The notion of $\theta $-congruent numbers generalises the classical congruent number problem. A positive integer n is $\theta $-congruent if it is the area of a rational triangle with an angle $\theta $ whose cosine is rational. Das and Saikia [‘On $\theta $-congruent numbers over real number fields’, Bull. Aust. Math. Soc. 103(2) (2021), 218–229] established criteria for numbers to be $\theta $-congruent over certain real number fields and concluded their work by posing four open questions regarding the relationship between $\theta $-congruent and properly $\theta $-congruent numbers. In this work, we provide complete answers to those questions. Indeed, we remove a technical assumption from their result on fields with degrees coprime to six, provide a definitive answer for real cubic fields without congruence restrictions, extend the analysis to fields of degree six and examine the exceptional cases $n=1, 2, 3$ and $6$.

Ibogaine is a psychedelic alkaloid without an approved indication. Observational clinical research shows linkages between single administration of ibogaine and relief of symptoms of neuropsychiatric conditions including substance use disorder, multiple sclerosis, and traumatic brain injury. Ibogaine has multi-receptor actions, but the neurobiological mechanisms underlying such putative effects is unknown. Here we review and discuss the relevant literature, focusing on remyelination and metabolic restoration. We provide evidence that ibogaine upregulates markers of myelination following opioid administration; that conditions such as opioid use disorder, multiple sclerosis and traumatic brain injury are characterized by white matter pathology; that decreased myelination is related to dysregulated metabolic homeostasis, ischemia and hypoxia which may also play a role in these disorders. We conclude that multi-receptor actions of ibogaine, especially its affinities for the NMDA, kappa opioid and sigma receptors, in turn account for reduction in excitotoxicity, metabolic regulation, lasting neuroplasticity and immunomodulation that facilitates neuronal repair and remyelination providing a rationale for future investigation of its use as a therapeutic agent for these common central nervous system disorders.

The set of sums of two squares plays a significant role in number theory. We establish the existence of several rich monochromatic configurations in the natural numbers by exploiting algebraic structures induced by the set of sums of two squares. The proofs rely on algebraic properties arising from the induced structures on the Stone–Čech compactification of the natural numbers.

The widespread use of atrazine in corn since the 1960s has raised environmental concerns, such as ground and surface water contamination. The U.S. Environmental Protection Agency has proposed label restrictions on atrazine to address these concerns and requires applicators to achieve herbicide mitigation points before applying herbicides. One way to achieve mitigation points is to reduce the proportion of the field that is treated. Therefore, research was conducted in 2023 in Arkansas, Mississippi, Tennessee, North Carolina, Indiana, and Virginia, and in 2024 in Arkansas, Tennessee, and Indiana, to determine whether targeted applications can mitigate atrazine use in corn while maintaining weed control levels comparable to those achieved with broadcast applications. All plots, except the nontreated control, received paraquat and S-metolachlor immediately after planting in 2023, with amicarbazone and metribuzin added in 2024. Combinations of atrazine, glyphosate, and mesotrione were applied postemergence either broadcast, target-applied to emerged weeds, or a combination of broadcast and target-applied. Targeted applications of herbicides did not differ in weed control, including Palmer amaranth and morningglory species, compared to broadcast applications of the same active ingredients. No injury or differences in corn grain yield were observed. Targeted applications in 2023 covered 86% of the area, on average, while 52% of the area was sprayed on average in 2024. Differences in the area sprayed during the targeted application between years can be attributed to the reduced area of weed emergence from a more robust residual herbicide combination in 2024. Based on this research, targeted spray technology can reduce atrazine use in corn while providing weed control comparable to that achieved with broadcast applications.

