological importance in riparian, mixed, and recently disturbed forests in the Pacific Northwest of North America. The alder bark beetle, Alniphagus aspericollis (LeConte) (Coleoptera: Curculionidae: Scolytinae), is an insect that infests and kills red alder throughout its range. Recent observations in southwestern British Columbia, Canada, have indicated that widespread red alder mortality may be attributed to attacks by the alder bark beetle. The most studied defence compound in red alder is oregonin, a diarylheptanoid xyloside. Past studies have shown oregonin to generally inhibit lepidopteran herbivory, but no research has investigated its effects on subcortical insects, such as the alder bark beetle. We hypothesised that high oregonin content is related to resistance to alder bark beetle colonisation in red alder. In support of our hypothesis, we found that the phloem oregonin content of trees that were successfully colonised by the alder bark beetle was significantly lower than that of trees that were not attacked and those that resisted colonisation. These results suggest that oregonin may be a defence metabolite in red alder phloem, although further studies are needed to evaluate how oregonin could influence beetle colonisation success.

We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals.

Maternal nutrition can influence offspring metabolism through metabolic programming, potentially leading to long-term disorders such as obesity and type 2 diabetes. However, the cellular- and tissue-level mechanisms involved in the metabolic programming, particularly regarding the endocrine pancreas, remain unclear. This study investigated the effects of maternal high-fat (HF) diet exposure on the biometric/metabolic profiles, β-cell morphometry, insulin secretion, and islet levels of the SNARE protein VAMP-2 and cytoskeletal F-actin, both critical to insulin granule exocytosis, in mouse offspring. Female C57BL6 mice were fed either a control (CON, 4.5% lipids) or a HF diet (35% lipids) during pregnancy and lactation. The offspring from both groups were evaluated at 3, 12, and 90 days of age. The offspring from HF diet-fed mothers exhibited significantly lower body weight from day 3 and increased visceral adiposity, hyperinsulinemia, glucose intolerance, and insulin resistance, associated with no significant changes in postprandial glycemia by adulthood. These alterations were accompanied by significant morphometric changes in the endocrine pancreas, including a reduction in total islet area, β-cell area, and β-cell number per islet, detectable from day 3 until adulthood. Additionally, adult islets from HF offspring showed elevated cellular F-actin labeling and reduced VAMP-2 protein levels, correlating with impaired glucose-stimulated insulin secretion in vitro. In conclusion, maternal HF diet exposure leads to metabolic disturbances and impaired β-cell function in offspring. These include reduced β-cell mass and secretory capacity, potentially due to an impaired cytoskeletal organization and insulin granule exocytosis, highlighting the long-term impact of maternal nutrition on offspring health.

Ever since John L. Austin, ‘performativity’ has meant many things to many scholars—something that did not change when phrases like ‘performativity of science’ became popular, obscuring various debates in philosophy of science. In this paper, I revisit Austin’s original use of the term and propose a nomenclature of three kinds of performativity in science. This revises earlier attempts to identify ‘authentic’ or ‘genuine’ performativity in science and instead advances an integrative disambiguation—one that preserves what scholars in STS and philosophy of science have found helpful about the concept while addressing demonstrable conceptual conflations.

This article introduces the concept of the inter-factor zone, defined as a bounded transitional phase that complements the traditional push and pull factor theory by incorporating the dynamics of uncertainty and the impact of contingent events in migration processes. Using the case of the political emigration of Czechoslovaks to Switzerland following the Warsaw Pact invasion in 1968, this study analyses how decision-making during this transitional phase was shaped by structural factors, institutional support, and unforeseen events. The inter-factor zone is empirically traced primarily in transit settings, where departure has occurred but a stable destination orientation has not yet been established. While this article primarily focuses on Switzerland, the analysis also considers Austria, particularly Vienna, as a crucial transit context where many emigrants made pivotal decisions before continuing their journeys. Based on qualitative analysis of 35 biographical narratives and historical documents, the research highlights the critical role of transit countries and humanitarian organizations in shaping migrants’ options and interpretations under conditions of suspended orientation. This study enhances our understanding of migration complexity, offers a novel perspective on the significance of this transitional phase, and provides conceptual insights for contemporary migration scholarship and policy debates concerning refugee reception and integration.

This work presents a broadband two-stage pseudo-differential low-noise amplifier (LNA) fabricated in an advanced 130-nm SiGe BiCMOS technology with $f{_t}$/$f_{max}$ of 470/650 GHz. The design combines Electromagnetic (EM)-based device co-simulations with novel broadband transformer matching networks. The input transformer employs asymmetric broadside-coupled lines to achieve wideband impedance transformation with insertion losses below 2 dB. The novel interstage and output transformers are designed as tapered asymmetric broadside coupled lines, providing a distributed transformation with a high impedance transformation ratio of 5:1 and 4:1, respectively, over a bandwidth (BW) of 100 GHz. The LNA provides a peak small-signal gain of 11.8 dB at 295 GHz with a 111 GHz 3-dB bandwidth spanning 211–322 GHz. The simulated noise figure is between 9.7 dB at 226 GHz and 14 dB at 330 GHz. The LNA has a saturated output power of 4.65 dBm at 280 GHz and an $OP_{1dB}$ of 3.6 dBm, including balun losses and consumes 118 mW DC power. It has a measured group delay (GD) variation of $\pm 3.8$ ps, making it suitable for broadband wireless communication.

