We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to conjugation in inverse semigroups. Subsequently, we prove that solvable and nilpotent inverse semigroups are groups.

Generative AI (GenAI) offers potential for English language teaching (ELT), but it has pedagogical limitations in multilingual contexts, often generating standard English forms rather than reflecting the pluralistic usage that represents diverse sociolinguistic realities. In response to mixed results in existing research, this study examines how ChatGPT, a text-based generative AI tool powered by a large language model (LLM), is used in ELT from a Global Englishes (GE) perspective. Using the Design and Development Research approach, we tested three ChatGPT models: Basic (single-step prompts); Refined 1 (multi-step prompting); and Refined 2 (GE-oriented corpora with advanced prompt engineering). Thematic analysis showed that Refined Model 1 provided limited improvements over Basic Model, while Refined Model 2 demonstrated significant gains, offering additional affordances in GE-informed evaluation and ELF communication, despite some limitations (e.g., defaulting to NES norms and lacking tailored GE feedback). The findings highlight the importance of using authentic data to enhance the contextual relevance of GenAI outputs for GE language teaching (GELT). Pedagogical implications include GenAI–teacher collaboration, teacher professional development, and educators’ agentive role in orchestrating diverse resources alongside GenAI.

Using Danish register data, we study whether individuals save enough to maintain almost all (90%) of their pre-retirement consumption. We find that 85 percent do, largely due to mandatory labour market pension contributions. The remaining 15 percent are less likely to have mandatory pension schemes and do not compensate for the lack thereof via voluntary private savings. However, mandatory contributions come at the cost of lower consumption and non-retirement savings during working years. Individuals experiencing the largest increases in mandatory pension contributions accumulate less non-retirement wealth and consume less before retirement compared to those with small increases.

In this work, we study rates of mixing for small independent and identically distributed random perturbations of contracting Lorenz maps sufficiently close to a Rovella parameter. By using a random Young tower construction, we prove that this random system has exponential decay of correlations.

We establish the pointwise equidistribution of self-similar measures in the complex plane. Let $\beta \in \mathbb Z[\mathrm{i}]$, whose complex conjugate $\overline{\beta}$ is not a divisor of β, and $T \subset \mathbb Z[\mathrm{i}]$ a finite subset. Let µ be a non-atomic self-similar measure with respect to the IFS $\big\{f_{t}(z)=\frac{z+t}{\beta}\colon t\in T\big\}$. For $\alpha \in \mathbb Z[\mathrm{i}]$, if α and β are relatively prime, then we show that the sequence $(\alpha^n z)_{n\ge 1}$ is equidistributed modulo one for µ-almost everywhere $z \in \mathbb{C}$. We also discuss normality of radix expansions in Gaussian integer base, and obtain pointwise normality. Our results generalize partially the classical results in the real line to the complex plane.

The effect of the bio-inspired leading-edge modifications on the aerodynamic performance of non-slender delta wing models was investigated in a low-speed wind tunnel using force and surface pressure measurements. The measurements were performed at a Reynolds number of $Re = 1 \times {10^5}$ over an angle-of-attack range from $ - 4^\circ $ to $30^\circ $. Seven different sharp-edged delta wing models with a 45-degree sweep angle (${\rm{\varLambda }}$), including a base wing, were used to study the effect of sinusoidal and saw-tooth leading-edge modifications. Sinusoidal leading-edge wing designs were inspired by the leading-edge tubercles of the humpback whale’s pectoral fins. The results indicate that the bio-inspired wing modifications resulted in a delay in the stall angle by 4 degrees, smoother stall characteristics, a higher maximum lift coefficient, and increased post-stall lift. The drag coefficient of the modified wings was observed as higher than that of the base wing model. Regarding the longitudinal static stability, leading-edge modifications decreased the stability of the wing as the angle-of-attack surpassed $\alpha = 17^\circ $.

