We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with a particular emphasis on the set $D'$ comprised of differences between successive elements. In particular, if the burden of the structure is at most n, then the result of applying the operation $D \mapsto D'\ n$ times must be a finite set (Theorem 1.1). In the case when the structure is densely ordered and has burden $2$, we show that any definable unary discrete set must be definable in some elementary extension of the structure $\langle \mathbb{R}; <, +, \mathbb{Z} \rangle $ (Theorem 1.3).

We study possible Scott sentence complexities of linear orderings using two approaches. First, we investigate the effect of the Friedman–Stanley embedding on Scott sentence complexity and show that it only preserves $\Pi ^{\mathrm {in}}_{\alpha }$ complexities. We then take a more direct approach and exhibit linear orderings of all Scott sentence complexities except $\Sigma ^{\mathrm {in}}_{3}$ and $\Sigma ^{\mathrm {in}}_{\lambda +1}$ for $\lambda $ a limit ordinal. We show that the former cannot be the Scott sentence complexity of a linear ordering. In the process we develop new techniques which appear to be helpful to calculate the Scott sentence complexities of structures.

The 1814 memoir of missionary wife Harriet Newell was important for awakening the early nineteenth-century American Evangelical imagination on behalf of the burgeoning missionary cause. As young women ‘read the self’ and patterned their lives according to the literary examples they encountered, Newell's memoir used the language of ‘usefulness’ as a powerful theological plot. This article hopes to address the lacuna of scholarship regarding the theological aspects of Newell's writing and how it was those aspects in particular which subsequent generations venerated in the creation of missionary wife memoirs.

This paper explores the use of mediation in medical treatment disputes through the lens of therapeutic justice (TJ), a concept developed in the 1990s to consider the therapeutic and anti-therapeutic effects of justice systems. The paper argues that mediation may be a mechanism for achieving therapeutic effects for people involved in medical treatment disputes. In doing so, the paper highlights the conflict that can often arise between healthcare professionals, family members and patients in medical treatment disputes and the related difficulties with using litigation to resolve this type of conflict. It has been suggested by judges, academics and policy-makers that mediation might be a better way of resolving conflict in these cases. While mediation and TJ have much in common, the paper explores the many tensions between them, considering ways in which mediation might need to be done differently to achieve therapeutic aims. Finally, the paper identifies six TJ features against which mediation can be tested to consider whether it can live up to the claims that it can be used to resolve medical treatment disputes more therapeutically.

The blow-up of the anticanonical base point on a del Pezzo surface S of degree 1 gives rise to a rational elliptic surface $\mathscr {E}$ with only irreducible fibers. The sections of minimal height of $\mathscr {E}$ are in correspondence with the $240$ exceptional curves on S. A natural question arises when studying the configuration of these curves: if a point on S is contained in “many” exceptional curves, is it torsion on its fiber on $\mathscr {E}$? In 2005, Kuwata proved for the analogous question on del Pezzo surfaces of degree $2$, where there are 56 exceptional curves, that if “many” equals $4$ or more, the answer is yes. In this paper, we prove that for del Pezzo surfaces of degree 1, the answer is yes if ‘many’ equals $9$ or more. Moreover, we give counterexamples where a non-torsion point lies in the intersection of $7$ exceptional curves. We give partial results for the still open case of 8 intersecting exceptional curves.

The so-called “Prakhon Chai Hoard” is one of Southeast Asia’s most infamous cases of looting. The story begins in 1964 when a cache of Buddhist bronzes from Northeast Thailand appeared on the international art market via the auction house Spink & Son, London. They quickly ended up in museums and private collections throughout the US and Europe. The exact findspot was unclear but soon became associated with an unidentified temple in Prakhon Chai district in Buriram province. The moniker “Prakhon Chai Hoard/bronzes” subsequently took hold, becoming commonplace in museum displays, dealer/auction house catalogs, and art historical discourse. However, in 2002, it was revealed the temple in question was Plai Bat II in Lahan Sai district.

This article untangles the many myths and misunderstandings surrounding this act of looting. It does so by reviewing the extant literature in light of information revealed by criminal investigations into the late Douglas Latchford from 2012 onwards, and presenting conclusions drawn from our decade-long documentation of villager testimonies at Plai Bat II (2014–2024).

