We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove existence and uniqueness of pseudo-trisections, and further establish a one-to-one correspondence between pseudo-trisections and their diagrammatic representations. We next introduce the concept of pseudo-bridge trisections of neatly embedded surfaces in smooth oriented compact 4-manifolds. We develop a diagrammatic theory of pseudo-bridge trisections and provide examples of computations of invariants of neatly embedded surfaces in 4-manifolds using said diagrams.

In this article, we present a simulation tool for modeling a quasi-optical bench for material characterization. The model uses a Gaussian beam expansion and tracking analysis, together with a modal analysis to enable a comparison of the simulated reflection and transmission S-parameters to the ones measured with a 4-port vector network analyzer. A Thru-Reflect-Line calibration is performed to de-embed the simulated S-parameters of a dielectric slab located between two lens antennas, showing good agreement with the analytical slab model used for experimental permittivity extraction.

This article examines the relationship between legality and legitimacy in postcolonial constitution-making, focusing on Singapore's two stages of sovereignty transfer from colonial rule to independent statehood: its decolonisation from Britain in 1963, achieved through merger with Malaysia, and its separation from Malaysia in 1965. The article shows how different forms of legitimacy were established and sustained during these transitions. The first independence was characterised by legal continuity and political legitimacy, solidified through peaceful negotiations and the strategic use of a 1962 referendum that helped mitigate internal opposition. By contrast, the second independence in 1965 was a ‘legal revolution’, as neither the Malaysian Federal Constitution nor the State of Singapore Constitution 1963 provided for secession and the People's Action Party (PAP) government lacked an explicit public mandate to negotiate the secession. This break in legal continuity required new sources of (revolutionary) legitimacy, which the PAP government secured through subsequent electoral dominance, constitutional consolidation, and political manoeuvres. This article underscores the fact that legitimacy in making, amending, and consolidating constitutions is inherently transient and unstable, requiring continuous renewal through various political and legal mechanisms.

We demonstrate the existence of K-multimagic squares of order N consisting of $N^2$ distinct integers whenever $N> 2K(K+1)$. This improves our earlier result [D. Flores, ‘A circle method approach to K-multimagic squares’, preprint (2024), arXiv:2406.08161] in which we only required $N+1$ distinct integers. Additionally, we present a direct method by which our analysis of the magic square system may be used to show the existence of $N \times N$ magic squares consisting of distinct kth powers when

$$ \begin{align*}N> \begin{cases} 2^{k+1} & \text{if}\ 2 \leqslant k \leqslant 4, \\ 2 \lceil k(\log k + 4.20032) \rceil & \text{if}\ k \geqslant 5, \end{cases}\end{align*} $$

improving on a recent result by Rome and Yamagishi [‘On the existence of magic squares of powers’, preprint (2024), arxiv:2406.09364].

Inspired by work of Andrews and Newman [‘Partitions and the minimal excludant’, Ann. Comb. 23 (2019), 249–254] on the minimal excludant or ‘mex’ of partitions, we define four new classes of minimal excludants for overpartitions and establish relations to certain functions due to Ramanujan.

It is well-attested that floating tones can associate across a word boundary, but it is typologically unusual for floating weight units to do so. The Nuer language presents a floating suprasegmental component (FSC), which is part of lexical morphemes, and includes a unit of quantity and a High tone. This component is located at the left edge of nouns and is realised primarily across a word boundary on a preceding vowel. This article examines the FSC through a phonological analysis and a production study with eight speakers. These investigations reveal how the FSC interacts with the specifications for vowel length and tone of the adjacent context. Specifically, the weight unit of the FSC lengthens a preceding word-final short vowel, and its High tone combines in a compositional manner with tone of this preceding context. Comparisons with related languages suggest that the FSC developed out of a word-initial vowel /a/.

We give a brief overview of the special issue of MSCS “Advances in Homotopy Type Theory.”

Let C and W be two integer sets. If $C+W=\mathbb {Z}$, then we say that C is an additive complement to W. If no proper subset of C is an additive complement to W, then we say that C is a minimal additive complement to W. We study the existence of a minimal additive complement to $W=\{w_i\}_{i=1}^{\infty}$ when W is not eventually periodic and $w_{i+1}-w_{i}\in \{2,3\}$ for all i.

Land-use changes are considered one of the main drivers of biodiversity loss. Agricultural intensification, pastoral abandonment, and changes in forest management have led to the homogenisation of landscapes. In particular, the encroachment of grasslands and the densification of forests that are no longer pastured threaten species that require multiple habitats to nest and forage, such as the European Nightjar Caprimulgus europaeus. Whereas previous studies have focused on understanding factors influencing the decrease of nightjars at regional or national scales, here, we aimed to assess fine-scaled habitat selection by nightjars within nesting and foraging sites based on high-resolution GPS tracking data. Vegetation structure and composition were quantified in the field. In the nesting habitat, nightjars prefer open forests with a low percentage of trees and where the ground is not covered by more than 40% of grass and crawling bushes (dwarf bushes such as Juniperus species). In contrast, when foraging, nightjars select open grasslands and biodiversity-friendly managed vineyards, both richly structured, i.e. interspersed or surrounded by other land-use types such as hedges or isolated trees. Both the nesting and foraging habitats are currently threatened, either by the abandonment of forest management, which makes stands denser and more homogeneous, or through agricultural intensification, which reduces land-use diversity. Clear habitat-specific management recommendations and political incentives are needed to simultaneously preserve and/or restore these critical habitats, which are important for nightjars that use complementary resources for nesting and foraging.

This article proposes to connect the history of European integration with that of protest movements. Drawing on a transnational approach, it highlights a double link between the protest movements of spring 1968 in France and autumn 1969 in West Germany and the rise of the European Economic Community. Firstly, the completion of the common market on 1 July 1968 increased competition between European economies, fostering social demands on the eve of the protest. Secondly, the economic consequences of May 1968, both in France and in West Germany, underlined the new interdependencies of French and German societies within the common market. The need for convergence towards a ‘community of stability’ paved the way for negotiations on an economic and monetary union after the relaunch at the Congress of The Hague in December 1969.

Morphological knowledge refers to the ability to recognize and use morphemes correctly in syntactic contexts and word formation. This is crucial for learning a morphologically rich language like Finnish, which features both agglutinative and fusional morphology. In Finnish, agglutination occurs in forms like aamu: aamu+lla (‘morning: in the morning’), where a suffix is transparently added. Fusional features, as seen in ilta: illa+lla (‘evening: in the evening’), involve allomorphic stem changes that reduce transparency. We investigated the challenges posed by stem allomorphy for word recognition in isolation and in context for L2 learners and L1 speakers of Finnish. In a lexical decision task, L2 speakers had longer response times and higher error rates for semitransparent inflections, while L1 speakers showed longer response times for both transparent and semitransparent inflection types. In sentence reading, L2 speakers exhibited longer fixation times for semitransparent forms, whereas L1 speakers showed no significant effects. The results suggest that the challenges in L2 inflectional processing are more related to fusional than agglutinative features of the Finnish language.