The integration of phenotypic, genomic and pedigree data into a single-step model for predicting genomically enhanced estimated breeding values (GEBVs) has become crucial for the accurate genetic evaluation of dairy cattle. This study compared two widely used software implementations, MiXBLUP and BLUPF90IOD3, for the prediction of breeding values using the single-step G-BLUP model based on data from the Polish national evaluation for stature. Four core animal sets were tested, which differed in the selection of bulls and cows. The GEBVs were predicted and validated using different subsets of the population. Both software packages resulted in high correlations (0.89 and 0.97) between full and truncated dataset predictions and similar validation performance, with MiXBLUP exhibiting slightly greater consistency across different sets of core animals. The ranking of the top 50 bulls remained stable across the implementations. This study concludes that both software implementations provide comparable GEBV predictions, suggesting that software choice should consider computational efficiency, cost and modeling flexibility, with MiXBLUP offering additional options for GEBV estimation.

We report a new species of stem ibis (Threskiornithidae) from the early Eocene Fossil Butte Member of the Green River Formation. Rhynchaeites mcfaddeni n. sp. is represented by an articulated partial skeleton and was a diminutive species, with an estimated body mass of under 300 g. The holotype specimen is preserved in an unusual manner, leaving the skull, presacral vertebral column, wings, and feet in approximate life position despite the loss of the trunk, pelvis, tail, and upper legs. This peculiar mode of preservation may represent a case of the “stick ‘n’ peel” model of preservation, by which a portion of a carcass becomes firmly adhered to the sediment by substances released during decay. Like other members of the stem ibis genus Rhynchaeites, Rhynchaeites mcfaddeni n. sp. lacks the dense pitting of the bill tip associated with abundant Herbst corpuscles, which is developed in extant ibises. However, the new species differs from all stem and crown ibises in possessing a sharply tapering beak tip, which suggests a unique mode of foraging, possibly including prying mollusks from their shells. Given that Rhynchaeites messelensis Wittich, 1898 is one of the most common birds in the prolific Messel deposits but Rhynchaeites mcfaddeni n. sp. is represented by a single specimen after more than 50 years of intense collecting in the Green River Formation, it is likely the two species had divergent foraging strategies, with the former perhaps feeding closer to the lake margin and the latter in streams.

UUID: http://zoobank.org/60d25b3b-9c76-4553-99c4-a390d3a5548d

We report an exceptionally early diagnosis of a Kommerell diverticulum on the first day of life, distinguished by unusual mid-ductal aneurysmal dilatation of the patent ductus arteriosus. Serial echocardiography documented the serial evolution of spontaneous ductal closure and thrombosis formation. CT confirmed a right aortic arch with a retroesophageal Kommerell diverticulum. The infant remains asymptomatic under close surveillance. This case represents one of the youngest reported cases with serial imaging documentation, providing unique insights into the early natural history and highlighting management challenges in asymptomatic neonatal patients.

This study examines whether behaviourally informed training can improve the effectiveness of phone-based tax debt collection in a public-sector setting. In collaboration with the Bulgarian National Revenue Agency, we implemented a two-day training programme for call centre agents focused on persuasion, negotiation and behavioural influence techniques derived from behavioural science and nudge theory. The impact of the intervention is assessed using descriptive comparisons of monthly aggregated debt-collection performance indicators before and after the training. We find that, following the intervention, trained agents achieved markedly better outcomes relative to pre-intervention periods, including an increase of approximately 20% in the total amount of debt collected over the subsequent three months and a higher rate of secured payment agreements. Notably, these improvements contrast with historical seasonal patterns that typically show a decline in collections during the same period. While the analysis is descriptive and does not permit definitive causal inference, the results provide strong indicative evidence that targeted behavioural training can enhance compliance outcomes in live, interpersonal interactions. The study contributes to the behavioural public policy and persuasion literatures by extending behavioural insights beyond written or digital nudges to real-time, conversational settings. From a practical perspective, the findings highlight the potential value of soft-skills and behavioural training for frontline public servants as a scalable and cost-effective tool for improving tax administration performance.

