The almost sure convergence of ergodic averages in Birkhoff’s pointwise ergodic theorem is known to fail in the finitely additive setting. We introduce a natural reformulation of almost sure convergence suitable for finitely additive measures, which we call finite almost sure convergence. Unlike the classical formulation, finite almost sure convergence only involves measures of finite unions and intersections, making it well adapted to finitely additive spaces. Using this notion, we extend the pointwise ergodic theorem to finitely additive probability spaces. Our proof relies on demonstrating that several quantitative generalizations of the pointwise ergodic theorem remain valid in the finitely additive setting via an extension of the Calderón transference principle. The result then follows by exploiting the relationships between quantitative notions of almost sure convergence developed by the author and Powell [On quantitative convergence for stochastic processes: crossings, fluctuations and martingales. Trans. Amer. Math. Soc. Series B 12 (2025), 974–1019].

In response to the sustained decline in academic psychiatry posts and infrastructure across the UK, the Royal College of Psychiatrists’ Academic Strategy proposes seven strategic pillars to rebuild workforce capacity through collaboration and innovation, and argues for revitalising the discipline that is essential for scientific leadership, excellence and mental healthcare.

This paper considers the neglected history of Arwa Salih, a leader in the underground Egyptian Communist Workers Party in the 1970s. Women’s role in leading student strikes and underground communist activism has been marginalized in the accounts of the movement, but Salih’s case is marked by deliberate silence. Salih’s intimate history of the movement in her memoir al-Mubtasirun: Dafatir Wahida min Jil al-Haraka al-Tullabiyya (1996; The Stillborn: Notebooks of a Woman from the Student-Movement Generation, trans. Samah Selim, 2018) underlines the historical factors contributing to the depoliticization of the private sphere in Marxist organizations. Although not a feminist, Salih questions the quest for national liberation alongside reinforcement of gendered, traditional family values. Drawing on oral history interviews in an environment shaped by suspicion, with narrators close to Salih until her suicide in 1997, I seek to fill gaps in this historiography and explain the reasons Egyptian Marxists struggled to reconcile the fight for liberation, for which they have paid immense sacrifices, with gender equality.

This article examines the tenure and legacy of Francisco Núñez de la Vega, a Dominican friar who served as Bishop of Chiapas and Soconusco in New Spain from 1682 to 1706. During his career, Núñez investigated allegations of idolatry and non-orthodox rituals practiced by Indigenous ritual specialists in his diocese. These investigations formed the basis of an influential sermon written in 1698 known as the Ninth Pastoral Letter (Carta Novena Pastoral), which inveighed against the magical powers of Indigenous shapeshifters, diviners, and healers pejoratively referred to as nahualistas. These nahualistas held sway in local Indigenous communities long before Europeans invaded the Americas, and they provided an alternative to the good–evil binary endorsed by the Church. This article examines five criminal cases in Chiapas to highlight the influence of Indigenous ritual specialists and the nahualli figure more broadly in the colonial era. Two of these cases (1685 and 1696) took place during Núñez’s tenure as bishop and shed light on his understanding of Native religious beliefs and practices, which had been shaped by European writings on witchcraft since the Middle Ages. The three remaining criminal cases (1721, 1778, and 1801) reveal that Dominican clergy continued to consult Núñez’s Ninth Pastoral Letter long after his death whenever charges of idolatry and nahualism arose. Lastly, this article considers how Núñez attempted to convert his parishioners and how Indigenous ritual specialists continued to influence village life while living in the bishop’s shadow.

This article challenges the narrative of ubiquitous late medieval Christian anti-Judaism by presenting Pablo de Santa Maria’s remarkably nuanced portrayal of Judaism (c. 1400–1430). Pablo, the rabbi of Burgos who had become its bishop, lived and wrote at the intersection of Judaism and Christianity. While longstanding historiographical misconceptions about the nature of Pablo’s intellectual and pastoral project have stifled interest in Pablo’s prolific Latin writings, recently scholars like Yosi Yisraeli have argued that these Latin writings actually contain intellectual innovations of profound importance to the development of Christian Hebraism. This article reads Pablo’s Latin writings not primarily within the Christian intellectual tradition but rather as a response to the contemporary phenomenon of large-scale Jewish baptism. Pablo was seeking to negotiate the integration of these baptized Jews into Christianity, which required him to construct positive narratives about Judaism to dispute (or at least complicate) the prevalent negative narratives. More broadly, while recent scholarship has treated Christian narratives of Judaism as emanating from intra-Christian disputes, this article suggests Christian views of Judaism were in fact formed and contested through the persons and identities of baptized Jews.

