My Mathematical Association Presidential Address focused on maths education in the context of the current environment in England. However, many of the issues are relevant to other UK nations and maths education more widely.

Colostrum (CM) and transition milk (TM) are crucial for neonatal development but knowledge about the changes in their composition in dairy goats is still limited. The aim of this study was to characterise the immunological, lipid and microbial changes from CM to TM in Guanzhong dairy goats, an indigenous, highly productive Chinese breed. Milk samples were collected from eight primiparous goats at day 0 (CM) and day 7 (TM) postpartum. Immunoglobulin concentrations (IgG, IgA, IgM) were measured by ELISA, long-chain saturated fatty acids (FA) were analysed by gas chromatography, and bacterial communities were profiled by 16S rRNA gene amplicon sequencing. Microbial functions were inferred using PICRUSt2 (Phylogenetic Investigation of Communities by Reconstruction of Unobserved States) software based on KEGG (Kyoto Encyclopedia of Genes and Genomes) orthologs. Immunoglobulin concentrations declined significantly from CM to TM, reflecting a transition from immunoprotection to food supply. The TM had increased concentrations of long-chain saturated FA, particularly palmitic acid (C16:0) and stearic acid (C18:0) and higher concentrations of branched-chain FA, suggesting an adaptation to the growing energy demands of the newborn. Although overall microbial diversity was stable, taxonomic shifts were observed. CM was enriched in Emticicia, which may be involved in oligosaccharide degradation, while TM had higher abundance of Faecalibacterium, Ruminococcus and Salinicoccus, genera associated with SCFA production and intestinal development. Functional predictions indicated enrichment of cold shock and haem biosynthetic pathways in CM and enhanced carbohydrate degradation pathways in TM. Correlation analyses revealed relationships between specific FA and bacterial genera, suggesting interactions between host, microbes and nutrients that may influence milk functionality. This integrative analysis of milk components during early lactation provides new insights into the compositional and functional dynamics of goat milk.

This study examined the effects of fat content (0.1%, 1.5%, 3%, and 3.5%), heat treatment (pasteurization and UHT), and vitamin D supplementation on the physicochemical, microbiological, and sensory characteristics of yoghurt over 21 days. Yoghurts with higher fat content generally received higher sensory acceptability scores (7–8), exhibited less syneresis (14.75–22.48%) and higher whiteness index; 0.1%-fat had the highest syneresis (51.28%) and lowest whiteness (80.77) (p < 0.05). Although pasteurised yoghurt exhibited slightly better firmness (1.77 N) than UHT (1.61 N), no significant effect of heat treatment was found (p > 0.05). Sensory preference was for 3% and 3.5%-fat and pasteurised variety, especially for consistency. All yoghurts maintained viable lactic acid bacteria counts >10⁷ cfu/g throughout the storage period. The vitamin D addition resulted in a 6% average higher syneresis rate (p > 0.05) and a nearly 4% higher whiteness index (p < 0.05). This study shows that it is possible to obtain yoghurts with enhanced properties by optimizing the fat content and heat treatment conditions applied, and it also directs future studies on the effect of vitamin D addition on yoghurt properties.

Michael Sata’s presidency in Zambia (2011–14) marked a notable attempt to revive statist development ideas rooted in the country’s postindependence era. While the preceding MMD government had begun reintroducing limited state intervention, its commitment remained constrained. Sata, by contrast, articulated a more assertive vision of state-led development, echoing the UNIP-era model under Kenneth Kaunda. Drawing on policy documents, speeches, and survey data, this article situates Sata’s politics and policies within broader public dissatisfaction with neoliberal reforms and highlights enduring tensions in Africa’s poststructural adjustment era between market-oriented policies and demands for greater state involvement.

