Number theory and especially primes are an infinite source of inspirational ideas in elementary mathematics. Many of these ideas can be understood and some also explained with very basic mathematical knowledge. In our paper we explain the cycle which appears between the first six multiples of the decimal expression of and explore an inspiringly simple relation between primes, which somehow makes them gather into mysterious groups. And while exploring these simple questions, we are led to unveil some aspects of the power and limits of human mind and those of a computer.

The 1892 collision between the British merchant ship Ravenna and the Japanese torpedo boat Chishima generated a three-year legal debate over jurisdiction in territorial waters. Challenging the conventional notion that the coastal State enjoyed full sovereignty over its maritime territory, this article argues that contested jurisdiction in territorial waters was ubiquitous at the turn of the twentieth century. In addition to imperialism, which played a pivotal role in transforming the coastal waters of semi-colonial countries into overlapping legal zones, political speculations and the absence of a uniform legal standard also put the coastal State's assertion of maritime sovereignty into question. On the one hand, semi-colonial states, such as the Meiji government, sometimes strategically avoided asserting maritime sovereignty when they deemed it appropriate for national interests. On the other hand, there was also a wide cleavage of opinions among Western powers regarding coastal jurisdiction. Scrutinizing the entangled currents of imperialism, political speculations and maritime laws in the Chishima case, this article contributes to the burgeoning scholarship on the polycentric oceanic world by displaying the rarely discussed contested jurisdiction in territorial waters before World War II.

According to International Union for the Conservation of Nature (IUCN) guidelines, all species must be assessed against all criteria during the Red Listing process. For organismal groups that are diverse and understudied, assessors face considerable challenges in assembling evidence due to difficulty in applying definitions of key terms used in the guidelines. Challenges also arise because of uncertainty in population sizes (Criteria A, C, D) and distributions (Criteria A2/3/4c, B). Lichens, which are often small, difficult to identify, or overlooked during biodiversity inventories, are one such group for which specific difficulties arise in applying Red List criteria. Here, we offer approaches and examples that address challenges in completing Red List assessments for lichens in a rapidly changing arena of data availability and analysis strategies. While assessors still contend with far from perfect information about individual species, we propose practical solutions for completing robust assessments given the currently available knowledge of individual lichen life-histories.

This article explores the Department of Education's programme of co-operation and rationalisation within the Irish post-primary school sector during the period 1966–70. Through a systematic analysis of government files and private convent archival collections, especially those of the Presentation Sisters, combined with oral history interviews, this study provides a unique insight into how co-operation and rationalisation in the post-primary sector were reconciled at ground level. It exposes the previously hidden history of voluntary secondary school authorities and the role they played in educational reform during the 1960s and explores how individual school authorities received, responded to and reacted to this new government initiative. To a large extent, the success of co-operation and rationalisation depended on the willingness of school authorities to accept and comply with departmental directives. This study, thus, expands understandings of the history of the Irish education system in general and of the reform period (c.1957‒72) in particular.

This research paper focuses on enrichment of yoghurt containing probiotic Lactobacillus casei with persimmon (Diospyros kaki) powder in concentrations of 0 (Control) and then 0.5, 1.0, 1.5 and 2.0% (A–D respectively) and determination of some characteristics of the product during refrigerated storage for 21 d. Powder addition affected the color characteristics, textural properties, titratable acidity and water-holding capacity values. The viability of both yoghurt bacteria (Lactobacillus delbrueckii subsp. bulgaricus and Streptococcus thermophilus) and L. casei increased proportionally to adding persimmon powder for all storage days. Furthermore, addition of fruit powder increased short-chain fatty acid and polyunsaturated fatty acid contents. According to sensory analysis results, sample D had the lowest scores from the panelists, whereas the Control together with samples B and C were the most liked yoghurts in terms of flavor characteristics. In terms of overall acceptability, all of the samples received scores over three points on a five-point scale throughout storage. This study indicates that persimmon powder enriched yoghurt is a good vehicle for L. casei and yoghurt bacteria with improved fatty acid profile and acceptable sensory characteristics.

This research paper presents the characterization of an enterocin-producing Enterococcus durans MF5 isolate and the determination of the in vitro antilisterial activity of enterocin produced by this isolate, named Ent-MF5. PCR-based screening for bacteriocin biosynthetic genes revealed that E. durans MF5 harbors multiple enterocin-encoding genes (ent A, B, P and X), classified as class II bacteriocins and enterocin-P of Enterococcus faecium (sharing up to 99% similarity at the genetic level). E. durans MF5 is sensitive to eight clinically important antibiotics and does not possess cytolysin activator -cylA, gelatinase -gelE and hyaluronidase -hylA virulence genes. The antilisterial activity of Ent-MF5 was abolished by trypsin, α-chymotrypsin, protease and proteinase-K. Ent-MF5 showed thermal and pH stability. In addition, the activity of Ent-MF5 was unaffected in the presence of various surfactants (1% SDS, Triton X-100, Tween 20, and Tween 80). Ent-MF5 exhibited antimicrobial activity against Listeria monocytogenes, Listeria innocua, Listeria ivanovii and Listeria seeligeri at concentrations as low as 0.13 μg/ml. Ent-MF5 had a bactericidal effect against L. monocytogenes with a significant reduction in surviving cells at concentrations equal to or greater than 0.13 μg/ml. A 75–100% reduction in L. monocytogenes growth and bactericidal effect determined by CFU counts was observed following treatment with Ent-MF5 at 4.47 μg/ml at time points starting at 2 and 4 h, respectively. Ent-MF5 action is associated with Listeria cell membrane damage, as observed by flow cytometry and fluorescence microscopy. Thus, the effective antilisterial activity and stability of Ent-MF5 presents promising perspectives for application as biopreservatives in the food industry.

This article, based on an oral presentation in virtual format by the author at its Annual General Meeting in February 2024, summarizes the activities of the British School at Athens with a focus on the calendar year 2023. It gives us great pleasure to present the innovative and varied work of BSA sponsored field and research projects, the Fitch Laboratory, Knossos Research Centre, archive, and library as well as the inspiring work of the School students, post docs, and fellows.

This report presents the first in-depth publication of preliminary data from Oued Beht, northwest Morocco, a remarkable site initially identified in the 1930s and now newly investigated. It is based on fieldwork undertaken in 2021–2022 (photogrammetry, survey and excavation), and associated study and analyses. Oued Beht is shown to be a large site of ca. 9–10 hectares in main extent, with many deep pits and convincing evidence for a full package of domesticated crops and animals. Its material culture is abundant and dense, comprising ceramics (including a local painted tradition hitherto barely attested in northwest Africa but comparable to finds in Iberia), numerous polished stone axes, grinding stones and other macrolithics, and a chipped-stone industry. Radiocarbon dates so far cluster at ca. 3400–2900 BC, but there are also indications of earlier and later prehistoric activity. What social activities Oued Beht reflects remains open to interpretation, but it emerges as a phenomenon of strong comparative interest for understanding the wider dynamics of north Africa and the Mediterranean during the fourth and third millennia BC.