The co-creation of new knowledge by combining traditional ecological knowledge and citizen science can empower communities to cope with impending and irreversible changes. However, scholar-activists walk a fine line between driving communities into fields that they are unfamiliar and uncomfortable with, and sharing their wealth of knowledge. This paper uses an autoethnographic approach to reflect on my experience as a researcher deeply involved in community organising in a rural fishing village in southwest Johor, Malaysia, and the tightrope I walked to provide locals with access to resources, networks, and materials, and to amplify their work through myriad media. My accidental scholar-activism is the outcome of 17 years immersed in this community, initially as an environmental education facilitator, then as the community found its voice, as a supporter of efforts to participate in and benefit from the development encroaching onto its neighbourhood and natural habitats. While the villagers simply wanted to safeguard nature-based livelihoods despite increasing habitat destruction and climate change impacts, my work in the background effectively empowered them to overcome restrictive power structures and improve social justice. This was an unplanned social movement that took on a life of its own, analysed through engaged and participative ethnography. While the community made headway in effective and impactful change, the journey demonstrated some failures in youth engagement, but unexpected success with the fishermen. Throughout it all, I questioned the wisdom of my providing people with a near-impossible vision of surmounting entrenched power structures, and the contravention of conservative cultural and gender norms.

This is a corrigendum to ‘An uncountable Furstenberg–Zimmer structure theory’ [Ergod. Th. & Dynam. Sys. 43(7) (2023), 2404–2436]. We report two issues in that paper. First, Lemma A.5 and Proposition A.6 in the Appendix, which supported a spectral analysis of conditional Hilbert–Schmidt operators, are incorrect. These results were used in the proof of Lemma 4.4, which establishes part of the equivalences in Theorem 4.1. We provide a correction for this issue here. While the proof strategy of Lemma 4.4 remains valid, the details have been revised using known auxiliary results in the non-commutative setting of tracial von Neumann algebras, replacing the faulty arguments from the Appendix. Second, the proof of the implication $\mathrm{(iii)} \Rightarrow \mathrm{(iii)}'$ in Lemma 4.10 is incorrect. We supply a new argument to address this. We also take this opportunity to correct several minor issues that have come to our attention since the paper’s publication. A fully revised version, including these corrections, as well as updated references and some fixed typos, is now available on arXiv.

The informal exit of the United States from the WTO under Trump is the culmination of US frustration with the organization's legislative and judicial rigidity, a frustration that has been building on a bipartisan basis for two decades. The WTO's commitment to a single undertaking, its reliance on consensus-based decision making, and an activist Appellate Body that imposed de facto stare decisis eroded political support for WTO rules in the United States and opened the door for political opportunists to cast them aside. We argue that the original GATT was, on balance, a more flexible and politically savvy bargain despite its imperfections. The 30-year history of the WTO that replaced it suggests the folly of trying to rein in powerful countries with a ‘rules-based’ institution, at least when the rules are unable to adjust to political shocks.

This paper investigates the asymptotic properties of parameter estimation for the Ewens–Pitman partition with parameters $0\lt\alpha\lt1$ and $\theta\gt-\alpha$. Specifically, we show that the maximum-likelihood estimator (MLE) of $\alpha$ is $n^{\alpha/2}$-consistent and converges to a variance mixture of normal distributions, where the variance is governed by the Mittag-Leffler distribution. Moreover, we show that a proper normalization involving a random statistic eliminates the randomness in the variance. Building on this result, we construct an approximate confidence interval for $\alpha$. Our proof relies on a stable martingale central limit theorem, which is of independent interest.

In Transparency and Reflection, Matthew Boyle offers a Sartrean account of prereflective self-awareness to explain the essential link between self-consciousness and rationality, moving away from standard Kantian interpretations that he claims presuppose rather than explain this connection. I argue that Boyle’s account provides useful tools for re-interpreting Kant’s claim that the “I think” must accompany all representations as a form of nonpositional consciousness. I also aim to show that Boyle’s model risks fragmenting the unity of the subject across different representational domains, and that Kant’s account (construed as a kind of prereflective consciousness) has the resources to address this challenge.

