It is shown that if $\{H_n\}_{n \in \omega}$ is a sequence of groups without involutions, with $1 \lt |H_n| \leq 2^{\aleph_0}$, then the topologist’s product modulo the finite words is (up to isomorphism) independent of the choice of sequence. This contrasts with the abelian setting: if $\{A_n\}_{n \in \omega}$ is a sequence of countably infinite torsion-free abelian groups, then the isomorphism class of the product modulo sum $\prod_{n \in \omega} A_n/\bigoplus_{n \in \omega} A_n$ is dependent on the sequence.

This paper evaluates the UK Government’s decision to increase the main form of social security by £20 per week during the coronavirus disease 2019 (COVID-19) pandemic, exploring whether increasing the generosity of social security for some, but not all, claimants affected food insecurity. Using the Family Resources Survey, we found a decline of about 7 percentage points in food insecurity amongst benefit claimants affected by the uplift compared with claimants not affected (95% CI −13.9 to −0.9%). This association did not change substantively following adjustment for covariates, nor when the model was re-estimated using matching methods. Results were not driven by changes in the composition of claimants over time. These analyses suggest food insecurity could be reduced if the generosity of the social security system increased. In actuality, the UK government went in the opposite direction, removing the £20 uplift in October 2021, potentially exposing claimants to higher rates of food insecurity again.

The COVID-19 pandemic significantly challenged the mental health of children and adolescents, with existing research highlighting the negative effects of restrictive measures to control the virus’s spread. However, in the specific context of this pandemic, there is limited understanding of how these difficulties have persisted over time after the situation was fully restored. This study sought to evaluate the pandemic’s impact on psychological symptoms in children from Italy, Spain, and Portugal across five-time points (2, 5, and 8 weeks, 6 months, and three and a half years after the pandemic’s onset). A total of 1613 parents completed the Psychological Impact of COVID-19 and Confinement on Children and Adolescents Scale, reporting symptoms in their children aged 3–17 years (39.2% female). The findings reveal an initial surge in psychological difficulties—anxiety, mood, sleep, behavioral, eating, and cognitive disturbances—followed by improvements in these domains three and a half years later. By September 2023, Spanish children experienced more significant reductions in symptoms compared to their Italian and Portuguese peers. While the COVID-19 pandemic has been a prolonged crisis, with varying impacts over time and across regions depending on the strictness of restrictions, the trends suggest a gradual improvement in the psychological well-being of children and adolescents.

Despite internet use potentially reducing loneliness among older adults during the Covid-19 pandemic, quantitative research in this area is limited. Our study addresses this gap by exploring how internet use affects loneliness worsening in old age across Europe from a gendered perspective. We adopt a comprehensive approach, considering individual and contextual factors. Using multi-level modelling, we analyse data from the Survey of Health, Ageing and Retirement in Europe (Wave 8 and Corona Survey 1), supplemented by the Oxford Covid-19 Government Response Tracker and the Eurostat Digital Agenda Scoreboard Key Indicators. The empirical analysis has revealed gender-specific differences in the relationship between internet use and the worsening of loneliness among older people during the pandemic, with internet use contributing to increased loneliness for older women, but not for men. In addition, our study indicates that while the contextual factors, namely the severity of the contingency measures and the quality of the internet connection, are not moderators of the relationship between internet use and loneliness worsening, the stringency index specifically exacerbates loneliness in women. These findings contribute to the development of more effective and targeted interventions to combat loneliness worsening and promote wellbeing among older women, particularly in the context of global health crises such as the Covid-19 pandemic.

A desire to preserve its ontological security was crucial in France’s decision to leave Algeria. France neither militarily lost the Algerian War (1954–62), nor were the financial costs of war too burdensome to bear. Instead, the contradictions between two narrative strands of France’s sense of self – liberal-democratic universalism and white European ethnonationalism – came unravelled, sparking a crisis of ontological security. These two narrative strands were rewoven together around the decision to leave Algeria, which saved France from facing a true reckoning about its sense of self and the dynamics of colonialism that had pushed France to create a racial hierarchy that contradicted French republican values. Algeria shows that ontological security can be preserved by using narrative strands to create the impression of stability amid profound changes. Additionally, in critical situations during periods of great global political change, shedding certain role-identities (such as being a colonial power) can help states recover ontological security. France’s pivot away from its colonial empire under President Charles de Gaulle is an example of such a transition away from a specific role-identity that was narrated in such a way that it actually – and paradoxically – projected stability.

