For a group G and $m\ge 1$, $G^m$ denotes the subgroup generated by the elements $g^m$, where g runs through G. The subgroups not of the form $G^m$ are called nonpower subgroups. We extend the classification of groups with few nonpower subgroups from groups with at most nine nonpower subgroups to groups with at most 13 nonpower subgroups.

Recent developments in spatial audio and immersive technologies have expanded creative possibilities for composers and sound artists. This article presents a novel prototype of a spherical microphone with an ellipsoid casing and ten motorised condenser capsules, each capable of real-time adjustment of orientation and polar pattern. Unlike fixed-pattern or conventional ambisonic arrays, this design enables dynamic control over spatial coverage and directivity, offering new opportunities for multichannel recording, live performance and interactive sound art. While software-based spatialisation offers some flexibility, physical reconfiguration of capsules provides superior responsiveness and avoids latency, phase artefacts or resolution loss. This is especially critical in performance contexts where immediate acoustic adaptation is required. The system allows direct manipulation of capsule parameters during rehearsal or installation, effectively transforming the microphone into a performative instrument. The article compares the prototype with existing commercial ambisonic microphones, highlighting its distinctive advantages in workflow and compositional strategy. Use-case scenarios demonstrate how real-time control over spatial parameters enhances both technical precision and artistic expressiveness. The article concludes with a discussion of future directions, including collaborative testing with practitioners and integration into creative environments where spatial transparency, fidelity and interactivity are essential.

Under the Generalised Riemann Hypothesis (GRH), any element in the multiplicative group of a number field K that is globally primitive (i.e., not a perfect power in $K^*$) is a primitive root modulo a set of primes of K of positive density.

For elliptic curves $E/K$ that are known to have infinitely many primes ${\mathfrak{p}}$ of cyclic reduction, possibly under GRH, a globally primitive point $P\in E(K)$ may fail to generate any of the point groups $E(k_{\mathfrak{p}})$. We describe this phenomenon in terms of an associated Galois representation $\rho_{E/K, P}\,:\,G_K\to\mathrm{GL}_3({\widehat {{\mathbf{Z}}}})$, and use it to construct non-trivial examples of global points on elliptic curves that are locally imprimitive.

The regulation of groundwater remains underdeveloped globally and often lags behind the domestic governance of surface water. As a result, groundwater is often subject to unfettered extraction, uses, and contamination. A clear understanding of ownership is central to the success of domestic regulations. However, the types of ownership regime in place in nations around the world are poorly documented in the academic literature. This study addresses that gap through a comparative analysis of domestic groundwater ownership regimes across ten jurisdictions in nine countries spanning five continents. It identifies three dominant models of groundwater ownership: private ownership, public ownership, and non-ownership with public oversight. It then examines how these ownership doctrines impact key dimensions of groundwater governance, including the nature and transferability of the ownership right, the level of government at which regulation takes place, implications for rights of use, and interactions with customary and Indigenous rights. Doing so offers unique insight into how nations with different legal traditions, governance structures, and customary practices address the ownership of groundwater resources. It also suggests that different ownership (and non-ownership) models can have distinct implications for other aspects of groundwater governance.

This musing explores the neoliberalization of addiction recovery and its implications for queer subjects, their affects and attachments. The author examines the ways in which neoliberal ideology usurps the critical potential of trauma-informed theory and practice in the context of addiction recovery, and offers a queer reading of the affects of addiction experienced as a negotiation of this tension. How do queer experiences both challenge and reflect the neoliberal ethos informing contemporary frameworks for addiction recovery? Through a media analysis of the Netflix mini-series, Feel Good, which depicts an experience of queer addiction and codependency, the author illustrates how a representation of queer affect is mediated by neoliberal formulations of subjectivity and pathology. A theoretical framework combining critical addiction studies and feminist affect studies is employed to examine the challenges and possibilities for queer subjects whose experiences at the intersection of systemic oppression and addictive attachment have the potential to subvert the neoliberalization of addiction recovery.

This note presents a new supplement for Euripides, Protesilaus fr. 646a Kannicht.

While transcatheter atrial septal defect closure is routinely performed, acute biventricular failure is an extraordinary complication in adolescents, with only anecdotal reports in the literature. We present a 16-year-old male with borderline left ventricular systolic function and biventricular diastolic dysfunction who developed transient severe biventricular failure immediately following Amplatzer Septal Occluder (Abbott, Plymouth, MN, USA) deployment. Preprocedural echocardiography revealed right ventricular dilation, a D-shaped septum in diastole. Intraprocedural haemodynamic assessment demonstrated elevated right ventricular diastolic pressures (right ventricular minimal diastolic pressure: 11 mmHg; end-diastolic pressure: 17 mmHg). Haemodynamic collapse occurred within minutes of device release, necessitating emergent dopamine infusion and urgent coronary angiography to rule out device-related complications. Remarkably, ventricular function normalised within 2 hours, enabling extubation the same day. Reports of transient biventricular failure following atrial septal defect closure in adolescents without comorbidities are exceedingly rare, underscoring the critical role of preexisting diastolic dysfunction in precipitating acute decompensation. This case advocates for preprocedural balloon occlusion testing and vigilant haemodynamic monitoring in adolescents with impaired ventricular compliance to mitigate catastrophic outcomes.