With the evolution from 5G to 6G and the popularization of carrier aggregation technology, mobile terminal devices face challenges in miniaturizing multiplexers and handling concurrent signals across a wide-bandgap. This study proposes a numerical de-embedding design method. By precisely calculating and compensating for the parasitic loads, it achieves deterministic synthesis of matching networks. Based on this method, we designed and fabricated a monolithic integrated surface acoustic wave triplexer on a lithium tantalite on insulator (LTOI) substrate for dual-frequency GPS L1/L5 positioning and Bluetooth (BT) communication. To suppress a specific spurious mode on the LTOI substrate and improve the isolation, a notch inductor structure was embedded into the design. The monolithic integrated triplexer measures 2.5 mm × 2.0 mm × 0.6 mm after packaging. The insertion loss is less than 1.6 dB in both the L1 and L5 bands. In the BT band, the average loss within any 18 MHz range of the passband is below 2.5 dB. The return loss for all three channels is better than −10 dB, while the isolation between channels is maintained at ≈40 dB. The successful fabrication of this triplexer not only validates the design method but also demonstrates its potential for application in miniaturized wearable devices.

In this article, I consider Bernard Lonergan (1904–1984) and Max Horkheimer (1896–1973) on the topic of social decline, focusing on the relationship between what Lonergan called “conceptualism” and what Horkheier called “instrumental reason.” I will argue that conceptualism and instrumental reason are distinct conscious intentional phenomena that collude in generating social decline. For the sake of convenience and clarity, I will categorize (with some qualifications) this collusive relationship between conceptualism and instrumental reason as one of “elective affinity.” I will advance my argument, first, by articulating Lonergan’s critique of conceptualism in his Verbum articles. Next, I will turn to Horkheimer’s account and critique of instrumental reason. We will see a striking example of the convergence of conceptualism and instrumental reason in Louis Billot, SJ (1846–1931), a neo-Scholastic theologian and cardinal mentioned specifically by Lonergan and generically by Horkheimer. I will then locate conceptualism and instrumental reason within Lonergan’s theory of intentionality analysis, specifically the levels of consciousness, and will elaborate on their elective affinity. Finally, within the parameters of Lonergan’s account of social decline, I will outline how their collusion generates social decline.

Medieval Roman frontier management remains understudied, and only rarely have digital humanities methods been applied to it. This article examines a moment in Roman–Fatimid imperial competition in Syria in the early 1030s by using Geographic Information Systems (GIS) analysis. The Syrian Coastal Mountains south of Antioch were the location of a failed Roman attempt to establish Naṣr ibn Musharraf as a client. As relations broke down, he sought Fatimid support. The brief ensuing conflict is revelatory of long-term patterns in frontier management, while spatial analysis within a GIS framework provides insight into the role of geomorphology in how these events unfolded.

We show that the quasilinear Schrödinger equation $-\epsilon ^{2}\Delta u + Q(x)u -\Delta (u^{2})u= h(u)$ in $\mathbb{R}^{N}$ has $\wp$ solutions related to the $\wp$ global minima of the potential $Q$. We work with the Nehari manifold associated with the energy functional. We evaluate the energy of the solutions to distinguish them from each other.

The history of post-war climate science has been written with a strong focus on the role of global geopolitics and climate models. In this article, I will broaden this perspective with a smaller-scale approach and a different technology. Drawing on the history of a radiocarbon dating laboratory in Switzerland, I show, on one hand, how local political and cultural contexts could influence the development of climate science and, on the other, how research technology beyond computer modelling also played a crucial role in this development. I argue that such a smaller-scale approach can help us to better understand the process of the interdisciplinarization of climate science, as well as the role of technology in this process.

The Little Ice Age (LIA, ∼1400–1850 CE) was characterized by colder winters and more frequent extreme weather events in the Northern Hemisphere. While changes in ocean circulation likely contributed to global cooling, the specific mechanisms remain poorly understood. Here, we investigate how ocean circulation changed before, during, and after the LIA using marine sediment cores from the Laurentian Channel in the lower St. Lawrence Estuary. We first established a Mg/Ca–temperature calibration for Globobulimina auriculata using instrumental temperature data and a century-old box core. Applying this calibration to a longer piston core, we reconstructed bottom-water temperatures during the LIA. Coupling these results with existing δ1⁸O calcite data allowed us to isolate the δ1⁸O seawater signal, which reflects changes in the relative contributions of the Labrador Current and Gulf Stream. Our results indicate an increase of fresh and cold Labrador Sea–derived waters around 1500 CE. Throughout most of the LIA, we observed a slow and steady warming of the bottom water associated with a gradual increase in the proportion of Atlantic-derived waters until ∼1850 CE. The ∼1800–1950 CE interval shows high-amplitude variability, including a sudden freshening event at the LIA’s end. After 1950 CE, regional warming dominates, consistent with previous studies documenting increased Atlantic influence over the Canadian shelf.