Since Cannon, inspired by Bernard’s discussion of the conditions required for free and independent life, introduced the term homeostasis, many have embraced it as the main theoretical principle guiding physiology and medicine. Nonetheless, critics have argued that homeostasis is too limiting and have advanced a variety of alternative concepts such as heterostasis, rheostasis, and allostasis. We argue that the critics target a much narrower understanding of homeostasis put forward by the cyberneticists and that Bernard and Cannon embraced a far broader understanding that can accommodate the alternatives advanced by the critics and provide an integrated theoretical framework for physiology.

We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound (the conductor). For many numerical semigroups, including all symmetric numerical semigroups, our upper bound is tight. Our construction uses combinatorially structured matrices and is parametrised by Kunz coordinates, which are central to enumerative problems in the study of numerical semigroups.

This paper advances a theory of disease as domino dysfunction. It is often argued that diseases are biological dysfunctions. However, a theory of disease as biological dysfunction is complicated by some plausible cases of dysfunction that seem clearly non-pathological. I argue that pathological conditions are not just dysfunctions but domino dysfunctions, and that domino dysfunctions can be distinguished on principled biological grounds from non-pathological dysfunctions. I then show how this theory can make sense of the problem cases; they are not diseases because they are not domino dysfunctions.

In this study, we propose hierarchical inconsistency among family-member top leaders as a novel structural reason for nonfamily executives' high compensation in family firms. Hierarchical inconsistency among family-member top leaders is observed when the head in the formal business hierarchy is not ranked the highest among family-member executives and directors in the informal family hierarchy. We argue that this structure triggers contestations between the heads of the two hierarchies, adding complexity and challenges to nonfamily executives' jobs. Family firms with hierarchical inconsistency among family-member top leaders need to offer higher compensation to make up for the demanding features of these professional managers' work. The positive relationship between hierarchical inconsistency and nonfamily executives' compensation is weaker when the proportion of female family-member executives and directors is high and when the formal head's tenure is long. We use data from publicly listed family firms in China to test our arguments. Our study contributes to family business research by suggesting how the interplay between family relationships and formal organizational structures influences job features and compensation decisions.

We investigated the accuracy and completeness of four large language model (LLM) artificial intelligence tools. Most LLMs provided acceptable answers to commonly asked infection prevention questions (accuracy 98.9%, completeness 94.6%). The use of LLMs to supplement infection prevention consults should be further explored.

We study the incidence of Social Security taxes on teacher wages and employment. On average, we estimate teachers with Social Security coverage take home 9.6 percent less in wages than observationally similar teachers in similar districts without Social Security coverage. This accounts for about three-fourths of the 12.4-percent total Social Security tax. Moreover, our analysis suggests this is likely a lower-bound estimate of the true incidence of Social Security taxes – under reasonable assumptions, we cannot rule out full (100%) tax incidence on teacher wages. We find no evidence of tax incidence on teacher staffing levels.

This paper presents a systematic design approach for developing a semiflexible multiple-input–multiple-output antenna system operating in the millimeter wave frequency spectrum, specifically designed for body-worn applications in biotechnologies. The designed antenna features dual flower-shaped antenna radiators placed in a spatial diversity configuration. Strategic modifications have been implemented by integrating dual crescent-shaped slots in the ground layer to attain the targeted frequency band of 25.7–30.6 GHz. Later, the upper edge of the ground plane is truncated in order to achieve circularly polarized radiation characteristics at 29.4 GHz with 3 dB ARBW of 0.6 GHz (29.1–29.7 GHz). The realization of circular polarization in the antenna geometry is validated through the analysis of characteristic mode theory. A maximum gain of 5.6 dBi is attained along with a port isolation of >30 dB. The proposed antenna undergoes analysis to assess its performance in the bending conditions and specific absorption rate, besides validation of diversity metrics encompassing envelope correlation coefficient, diversity gain, channel capacity loss, total active reflection coefficient, and mean effective gain has also been conducted. Finally, the proposed antenna structure is fabricated, and its performance is validated and subsequently compared with that of its simulated counterpart.