Ballantine et al. [‘Partitions and elementary symmetric polynomials: an experimental approach’, Ramanujan J. 66(2) (2025), Article no. 34] proposed two conjectures on the injectivity of a class of maps ${pre}_k$ defined on integer partitions. These maps arise from applying the sequence of elementary symmetric polynomials to integer partitions. We provide an infinite family of examples to disprove the conjecture for $k\ge 3$ and state a modified version of it. Throwing fresh light on this class of maps, we study the inter-relationships between them, deviating from the approaches so far, which study these maps one at a time. While the conjecture for $k=2$ has now been settled, we provide alternate proofs of three subcases. We also discuss lower bounds for the number of partitions of n that are in the image of the map $pre_2$.

In 1942 and 1943, Orson Welles produced the radio series Hello Americans, sponsored by the Office of Inter-American Affairs, as part of his efforts as a wartime goodwill ambassador. The twelve thirty-minute episodes explore various regions of Central and South America – including Brazil, the Andes, the Caribbean, and Mexico – and address themes of history and culture. This article examines the sonic strategies – encompassing music and sound – that Welles employed to promote a Pan-Americanist agenda within Hello Americans, focusing on how radio as a medium becomes a site of transatlantic encounter. How does Welles’s use of sound and music shape and communicate a particular vision of Latin American identity within the broader context of Pan-American cultural exchanges? This analysis explores how sonic elements serve as tools of cultural diplomacy during moments of encounter, illustrating how music and sound can foster understanding while also constructing idealized images of Latin America and the Caribbean.

This paper examines environmentalism among 3229 clergy and lay people from the Church of England who took part in the online Church 2024 survey. Three scales of pro-environmentalism were developed: a six-item scale of concern for the environment, a seven-item scale of willingness to make sacrifices for the environment and a seven-item scale of pro-environmental behaviour. Concern was highest for pollution or the loss of natural habitats and lowest for over-population. Participants were most willing to see more onshore windfarms and least willing to see restriction in economic growth. Pro-environmental attitudes and behaviours were more evident among women than men, among older than younger people, among those with preference for intuition over sensing and preference for feeling over thinking and among those with higher levels of education. Clergy were more willing to make sacrifices and showed more activism than laity but had similar levels of concern. Evangelicals had lower scores than other traditions, which reflected their more conservative doctrinal and moral stance. Implications of the findings for promoting the Church’s Green agenda are discussed.

A growing body of research suggests that a person’s field of education shapes their political worldview. Yet basic questions remain unanswered. How strongly is the content of education associated with political attitudes relative to income, gender, ethnicity, and, most importantly, level of education? Which political orientations are most closely linked to field, and which are not? Using original and public surveys from the United States and Europe, we show that the human-centeredness of a field is strongly related to liberal positions on a wide range of political attitudes. The association with field is comparable to, and sometimes larger than, the association with level of education. However, the theory we propose has clear scope conditions: field of education is not systematically associated with interest in politics, efficacy, participation, or affective party identification.

Where central state authority is limited, local leaders play a crucial role in political mobilization. But why are some leaders more effective than others? Dominant explanations emphasize leader characteristics, such as social centrality and shared social identity with voters, or individuals’ traits like wealth and gender. We argue that a critical factor has been overlooked: the breadth of leaders’ perceived influence across various domains of individuals’ lives. We introduce and test the concept of encompassing authority – the extent to which individuals perceive a leader as influencing multiple aspects of their lives. Drawing on original survey data from Zambia’s 2021 elections, we examine three types of local mobilizers: religious leaders, chiefs, and local councillors. We show that encompassing authority predicts mobilization in campaigns and community meetings independently of leader and individual characteristics. We identify three mechanisms that explain this effect: belief in the leader’s legitimacy, fear of sanctions for noncompliance, and confidence in the leader’s ability to coordinate collective action. By conceptualizing authority as a dyadic, relational property rather than fixed characteristics of leaders or individuals, our study offers new insights into the underpinnings of political mobilization and opens avenues for future work.

Let $[q] = \{0,1,\ldots ,q-1\}$, let $\Delta [q]$ denote the simplex of probability measures on $[q]$, and let $\gamma$ denote the Lebesgue measure normalized on $\Delta [q]$. We prove that for any symmetric monotone function ${\kern1pt}f \colon{\kern-1pt} [q]^n \to [q]$ and any $a \in [q]$, we have

\begin{equation*} \gamma (\{\mu \in \Delta [q]\;\vert \;\mathbb{P}_{x\sim \mu ^{\otimes n}}[\,f(x)=a] \in (\varepsilon ,1-\varepsilon )\}) = O(1/\log n)\text{.} \end{equation*}

We also show that this bound is tight. This improves Kalai and Mossel's previous bound of $O(\!\log \log n/\log n)$ and answers their question completely.

This article aims to show that Ingeborg Maus’s interpretation of Kant’s political philosophy re-establishes Kant as a radical thinker of democracy in the canon of democratic theory, from which Cold War liberalism had excluded him. Using the concept ‘social superego’, Maus argues that trust in elitist authorities is foreign to Kant’s republican politics. In a comparison with Arthur Ripstein, it is shown why Maus rejects the right to resistance and the right to revolution as residues of authoritarian democracy justifications. Finally, the thesis is put forward that populism is a new form of such a superego and that the theory of popular sovereignty is also an effective antidote to it.