The present study documents coastal processes of movement and subsidence that affect the clayey sediments of the exposed mudflats (‘mudflat sediments’) on the receding western shore of the Deep Dead Sea (‘western Dead Sea shore’) and the formation of subsidence features: subsidence strips and clustered sinkholes. The properties of the clayey sediments that promote movement and subsidence and the development of the subsidence features in the exposed mudflats are the unconsolidated fine-particle texture composed of clay and carbonate minerals, their being dry near the surface and wet at the subsurface, their soaking with saline water and brine and the abundance of smectitic clays saturated with sodium and magnesium. Field observations indicate that narrow subsidence strips with/without clustered sinkholes were developed by movement and subsidence in mudflat sediments via lateral spreading. Wide subsidence strips with clustered sinkholes were developed via increased subsidence in mudflat sediments due to the progress of dissolution within a subsurface rock–salt unit. The emergence of sinkholes occurs via subsidence of mudflat sediments into subsurface cavities resulting from dissolution within a subsidence rock–salt unit. The coastal processes on the receding Dead Sea shore and the formation of the subsidence features are part of the adjustment of the Dead Sea periphery to the lowering of the base level. A contribution of slow mass movement seaward to the coastal processes on the receding Dead Sea shore is indicated.

In the autumn of 1934, Bishop Johannes Geisler of Brixen/Bressanone denied two Italian-speaking priests, Carlo Torello and Giuseppe Ricci, permission to teach within his predominantly German-speaking diocese. In response, Benito Mussolini threatened to expel all Church representatives from the state education system and, by extension, to unravel the recently signed Lateran Accords. Untangling the motivations behind Geisler’s decision, the escalating tensions it precipitated, and, ultimately, the discussions that led to its quiet resolution reveal much about Fascist and Church ambitions in the newly annexed territory of Trentino-South Tyrol. This ‘Torello-Ricci Affair’ provides a micro-historical lens with which to better understand the political and cultural infrastructures of power in interwar South Tyrol and their relationship to institutions in Rome. In particular, it illustrates the ongoing battle between civil and religious officials to assert moral authority within the region, most importantly as it regarded the education of its children.

In this paper, a novel special structure derived from the double-slider mechanism is presented and apply it to the design of a parallel mechanism, endowing the designed parallel mechanism with reconfigurable characteristics. First, a comprehensive analysis of the motion modes of the double-slider mechanism is carried out. By ingeniously varying the slider structure of the double-slider mechanism, a special structure capable of three distinct motion modes is obtained. This special structure is then integrated into the 3UPU parallel mechanism. As a result, the redesigned 3UPU parallel mechanism exhibits reconfigurability and can seamlessly switch among the three motion modes. Subsequently, the inverse kinematics, workspace, and singular pose of the parallel mechanism in these three modes are meticulously analyzed. Moreover, the Jacobian matrix is utilized to evaluate its flexibility and load-bearing performance. The analysis reveals that in different motion modes, all performance indicators of the mechanism are remarkable, indicating a promising application prospect. Finally, a prototype is fabricated using 3D printing technology to further validate the effectiveness of the proposed special structure. Additionally, its versatility is further explored and analyzed in-depth.

Inspired by Nakamura’s work [36] on $\epsilon $-isomorphisms for $(\varphi ,\Gamma )$-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for L-analytic Lubin-Tate $(\varphi _L,\Gamma _L)$-modules over (relative) Robba rings for any finite extension L of $\mathbb {Q}_p.$ In contrast to Kato’s and Nakamura’s setting, our conjecture involves L-analytic cohomology instead of continuous cohomology within the generalized Herr complex. Similarly, we restrict to the identity components of $D_{cris}$ and $D_{dR},$ respectively. For rank one modules of the above type or slightly more generally for trianguline ones, we construct $\epsilon $-isomorphisms for their Lubin-Tate deformations satisfying the desired interpolation property.

Douglas has argued that if values were accorded a “direct” role during the “internal” phases of science, this would amount to “wishful thinking” in place of evidence. This article draws on two claims that jointly threaten this position. First, building a cogent ethical case in favor of a claim about what ought to happen is not a simple matter of saying what one wishes were true; a good ethical case has a kind of discipline to it. Second, some theorists have argued that scientists do and should defend “mixed hypotheses,” that is, hypotheses that implicate both factual and evaluative content.

There is much to praise in Freedom from Fear, including Kahan’s compelling case that liberalism must be studied in relation to the concrete conditions which shaped liberal fears and hopes; his fair-minded exploration of liberalism’s complex relationships with democracy, religion, imperialism, feminism, and economic transformation; and his recovery of important, oft-neglected figures. But, as Kahan reminds us, liberalism valorizes conflict. Accordingly, I dwell on my disagreement or doubts concerning Kahan’s definition of liberalism, his depiction of liberalism’s “third wave,” and his suggestions for liberalism’s response to populism.