A considerable knowledge gap exists in relation to the presence and even existence of seagrass within Northern Ireland’s waters. Peer-reviewed publications on the historical ecology of seagrass are scarce and a collated timeline of references directly focusing on Northern Irish seagrasses does not exist. Recognising abiotic and biotic induced environmental change within key marine features such as seagrass is vital when attempting to measure the biodiversity and carbon sequestration services they provide. The research undertaken during this study identified three distinct periods within the archival records, which could be matched to the ecological history of seagrass in Northern Ireland. The first period (extensive and dense seagrass meadows from 1790 to 1880) was characterised by extensive seagrass meadows which were dense and healthy. The second period (degradation from 1880 to 1940) saw the beginnings of decline in seagrass from the 1790s, initially from anthropogenic influences and later from the seagrass wasting disease) and the final period (signs of recovery from 1940 to present day) showed small amounts of local regrowth of seagrass but at far reduced densities compared to the historical baseline described. These three defined periods all delivered varying degrees of anthropogenic stressors which determined the conservational health of seagrass in Northern Ireland. Seagrass habitats have become integral components in future-proofing the coastal marine environment against the effects of climate change and its associated impacts. Therefore, it is envisaged that the historical baseline that this manuscript provides will greatly benefit habitat managers in protecting, repairing, and restoring lost seagrass meadows.

It is a well known and easily verifiable fact that not all integer triangles have integer areas. Consider the triangles with sides {9, 10, 17}, {13, 14, 15}, {5, 7, 8} and {6, 7, 9} with respective areas 36, 84, and . The first two, whose areas are integers, are called Heronian triangles. The second triangle also has the additional property that its sides are consecutive integers and is an example of a Brahmagupta triangle, named after an Indian mathematician, born in AD 598. These are called Super-Heronian triangles in [1] and a method is developed there for generating examples of such triangles.

The Blue Shield UK Underwater Heritage Working Group (UHWG) is dedicated to protecting underwater cultural heritage in crisis, both within the United Kingdom (UK), UK Overseas Territories and internationally. In pursuit of this mission, the UHWG’s objectives are threefold:

We prove the conjecture of Franceschini and Lorenzini [‘Fat points of $\mathbb P^n$ whose support is contained in a linear proper subspace’, J. Pure and Appl. Algebra 160 (2001), 169–182] about the regularity index of fat points of $\mathbb P^n$ whose support is contained in a linear proper subspace.

This article focuses on passages in which Confucius is portrayed in dialogue with Lord Ai of Lu (r. 494–468 bce), found scattered throughout a range of early texts, most centrally in the Li ji, the Da Dai Li ji, and the Xunzi. Examining intertextual connections among these dialogues and related texts, both received and excavated, it seeks to adduce evidence to determine whether their particular shared narrative frame might be original and integral to the content of these texts, as well as to reveal their close links with other early Confucian texts that hold important implications for the dating of all these interrelated texts.

Earth–outer space interactions challenge conventional legal structures through dynamics that transcend jurisdictional boundaries and temporal scales. International law historically operates through specific spatiotemporal assumptions: geometric space, chronometric time, and cartographic politics. These elements structure how legal authority is conceptualised and enacted. This study recognizes the interconnectedness between Earth and outer space, positioning legal thought and practice within planetary and cosmic contexts. This integrative framework moves beyond anthropocentric and state-centric paradigms to address the indeterminate nature of multifaceted systems. The research employs an interdisciplinary methodology that integrates legal theory and doctrine, systems engineering, and systems science to analyse emergent phenomena such as orbital debris dynamics. The study concludes that addressing Earth–outer space interactions effectively requires not merely integrating existing legal regimes but reconceptualizing core legal concepts to align better with complex, multi-scalar and emergent dynamics.

Self-working card tricks have been a staple for budding magicians and entire books have been written about them, e.g. Fulves [1]. Lately selfworking card tricks have become common fodder for social media. In this note, we generalise two such card tricks (from [2] and [3]) that are based on the Australian shuffle.

Mental health, like physical health, represents an important resource for participating in politics. We bring new insights from six surveys from five different countries (Britain, Germany, the Netherlands, Switzerland, and the United States) that combine diversified questions on mental health problems and political participation. Unlike previous research on depression, we find only limited evidence for the Resource Hypothesis that mental health problems reduce political participation, except in the case of voting and only in some samples. Instead, we find mixed evidence that mental health problems and their comorbidity (experiencing multiple problems) are associated with increased political participation. Our study leads us to more questions than answers: are the measures available in public opinion surveys appropriate for the task? Do general survey samples adequately capture people with mental disorders? And is the assumption that poor mental health reduces political participation wrong?

We developed a method called “component decomposition” to extract the pattern of each component of the sample from the multiple powder X-ray diffraction data. Using the component decomposition and the Direct Derivation Method™, we analyze the behavior of phase transitions of trehalose during the changes in temperature and humidity. Because we do not require databases or standard samples, this method is a powerful tool for the quantification of polymorphs in samples containing multiple polymorphs.