Rare Earth Elements (REEs) are essential for green energy technologies and defense systems, yet global supply chains remain concentrated in China. This has intensified geopolitical competition for alternative sources, positioning the Arctic as a strategic frontier, as retreating ice exposes mineral deposits. A comprehensive discourse analysis of strategic documents, scholarly literature, and media sources from 2010 to 2025 reveals a dramatic shift from geological characterization and economic speculation to urgent securitization and strategic alliance formation. Academic research has evolved from establishing natural baselines to governance and social conflict analysis. Media coverage of REE in the Arctic peaked in 2025, with rising emphasis on governance, sovereignty, geopolitics, and Greenland’s strategic position. Critical gaps persist in addressing Indigenous rights, holistic impact assessments, and Arctic-specific innovation. Sustainable Arctic REE development requires integrated frameworks that balance geopolitical imperatives with environmental protection and Indigenous self-determination, preventing the region from becoming a sacrifice zone for global decarbonization.

This study investigates experimental luthiery and sound art practices in Latin America through the lenses of postcolonial theory and acoustemology. Within this framework, the musical instrument is conceptualised as a sound-producing object and an active site of cultural representation, historical memory and resistance. These practices, diverging from conventional luthiery traditions, embrace collective, conceptual and material-based modes of production, establishing alternative knowledge systems through sound. Drawing on the works of artists, such as Walter Smetak, Marco Antônio Guimarães, Joaquín Orellana, Wilson Sukorski and Tania Candiani, this study explores how sound mediates relationships with space, the body, memory and technology. Conceptual instrument design is thereby positioned as an aesthetic-political tool developed in parallel with transformations in auditory regimes and responding to epistemic inequalities. This study also focuses on modes of production shaped by technological exclusion, gender and postcolonial identity formation. Experimental luthiery in Latin America is presented as a field of artistic expression and a multilayered epistemic site for the generation of alternative knowledge systems, political subjectivities and spatial justice strategies.

This article will use the records of the Slave Compensation Commission to examine how women experienced and negotiated property- and slave-ownership in nineteenth-century Britain. Demonstrating that women played a crucial role in facilitating the transmission of wealth rooted in enslavement into metropolitan society, it will show how they utilized, manipulated—and were restricted by—the financial mechanisms and legal frameworks that underpinned the British economy. Women’s engagement with the compensation process illustrates both the economic opportunities open to middle- and upper-class women in the early nineteenth century and the ways that female property ownership was mediated and constrained. But we cannot elide the nature of this particular form of “property.” These women were significant players in a system dependent on the violent exploitation of other human beings. The article shows the different ways that British women claimed enslaved people as property: how they used racialized violence to negotiate and wield power in a patriarchal society and to claim, establish, and reinforce their own potentially precarious positions. In doing so, it demonstrates the importance of interrogating the complex nexus of power relations—gendered, racialized, and classed—that shaped how female property- and wealth-holders thought, acted, and behaved in nineteenth-century Britain.

Allocapnia pygmaea Burmeister (Plecoptera: Capniidae) is a winter-active stonefly in North America. Despite the adult’s winter emergence, little is documented about the insect’s cold tolerance and cryoprotective biochemistry. To better understand the cold tolerance of this winter-active stonefly, we collected adult A. pygmaea in Antigonish, Nova Scotia, Canada, during March or April in both 2023 and 2024. Following different cold exposures, we measured the lower limits of activity (–9.3 °C) and the temperature at which internal freezing occurs (–11.9 °C), and we confirmed that A. pygmaea could survive subzero temperatures unless they froze. In control (field-collected) and cold-shocked stoneflies, we assayed the following putative cryoprotectants: proline, glycerol, myo-inositol, trehalose, and glucose. We detected little effect of cold shock on most cryoprotectants, except for the polyols glycerol and myo-inositol, which decreased in concentration following cold shock. These findings improve our current understanding of Capniid cold tolerance, confirm that A. pygmaea uses a freeze-avoidant strategy, and lay a foundation for future studies on how these insects may use cryoprotectants for winter activity.

This paper studies the $4$-ranks of narrow class groups in certain families of quadratic fields. We prove that for any positive integer n, there exists an integer $s_\lambda (n)$ depending on n and the sign $\lambda $ of the fundamental discriminant D, such that for any choice of $s_\lambda (n)$ integers $t_1, \ldots , t_{s_\lambda (n)}$, there are infinitely many D for which the narrow class group of $\mathbb {Q}(\sqrt {D + t_i})$ has $4$-rank bounded by n for all i. This result extends previous work on $3$-ranks to the case of $4$-ranks.