Structural changes like globalisation and technical change have empowered business actors in global governance. Yet to become leaders of global governance rather than mere participants, business actors need to legitimise themselves as working for the public good rather than for the maximisation of profit alone. This paper argues that business power becomes authority through the gradual diffusion of ideals of global governance that legitimate the leadership of business actors. We use the concepts of cultural capital and symbolic capital developed by Pierre Bourdieu to conceptualise the construction of business authority. However, we also expand on existing Bourdieusian accounts, which focus on authority construction within fields, by showing how business actors leverage globalisation and technical change to frame discourses that construct their authority across fields of governance. To demonstrate this, we focus on the case of the World Economic Forum (WEF), which has accumulated enough cultural capital to deploy two particularly influential discourses – multistakeholderism and the 4th Industrial Revolution. We show that, by making sense of complex situations, these discourses functioned as symbolic capital and legitimised both the WEF’s own authority and that of business actors more broadly.

The Monte Carlo methods are frequently employed to evaluate the overall characteristics of non-monotonic, non-linear, non-superpositional performance functions. However, the multi-parameter, multi-objective spacecraft separation dynamics model is not amenable to decoupling to produce a result. This paper presents a parametric objective function that can be sampled. It combines the reliability analysis of the complex non-linear spacecraft separation model with Automated Dynamic Analysis of Mechanical Systems (ADAMS) and uses the Monte Carlo method to obtain the separation performance of the spacecraft separation system reliability profile, that is to say, the distribution of separation performance. The performance distribution of the spacecraft separation system was determined and parameters such as spring separation force, spring line of action, module mass and module centre of mass position were found to have a significant effect on the spacecraft separation dynamics by Adaboost machine learning regression.

In early 2023 Kellie-Jay Keen-Minshull—also known as Posie Parker—took her “Let Women Speak” tour throughout Australasia. One of those rallies made international headlines due to the attendance of a small group of neo-Nazis (members of the National Socialist Network) who proceeded to perform Nazi salutes on the steps of Parliament House and on the surrounding streets. At that very same rally an academic philosopher, Holly Lawford-Smith, gave a speech in support of gender-critical feminism. This paper is my attempt to make sense of that moment, through critical engagement with Lawford-Smith’s book Gender-Critical Feminism. Since Lawford-Smith positions her book as a philosophical foundation for the gender-critical movement, my primary goal is to show that this philosophical foundation is both metaphysically and politically flawed. My secondary goal is to consider whether, and if so how, enactment of the philosophical views developed in that book would move us closer to the oppressive world neo-Nazis are trying to bring about.

We consider the nonlocal differential equation

\begin{equation*}-A\left(\int_0^1b(1-s)\big(u(s)\big)^{p(s)}\ ds\right)u''(t)=\lambda f\big(t,u(t)\big)\text{, }t\in(0,1),\end{equation*}

which is a one-dimensional Kirchhoff-like equation with a nonlocal convolution coefficient. The novelty of our work involves allowing a variable growth term in the nonlocal coefficient. By relating the variable growth problem to a constant growth problem, we are able to deduce the existence of at least one positive solution to the differential equation when equipped with boundary data. Our methodology relies on topological fixed point theory. Because our results treat both the convex and concave regimes, together with both the variable growth and constant growth regimes, our results provide a unified framework for one-dimensional Kirchhoff-type problems.

This article analyzes the interplay between medicine and politics in East Germany. It analyzes the meetings of the Politburo medical commissions (1958–60) to frame and define the habitus of a generation, the “Tenners” (born 1910–20), which included most of the experts in the Politburo meetings. This generation consisted of politically committed doctors who were also influential medical scholars, many with international reputations. The Politburo meetings revealed major quarrels between these experts and the Party. The communiqué (1960) issued by the Politburo showed a partial victory for the experts, because the Party acknowledged many of their claims, proving that “totalitarian” interpretations do not hold. However, this was not a victory of medicine over politics. The experts formulated their claims by combining medical and political arguments and defended the jurisdiction of their medical expertise over the Party, precisely because they believed it could more decisively contribute to achieving the goals of socialism.