This communication addresses the hypothesis that silver nanoparticles obtained by green synthesis (G-AgNPs), using an aqueous extract of chicory, have antibacterial activity against bovine mastitis-associated strains and may inhibit their adherence capacity. Bovine mastitis is among the diseases with the greatest economic impact worldwide. Multifactorial in nature, it is usually associated with infection caused by bacterial species such as Staphylococcus aureus, coagulase-negative staphylococci, Streptococcus uberis, and Escherichia coli. Antibiotics are currently the main line of treatment, but in order to offset the emergence of resistance, alternative compounds and nanomaterials are being researched for prevention and control. In this study, bacteria that cause bovine mastitis were molecularly identified by groEL gene PCR-RFLP. Then, G-AgNPs were produced using an aqueous extract of chicory as a reducing and stabilizing agent. The nanoparticles showed powerful antibacterial activity, but they did not seem to reduce the adherence of pathogens to MAC-T cells that had been preincubated with a sub-MIC concentration of G-AgNPs. Nevertheless, very low concentrations (21-30 pM) were needed for the antibacterial effect to take place, which makes G-AgNPs promising candidates for the control of bovine mastitis.

Part of a series of longitudinal studies of churchgoing in British towns and cities, this article traces the statistical history of church attendance in London over the past two hundred years. Among other sources, it utilises national religious censuses in 1851 and 1979–2005 and metropolitan ones in 1886–7, 1902–3, 1933–4 and 2012, presenting results as an index of attendance (IA), expressing attendances as percentage of population. Throughout the late nineteenth and twentieth centuries, London’s IAs fell continuously and were mostly below those in other conurbations. Following an uptick around the millennium, net decline resumed after 2012.

In 1408, as the Great Western Schism entered its fourth decade, the Parisian community of Celestine monks asked Pierre d’Ailly to write a life of their founder, Pietro Morrone, who served as Pope Celestine V in 1294. D’Ailly found in him an example that suited his times: a pope could resign without damage to the Church at large. With cardinals from both obediences ready to withdraw support from Avignon’s Benedict XIII and Rome’s Gregory XII, both of whom resisted resignation, d’Ailly made his case for papal resignation via his life of Celestine V.

This paper broaches ‘natural theology’ in terms of the conceptual systems through which revelation is understood, as opposed to questions regarding the sources of revelation. I do so by analysing Barth’s rejection of natural theology in terms of what it can mean to treat a logic of prior possibility as determining what revelation’s conditions of possibility must be. I begin by reading Emil Brunner’s ‘Nature and Grace’ alongside Ludwig Wittgenstein’s reflections on mathematical necessity in order to show that Brunner’s thinking of possibility subordinates the necessities of revelation to what Wittgenstein calls ‘the logical machine’. I then argue that Barth’s rejection of natural theology involves rejecting the workings of this machine and so rejecting the axiomatic force of prior possibility for theology. I conclude by tracing two consequences of this rejection, one related to creativity, the other to political crisis.

This Article is an exposition of two very old theorems. One was first proved by A. A. Markov in 1889 [1], the other by S. N. Bernstein in 1912 [2]. Both Markov (1856–1922) and Bernstein (1880–1968) were authors of numerous pioneering works: there are many other results designated Markov’s theorem or Bernstein’s theorem (or Bernstein’s inequality) in their respective subject areas. “Markov chains” have become a standard concept in probability theory, and “Bernstein polynomials” a standard one in approximation theory.

Psychedelic medicines hold the promise of therapeutic benefit for many suffering from serious unmet mental health needs, leading to substantial demand even before these drugs receive FDA approval based on demonstrated safety and effectiveness for particular conditions. Recognizing FDA approval as the ideal path for psychedelics intended for medical use and drawing on lessons from medical marijuana, we encourage policymakers to balance the need for evidence, the importance of patient safeguards, and the desire for speed. They should increase support for psychedelic research, reject approaches that could inhibit that research, explore improvements to FDA’s existing pre-approval access pathway, and avoid politically motivated FDA approval of psychedelic medicines.

By observing China’s domestic media landscape and state policies during the COVID-19 pandemic, this paper proposes the concept of “propaganda state 2.0” as a framework for exploring autocratic state propaganda from a holistic perspective. It contends that state propaganda in China remains an agitprop apparatus deeply embedded in the totality of the authoritarian regime, which it both serves and is served by. This system performs both conventional persuasion and indoctrination functions, as well as fulfilling the now underestimated mission of agitation, which can enhance the credibility of propaganda messages. This framework emphasizes the legacies of China’s past “propaganda state” and effectively explains how the party-state transformed the pandemic into opportunities to win popular support, and how this resulted in a debacle. Theoretically, the article highlights how state propaganda in contemporary China can shape, if not dictate, state policy, while serving as a more organic framework that bridges the “hard” and “soft” propaganda literatures.