New information on the growth analysis for different cassava genotypes grown under different irrigation managements during the early growth phase could support decision-making to improve crop productivity. This study aimed to determine the performance of 20 cassava genotypes grown under different irrigation management practices during the early growth phase. A strip-plot design with four replications was used during two growing seasons (2019/2020 and 2020/2021). Three levels of irrigation from 30 to 180 days after planting (DAP) were assigned as factor A (W1 = 100%, W2 = 60% and W3 = 20% of the crop water requirement), whereas 20 cassava genotypes were assigned as factor B. Crop data were recorded on SPAD chlorophyll meter reading (SCMR), specific leaf area (SLA) and leaf area index (LAI) at 180 and 330 DAP, relative growth rate (RGR) from 180 to 330 DAP and harvest index (HI) at 330 DAP. The genotypes CMR36-31-381 and Huay Bong 90 had high values of HI, indicating a good partitioning of photosynthate to the storage root. These two genotypes also showed superior performances in terms of SCMR, SLA and RGR inW2 and W3 treatments when compared to the other genotypes. They also had LAI values within the optimum range during the period of maximum canopy size. Therefore, the genotypes CMR36-31-381 and Huay Bong 90 could be used as genetic resources to improve cassava productivity under different irrigation levels.

This article explores the multifaceted landscape of music literacy education in South African secondary schools through an anagrammatic lens. Music literacy education is symbolised by the anagrams ‘NAOUIEDCT’ and ‘RCSSEOEUR’, encapsulating resource-related, cultural and pedagogical complexities. This comparison of music literacy education to anagrams creates an interesting analogy that can shed light on the complexity and challenges inherent in the situation. It aims to unravel these complexities, like solving a multifaceted puzzle. Thus, the result of this qualitative interpretive research project is the transformation of a complex challenge (conundrum) into symbolic puzzles (anagrams), aiming to decipher the intricacies of music literacy education. This methodology offers an approach to foster engagement and collaborative work toward future solutions. Through a comprehensive exploration, this research aims to unravel the layers of challenges inherent in Music Education, offering insights and recommendations for a nuanced and enriched educational experience. The data for this research project were collected through semi-structured interviews and, consequently, a thematic content analysis was carried out, first in a descriptive level of analysis, followed by a conceptual level of analysis. Computer-aided qualitative analysis software, namely ATLAS.tiTM23, played a valuable and significant role in both the literature review and thematic content analysis phases of this study.

In this paper, we study the employment of $\Sigma _1$-sentences with certificates, i.e., $\Sigma _1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some detail and illustrate their use by reproving some classical results and proving some new ones. An example of such a classical result is Vaught’s theorem of the strong effective inseparability of $\mathsf {R}_0$.

We also develop the new idea of a theory being $\mathsf {R}_{0\mathsf {p}}$-sourced. Using this notion, we can transfer a number of salient results from $\mathsf {R}_0$ to a variety of other theories.

This research aimed to develop biomarkers for estimating ammonia (NH3) emissions from dairy cattle manure over a 15-day in vitro incubation system. To generate different levels of NH3 emissions, the experiment utilized four manure experimental groups: 1 urinary nitrogen (U) to 1 faecal nitrogen (F) ratio (CT), 2 U to 1 F ratio (2U1F), and CT and 2U1F with lignite application (CT + L and 2U1F + L, respectively). The addition of lignite to ruminant manure aimed to enhance environmental sustainability through its beneficial properties. Three biomarkers, nitrogen (N) isotopic fractionation (δ15N), N: potassium (K) ratio, and N: phosphorus (P) ratio, were investigated. Manure δ15N increased linearly when NH3 emission increased in CT and 2U1F groups (R2 = 0.79 and 0.90, respectively; P ≤ 0.001), while manure N: P decreased when NH3 emission increased in CT + L and 2U1F + L groups (R2 = 0.73 and 0.85, respectively; P ≤ 0.001). No useful relationship was found between N: K and NH3 emission, apart from in 2U1F group (R2 = 0.84; P ≤ 0.001). The experiment found manure δ15N and N: P are complementary biomarkers to predict NH3 emissions, from non-lignite and lignite groups, respectively.