This study investigated changes in serum folate and B12, and associations with endurance performance and bone outcomes, in women during military training. Women (n = 137) had serum folate and B12, haematological markers, and endurance performance (2.4 km run) measured at the start (week 1) and end (week 13) of British Army basic training. Whole-body areal bone mineral density and markers of bone metabolism were measured at week 1. Training decreased serum folate (mean change [95% CI], −2.3 [−3.0, −1.6] nmol∙L-1, p < 0.001), B12 (−16 [−32, 0] pmol∙L-1, p = 0.042), haemoglobin (−0.7 [−0.9, −0.5] g∙dL-1, p < 0.001), and red blood cell (RBC) count (−0.2 [−0.3, −0.2] × 10^9∙L-1, p < 0.001), but had no effect on mean corpuscular volume (p = 0.438) or erythrocyte distribution width (p = 0.088). There was no association between serum folate, serum B12, haemoglobin, or RBC count with run time (p ≥ 0.518). Serum B12 was not associated with areal bone mineral density or bone metabolism at week 1 (p ≥ 0.152). Higher serum folate was associated with lower plasma c-telopeptide cross-links of type I collagen (standardised β [95% CI] = −0.31 [−0.48, −0.15], p < 0.001), but not whole-body bone mineral density or plasma procollagen type I N-terminal propeptide (p ≥ 0.152). Serum folate and B12 decreased after military training in women, resulting in a high prevalence of folate deficiencies at the end of training. Low serum folate may contribute to increased bone resorption, the implications of which are unclear.

Dr. Mark Rupp served as Medical Director of the Infection Prevention Department at Nebraska Medicine for 28 years and as Chief of the Division of Infectious Diseases for 14 years before assuming his current role as Interim Chair of the Department of Internal Medicine at the University of Nebraska Medical Center (UNMC) in 2025. He is a Past President of the Society for Healthcare Epidemiology of America (SHEA; 2009) and delivered the SHEA Lecture at IDWeek 2020.

Dr. Rupp has authored more than 200 peer-reviewed articles, 48 book chapters, three textbooks, and holds three U.S. patents. He is an internationally recognized expert in clinical infectious diseases and healthcare epidemiology and is a frequent national and international speaker, educator, and media contributor.

Authoritarian regimes have increasingly leveraged foreign media to project influence within democracies, yet evidence of these co-opted outlets’ actual effects remains scarce. This study presents findings from a field experiment conducted during Taiwan’s 2020 general election, assessing the impact of The China Times, a Beijing-backed media conglomerate, on voter behavior and attitudes. The experiment incentivized participants to engage in sustained consumption of real-time news from this outlet in the weeks leading up to the election. Results from a panel survey linked to individual-level web-tracking data reveal that exposure to The China Times sways voters in favor of the People’s Republic of China (PRC). These effects, however, are primarily driven by nonpartisan and PRC-friendly voters. To the extent that I find effects among PRC-skeptics, they show evidence of backfiring. As Beijing’s media co-optation extends beyond Taiwan, my findings have broader implications for understanding the effectiveness and limitations of authoritarian influence operations.

This article explores the Detached Papers of the Company of Merchants Trading to Africa, an underused sub-series within The National Archives’ T 70 collection. These records offer a unique and detailed insight into the British administration of West African forts, and the lives of enslaved people forced to work in these fortifications. While the Royal African Company has been the subject of extensive scholarship, the Company of Merchants – its successor – remains understudied. Through letters, minute books, fort lists, and financial records, the Detached Papers, recently catalogued at item level for the first time, provide a critical and untapped source on the eighteenth-century Atlantic world, revealing overlooked narratives of local relationships, familial networks, and the operational structures that underpinned the transatlantic trade in enslaved Africans. This article focuses on three key areas to exemplify the importance of these records for future research: the cultural and political life of the Fante; the networks and influence of Company Governor Richard Miles; and the identities and experiences of enslaved people in British-controlled forts. By engaging with the fragmentary nature of these records, the article interrogates archival silences to surface the submerged histories of exploitation, agency, and survival within the archives of enslavement.